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[Illustration:

  MARY SOMERVILLE
  J. COOPER S^c.
]




                                   ON

                             THE CONNEXION

                                   OF

                         THE PHYSICAL SCIENCES.

                          BY MARY SOMERVILLE,

              AUTHORESS OF ‘MECHANISM OF THE HEAVENS,’ AND
                         ‘PHYSICAL GEOGRAPHY.’

                         ---------------------

“No natural phenomenon can be adequately studied in itself alone—but, to
be understood, it must be considered as it stands connected with all
Nature.”—BACON.

                         ---------------------

                   Ninth Edition, completely Revised.




                                LONDON:
                     JOHN MURRAY, ALBEMARLE STREET.
                                 1858.

                _The right of Translation is reserved._




  LONDON: PRINTED BY W. CLOWES AND SONS, DUKE STREET, STAMFORD STREET,
                           AND CHARING CROSS.




                         This Book is Dedicated

                                   TO

                           HER DEAR CHILDREN,

                     BY THEIR AFFECTIONATE MOTHER,

                                                        MARY SOMERVILLE.

_Florence, Nov. 1, 1858._




                               CONTENTS.


INTRODUCTION

                                                                  Page 1


                               SECTION I.

Attraction of a Sphere—Form of Celestial Bodies—Terrestrial Gravitation
  retains the Moon in her Orbit—The Heavenly Bodies move in Conic
  Sections—Gravitation Proportional to Mass—Gravitation of the Particles
  of Matter—Figure of the Planets—How it affects the Motions of their
  Satellites—Rotation and Translation impressed by the same
  Impulse—Motion of the Sun and Solar System

                                                                       4


                              SECTION II.

Elliptical Motion—Mean and True
  Motion—Equinoctial—Ecliptic—Equinoxes—Mean and True Longitude—Equation
  of Centre—Inclination of the Orbits of Planets—Celestial
  Latitude—Nodes—Elements of an Orbit—Undisturbed or Elliptical
  Orbits—Great Inclination of the Orbits of the New Planets—Universal
  Gravitation the Cause of Perturbations in the Motions of the Heavenly
  Bodies—Problem of the Three Bodies—Stability of Solar System depends
  upon the Primitive Momentum of the Bodies

                                                                       8


                              SECTION III.

Perturbations, Periodic and Secular—Disturbing Action equivalent to
  three Partial Forces—Tangential Force the cause of the Periodic
  Inequalities in Longitude, and Secular Inequalities in the Form and
  Position of the Orbit in its own Plane—Radial Force the cause of
  Variations in the Planet’s Distance from the Sun—It combines with the
  Tangential Force to produce the Secular Variations in the Form and
  Position of the Orbit in its own Plane—Perpendicular Force the cause
  of Periodic Perturbations in Latitude, and Secular Variations in the
  Position of the Orbit with regard to the Plane of the Ecliptic—Mean
  Motion and Major Axis Invariable—Stability of System—Effects of a
  Resisting Medium—Invariable Plane of the Solar System and of the
  Universe—Great Inequality of Jupiter and Saturn

                                                                      13


                              SECTION IV.

Theory of Jupiter’s Satellites—Effects of the Figure of Jupiter upon his
  Satellites—Position of their Orbits—Singular Laws among the Motions of
  the first Three Satellites—Eclipses of the Satellites—Velocity of
  Light—Aberration—Ethereal Medium—Satellites of Saturn and Uranus

                                                                      27


                               SECTION V.

Lunar Theory—Periodic Perturbations of the Moon—Equation of
  Centre—Evection—Variation—Annual Equation—Direct and Indirect
  Action of Planets—The Moon’s Action on the Earth disturbs her
  own Motion—Excentricity and Inclination of Lunar Orbit
  invariable—Acceleration—Secular Variation in Nodes and
  Perigee—Motion of Nodes and Perigee inseparably connected with
  the Acceleration—Nutation of Lunar Orbit—Form and Internal
  Structure of the Earth determined from it—Lunar, Solar, and
  Planetary Eclipses—Occultations and Lunar Distances—Mean
  Distance of the Sun from the Earth obtained from Lunar
  Theory—Absolute Distances of the Planets, how found

                                                                      34


                              SECTION VI.

Form of the Earth and Planets—Figure of a Homogeneous Spheroid in
  Rotation—Figure of a Spheroid of variable Density—Figure of the Earth,
  supposing it to be an Ellipsoid of Revolution—Mensuration of a Degree
  of the Meridian—Compression and Size of the Earth from Degrees of
  Meridian—Figure of Earth from the Pendulum

                                                                      44


                              SECTION VII.

Parallax—Lunar Parallax found from Direct Observation—Solar Parallax
  deduced from the Transit of Venus—Distance of the Sun from the
  Earth—Annual Parallax—Distance of the Fixed Stars

                                                                      52


                             SECTION VIII.

Masses of Planets that have no Satellites determined from their
  Perturbations—Masses of the others obtained from the Motions of their
  Satellites—Masses of the Sun, the Earth, of Jupiter and of the Jovial
  System—Mass of the Moon—Real Diameters of Planets, how obtained—Size
  of Sun, Densities of the Heavenly Bodies—Formation of Astronomical
  Tables—Requisite Data and Means of obtaining them

                                                                      55


                              SECTION IX.

Rotation of the Sun and Planets—Saturn’s Rings—Periods of the Rotation
  of the Moon and other Satellites equal to the Periods of their
  Revolutions—Form of Lunar Spheroid—Libration, Aspect, and Constitution
  of the Moon—Rotation of Jupiter’s Satellites

                                                                      65


                               SECTION X.

Rotation of the Earth invariable—Decrease in the Earth’s mean
  Temperature—Earth originally in a state of Fusion—Length of Day
  constant—Decrease of Temperature ascribed by Sir John Herschel to the
  variation in the Excentricity of the Terrestrial Orbit—Difference in
  the Temperature of the two Hemispheres erroneously ascribed to the
  Excess in the Length of Spring and Summer in the Southern Hemisphere;
  attributed by Sir Charles Lyell to the Operation of existing
  Causes—Three principal Axes of Rotation—Position of the Axis of
  Rotation on the Surface of the Earth invariable—Ocean not sufficient
  to restore the Equilibrium of the Earth if deranged—Its Density and
  mean Depth—Internal Structure of the Earth

                                                                      71


                              SECTION XI.

Precession and Nutation—Their Effects on the Apparent Places of the
  Fixed Stars

                                                                      79


                              SECTION XII.

Mean and Apparent Sidereal Time—Mean and Apparent Solar Time—Equation of
  Time—English and French Subdivisions of Time—Leap Year—Christian
  Era—Equinoctial Time—Remarkable Eras depending upon the Position of
  the Solar Perigee—Inequality of the Lengths of the Seasons in the two
  Hemispheres—Application of Astronomy to Chronology—English and French
  Standards of Weights and Measures

                                                                      83


                             SECTION XIII.

Tides—Forces that produce them—Origin and Course of Tidal Wave—Its
  Speed—Three kinds of Oscillations in the Ocean—The Semidiurnal
  Tides—Equinoctial Tides—Effects of the Declination of the Sun and
  Moon—Theory insufficient without Observation—Direction of the Tidal
  Wave—Height of Tides—Mass of Moon obtained from her Action on the
  Tides—Interference of Undulations—Impossibility of a Universal
  Inundation—Currents

                                                                      91


                              SECTION XIV.

Molecular Forces—Permanency of the ultimate Particles of
  Matter—Interstices—Mossotti’s Theory—Rankin’s Theory of Molecular
  Vortices—Gases reduced to Liquids by Pressure—Gravitation of
  Particles—Cohesion—Crystallization—Cleavage—Isomorphism—Minuteness of
  the Particles—Height of Atmosphere—Chemical Affinity—Definite
  Proportions and Relative Weights of Atoms—Faraday’s Discovery with
  regard to Affinity—Capillary Attraction

                                                                     102


                              SECTION XV.

Analysis of the Atmosphere—Its pressure—Law of Decrease in
  Density—Law of Decrease in Temperature—Measurement of Heights
  by the Barometer—Extent of the Atmosphere—Barometrical
  Variations—Oscillations—Trade-Winds—Cloud-Ring—Monsoons—Rotation of
  Winds—Laws of Hurricanes

                                                                     117


                              SECTION XVI.

Sound—Propagation of Sound illustrated by a Field of Standing
  Corn—Nature of Waves—Propagation of Sound through the
  Atmosphere—Intensity—Noises—A Musical Sound—Quality—Pitch—Extent of
  Human Hearing—Velocity of Sound in Air, Water, and Solids—Causes of
  the Obstruction of Sound—Law of its Intensity—Reflection of
  Sound—Echoes—Thunder—Refraction of Sound—Interference of Sounds

                                                                     129


                             SECTION XVII.

Vibration of Musical Strings—Harmonic Sounds—Nodes—Vibration of Air in
  Wind-Instruments—Vibration of Solids—Vibrating
  Plates—Bells—Harmony—Sounding Boards—Forced
  Vibrations—Resonance—Speaking Machines

                                                                     140


                             SECTION XVIII.

Refraction—Astronomical Refraction and its Laws—Formation of Tables of
  Refraction—Terrestrial Refraction—Its Quantity—Instances of
  Extraordinary Refraction—Reflection—Instances of Extraordinary
  Reflection—Loss of Light by the Absorbing Power of the
  Atmosphere—Apparent Magnitude of Sun and Moon in the Horizon

                                                                     153


                              SECTION XIX.

Constitution of Light according to Sir Isaac Newton—Absorption of
  Light—Colours of Bodies—Constitution of Light according to Sir David
  Brewster—New Colours—Fraunhofer’s Dark Lines—Dispersion of Light—The
  Achromatic Telescope—Homogeneous Light—Accidental and Complementary
  Colours—M. Plateau’s Experiments and Theory of Accidental Colours

                                                                     159


                              SECTION XX.

Interference of Light—Undulatory Theory of Light—Propagation of
  Light—Newton’s Rings—Measurement of the Length of the Waves of Light,
  and of the Frequency of the Vibrations of Ether for each
  Colour—Newton’s Scale of Colours—Diffraction of Light—Sir John
  Herschel’s Theory of the Absorption of Light—Refraction and Reflection
  of Light

                                                                     167


                              SECTION XXI.

Polarization of Light—Defined—Polarization by Refraction—Properties of
  the Tourmaline—Double Refraction—All doubly Refracted Light is
  Polarized—Properties of Iceland Spar—Tourmaline absorbs one of the two
  Refracted Rays—Undulations of Natural Light—Undulations of Polarized
  Light—The Optic Axes of Crystals—M. Fresnel’s Discoveries on the Rays
  passing along the Optic Axis—Polarization by Reflection

                                                                     179


                             SECTION XXII.

Phenomena exhibited by the Passage of Polarized Light through Mica and
  Sulphate of Lime—The Coloured Images produced by Polarized Light
  passing through Crystals having one and two Optic Axes—Circular
  Polarization—Elliptical Polarization—Discoveries of MM. Biot, Fresnel,
  and Professor Airy—Coloured Images produced by the Interference of
  Polarized Rays—Fluorescence

                                                                     186


                             SECTION XXIII.

Objections to the Undulatory Theory, from a difference in the Action of
  Sound and Light under the same circumstances, removed—The Dispersion
  of Light according to the Undulatory Theory—Arago’s final proof that
  the Undulatory Theory is the Law of Nature

                                                                     199


                             SECTION XXIV.

Chemical or Photographic Rays of Solar Spectrum—Scheele, Ritter, and
  Wollaston’s Discoveries—Wedgwood’s and Sir Humphry Davy’s Photographic
  Pictures—The Calotype—The Daguerreotype—The Chromatype—The
  Cyanotype—Collodion—Sir John Herschel’s Discoveries in the Chemical
  Spectrum—M. Becquerel’s Discoveries of Inactive Lines in ditto—Thermic
  Spectrum—Phosphoric Spectrum—Electrical Properties—Parathermic
  Rays—Moser and Hunt’s Experiments—General Structure and antagonist
  Properties of Solar Spectrum—Defracted Spectrum

                                                                     203


                              SECTION XXV.

Size and Constitution of the Sun—The Solar Spots—Intensity of the
  Sun’s Light and Heat—The Sun’s Atmosphere—His influence on the
  Planets—Atmospheres of the Planets—The Moon has none—Lunar
  heat—The Differential Telescope—Temperature of Space—Internal
  Heat of the Earth—Zone of constant Temperature—Increase of Heat
  with the Depth—Central Heat—Volcanic Action—Quantity of Heat
  received from the Sun—Isogeothermal Lines—Line of Perpetual
  Congelation—Climate—Isothermal Lines—Same quantity of Heat
  annually received and radiated by the Earth

                                                                     224


                             SECTION XXVI.

Influence of Temperature on Vegetation—Vegetation varies with the
  Latitude and Height above the Sea—Geographical Distribution of Land
  Plants—Distribution of Marine Plants—Corallines, Shell-fish, Reptiles,
  Insects, Birds, and Quadrupeds—Varieties of Mankind, yet identity of
  Species

                                                                     248


                             SECTION XXVII.

Terrestrial Heat—Radiation—Transmission—Melloni’s experiments—Heat
  in Solar Spectrum—Polarization of Heat—Nature of
  Heat—Absorptions—Dew—Rain—Combustion—Expansion—Compensation
  Pendulum—Transmission through Crystals—Propagation—Dynamic Theory
  of Heat—Mechanical equivalent of Heat—Latent Heat is the Force of
  Expansion—Steam—Work performed by Heat—Conservation of
  Force—Mechanical Power in the Tides—Dynamical Power of
  Light—Analogy between Light, Heat, and Sound

                                                                     257


                            SECTION XXVIII.

Common or Static Electricity, or Electricity of Tension—A Dual
  Power—Methods of exciting it—Attraction and
  Repulsion—Conduction—Electrics and
  Non-electrics—Induction—Dielectrics—Tension—Law of the Electric
  Force—Distribution—Laws of Distribution—Heat of Electricity—Electrical
  Light and its Spectrum—Velocity—Atmospheric Electricity—Its
  cause—Electric Clouds—Violent effects of Lightning—Back
  Stroke—Electric Glow—Phosphorescence

                                                                     282


                             SECTION XXIX.

Voltaic Electricity—The Voltaic Battery—Intensity—Quantity—Static
  Electricity, and Electricity in Motion—Luminous Effects—Mr.
  Grove on the Electric Arc and Light—Decomposition of Water—Formation
  of Crystals by Voltaic Electricity—Photo-galvanic
  Engraving—Conduction—Heat of Voltaic Electricity—Electric Fish

                                                                     297


                              SECTION XXX.

Discovery of Electro-magnetism—Deflection of the Magnetic Needle by a
  Current of Electricity—Direction of the Force—Rotatory Motion by
  Electricity—Rotation of a Wire and a Magnet—Rotation of a Magnet about
  its Axis—Of Mercury and Water—Electro-Magnetic Cylinder or
  Helix—Suspension of a Needle in a Helix—Electro-Magnetic
  Induction—Temporary Magnets—The Galvanometer

                                                                     312


                             SECTION XXXI.

Electro-Dynamics—Reciprocal Action of Electric Currents—Identity of
  Electro-Dynamic Cylinders and Magnets—Differences between the Action
  of Voltaic Electricity and Electricity of Tension—Effects of a Voltaic
  Current—Ampère’s Theory—Dr. Faraday’s Experiment of Electrifying and
  Magnetising a Ray of Light

                                                                     316


                             SECTION XXXII.

Magneto-Electricity—Volta-Electric Induction—Magneto-Electric
  Induction—Identity in the Action of Electricity and
  Magnetism—Description of a Magneto-Electric Apparatus and its
  Effects—Identity of Magnetism and Electricity—The Submarine Telegraph

                                                                     322


                            SECTION XXXIII.

Electricity produced by Rotation—Direction of the Currents—Electricity
  from the Rotation of a Magnet—M. Arago’s Experiment explained—Rotation
  of a Plate of Iron between the Poles of a Magnet—Relation of
  Substances to Magnets of three Kinds—Thermo-Electricity

                                                                     330


                             SECTION XXXIV.

Magnetism a Dual Power—Antithetic Character of Paramagnetism and
  Diamagnetism—The Earth Paramagnetic—Properties of Paramagnetic
  Bodies—Polarity—Induction—Lines of Magnetic Force—Currents of
  Electricity induced by them—Proved to be Closed Curves—Analogy and
  Identity of Electricity and Magnetism—Terrestrial Magnetism—Mean
  Values of the Three Magnetic Elements—Their Variations in Double
  Progression proved to consist of Two Superposed Variations—Discovery
  of the Periodicity of the Magnetic Storms—The Decennial Period of the
  Magnetic Elements the same with that of the Solar Spots—Magnetism of
  the Atmosphere—Diamagnetism—Action of Electro-Magnetism on
  Paramagnetic, Diamagnetic Bodies, and on Copper, very different—Proof
  of Diamagnetic Polarity and Induction—Magnecrystallic Action—Effects
  of Compression, Heat, and Cleavage on Magnetic Bodies—Mutual
  Dependence of Light, Heat, Electricity, &c. &c.—The Conservation of
  Force and the Permanency of Matter Primary Laws of Nature—Definition
  of Gravity not according to that Law—Gravity only the Residual Force
  of a Universal Power—Magnetism of the Ethereal Medium

                                                                     335


                             SECTION XXXV.

Ethereal Medium—Comets—Do not disturb the Solar System—Their Orbits and
  Disturbances—M. Faye’s Comet probably the same with Lexel’s—Periods of
  other three known—Acceleration in the mean Motions of Encke’s and
  Biela’s Comets—The Shock of a Comet—Disturbing Action of the Earth and
  Planets on Encke’s and Biela’s Comets—Velocity of Comets—The Comet of
  1264—The great Comet of 1343—Physical Constitution—Shine by borrowed
  Light—Estimation of their Number

                                                                     358


                             SECTION XXXVI.

The Fixed Stars—Their Number—The Milky Way—Double Stars—Binary
  Systems—Their Orbits and Periodic Times—Colours of the Stars—Stars
  that have vanished—Variable Stars—Variation in Sun’s Light—Parallax
  and Distances of the Fixed Stars—Masses of the Stars—Comparative Light
  of the Stars—Proper Motions of the Stars—Apparent Motions of the
  Stars—Motion and Velocity of the Sun and Solar System—The Nebulæ—Their
  Number—Catalogue of them—Consist of Two Classes—Diffuse
  Nebulæ—Definitely formed Nebulæ—Globular Clusters—Splendour of Milky
  Way—Distribution of the Nebulæ—The Magellanic Clouds—Nebulæ round η
  Argûs—Constitution of Nebulæ, and the Forces that maintain
  them—Meteorites and Shooting Stars

                                                                     384


                            SECTION XXXVII.

Diffusion of Matter through Space—Gravitation—Its Velocity—Simplicity of
  its Laws—Gravitation independent of the Magnitude and Distances of the
  Bodies—Not impeded by the intervention of any Substance—Its Intensity
  invariable—General Laws—Recapitulation and Conclusion

                                                                     424


NOTES

                                                                     429


INDEX

                                                                     479




                             THE CONNECTION

                                   OF

                         THE PHYSICAL SCIENCES.




                             INTRODUCTION.


SCIENCE, regarded as the pursuit of truth, must ever afford occupation
of consummate interest, and subject of elevated meditation. The
contemplation of the works of creation elevates the mind to the
admiration of whatever is great and noble; accomplishing the object of
all study, which, in the eloquent language of Sir James Mackintosh, “is
to inspire the love of truth, of wisdom, of beauty—especially of
goodness, the highest beauty—and of that supreme and eternal Mind, which
contains all truth and wisdom, all beauty and goodness. By the love or
delightful contemplation and pursuit of these transcendent aims, for
their own sake only, the mind of man is raised from low and perishable
objects, and prepared for those high destinies which are appointed for
all those who are capable of them.”

Astronomy affords the most extensive example of the connection of the
physical sciences. In it are combined the sciences of number and
quantity, of rest and motion. In it we perceive the operation of a force
which is mixed up with everything that exists in the heavens or on
earth; which pervades every atom, rules the motions of animate and
inanimate beings, and is as sensible in the descent of a rain-drop as in
the falls of Niagara; in the weight of the air, as in the periods of the
moon. Gravitation not only binds satellites to their planet, and planets
to the sun, but it connects sun with sun throughout the wide extent of
creation, and is the cause of the disturbances, as well as of the order
of nature; since every tremor it excites in any one planet is
immediately transmitted to the farthest limits of the system, in
oscillations which correspond in their periods with the cause producing
them, like sympathetic notes in music, or vibrations from the deep tones
of an organ.

The heavens afford the most sublime subject of study which can be
derived from science. The magnitude and splendour of the objects, the
inconceivable rapidity with which they move, and the enormous distances
between them, impress the mind with some notion of the energy that
maintains them in their motions, with a durability to which we can see
no limit. Equally conspicuous is the goodness of the great First Cause,
in having endowed man with faculties, by which he can not only
appreciate the magnificence of His works, but trace, with precision, the
operation of His laws, use the globe he inhabits as a base wherewith to
measure the magnitude and distance of the sun and planets, and make the
diameter (Note 1) of the earth’s orbit the first step of a scale by
which he may ascend to the starry firmament. Such pursuits, while they
ennoble the mind, at the same time inculcate humility, by showing that
there is a barrier which no energy, mental or physical, can ever enable
us to pass: that, however profoundly we may penetrate the depths of
space, there still remain innumerable systems, compared with which,
those apparently so vast must dwindle into insignificance, or even
become invisible; and that not only man, but the globe he inhabits—nay,
the whole system of which it forms so small a part—might be annihilated,
and its extinction be unperceived in the immensity of creation.

A complete acquaintance with physical astronomy can be attained by those
only who are well versed in the higher branches of mathematical and
mechanical science (N. 2), and they alone can appreciate the extreme
beauty of the results, and of the means by which these results are
obtained. It is nevertheless true, that a sufficient skill in analysis
(N. 3) to follow the general outline—to see the mutual dependence of the
different parts of the system, and to comprehend by what means the most
extraordinary conclusions have been arrived at,—is within the reach of
many who shrink from the task, appalled by difficulties, not more
formidable than those incident to the study of the elements of every
branch of knowledge. There is a wide distinction between the degree of
mathematical acquirement necessary for making discoveries, and that
which is requisite for understanding what others have done.

Our knowledge of external objects is founded upon experience, which
furnishes facts; the comparison of these facts establishes relations,
from which the belief that like causes will produce like effects leads
to general laws. Thus, experience teaches that bodies fall at the
surface of the earth with an accelerated velocity, and with a force
proportional to their masses. By comparison, Newton proved that the
force which occasions the fall of bodies at the earth’s surface is
identical with that which retains the moon in her orbit; and he
concluded, that, as the moon is kept in her orbit by the attraction of
the earth, so the planets might be retained in their orbits by the
attraction of the sun. By such steps he was led to the discovery of one
of those powers with which the Creator has ordained that matter should
reciprocally act upon matter.

Physical astronomy is the science which compares and identifies the laws
of motion observed on earth with the motions that take place in the
heavens: and which traces, by an uninterrupted chain of deduction from
the great principle that governs the universe, the revolutions and
rotations of the planets, and the oscillations (N. 4) of the fluids at
their surfaces; and which estimates the changes the system has hitherto
undergone, or may hereafter experience—changes which require millions of
years for their accomplishment.

The accumulated efforts of astronomers, from the earliest dawn of
civilization, have been necessary to establish the mechanical theory of
astronomy. The courses of the planets have been observed for ages, with
a degree of perseverance that is astonishing, if we consider the
imperfection and even the want of instruments. The real motions of the
earth have been separated from the apparent motions of the planets; the
laws of the planetary revolutions have been discovered; and the
discovery of these laws has led to the knowledge of the gravitation
(N. 5) of matter. On the other hand, descending from the principle of
gravitation, every motion in the solar system has been so completely
explained, that the laws of any astronomical phenomena that may
hereafter occur are already determined.




                               SECTION I.

Attraction of a Sphere—Form of Celestial Bodies—Terrestrial Gravitation
  retains the Moon in her Orbit—The Heavenly Bodies move in Conic
  Sections—Gravitation Proportional to Mass—Gravitation of the Particles
  of Matter—Figure of the Planets—How it affects the Motions of their
  Satellites—Rotation and Translation impressed by the same
  Impulse—Motion of the Sun and Solar System.


IT has been proved by Newton, that a particle of matter (N. 6) placed
without the surface of a hollow sphere (N. 7) is attracted by it in the
same manner as if the mass of the hollow sphere, or the whole matter it
contains, were collected into one dense particle in its centre. The same
is therefore true of a solid sphere, which may be supposed to consist of
an infinite number of concentric hollow spheres (N. 8). This, however,
is not the case with a spheroid (N. 9); but the celestial bodies are so
nearly spherical, and at such remote distances from one another, that
they attract and are attracted as if each were condensed into a single
particle situate in its centre of gravity (N. 10)—a circumstance which
greatly facilitates the investigation of their motions.

Newton has shown that the force which retains the moon in her orbit is
the same with that which causes heavy substances to fall at the surface
of the earth. If the earth were a sphere, and at rest, a body would be
equally attracted, that is, it would have the same weight at every point
of its surface, because the surface of a sphere is everywhere equally
distant from its centre. But, as our planet is flattened at the poles
(N. 11), and bulges at the equator, the weight of the same body
gradually decreases from the poles, where it is greatest, to the
equator, where it is least. There is, however, a certain mean (N. 12)
latitude (N. 13), or part of the earth intermediate between the pole and
the equator, where the attraction of the earth on bodies at its surface
is the same as if it were a sphere; and experience shows that bodies
there fall through 16·0697 feet in a second. The mean distance (N. 14)
of the moon from the earth is about sixty times the mean radius (N. 15)
of the earth. When the number 16·0697 is diminished in the ratio (N. 16)
of 1 to 3600, which is the square of the moon’s distance (N. 17) from
the earth’s centre, estimated in terrestrial radii, it is found to be
exactly the space the moon would fall through in the first second of her
descent to the earth, were she not prevented by the centrifugal force
(N. 18) arising from the velocity with which she moves in her orbit. The
moon is thus retained in her orbit by a force having the same origin,
and regulated by the same law, with that which causes a stone to fall at
the earth’s surface. The earth may, therefore, be regarded as the centre
of a force which extends to the moon; and, as experience shows that the
action and reaction of matter are equal and contrary (N. 19), the moon
must attract the earth with an equal and contrary force.

Newton also ascertained that a body projected (N. 20) in space (N. 21)
will move in a conic section (N. 22), if attracted by a force proceeding
from a fixed point, with an intensity inversely as the square of the
distance (N. 23); but that any deviation from that law will cause it to
move in a curve of a different nature. Kepler found, by direct
observation, that the planets describe ellipses (N. 24), or oval paths,
round the sun. Later observations show that comets also move in conic
sections. It consequently follows that the sun attracts all the planets
and comets inversely as the square of their distances from its centre;
the sun, therefore, is the centre of a force extending indefinitely in
space, and including all the bodies of the system in its action.

Kepler also deduced from observation that the squares of the periodic
times (N. 25) of the planets, or the times of their revolutions round
the sun, are proportional to the cubes of their mean distances from its
centre (N. 26). Hence the intensity of gravitation of all the bodies
towards the sun is the same at equal distances. Consequently,
gravitation is proportional to the masses (N. 27); for, if the planets
and comets were at equal distances from the sun, and left to the effects
of gravity, they would arrive at his surface at the same time (N. 28).
The satellites also gravitate to their primaries (N. 29) according to
the same law that their primaries do to the sun. Thus, by the law of
action and reaction, each body is itself the centre of an attractive
force extending indefinitely in space, causing all the mutual
disturbances which render the celestial motions so complicated, and
their investigation so difficult.

The gravitation of matter directed to a centre, and attracting directly
as the mass and inversely as the square of the distance, does not belong
to it when considered in mass only; particle acts on particle according
to the same law when at sensible distances from each other. If the sun
acted on the centre of the earth, without attracting each of its
particles, the tides would be very much greater than they now are, and
would also, in other respects, be very different. The gravitation of the
earth to the sun results from the gravitation of all its particles,
which, in their turn, attract the sun in the ratio of their respective
masses. There is a reciprocal action likewise between the earth and
every particle at its surface. The earth and a feather mutually attract
each other in the proportion of the mass of the earth to the mass of the
feather. Were this not the case, and were any portion of the earth,
however small, to attract another portion, and not be itself attracted,
the centre of gravity of the earth would be moved in space by this
action, which is impossible.

The forms of the planets result from the reciprocal attraction of their
component particles. A detached fluid mass, if at rest, would assume the
form of a sphere, from the reciprocal attraction of its particles. But
if the mass revolve about an axis, it becomes flattened at the poles and
bulges at the equator (N. 11), in consequence of the centrifugal force
arising from the velocity of rotation (N. 30); for the centrifugal force
diminishes the gravity of the particles at the equator, and equilibrium
can only exist where these two forces are balanced by an increase of
gravity. Therefore, as the attractive force is the same on all particles
at equal distances from the centre of a sphere, the equatorial particles
would recede from the centre, till their increase in number balance the
centrifugal force by their attraction. Consequently, the sphere would
become an oblate or flattened spheroid, and a fluid, partially or
entirely covering a solid, as the ocean and atmosphere cover the earth,
must assume that form in order to remain in equilibrio. The surface of
the sea is, therefore, spheroidal, and the surface of the earth only
deviates from that figure where it rises above or sinks below the level
of the sea. But the deviation is so small, that it is unimportant when
compared with the magnitude of the earth; for the mighty chain of the
Andes, and the yet more lofty Himalaya, bear about the same proportion
to the earth that a grain of sand does to a globe three feet in
diameter. Such is the form of the earth and planets. The compression
(N. 31) or flattening at their poles is, however, so small, that even
Jupiter, whose rotation is the most rapid, and therefore the most
elliptical of the planets, may, from his great distance, be regarded as
spherical. Although the planets attract each other as if they were
spheres, on account of their distances, yet the satellites (N. 32) are
near enough to be sensibly affected in their motions by the forms of
their primaries. The moon, for example, is so near the earth, that the
reciprocal attraction between each of her particles, and each of the
particles in the prominent mass at the terrestrial equator, occasions
considerable disturbances in the motions of both bodies; for the action
of the moon on the matter at the earth’s equator produces a nutation
(N. 33) in the axis (N. 34) of rotation, and the reaction of that matter
on the moon is the cause of a corresponding nutation in the lunar orbit
(N. 35).

If a sphere at rest in space receive an impulse passing through its
centre of gravity, all its parts will move with an equal velocity in a
straight line; but, if the impulse does not pass through the centre of
gravity, its particles, having unequal velocities, will have a rotatory
or revolving motion, at the same time that it is translated (N. 36) in
space. These motions are independent of one another; so that a contrary
impulse, passing through its centre of gravity, will impede its
progress, without interfering with its rotation. The sun rotates about
an axis, and modern observations show that an impulse in a contrary
direction has not been given to his centre of gravity, for he moves in
space, accompanied by all those bodies which compose the solar system—a
circumstance which in no way interferes with their relative motions;
for, in consequence of the principle that force is proportional to
velocity (N. 37), the reciprocal attractions of a system remain the same
whether its centre of gravity be at rest, or moving uniformly in space.
It is computed that, had the earth received its motion from a single
impulse, that impulse must have passed through a point about twenty-five
miles from its centre.

Since the motions of rotation and translation of the planets are
independent of each other, though probably communicated by the same
impulse, they form separate subjects of investigation.




                              SECTION II.

Elliptical Motion—Mean and True
  Motion—Equinoctial—Ecliptic—Equinoxes—Mean and True Longitude—Equation
  of Centre—Inclination of the Orbits of Planets—Celestial
  Latitude—Nodes—Elements of an Orbit—Undisturbed or Elliptical
  Orbits—Great Inclination of the Orbits of the New Planets—Universal
  Gravitation the Cause of Perturbations in the Motions of the Heavenly
  Bodies—Problem of the Three Bodies—Stability of Solar System depends
  upon the Primitive Momentum of the Bodies.


A PLANET moves in its elliptical orbit with a velocity varying every
instant, in consequence of two forces, one tending to the centre of the
sun, and the other in the direction of a tangent (N. 38) to its orbit,
arising from the primitive impulse given at the time when it was
launched into space. Should the force in the tangent cease, the planet
would fall to the sun by its gravity. Were the sun not to attract it,
the planet would fly off in the tangent. Thus, when the planet is at the
point of its orbit farthest from the sun, his action overcomes the
planet’s velocity, and brings it towards him with such an accelerated
motion, that at last it overcomes the sun’s attraction, and, shooting
past him, gradually decreases in velocity until it arrives at the most
distant point, where the sun’s attraction again prevails (N. 39). In
this motion the _radii vectores_ (N. 40), or imaginary lines joining the
centres of the sun and the planets, pass over equal areas or spaces in
equal times (N. 41).

The mean distance of a planet from the sun is equal to half the major
axis (N. 42) of its orbit: if, therefore, the planet described a circle
(N. 43) round the sun at its mean distance, the motion would be uniform,
and the periodic time unaltered, because the planet would arrive at the
extremities of the major axis at the same instant, and would have the
same velocity, whether it moved in the circular or elliptical orbit,
since the curves coincide in these points. But in every other part the
elliptical, or true motion (N. 44), would either be faster or slower
than the circular or mean motion (N. 45). As it is necessary to have
some fixed point in the heavens from whence to estimate these motions,
the vernal equinox (N. 46) at a given epoch has been chosen. The
equinoctial, which is a great circle traced in the starry heavens by the
imaginary extension of the plane of the terrestrial equator, is
intersected by the ecliptic, or apparent path of the sun, in two points
diametrically opposite to one another, called the vernal and autumnal
equinoxes. The vernal equinox is the point through which the sun passes
in going from the southern to the northern hemisphere; and the autumnal,
that in which he crosses from the northern to the southern. The mean or
circular motion of a body, estimated from the vernal equinox, is its
mean longitude; and its elliptical, or true motion, reckoned from that
point, is its true longitude (N. 47): both being estimated from west to
east, the direction in which the bodies move. The difference between the
two is called the equation of the centre (N. 48); which consequently
vanishes at the apsides (N. 49), or extremities of the major axis, and
is at its maximum ninety degrees (N. 50) distant from these points, or
in quadratures (N. 51), where it measures the excentricity (N. 52) of
the orbit; so that the place of the planet in its elliptical orbit is
obtained by adding or subtracting the equation of the centre to or from
its mean longitude.

The orbits of the principal planets have a very small obliquity or
inclination (N. 53) to the plane of the ecliptic in which the earth
moves; and, on that account, astronomers refer their motions to this
plane at a given epoch as a known and fixed position. The angular
distance of a planet from the plane of the ecliptic is its latitude
(N. 54), which is south or north according as the planet is south or
north of that plane. When the planet is in the plane of the ecliptic,
its latitude is zero; it is then said to be in its nodes (N. 55). The
ascending node is that point in the ecliptic through which the planet
passes in going from the southern to the northern hemisphere. The
descending node is a corresponding point in the plane of the ecliptic
diametrically opposite to the other, through which the planet descends
in going from the northern to the southern hemisphere. The longitude and
latitude of a planet cannot be obtained by direct observation, but are
deduced from observations made at the surface of the earth by a very
simple computation. These two quantities, however, will not give the
place of a planet in space. Its distance from the sun (N. 56) must also
be known; and, for the complete determination of its elliptical motion,
the nature and position of its orbit must be ascertained by observation.
This depends upon seven quantities, called the elements of the orbit
(N. 57). These are, the length of the major axis, and the excentricity,
which determine the form of the orbit; the longitude of the planet when
at its least distance from the sun, called the longitude of the
perihelion; the inclination of the orbit to the plane of the ecliptic,
and the longitude of its ascending node: these give the position of the
orbit in space; but the periodic time, and the longitude of the planet
at a given instant, called the longitude of the epoch, are necessary for
finding the place of the body in its orbit at all times. A perfect
knowledge of these seven elements is requisite for ascertaining all the
circumstances of undisturbed elliptical motion. By such means it is
found that the paths of the planets, when their mutual disturbances are
omitted, are ellipses nearly approaching to circles, whose planes,
slightly inclined to the ecliptic, cut it in straight lines, passing
through the centre of the sun (N. 58). The orbits of the
recently-discovered planets deviate more from the ecliptic than those of
the ancient planets: that of Pallas, for instance, has an inclination of
34° 42ʹ 29·8ʺ to it; on which account it is more difficult to determine
their motions.

Were the planets attracted by the sun only, they would always move in
ellipses, invariable in form and position; and because his action is
proportional to his mass, which is much larger than that of all the
planets put together, the elliptical is the nearest approximation to
their true motions. The true motions of the planets are extremely
complicated, in consequence of their mutual attraction, so that they do
not move in any known or symmetrical curve, but in paths now approaching
to, now receding from, the elliptical form; and their radii vectores do
not describe areas or spaces exactly proportional to the time, so that
the areas become a test of disturbing forces.

To determine the motion of each body, when disturbed by all the rest, is
beyond the power of analysis. It is therefore necessary to estimate the
disturbing action of one planet at a time, whence the celebrated problem
of the three bodies, originally applied to the moon, the earth, and the
sun—namely, the masses being given of three bodies projected from three
given points, with velocities given both in quantity and direction; and
supposing the bodies to gravitate to one another with forces that are
directly as their masses, and inversely as the squares of the distances,
to find the lines described by these bodies, and their positions at any
given instant; or, in other words, to determine the path of a celestial
body when attracted by a second body, and disturbed in its motion round
the second body by a third—a problem equally applicable to planets,
satellites, and comets.

By this problem the motions of translation of the celestial bodies are
determined. It is an extremely difficult one, and would be infinitely
more so if the disturbing action were not very small when compared with
the central force; that is, if the action of the planets on one another
were not very small when compared with that of the sun. As the
disturbing influence of each body may be found separately, it is assumed
that the action of the whole system, in disturbing any one planet, is
equal to the sum of all the particular disturbances it experiences, on
the general mechanical principle, that the sum of any number of small
oscillations is nearly equal to their simultaneous and joint effect.

On account of the reciprocal action of matter, the stability of the
system depends upon the intensity of the primitive momentum (N. 59) of
the planets, and the ratio of their masses to that of the sun; for the
nature of the conic sections in which the celestial bodies move depends
upon the velocity with which they were first propelled in space. Had
that velocity been such as to make the planets move in orbits of
unstable equilibrium (N. 60), their mutual attractions might have
changed them into parabolas, or even hyperbolas (N. 22); so that the
earth and planets might, ages ago, have been sweeping far from our sun
through the abyss of space. But as the orbits differ very little from
circles, the momentum of the planets, when projected, must have been
exactly sufficient to ensure the permanency and stability of the system.
Besides, the mass of the sun is vastly greater than that of any planet;
and as their inequalities bear the same ratio to their elliptical
motions that their masses do to that of the sun, their mutual
disturbances only increase or diminish the excentricities of their
orbits by very minute quantities; consequently the magnitude of the
sun’s mass is the principal cause of the stability of the system. There
is not in the physical world a more splendid example of the adaptation
of means to the accomplishment of an end than is exhibited in the nice
adjustment of these forces, at once the cause of the variety and of the
order of Nature.




                              SECTION III.

Perturbations, Periodic and Secular—Disturbing Action equivalent to
  three Partial Forces—Tangential Force the cause of the Periodic
  Inequalities in Longitude, and Secular Inequalities in the Form and
  Position of the Orbit in its own Plane—Radial Force the cause of
  Variations in the Planet’s Distance from the Sun—It combines with the
  Tangential Force to produce the Secular Variations in the Form and
  Position of the Orbit in its own Plane—Perpendicular Force the cause
  of Periodic Perturbations in Latitude, and Secular Variations in the
  Position of the Orbit with regard to the Plane of the Ecliptic—Mean
  Motion and Major Axis Invariable—Stability of System—Effects of a
  Resisting Medium—Invariable Plane of the Solar System and of the
  Universe—Great Inequality of Jupiter and Saturn.


THE planets are subject to disturbances of two kinds, both resulting
from the constant operation of their reciprocal attraction: one kind,
depending upon their positions with regard to each other, begins from
zero, increases to a maximum, decreases, and becomes zero again, when
the planets return to the same relative positions. In consequence of
these, the disturbed planet is sometimes drawn away from the sun,
sometimes brought nearer to him: sometimes it is accelerated in its
motion, and sometimes retarded. At one time it is drawn above the plane
of its orbit, at another time below it, according to the position of the
disturbing body. All such changes, being accomplished in short periods,
some in a few months, others in years, or in hundreds of years, are
denominated periodic inequalities. The inequalities of the other kind,
though occasioned likewise by the disturbing energy of the planets, are
entirely independent of their relative positions. They depend upon the
relative positions of the orbits alone, whose forms and places in space
are altered by very minute quantities, in immense periods of time, and
are therefore called secular inequalities.

The periodical perturbations are compensated when the bodies return to
the same relative positions with regard to one another and to the sun:
the secular inequalities are compensated when the orbits return to the
same positions relatively to one another and to the plane of the
ecliptic.

Planetary motion, including both these kinds of disturbance, may be
represented by a body revolving in an ellipse, and making small and
transient deviations, now on one side of its path, and now on the other,
whilst the ellipse itself is slowly, but perpetually, changing both in
form and position.

The periodic inequalities are merely transient deviations of a planet
from its path, the most remarkable of which only lasts about 918 years;
but, in consequence of the secular disturbances, the apsides, or
extremities of the major axes of all the orbits, have a direct but
variable motion in space, excepting those of the orbit of Venus, which
are retrograde (N. 61), and the lines of the nodes move with a variable
velocity in a contrary direction. Besides these, the inclination and
excentricity of every orbit are in a state of perpetual but slow change.
These effects result from the disturbing action of all the planets on
each. But, as it is only necessary to estimate the disturbing influence
of one body at a time, what follows may convey some idea of the manner
in which one planet disturbs the elliptical motion of another.

Suppose two planets moving in ellipses round the sun; if one of them
attracted the other and the sun with equal intensity, and in parallel
directions (N. 62), it would have no effect in disturbing the elliptical
motion. The inequality of this attraction is the sole cause of
perturbation, and the difference between the disturbing planet’s action
on the sun and on the disturbed planet constitutes the disturbing force,
which consequently varies in intensity and direction with every change
in the relative positions of the three bodies. Although both the sun and
planet are under the influence of the disturbing force, the motion of
the disturbed planet is referred to the centre of the sun as a fixed
point, for convenience. The whole force (N. 63) which disturbs a planet
is equivalent to three partial forces. One of these acts on the
disturbed planet, in the direction of a tangent to its orbit, and is
called the tangential force: it occasions secular inequalities in the
form and position of the orbit in its own plane, and is the sole cause
of the periodical perturbations in the planet’s longitude. Another acts
upon the same body in the direction of its radius vector, that is, in
the line joining the centres of the sun and planet, and is called the
radial force: it produces periodical changes in the distance of the
planet from the sun, and affects the form and position of the orbit in
its own plane. The third, which may be called the perpendicular force,
acts at right angles to the plane of the orbit, occasions the periodic
inequalities in the planet’s latitude, and affects the position of the
orbit with regard to the plane of the ecliptic.

It has been observed, that the radius vector of a planet, moving in a
perfectly elliptical orbit, passes over equal spaces or areas in equal
times; a circumstance which is independent of the law of the force, and
would be the same whether it varied inversely as the square of the
distance, or not, provided only that it be directed to the centre of the
sun. Hence the tangential force, not being directed to the centre,
occasions an unequable description of areas, or, what is the same thing,
it disturbs the motion of the planet in longitude. The tangential force
sometimes accelerates the planet’s motion, sometimes retards it, and
occasionally has no effect at all. Were the orbits of both planets
circular, a complete compensation would take place at each revolution of
the two planets, because the arcs in which the accelerations and
retardations take place would be symmetrical on each side of the
disturbing force. For it is clear, that if the motion be accelerated
through a certain space, and then retarded through as much, the motion
at the end of the time will be the same as if no change had taken place.
But, as the orbits of the planets are ellipses, this symmetry does not
hold: for, as the planet moves unequably in its orbit, it is in some
positions more directly, and for a longer time, under the influence of
the disturbing force than in others. And, although multitudes of
variations do compensate each other in short periods, there are others,
depending on peculiar relations among the periodic times of the planets,
which do not compensate each other till after one, or even till after
many revolutions of both bodies. A periodical inequality of this kind in
the motions of Jupiter and Saturn has a period of no less than 918
years.

The radial force, or that part of the disturbing force which acts in the
direction of the line joining the centres of the sun and disturbed
planet, has no effect on the areas, but is the cause of periodical
changes of small extent in the distance of the planet from the sun. It
has already been shown, that the force producing perfectly elliptical
motion varies inversely as the square of the distance, and that a force
following any other law would cause the body to move in a curve of a
very different kind. Now, the radial disturbing force varies directly as
the distance; and, as it sometimes combines with and increases the
intensity of the sun’s attraction for the disturbed body, and at other
times opposes and consequently diminishes it, in both cases it causes
the sun’s attraction to deviate from the exact law of gravity, and the
whole action of this compound central force on the disturbed body is
either greater or less than what is requisite for perfectly elliptical
motion. When greater, the curvature of the disturbed planet’s path, on
leaving its perihelion (N. 64), or point nearest the sun, is greater
than it would be in the ellipse, which brings the planet to its aphelion
(N. 65), or point farthest from the sun, before it has passed through
180°, as it would do if undisturbed. So that in this case the apsides,
or extremities of the major axis, advance in space. When the central
force is less than the law of gravity requires, the curvature of the
planet’s path is less than the curvature of the ellipse. So that the
planet, on leaving its perihelion, would pass through more than 180°
before arriving at its aphelion, which causes the apsides to recede in
space (N. 66). Cases both of advance and recess occur during a
revolution of the two planets; but those in which the apsides advance
preponderate. This, however, is not the full amount of the motion of the
apsides; part arises also from the tangential force (N. 63), which
alternately accelerates and retards the velocity of the disturbed
planet. An increase in the planet’s tangential velocity diminishes the
curvature of its orbit, and is equivalent to a decrease of central
force. On the contrary, a decrease of the tangential velocity, which
increases the curvature of the orbit, is equivalent to an increase of
central force. These fluctuations, owing to the tangential force,
occasion an alternate recess and advance of the apsides, after the
manner already explained (N. 66). An uncompensated portion of the direct
motion, arising from this cause, conspires with that already impressed
by the radial force, and in some cases even nearly doubles the direct
motion of these points. The motion of the apsides may be represented by
supposing a planet to move in an ellipse, while the ellipse itself is
slowly revolving about the sun in the same plane (N. 67). This motion of
the major axis, which is direct in all the orbits except that of the
planet Venus, is irregular, and so slow that it requires more than
109,830 years for the major axis of the earth’s orbit to accomplish a
sidereal revolution (N. 68), that is, to return to the same stars; and
20,984 years to complete its tropical revolution (N. 69), or to return
to the same equinox. The difference between these two periods arises
from a retrograde motion in the equinoctial point, which meets the
advancing axis before it has completed its revolution with regard to the
stars. The major axis of Jupiter’s orbit requires no less than 200,610
years to perform its sidereal revolution, and 22,748 years to accomplish
its tropical revolution from the disturbing action of Saturn alone.

A variation in the excentricity of the disturbed planet’s orbit is an
immediate consequence of the deviation from elliptical curvature, caused
by the action of the disturbing force. When the path of the body, in
proceeding from its perihelion to its aphelion, is more curved than it
ought to be from the effect of the disturbing forces, it falls within
the elliptical orbit, the excentricity is diminished, and the orbit
becomes more nearly circular; when that curvature is less than it ought
to be, the path of the planet falls without its elliptical orbit
(N. 66), and the excentricity is increased; during these changes, the
length of the major axis is not altered, the orbit only bulges out, or
becomes more flat (N. 70). Thus the variation in the excentricity arises
from the same cause that occasions the motion of the apsides (N. 67).
There is an inseparable connection between these two elements: they vary
simultaneously, and have the same period; so that, whilst the major axis
revolves in an immense period of time, the excentricity increases and
decreases by very small quantities, and at length returns to its
original magnitude at each revolution of the apsides. The terrestrial
excentricity is decreasing at the rate of about 40 miles annually; and,
if it were to decrease equably, it would be 39,861 years before the
earth’s orbit became a circle. The mutual action of Jupiter and Saturn
occasions variations in the excentricity of both orbits, the greatest
excentricity of Jupiter’s orbit corresponding to the least of Saturn’s.
The period in which these vicissitudes are accomplished is 70,414 years,
estimating the action of these two planets alone; but, if the action of
all the planets were estimated, the cycle would extend to millions of
years.

That part of the disturbing force is now to be considered which acts
perpendicularly to the plane of the orbit, causing periodic
perturbations in latitude, secular variations in the inclination of the
orbit, and a retrograde motion to its nodes on the true plane of the
ecliptic (N. 71). This force tends to pull the disturbed body above, or
push (N. 72) it below, the plane of its orbit, according to the relative
positions of the two planets with regard to the sun, considered to be
fixed. By this action, it sometimes makes the plane of the orbit of the
disturbed body tend to coincide with the plane of the ecliptic, and
sometimes increases its inclination to that plane. In consequence of
which, its nodes alternately recede or advance on the ecliptic (N. 73).
When the disturbing planet is in the line of the disturbed planet’s
nodes (N. 74), it neither affects these points, the latitude, nor the
inclination, because both planets are then in the same plane. When it is
at right angles to the line of the nodes, and the orbit symmetrical on
each side of the disturbing force, the average motion of these points,
after a revolution of the disturbed body, is retrograde, and
comparatively rapid: but, when the disturbing planet is so situated that
the orbit of the disturbed planet is not symmetrical on each side of the
disturbing force, which is most frequently the case, every possible
variety of action takes place. Consequently, the nodes are perpetually
advancing or receding with unequal velocity; but, as a compensation is
not effected, their motion is, on the whole, retrograde.

With regard to the variations in the inclination, it is clear, that,
when the orbit is symmetrical on each side of the disturbing force, all
its variations are compensated after a revolution of the disturbed body,
and are merely periodical perturbations in the planet’s latitude; and no
secular change is induced in the inclination of the orbit. When, on the
contrary, that orbit is not symmetrical on each side of the disturbing
force, although many of the variations in latitude are transient or
periodical, still, after a complete revolution of the disturbed body, a
portion remains uncompensated, which forms a secular change in the
inclination of the orbit to the plane of the ecliptic. It is true, part
of this secular change in the inclination is compensated by the
revolution of the disturbing body, whose motion has not hitherto been
taken into the account, so that perturbation compensates perturbation;
but still a comparatively permanent change is effected in the
inclination, which is not compensated till the nodes have accomplished a
complete revolution.

The changes in the inclination are extremely minute (N. 75), compared
with the motion of the nodes, and there is the same kind of inseparable
connection between their secular changes that there is between the
variation of the excentricity and the motion of the major axis. The
nodes and inclinations vary simultaneously; their periods are the same,
and very great. The nodes of Jupiter’s orbit, from the action of Saturn
alone, require 36,261 years to accomplish even a tropical revolution. In
what precedes, the influence of only one disturbing body has been
considered; but, when the action and reaction of the whole system are
taken into account, every planet is acted upon, and does itself act, in
this manner, on all the others; and the joint effect keeps the
inclinations and excentricities in a state of perpetual variation. It
makes the major axes of all the orbits continually revolve, and causes,
on an average, a retrograde motion of the nodes of each orbit upon every
other. The ecliptic (N. 71) itself is in motion from the mutual action
of the earth and planets, so that the whole is a compound phenomenon of
great complexity, extending through unknown ages. At the present time
the inclinations of all the orbits are decreasing, but so slowly, that
the inclination of Jupiter’s orbit is only about six minutes less than
it was in the age of Ptolemy.

But, in the midst of all these vicissitudes, the length of the major
axes and the mean motions of the planets remain permanently independent
of secular changes. They are so connected by Kepler’s law, of the
squares of the periodic times being proportional to the cubes of the
mean distances of the planets from the sun, that one cannot vary without
affecting the other. And it is proved, that any variations which do take
place are transient, and depend only on the relative positions of the
bodies.

It is true that, according to theory, the radial disturbing force should
permanently alter the dimensions of all the orbits, and the periodic
times of all the planets, to a certain degree. For example, the masses
of all the planets revolving within the orbit of any one, such as Mars,
by adding to the interior mass, increase the attracting force of the
sun, which, therefore, must contract the dimensions of the orbit of that
planet, and diminish its periodic time; whilst the planets exterior to
Mars’s orbit must have the contrary effect. But the mass of the whole of
the planets and satellites taken together is so small, when compared
with that of the sun, that these effects are quite insensible, and could
only have been discovered by theory. And, as it is certain that the
length of the major axes and the mean motions are not permanently
changed by any other power whatever, it may be concluded that they are
invariable.

With the exception of these two elements, it appears that all the bodies
are in motion, and every orbit in a state of perpetual change. Minute as
these changes are, they might be supposed to accumulate in the course of
ages, sufficiently to derange the whole order of nature, to alter the
relative positions of the planets, to put an end to the vicissitudes of
the seasons, and to bring about collisions which would involve our whole
system, now so harmonious, in chaotic confusion. It is natural to
inquire, what proof exists that nature will be preserved from such a
catastrophe? Nothing can be known from observation, since the existence
of the human race has occupied comparatively but a point in duration,
while these vicissitudes embrace myriads of ages. The proof is simple
and conclusive. All the variations of the solar system, secular as well
as periodic, are expressed analytically by the sines and cosines of
circular arcs (N. 76), which increase with the time; and, as a sine or
cosine can never exceed the radius, but must oscillate between zero and
unity, however much the time may increase, it follows that when the
variations have accumulated to a maximum by slow changes, in however
long a time, they decrease, by the same slow degrees, till they arrive
at their smallest value, again to begin a new course; thus for ever
oscillating about a mean value. This circumstance, however, would be
insufficient, were it not for the small excentricities of the planetary
orbits, their minute inclinations to the plane of the ecliptic, and the
revolutions of all the bodies, as well planets as satellites, in the
same direction. These secure the perpetual stability of the solar system
(N. 77). However, at the time that the stability was proved by La Grange
and La Place, the telescopic planets between Mars and Jupiter had not
been discovered; but La Grange, having investigated the subject under a
very general point of view, showed that, if a planetary system be
composed of very unequal masses, the whole of the larger would maintain
an unalterable stability with regard to the form and position of their
orbits, while the orbits of the lesser might undergo unlimited changes.
M. Le Verrier has applied this to the solar system, and has found that
the orbits of all the larger planets will for ever maintain an
unalterable stability in form and position; for, though liable to
mutations of very long periods, they return again exactly to what they
originally were, oscillating between very narrow limits; but he found a
zone of instability between the orbit of Mars, and twice the mean
distance of the earth from the sun,[1] or between 1·5 and 2·00;
therefore the position and form of the orbits of such of the telescopic
planets as revolve within that zone will be subject to unlimited
variations. But the orbits of those more remote from the sun than Flora,
or beyond 2·20, will be stable, so that their excentricities and
inclinations must always have been, and will always remain, very great,
since they must have depended upon the primitive conditions that
prevailed when these planetary atoms were launched into space. The 51st
of these small bodies, which was discovered, and the elements of its
orbit determined, by M. Valz, at Nimes, has a mean distance of 1·88; so
it revolves within the zone of instability. It has a shorter periodic
time than any of those previously discovered, and a greater
excentricity, with the exception of Nysa. Its orbit cuts that of Mars,
and comes nearer to the earth than the orbits of either Mars or Venus, a
circumstance which would be favourable for correcting the parallax of
the sun, or confirming its accuracy. The telescopic planets, numerous as
they are, have no influence on the motions of the larger planets, for
Jupiter has a diameter of 90,734 miles, while that of Pallas, his
nearest neighbour, is only 97 miles, little more than the distance from
London to Bath. The diameter of Mars, on the other side of the small
planets, is 4546 miles, and that of the earth 7925-1/2 miles, so that
the telescopic group are too minute to disturb the others. M. Le Verrier
found another zone of instability between Venus and the sun, on the
border of which Mercury is revolving, the inclination of whose orbit to
the plane of the ecliptic is about 7°, which is more than that of any of
the large planets. Neptune’s orbit is, no doubt, as stable as that of
any other of the large planets, as the inclination is very small, but he
will have periodical variations of very long duration from the
reciprocal attraction between him and Uranus, one especially of an
enormous duration, similar to those of Jupiter and Saturn, and, like
them, depending on the time of his revolution round the sun, being
nearly twice as long as that of Saturn. Mr. Adams has computed that
Neptune produces a periodical perturbation in the motion of Uranus,
whose duration is about 6800 years.

The equilibrium of the system, however, would be deranged if the planets
moved in a resisting medium (N. 78) sufficiently dense to diminish their
tangential velocity, for then both the excentricities and the major axes
of the orbits would vary with the time, so that the stability of the
system would be ultimately destroyed. The existence of an ethereal
medium is now proved; and, although it is so extremely rare that
hitherto its effects on the motions of the planets have been altogether
insensible, there can be no doubt that, in the immensity of time, it
will modify the forms of the planetary orbits, and may at last even
cause the destruction of our system, which in itself contains no
principle of decay, unless a rotatory motion from west to east has been
given to this medium by the bodies of the solar system, which have all
been revolving about the sun in that direction for unknown ages. This
rotation, which seems to be highly probable, may even have been coeval
with its creation. Such a vortex would have no effect on bodies moving
with it, but it would influence the motions of those revolving in a
contrary direction. It is possible that the disturbances experienced by
comets, which have already revealed the existence of this medium, may
also, in time, disclose its rotatory motion.

The form and position of the planetary orbits, and the motion of the
bodies in the same direction, together with the periodicity of the terms
in which the inequalities are expressed, assure us that the variations
of the system are confined within very narrow limits, and that, although
we do not know the extent of the limits, nor the period of that grand
cycle which probably embraces millions of years, yet they never will
exceed what is requisite for the stability and harmony of the whole; for
the preservation of which every circumstance is so beautifully and
wonderfully adapted.

The plane of the ecliptic itself, though assumed to be fixed at a given
epoch for the convenience of astronomical computation, is subject to a
minute secular variation of 45ʺ·7, occasioned by the reciprocal action
of the planets. But, as this is also periodical, and cannot exceed 2°
42ʹ, the terrestrial equator, which is inclined to it at an angle[2] of
23° 27ʹ 28ʺ·29, will never coincide with the plane of the ecliptic: so
there never can be perpetual spring (N. 79). The rotation of the earth
is uniform; therefore day and night, summer and winter, will continue
their vicissitudes while the system endures, or is undisturbed by
foreign causes.

                        Yonder starry sphere
              Of planets and of fix’d, in all her wheels,
              Resembles nearest mazes intricate,
              Eccentric, intervolved, yet regular,
              Then most, when most irregular they seem.

The stability of our system was established by La Grange: “a discovery,”
says Professor Playfair, “that must render the name for ever memorable
in science, and revered by those who delight in the contemplation of
whatever is excellent and sublime.” After Newton’s discovery of the
mechanical laws of the elliptical orbits of the planets, that of their
periodical inequalities, by La Grange, is, without doubt, the noblest
truth in the mechanism of the heavens; and, in respect of the doctrine
of final causes, it may be regarded as the greatest of all.

Notwithstanding the permanency of our system, the secular variations in
the planetary orbits would have been extremely embarrassing to
astronomers when it became necessary to compare observations separated
by long periods. The difficulty was in part obviated, and the principle
for accomplishing it established, by La Place, and has since been
extended by M. Poinsot. It appears that there exists an invariable plane
(N. 80), passing through the centre of gravity of the system, about
which the whole oscillates within very narrow limits, and that this
plane will always remain parallel to itself, whatever changes time may
induce in the orbits of the planets, in the plane of the ecliptic, or
even in the law of gravitation; provided only that our system remains
unconnected with any other. The position of the plane is determined by
this property—that, if each particle in the system be multiplied by the
area described upon this plane in a given time, by the projection of its
radius vector about the common centre of gravity of the whole, the sum
of all these products will be a maximum (N. 81). La Place found that the
plane in question is inclined to the ecliptic at an angle of nearly 1°
34ʹ 15ʺ, and that, in passing through the sun, and about midway between
the orbits of Jupiter and Saturn, it may be regarded as the equator of
the solar system, dividing it into two parts, which balance one another
in all their motions. This plane of greatest inertia, by no means
peculiar to the solar system, but existing in every system of bodies
submitted to their mutual attractions only, always maintains a fixed
position, whence the oscillations of the system may be estimated through
unlimited time. Future astronomers will know, from its immutability or
variation, whether the sun and his attendants are connected or not with
the other systems of the universe. Should there be no link between them,
it may be inferred, from the rotation of the sun, that the centre of
gravity (N. 82) of the system situate within his mass describes a
straight line in this invariable plane or great equator of the solar
system, which, unaffected by the changes of time, will maintain its
stability through endless ages. But, if the fixed stars, comets, or any
unknown and unseen bodies, affect our sun and planets, the nodes of this
plane will slowly recede on the plane of that immense orbit which the
sun may describe about some most distant centre, in a period which it
transcends the power of man to determine. There is every reason to
believe that this is the case; for it is more than probable that, remote
as the fixed stars are, they in some degree influence our system, and
that even the invariability of this plane is relative, only appearing
fixed to creatures incapable of estimating its minute and slow changes
during the small extent of time and space granted to the human race.
“The development of such changes,” as M. Poinsot justly observes, “is
similar to an enormous curve, of which we see so small an arc that we
imagine it to be a straight line.” If we raise our views to the whole
extent of the universe, and consider the stars, together with the sun,
to be wandering bodies, revolving about the common centre of creation,
we may then recognise in the equatorial plane passing through the centre
of gravity of the universe the only instance of absolute and eternal
repose.

All the periodic and secular inequalities deduced from the law of
gravitation are so perfectly confirmed by observation, that analysis has
become one of the most certain means of discovering the planetary
irregularities, either when they are too small, or too long in their
periods, to be detected by other methods. Jupiter and Saturn, however,
exhibit inequalities which for a long time seemed discordant with that
law. All observations, from those of the Chinese and Arabs down to the
present day, prove that for ages the mean motions of Jupiter and Saturn
have been affected by a great inequality of a very long period, forming
an apparent anomaly in the theory of the planets. It was long known by
observation that five times the mean motion of Saturn is nearly equal to
twice that of Jupiter; a relation which the sagacity of La Place
perceived to be the cause of a periodic irregularity in the mean motion
of each of these planets, which completes its period in nearly 918
years, the one being retarded while the other is accelerated; but both
the magnitude and period of these quantities vary, in consequence of the
secular variations in the elements of the orbits. Suppose the two
planets to be on the same side of the sun, and all three in the same
straight line, they are then said to be in conjunction (N. 83). Now, if
they begin to move at the same time, one making exactly five revolutions
in its orbit while the other only accomplishes two, it is clear that
Saturn, the slow-moving body, will only have got through a part of its
orbit during the time that Jupiter has made one whole revolution and
part of another, before they be again in conjunction. It is found that
during this time their mutual action is such as to produce a great many
perturbations which compensate each other, but that there still remains
a portion outstanding, owing to the length of time during which the
forces act in the same manner; and, if the conjunction always happened
in the same point of the orbit, this uncompensated inequality in the
mean motion would go on increasing till the periodic times and forms of
the orbits were completely and permanently changed: a case that would
actually take place if Jupiter accomplished exactly five revolutions in
the time Saturn performed two. These revolutions are, however, not
exactly commensurable; the points in which the conjunctions take place
are in advance each time as much as 8°·37; so that the conjunctions do
not happen exactly in the same points of the orbits till after a period
of 850 years; and, in consequence of this small advance, the planets are
brought into such relative positions, that the inequality, which seemed
to threaten the stability of the system, is completely compensated, and
the bodies, having returned to the same relative positions with regard
to one another and the sun, begin a new course. The secular variations
in the elements of the orbit increase the period of the inequality to
918 years (N. 84). As any perturbation which affects the mean motion
affects also the major axis, the disturbing forces tend to diminish the
major axis of Jupiter’s orbit, and increase that of Saturn’s, during one
half of the period, and the contrary during the other half. This
inequality is strictly periodical, since it depends upon the
configuration (N. 85) of the two planets; and theory is confirmed by
observation, which shows that, in the course of twenty centuries,
Jupiter’s mean motion has been accelerated by about 3° 23ʹ, and Saturn’s
retarded by 5° 13ʹ. Several instances of perturbations of this kind
occur in the solar system. One, in the mean motions of the Earth and
Venus, only amounting to a few seconds, has been recently worked out
with immense labour by Professor Airy. It accomplishes its changes in
240 years, and arises from the circumstance of thirteen times the
periodic time of Venus being nearly equal to eight times that of the
Earth. Small as it is, it is sensible in the motions of the Earth.

It might be imagined that the reciprocal action of such planets as have
satellites would be different from the influence of those that have
none. But the distances of the satellites from their primaries are
incomparably less than the distances of the planets from the sun, and
from one another. So that the system of a planet and its satellites
moves nearly as if all these bodies were united in their common centre
of gravity. The action of the sun, however, in some degree disturbs the
motion of the satellites about their primary.




                              SECTION IV.

Theory of Jupiter’s Satellites—Effects of the Figure of Jupiter upon his
  Satellites—Position of their Orbits—Singular Laws among the Motions of
  the first Three Satellites—Eclipses of the Satellites—Velocity of
  Light—Aberration—Ethereal Medium—Satellites of Saturn and Uranus.


THE changes which take place in the planetary system are exhibited on a
smaller scale by Jupiter and his satellites; and, as the period
requisite for the development of the inequalities of these moons only
extends to a few centuries, it may be regarded as an epitome of that
grand cycle which will not be accomplished by the planets in myriads of
ages. The revolutions of the satellites about Jupiter are precisely
similar to those of the planets about the sun; it is true they are
disturbed by the sun, but his distance is so great, that their motions
are nearly the same as if they were not under his influence. The
satellites, like the planets, were probably projected in elliptical
orbits: but, as the masses of the satellites are nearly 100,000 times
less than that of Jupiter; and as the compression of Jupiter’s spheroid
is so great, in consequence of his rapid rotation, that his equatorial
diameter exceeds his polar diameter by no less than 6000 miles; the
immense quantity of prominent matter at his equator must soon have given
the circular form observed in the orbits of the first and second
satellites, which its superior attraction will always maintain. The
third and fourth satellites, being farther removed from its influence,
revolve in orbits with a very small excentricity. And, although the
first two sensibly move in circles, their orbits acquire a small
ellipticity, from the disturbances they experience (N. 86).

It has been stated, that the attraction of a sphere on an exterior body
is the same as if its mass were united in one particle in its centre of
gravity, and therefore inversely as the square of the distance. In a
spheroid, however, there is an additional force arising from the bulging
mass at its equator, which, not following the exact law of gravity, acts
as a disturbing force. One effect of this disturbing force in the
spheroid of Jupiter is to occasion a direct motion in the greater axes
of the orbits of all his satellites, which is more rapid the nearer the
satellite is to the planet, and very much greater than that part of
their motion which arises from the disturbing action of the sun. The
same cause occasions the orbits of the satellites to remain nearly in
the plane of Jupiter’s equator (N. 87), on account of which the
satellites are always seen nearly in the same line (N. 88); and the
powerful action of that quantity of prominent matter is the reason why
the motions of the nodes of these small bodies are so much more rapid
than those of the planet. The nodes of the fourth satellite accomplish a
tropical revolution in 531 years, while those of Jupiter’s orbit require
no less than 36,261 years;—a proof of the reciprocal attraction between
each particle of Jupiter’s equator and of the satellites. In fact, if
the satellites moved exactly in the plane of Jupiter’s equator, they
would not be pulled out of that plane, because his attraction would be
equal on both sides of it. But, as their orbits have a small inclination
to the plane of the planet’s equator, there is a want of symmetry, and
the action of the protuberant matter tends to make the nodes regress by
pulling the satellites above or below the planes of their orbits; an
action which is so great on the interior satellites, that the motions of
their nodes are nearly the same as if no other disturbing force existed.

The orbits of the satellites do not retain a permanent inclination,
either to the plane of Jupiter’s equator, or to that of his orbit, but
to certain planes passing between the two, and through their
intersection. These have a greater inclination to his equator the
farther the satellite is removed, owing to the influence of Jupiter’s
compression; and they have a slow motion corresponding to secular
variations in the planes of Jupiter’s orbit and equator.

The satellites are not only subject to periodic and secular inequalities
from their mutual attraction, similar to those which affect the motions
and orbits of the planets, but also to others peculiar to themselves. Of
the periodic inequalities arising from their mutual attraction the most
remarkable take place in the angular motions (N. 89) of the three
nearest to Jupiter, the second of which receives from the first a
perturbation similar to that which it produces in the third; and it
experiences from the third a perturbation similar to that which it
communicates to the first. In the eclipses these two inequalities are
combined into one, whose period is 437·659 days. The variations peculiar
to the satellites arise from the secular inequalities occasioned by the
action of the planets in the form and position of Jupiter’s orbit, and
from the displacement of his equator. It is obvious that whatever alters
the relative positions of the sun, Jupiter, and his satellites, must
occasion a change in the directions and intensities of the forces, which
will affect the motions and orbits of the satellites. For this reason
the secular variations in the excentricity of Jupiter’s orbit occasion
secular inequalities in the mean motions of the satellites, and in the
motions of the nodes and apsides of their orbits. The displacement of
the orbit of Jupiter, and the variation in the position of his equator,
also affect these small bodies (N. 90). The plane of Jupiter’s equator
is inclined to the plane of his orbit at an angle of 3° 5ʹ 30ʺ, so that
the action of the sun and of the satellites themselves produces a
nutation and precession (N. 91) in his equator, precisely similar to
that which takes place in the rotation of the earth, from the action of
the sun and moon. Hence the protuberant matter at Jupiter’s equator is
continually changing its position with regard to the satellites, and
produces corresponding mutations in their motions. And, as the cause
must be proportional to the effect, these inequalities afford the means,
not only of ascertaining the compression of Jupiter’s spheroid, but they
prove that his mass is not homogeneous. Although the apparent diameters
of the satellites are too small to be measured, yet their perturbations
give the values of their masses with considerable accuracy—a striking
proof of the power of analysis.

A singular law obtains among the mean motions and mean longitudes of the
first three satellites. It appears from observation that the mean motion
of the first satellite, plus twice that of the third, is equal to three
times that of the second; and that the mean longitude of the first
satellite, minus three times that of the second, plus twice that of the
third, is always equal to two right angles. It is proved by theory,
that, if these relations had only been approximate when the satellites
were first launched into space, their mutual attractions would have
established and maintained them, notwithstanding the secular
inequalities to which they are liable. They extend to the synodic
motions (N. 92) of the satellites; consequently they affect their
eclipses, and have a very great influence on their whole theory. The
satellites move so nearly in the plane of Jupiter’s equator, which has a
very small inclination to his orbit, that the first three are eclipsed
at each revolution by the shadow of the planet, which is much larger
than the shadow of the moon: the fourth satellite is not eclipsed so
frequently as the others. The eclipses take place close to the disc of
Jupiter when he is near opposition (N. 93); but at times his shadow is
so projected with regard to the earth, that the third and fourth
satellites vanish and reappear on the same side of the disc (N. 94).
These eclipses are in all respects similar to those of the moon: but,
occasionally, the satellites eclipse Jupiter, sometimes passing like
obscure spots across his surface, resembling annular eclipses of the
sun, and sometimes like a bright spot traversing one of his dark belts.
Before opposition, the shadow of the satellite, like a round black spot,
precedes its passage over the disc of the planet; and, after opposition,
the shadow follows the satellite.

In consequence of the relations already mentioned in the mean motions
and mean longitudes of the first three satellites, they never can be all
eclipsed at the same time: for, when the second and third are in one
direction, the first is in the opposite direction; consequently, when
the first is eclipsed, the other two must be between the sun and
Jupiter. The instant of the beginning or end of an eclipse of a
satellite marks the same instant of absolute time to all the inhabitants
of the earth; therefore, the time of these eclipses observed by a
traveller, when compared with the time of the eclipse computed for
Greenwich, or any other fixed meridian (N. 95), gives the difference of
the meridians in time, and, consequently, the longitude of the place of
observation. The longitude is determined with extreme precision whenever
it is possible to convey the time instantaneously by means of
electricity from one place to another, since it obviates the errors of
clocks and chronometers. The eclipses of Jupiter’s satellites have been
the means of a discovery which, though not so immediately applicable to
the wants of man, unfolds one of the properties of light—that medium
without whose cheering influence all the beauties of the creation would
have been to us a blank. It is observed, that those eclipses of the
first satellite which happen when Jupiter is near conjunction (N. 96),
are later by 16ʹ 26ʺ·6 than those which take place when the planet is in
opposition. As Jupiter is nearer to us when in opposition by the whole
breadth of the earth’s orbit than when in conjunction, this circumstance
is to be attributed to the time employed by the rays of light in
crossing the earth’s orbit, a distance of about 190,000,000 of miles;
whence it is estimated that light travels at the rate of 192,000 miles
in one second. Such is its velocity, that the earth, moving at the rate
of nineteen miles in a second, would take two months to pass through a
distance which a ray of light would dart over in eight minutes. The
subsequent discovery of the aberration of light has fully confirmed this
astonishing result.

Objects appear to be situate in the direction of the rays which proceed
from them. Were light propagated instantaneously, every object, whether
at rest or in motion, would appear in the direction of these rays; but,
as light takes some time to travel, we see Jupiter in conjunction, by
means of rays that left him 16^m 26^s·6 before; but, during that time,
we have changed our position, in consequence of the motion of the earth
in its orbit: we therefore refer Jupiter to a place in which he is not.
His true position is in the diagonal (N. 97) of the parallelogram, whose
sides are in the ratio of the velocity of light to the velocity of the
earth in its orbit, which is as 192,000 to 19, or nearly as 10,000 to 1.
In consequence of the aberration of light, the heavenly bodies seem to
be in places in which they are not. In fact, if the earth were at rest,
rays from a star would pass along the axis of a telescope directed to
it; but, if the earth were to begin to move in its orbit with its usual
velocity, these rays would strike against the side of the tube; it
would, therefore, be necessary to incline the telescope a little, in
order to see the star. The angle contained between the axis of the
telescope and a line drawn to the true place of the star is its
aberration, which varies in quantity and direction in different parts of
the earth’s orbit; but, as it is only 20ʺ·481, it is insensible in
ordinary cases (N. 98).

The velocity of light deduced from the observed aberration of the fixed
stars perfectly corresponds with that given by the eclipses of the first
satellite. The same result, obtained from sources so different, leaves
not a doubt of its truth. Many such beautiful coincidences, derived from
circumstances apparently the most unpromising and dissimilar, occur in
physical astronomy, and prove connections which we might otherwise be
unable to trace. The identity of the velocity of light, at the distance
of Jupiter, and on the earth’s surface, shows that its velocity is
uniform; and as light consists in the vibrations of an elastic medium or
ether filling space, the uniformity of its velocity shows that the
density of the medium throughout the whole extent of the solar system
must be proportional to its elasticity (N. 99). Among the fortunate
conjectures which have been confirmed by subsequent experience, that of
Bacon is not the least remarkable, “It produces in me,” says the
restorer of true philosophy, “a doubt whether the face of the serene and
starry heavens be seen at the instant it really exists, or not till some
time later: and whether there be not, with respect to the heavenly
bodies, a true time and an apparent time, no less than a true place and
an apparent place, as astronomers say, on account of parallax. For it
seems incredible that the species or rays of the celestial bodies can
pass through the immense interval between them and us in an instant, or
that they do not even require some considerable portion of time.”

Great discoveries generally lead to a variety of conclusions: the
aberration of light affords a direct proof of the motion of the earth in
its orbit; and its rotation is proved by the theory of falling bodies,
since the centrifugal force it induces retards the oscillations of the
pendulum (N. 100) in going from the pole to the equator. Thus a high
degree of scientific knowledge has been requisite to dispel the errors
of the senses (N. 237).

The little that is known of the theories of the satellites of Saturn and
Uranus is, in all respects, similar to that of Jupiter. Saturn is
accompanied by eight satellites. The seventh is about the size of Mars,
and the eighth was simultaneously discovered by Mr. Bond in America, and
that distinguished astronomer Mr. Lassell, of Liverpool. The orbits of
the two last have a sensible inclination to the plane of the ring; but
the great compression of Saturn occasions the other satellites to move
nearly in the plane of his equator. So many circumstances must concur to
render the two interior satellites visible, that they have very rarely
been seen. They move exactly at the edge of the ring, and their orbits
never deviate from its plane. In 1789 Sir William Herschel saw them like
beads, threading the slender line of light which the ring is reduced to
when seen edgewise from the earth. And for a short time he perceived
them advancing off it at each end, when turning round in their orbits.
The eclipses of the exterior satellites only take place when the ring is
in this position. Mr. Lassell, with a powerful telescope, made by
himself, has seen Iapetus, the nearest of the two, on several occasions,
even when the opening of the ring was very wide, which made it extremely
difficult to see so minute an object. Of the situation of the equator of
Uranus we know nothing, nor of his compression; but the orbits of his
satellites are nearly perpendicular to the plane of the ecliptic; and,
by analogy, they ought to be in the plane of his equator. Uranus is so
remote that he has more the appearance of a planetary nebula than a
planet, which renders it extremely difficult to distinguish the
satellites at all; and quite hopeless without such a telescope as is
rarely to be met with even in observatories. Sir William Herschel
discovered the two that are farthest from the planet, and ascertained
their approximate periods, which his son afterwards determined to be
13^d 11^h 7^m 12^s·6 and 8^d 16^h 56^m 28^s·6 respectively. The
orbits of both seem to have an inclination of about 101°·2 to the plane
of the ecliptic. The two interior satellites are so faint and small, and
so near the edge of the planet, that they can with difficulty be seen
even under the most favourable circumstances: however, Mr. Lassell has
ascertained that the more distant of the two revolves about Uranus in 4
days, and that nearest to the planet in 2-1/2 days, and from a long and
minute examination he is convinced that the system only consists of four
satellites. Soon after Neptune was seen Mr. Lassell discovered the only
satellite known to belong to that planet. The satellites of Uranus and
Neptune, the two planets on the remotest verge of the solar system,
offer the singular and only instance of a revolution from east to west,
while all the planets and all the other satellites revolve from west to
east. Retrograde motion is occasionally met with in the comets and
double stars.




                               SECTION V.

Lunar Theory—Periodic Perturbations of the Moon—Equation of
  Centre—Evection—Variation—Annual Equation—Direct and Indirect
  Action of Planets—The Moon’s Action on the Earth disturbs her
  own Motion—Excentricity and Inclination of Lunar Orbit
  invariable—Acceleration—Secular Variation in Nodes and
  Perigee—Motion of Nodes and Perigee inseparably connected with
  the Acceleration—Nutation of Lunar Orbit—Form and Internal
  Structure of the Earth determined from it—Lunar, Solar, and
  Planetary Eclipses—Occultations and Lunar Distances—Mean
  Distance of the Sun from the Earth obtained from Lunar
  Theory—Absolute Distances of the Planets, how found.


OUR constant companion, the moon, next claims our attention. Several
circumstances concur to render her motions the most interesting, and at
the same time the most difficult to investigate, of all the bodies of
our system. In the solar system, planet troubles planet; but, in the
lunar theory, the sun is the great disturbing cause, his vast distance
being compensated by his enormous magnitude, so that the motions of the
moon are more irregular than those of the planets; and, on account of
the great ellipticity of her orbit, and the size of the sun, the
approximations to her motions are tedious and difficult, beyond what
those unaccustomed to such investigations could imagine. The average
distance of the moon from the centre of the earth is only 238,793 miles,
so that her motion among the stars is perceptible in a few hours. She
completes a circuit of the heavens in 27^d 7^h 43^m 11^s·5, moving
in an orbit whose excentricity is about 12,985 miles. The moon is about
four hundred times nearer to the earth than the sun. The proximity of
the moon to the earth keeps them together. For so great is the
attraction of the sun, that, if the moon were farther from the earth,
she would leave it altogether, and would revolve as an independent
planet about the sun.

The disturbing action (N. 101) of the sun on the moon is equivalent to
three forces. The first, acting in the direction of the line joining the
moon and earth, increases or diminishes her gravity to the earth. The
second, acting in the direction of a tangent to her orbit, disturbs her
motion in longitude. And the third, acting perpendicularly to the plane
of her orbit, disturbs her motion in latitude; that is, it brings her
nearer to, or removes her farther from, the plane of the ecliptic than
she would otherwise be. The periodic perturbations in the moon, arising
from these forces, are perfectly similar to the periodic perturbations
of the planets. But they are much greater and more numerous; because the
sun is so large, that many inequalities which are quite insensible in
the motions of the planets, are of great magnitude in those of the moon.
Among the innumerable periodic inequalities to which the moon’s motion
in longitude is liable, the most remarkable are, the Equation of the
Centre, which is the difference between the moon’s mean and true
longitude, the Evection, the Variation, and the Annual Equation. The
disturbing force which acts in the line joining the moon and earth
produces the Evection: it diminishes the excentricity of the lunar orbit
in conjunction and opposition, thereby making it more circular, and
augments it in quadrature, which consequently renders it more
elliptical. The period of this inequality is less than thirty-two days.
Were the increase and diminution always the same, the Evection would
only depend upon the distance of the moon from the sun; but its absolute
value also varies with her distance from the perigee (N. 102) of her
orbit. Ancient astronomers, who observed the moon solely with a view to
the prediction of eclipses, which can only happen in conjunction and
opposition, where the excentricity is diminished by the Evection,
assigned too small a value to the ellipticity of her orbit (N. 103). The
Evection was discovered by Ptolemy from observation, about A.D. 140. The
Variation produced by the tangential disturbing force, which is at its
maximum when the moon is 45° distant from the sun, vanishes when that
distance amounts to a quadrant, and also when the moon is in conjunction
and opposition; consequently, that inequality never could have been
discovered from the eclipses: its period is half a lunar month (N. 104).
The Annual Equation depends upon the sun’s distance from the earth: it
arises from the moon’s motion being accelerated when that of the earth
is retarded, and _vice versâ_—for, when the earth is in its perihelion,
the lunar orbit is enlarged by the action of the sun; therefore, the
moon requires more time to perform her revolution. But, as the earth
approaches its aphelion, the moon’s orbit contracts, and less time is
necessary to accomplish her motion—its period, consequently, depends
upon the time of the year. In the eclipses the Annual Equation combines
with the Equation of the Centre of the terrestrial orbit, so that
ancient astronomers imagined the earth’s orbit to have a greater
excentricity than modern astronomers assign to it.

The planets disturb the motion of the moon both directly and indirectly;
their action on the earth alters its relative position with regard to
the sun and moon, and occasions inequalities in the moon’s motion, which
are more considerable than those arising from their direct action; for
the same reason the moon, by disturbing the earth, indirectly disturbs
her own motion. Neither the excentricity of the lunar orbit, nor its
mean inclination to the plane of the ecliptic, have experienced any
changes from secular inequalities; for, although the mean action of the
sun on the moon depends upon the inclination of the lunar orbit to the
ecliptic, and the position of the ecliptic is subject to a secular
inequality, yet analysis shows that it does not occasion a secular
variation in the inclination of the lunar orbit, because the action of
the sun constantly brings the moon’s orbit to the same inclination to
the ecliptic. The mean motion, the nodes, and the perigee, however, are
subject to very remarkable variations.

From the eclipse observed at Babylon, on the 19th of March, seven
hundred and twenty-one years before the Christian era, the place of the
moon is known from that of the sun at the instant of opposition (N. 83),
whence her mean longitude may be found. But the comparison of this mean
longitude with another mean longitude, computed back for the instant of
the eclipse from modern observations, shows that the moon performs her
revolution round the earth more rapidly and in a shorter time now than
she did formerly, and that the acceleration in her mean motion has been
increasing from age to age as the square of the time (N. 105). All
ancient and intermediate eclipses confirm this result. As the mean
motions of the planets have no secular inequalities, this seemed to be
an unaccountable anomaly. It was at one time attributed to the
resistance of an ethereal medium pervading space, and at another to the
successive transmission of the gravitating force. But, as La Place
proved that neither of these causes, even if they exist, have any
influence on the motions of the lunar perigee (N. 102) or nodes, they
could not affect the mean motion; a variation in the mean motion from
such causes being inseparably connected with variations in the motions
of the perigee and nodes. That great mathematician, in studying the
theory of Jupiter’s satellites, perceived that the secular variation in
the elements of Jupiter’s orbit, from the action of the planets,
occasions corresponding changes in the motions of the satellites, which
led him to suspect that the acceleration in the mean motion of the moon
might be connected with the secular variation in the excentricity of the
terrestrial orbit. Analysis has shown that he assigned the true cause of
the acceleration.

It is proved that the greater the excentricity of the terrestrial orbit,
the greater is the disturbing action of the sun on the moon. Now, as the
excentricity has been decreasing for ages, the effect of the sun in
disturbing the moon has been diminishing during that time. Consequently
the attraction of the earth has had a more and more powerful effect on
the moon, and has been continually diminishing the size of the lunar
orbit. So that the moon’s velocity has been gradually augmenting for
many centuries to balance the increase of the earth’s attraction. This
secular increase in the moon’s velocity is called the Acceleration, a
name peculiarly appropriate at present, and which will continue to be so
for a vast number of ages; because, as long as the earth’s excentricity
diminishes, the moon’s mean motion will be accelerated; but when the
excentricity has passed its minimum, and begins to increase, the mean
motion will be retarded from age to age. The secular acceleration is now
about 11ʺ·9, but its effect on the moon’s place increases as the square
of the time (N. 106). It is remarkable that the action of the planets,
thus reflected by the sun to the moon, is much more sensible than their
direct action either on the earth or moon. The secular diminution in the
excentricity, which has not altered the equation of the centre of the
sun by eight minutes since the earliest recorded eclipses, has produced
a variation of about 1° 48ʹ in the moon’s longitude, and of 7° 12ʹ in
her mean anomaly (N. 107).

The action of the sun occasions a rapid but variable motion in the nodes
and perigee of the lunar orbit. Though the nodes recede during the
greater part of the moon’s revolution, and advance during the smaller,
they perform their sidereal revolution in 6793^d 9^h 23^m 9^s·3, or
about 18-6/10 years; and the perigee accomplishes a revolution, called
of the moon’s apsides, in 3232^d 13^h 48^m 29^s·6, or a little more
than nine years, notwithstanding its motion is sometimes retrograde and
sometimes direct: but such is the difference between the disturbing
energy of the sun and that of all the planets put together, that it
requires no less than 109,830 years for the greater axis of the
terrestrial orbit to do the same, moving at the rate of 11ʺ·8 annually.
The form of the earth has no sensible effect either on the lunar nodes
or apsides. It is evident that the same secular variation which changes
the sun’s distance from the earth, and occasions the acceleration in the
moon’s mean motion, must affect the nodes and perigee. It consequently
appears, from theory as well as observation, that both these elements
are subject to a secular inequality, arising from the variation in the
excentricity of the earth’s orbit, which connects them with the
Acceleration, so that both are retarded when the mean motion is
anticipated. The secular variations in these three elements are in the
ratio of the numbers 3, 0·735, and 1; whence the three motions of the
moon, with regard to the sun, to her perigee, and to her nodes, are
continually accelerated, and their secular equations are as the numbers
1, 4·702, and 0·612. A comparison of ancient eclipses observed by the
Arabs, Greeks, and Chaldeans, imperfect as they are, with modern
observations, confirms these results of analysis. Future ages will
develop these great inequalities, which at some most distant period will
amount to many circumferences (N. 108). They are, indeed, periodic; but
who shall tell their period? Millions of years must elapse before that
great cycle is accomplished.

The moon is so near, that the excess of matter at the earth’s equator
occasions periodic variations in her longitude, and also that remarkable
inequality in her latitude, already mentioned as a nutation in the lunar
orbit, which diminishes its inclination to the ecliptic when the moon’s
ascending node coincides with the equinox of spring, and augments it
when that node coincides with the equinox of autumn. As the cause must
be proportional to the effect, a comparison of these inequalities,
computed from theory, with the same given by observation, shows that the
compression of the terrestrial spheroid, or the ratio of the difference
between the polar and the equatorial diameters, to the diameter of the
equator, is 1/305·05. It is proved analytically, that, if a fluid mass
of homogeneous matter, whose particles attract each other inversely as
the squares of the distance, were to revolve about an axis as the earth
does, it would assume the form of a spheroid whose compression is 1/230.
Since that is not the case, the earth cannot be homogeneous, but must
decrease in density from its centre to its circumference. Thus the
moon’s eclipses show the earth to be round; and her inequalities not
only determine the form, but even the internal structure of our planet;
results of analysis which could not have been anticipated. Similar
inequalities in the motions of Jupiter’s satellites prove that his mass
is not homogeneous, and that his compression is 1/13·8. His equatorial
diameter exceeds his polar diameter by about 6000 miles.

The phases (N. 109) of the moon, which vary from a slender silvery
crescent soon after conjunction, to a complete circular disc of light in
opposition, decrease by the same degrees till the moon is again
enveloped in the morning beams of the sun. These changes regulate the
returns of the eclipses. Those of the sun can only happen in
conjunction, when the moon, coming between the earth and the sun,
intercepts his light. Those of the moon are occasioned by the earth
intervening between the sun and moon when in opposition. As the earth is
opaque and nearly spherical, it throws a conical shadow on the side of
the moon opposite to the sun, the axis of which passes through the
centres of the sun and earth (N. 110). The length of the shadow
terminates at the point where the apparent diameters (N. 111) of the sun
and earth would be the same. When the moon is in opposition, and at her
mean distance, the diameter of the sun would be seen from her centre
under an angle of 1918ʺ·1. That of the earth would appear under an angle
of 6908ʺ·3. So that the length of the shadow is at least three times and
a half greater than the distance of the moon from the earth, and the
breadth of the shadow, where it is traversed by the moon, is about
eight-thirds of the lunar diameter. Hence the moon would be eclipsed
every time she is in opposition, were it not for the inclination of her
orbit to the plane of the ecliptic, in consequence of which the moon,
when in opposition, is either above or below the cone of the earth’s
shadow, except when in or near her nodes. Her position with regard to
them occasions all the varieties in the lunar eclipses. Every point of
the moon’s surface successively loses the light of different parts of
the sun’s disc before being eclipsed. Her brightness therefore gradually
diminishes before she plunges into the earth’s shadow. The breadth of
the space occupied by the penumbra (N. 112) is equal to the apparent
diameter of the sun, as seen from the centre of the moon. The mean
duration of a revolution of the sun, with regard to the node of the
lunar orbit, is to the duration of a synodic revolution (N. 113) of the
moon as 223 to 19. So that, after a period of 223 lunar months, the sun
and moon would return to the same relative position with regard to the
node of the moon’s orbit, and therefore the eclipses would recur in the
same order were not the periods altered by irregularities in the motions
of the sun and moon. In lunar eclipses, our atmosphere bends the sun’s
rays which pass through it all round into the cone of the earth’s
shadow. And as the horizontal refraction (N. 114) or bending of the rays
surpasses half the sum of the semidiameters of the sun and moon, divided
by their mutual distance, the centre of the lunar disc, supposed to be
in the axis of the shadow, would receive the rays from the same point of
the sun, round all sides of the earth; so that it would be more
illuminated than in full moon, if the greater portion of the light were
not stopped or absorbed by the atmosphere. Instances are recorded where
this feeble light has been entirely absorbed, so that the moon has
altogether disappeared in her eclipses.

The sun is eclipsed when the moon intercepts his rays (N. 115). The
moon, though incomparably smaller than the sun, is so much nearer the
earth, that her apparent diameter differs but little from his, but both
are liable to such variations that they alternately surpass one another.
Were the eye of a spectator in the same straight line with the centres
of the sun and moon, he would see the sun eclipsed. If the apparent
diameter of the moon surpassed that of the sun, the eclipse would be
total. If it were less, the observer would see a ring of light round the
disc of the moon, and the eclipse would be annular, as it was on the
17th of May, 1836, and on the 15th of March, 1858. If the centre of the
moon should not be in the straight line joining the centres of the sun
and the eye of the observer, the moon might only eclipse a part of the
sun. The variation, therefore, in the distances of the sun and moon from
the centre of the earth, and of the moon from her node at the instant of
conjunction, occasions great varieties in the solar eclipses. Besides,
the height of the moon above the horizon changes her apparent diameter,
and may augment or diminish the apparent distances of the centres of the
sun and moon, so that an eclipse of the sun may occur to the inhabitants
of one country, and not to those of another. In this respect the solar
eclipses differ from the lunar, which are the same for every part of the
earth where the moon is above the horizon. In solar eclipses, the light
reflected by the atmosphere diminishes the obscurity they produce. Even
in total eclipses the higher part of the atmosphere is enlightened by a
part of the sun’s disc, and reflects its rays to the earth. The whole
disc of the new moon is frequently visible from atmospheric reflection.
During the eclipse of the 19th of March, 1849, the spots on the lunar
disc were distinctly visible, and during that of 1856 the moon was like
a beautiful rose-coloured ball floating in the ether: the colour is
owing to the refraction of the sun’s light passing through the earth’s
atmosphere.

In total solar eclipses the slender luminous arc that is visible for a
few seconds before the sun vanishes and also before he reappears,
resembles a string of pearls surrounding the dark edge of the moon; it
is occasioned by the sun’s rays passing between the tops of the lunar
mountains: it occurs likewise in annular eclipses.

A phenomenon altogether unprecedented was seen during the total eclipse
of the sun which happened on the 8th of July, 1842. The moon was like a
black patch on the sky surrounded by a faint whitish light or corona
about the eighth of the moon’s diameter in breadth, which is supposed to
be the solar atmosphere rendered visible by the intervention of the
moon. In this whitish corona there appeared three rose-coloured flames
like the teeth of a saw. Similar flames were also seen in the white
corona of the total eclipse which took place in 1851, and a long
rose-coloured chain of what appeared to be jagged mountains or sierras
united at the base by a red band seemed to be raised into the corona by
mirage; but there is no doubt that the corona and red phenomena belong
to the sun. This red chain was so bright that Mr. Airy saw it illuminate
the northern horizon through an azimuth of 90° with red light. M. Faye
attributes the rose-coloured protuberances to the constitution of the
sun, which, like Sir William Herschel, he conceives to be an
incandescent globe, consisting of two concentric parts of very unequal
density, the internal part being a dark spherical mass, the external a
very extensive atmosphere, at a certain height in which there is a
stratum of luminous clouds which constitutes the photosphere of the sun;
above this rises his real atmosphere, so rare as to be only visible as a
white aureola or corona during total and annular eclipses. M. Faye
conceives that from the central mass gaseous eruptions issue, which form
the spots by dissipating and partly extinguishing the luminous clouds,
and then rising into the rare atmosphere above that they appear as
rose-coloured protuberances during annular eclipses. He estimates that
the volume of these vapours sometimes surpasses that of the earth a
thousand or even two thousand times. Sir William Herschel attributed the
spots to occasional openings in the luminous coating, which seems to be
always in motion; but whatever the cause of the spots may be, it is
certainly periodical. The white corona and beads were seen during the
eclipse of the 15th March, 1858, but there were no rose-coloured
appearances, in England at least; but the sky was clouded, so that the
eclipse was only visible at intervals.

Planets sometimes eclipse one another. On the 17th of May, 1737, Mercury
was eclipsed by Venus near their inferior conjunction; Mars passed over
Jupiter on the 9th of January, 1591; and on the 30th of October, 1825,
the moon eclipsed Saturn. These phenomena, however, happen very seldom,
because all the planets, or even a part of them, are very rarely seen in
conjunction at once; that is, in the same part of the heavens at the
same time. More than 2500 years before our era the five great planets
were in conjunction. On the 15th of September, 1186, a similar
assemblage took place between the constellations of Virgo and Libra; and
in 1801 the Moon, Jupiter, Saturn, and Venus were united in the heart of
the Lion. These conjunctions are so rare, that Lalande has computed that
more than seventeen millions of millions of years separate the epochs of
the contemporaneous conjunctions of the six great planets.

The motions of the moon have now become of more importance to the
navigator and geographer than those of any other heavenly body, from the
precision with which terrestrial longitude is determined by occultations
of stars, and by lunar distances. In consequence of the retrograde
motion of the nodes of the lunar orbit, at the rate of 3ʹ 10ʺ·64 daily,
these points make a tour of the heavens in a little more than eighteen
years and a half. This causes the moon to move round the earth in a kind
of spiral, so that her disc at different times passes over every point
in a zone of the heavens extending rather more than 5° 9ʹ on each side
of the ecliptic. It is therefore evident that at one time or other she
must eclipse every star and planet she meets with in this space.
Therefore the occultation of a star by the moon is a phenomenon of
frequent occurrence. The moon seems to pass over the star, which almost
instantaneously vanishes at one side of her disc, and after a short time
as suddenly reappears on the other. A lunar distance is the observed
distance of the moon from the sun, or from a particular star or planet,
at any instant. The lunar theory is brought to such perfection, that the
times of these phenomena, observed under any meridian, when compared
with those computed for that of Greenwich, and given in the Nautical
Almanac, furnish the longitude of the observer within a few miles
(N. 95.)

From the lunar theory, the mean distance of the sun from the earth, and
thence the whole dimensions of the solar system, are known; for the
forces which retain the earth and moon in their orbits are respectively
proportional to the radii vectores of the earth and moon, each being
divided by the square of its periodic time. And, as the lunar theory
gives the ratio of the forces, the ratio of the distances of the sun and
moon from the earth is obtained. Hence it appears that the sun’s mean
distance from the earth is 399·7 or nearly 400 times greater than that
of the moon. The method of finding the absolute distances of the
celestial bodies, in miles, is in fact the same with that employed in
measuring the distances of terrestrial objects. From the extremities of
a known base (N. 116), the angles which the visual rays from the object
form with it are measured; their sum subtracted from two right angles
gives the angle opposite the base; therefore, by trigonometry, all the
angles and sides of the triangle may be computed—consequently the
distance of the object is found. The angle under which the base of the
triangle is seen from the object is the parallax of that object. It
evidently increases and decreases with the distance. Therefore the base
must be very great indeed to be visible from the celestial bodies. The
globe itself, whose dimensions are obtained by actual admeasurement,
furnishes a standard of measures with which we compare the distances,
masses, densities, and volumes of the sun and planets.




                              SECTION VI.

Form of the Earth and Planets—Figure of a Homogeneous Spheroid in
  Rotation—Figure of a Spheroid of variable Density—Figure of the Earth,
  supposing it to be an Ellipsoid of Revolution—Mensuration of a Degree
  of the Meridian—Compression and Size of the Earth from Degrees of
  Meridian—Figure of Earth from the Pendulum.


THE theoretical investigation of the figure of the earth and planets is
so complicated, that neither the geometry of Newton, nor the refined
analysis of La Place, has attained more than an approximation. The
solution of that difficult problem has been accomplished by our
distinguished countryman Mr. Ivory. The investigation has been conducted
by successive steps, beginning with a simple case, and then proceeding
to the more difficult. But, in all, the forces which occasion the
revolutions of the earth and planets are omitted, because, by acting
equally upon all the particles, they do not disturb their mutual
relations. A fluid mass of uniform density, whose particles mutually
gravitate to each other, will assume the form of a sphere when at rest.
But, if the sphere begins to revolve, every particle will describe a
circle (N. 117), having its centre in the axis of revolution. The planes
of all these circles will be parallel to one another and perpendicular
to the axis, and the particles will have a tendency to fly from that
axis in consequence of the centrifugal force arising from the velocity
of rotation. The force of gravity is everywhere perpendicular to the
surface (N. 118), and tends to the interior of the fluid mass; whereas
the centrifugal force acts perpendicularly to the axis of rotation, and
is directed to the exterior. And, as its intensity diminishes with the
distance from the axis of rotation, it decreases from the equator to the
poles, where it ceases. Now it is clear that these two forces are in
direct opposition to each other in the equator alone, and that gravity
is there diminished by the whole effect of the centrifugal force,
whereas, in every other part of the fluid, the centrifugal force is
resolved into two parts, one of which, being perpendicular to the
surface, diminishes the force of gravity; but the other, being at a
tangent to the surface, urges the particles towards the equator, where
they accumulate till their numbers compensate the diminution of gravity,
which makes the mass bulge at the equator, and become flattened at the
poles. It appears, then, that the influence of the centrifugal force is
most powerful at the equator, not only because it is actually greater
there than elsewhere, but because its whole effect is employed in
diminishing gravity, whereas, in every other point of the fluid mass, it
is only a part that is so employed. For both these reasons, it gradually
decreases towards the poles, where it ceases. On the contrary, gravity
is least at the equator, because the particles are farther from the
centre of the mass, and increases towards the poles, where it is
greatest. It is evident, therefore, that, as the centrifugal force is
much less than the force of gravity—gravitation, which is the difference
between the two, is least at the equator, and continually increases
towards the poles, where it is a maximum. On these principles Sir Isaac
Newton proved that a homogeneous fluid (N. 119) mass in rotation assumes
the form of an ellipsoid of revolution (N. 120), whose compression is
1/230. Such, however, cannot be the form of the earth, because the
strata increase in density towards the centre. The lunar inequalities
also prove the earth to be so constructed; it was requisite, therefore,
to consider the fluid mass to be of variable density. Including this
condition, it has been found that the mass, when in rotation, would
still assume the form of an ellipsoid of revolution (N. 120); that the
particles of equal density would arrange themselves in concentric
elliptical strata (N. 121), the most dense being in the centre; but that
the compression or flattening would be less than in the case of the
homogeneous fluid. The compression is still less when the mass is
considered to be, as it actually is, a solid nucleus, decreasing
regularly in density from the centre to the surface, and partially
covered by the ocean, because the solid parts, by their cohesion, nearly
destroy that part of the centrifugal force which gives the particles a
tendency to accumulate at the equator, though not altogether; otherwise
the sea, by the superior mobility of its particles, would flow towards
the equator and leave the poles dry. Besides, it is well known that the
continents at the equator are more elevated than they are in higher
latitudes. It is also necessary for the equilibrium of the ocean that
its density should be less than the mean density of the earth, otherwise
the continents would be perpetually liable to inundations from storms
and other causes. On the whole, it appears from theory, that a
horizontal line passing round the earth through both poles must be
nearly an ellipse, having its major axis in the plane of the equator,
and its minor axis coincident with the axis of the earth’s rotation
(N. 122). It is easy to show, in a spheroid whose strata are elliptical,
that the increase in the length of the radii (N. 123), the decrease of
gravitation, and the increase in the length of the arcs of the meridian,
corresponding to angles of one degree, from the poles to the equator,
are all proportional to the square of the cosine of the latitude
(N. 124). These quantities are so connected with the ellipticity of the
spheroid, that the total increase in the length of the radii is equal to
the compression or flattening, and the total diminution in the length of
the arcs is equal to the compression, multiplied by three times the
length of an arc of one degree at the equator. Hence, by measuring the
meridian curvature of the earth, the compression, and consequently its
figure, become known. This, indeed, is assuming the earth to be an
ellipsoid of revolution; but the actual measurement of the globe will
show how far it corresponds with that solid in figure and constitution.

The courses of the great rivers, which are in general navigable to a
considerable extent, prove that the curvature of the land differs but
little from that of the ocean; and, as the heights of the mountains and
continents are inconsiderable when compared with the magnitude of the
earth, its figure is understood to be determined by a surface at every
point perpendicular to the direction of gravitation, or of the
plumb-line, and is the same which the sea would have if it were
continued all round the earth beneath the continents. Such is the figure
that has been measured in the following manner:—

A terrestrial meridian is a line passing through both poles, all the
points of which have their noon contemporaneously. Were the lengths and
curvatures of different meridians known, the figure of the earth might
be determined. But the length of one degree is sufficient to give the
figure of the earth, if it be measured on different meridians, and in a
variety of latitudes. For, if the earth were a sphere, all degrees would
be of the same length; but, if not, the lengths of the degrees would be
greater, exactly in proportion as the curvature is less. A comparison of
the length of a degree in different parts of the earth’s surface will
therefore determine its size and form.

An arc of the meridian may be measured by determining the latitude of
its extreme points by astronomical observations (N. 125), and then
measuring the distance between them in feet or fathoms. The distance
thus determined on the surface of the earth, divided by the degrees and
parts of a degree contained in the difference of the latitudes, will
give the exact length of one degree, the difference of the latitudes
being the angle contained between the verticals at the extremities of
the arc. This would be easily accomplished were the distance
unobstructed and on a level with the sea. But, on account of the
innumerable obstacles on the surface of the earth, it is necessary to
connect the extreme points of the arc by a series of triangles (N. 126),
the sides and angles of which are either measured or computed, so that
the length of the arc is ascertained with much laborious calculation. In
consequence of the irregularities of the surface each triangle is in a
different plane. They must therefore be reduced by computation to what
they would have been had they been measured on the surface of the sea.
And, as the earth may in this case be esteemed spherical, they require a
correction to reduce them to spherical triangles. The officers who
conducted the trigonometrical survey, in measuring 500 feet of a base in
Ireland twice over, found that the difference in the two measurements
did not amount to the 800th part of an inch; and in the General Survey
of Great Britain, five bases were measured from 5 to 7 miles long, and
some of them 400 miles apart, yet, when connected by series of
triangles, the measured and computed lengths did not differ by more than
3 inches, an unparalleled degree of accuracy; but such is the accuracy
with which these operations are conducted.

Arcs of the meridian have been measured in a variety of latitudes in
both hemispheres, as well as arcs perpendicular to the meridian. From
these measurements it appears that the length of the degrees increases
from the equator to the poles, nearly in proportion to the square of the
sine of the latitude (N. 127). Consequently, the convexity of the earth
diminishes from the equator to the poles.

Were the earth an ellipsoid of revolution, the meridians would be
ellipses whose lesser axes would coincide with the axis of rotation, and
all the degrees measured between the pole and the equator would give the
same compression when combined two and two. That, however, is far from
being the case. Scarcely any of the measurements give exactly the same
results, chiefly on account of local attractions, which cause the
plumb-line to deviate from the vertical. The vicinity of mountains
produces that effect. One of the most remarkable anomalies of this kind
has been observed in certain localities of northern Italy, where the
action of some dense subterraneous matter causes the plumb-line to
deviate seven or eight times more than it did from the attraction of
Chimborazo, in the observations of Bouguer, while measuring a degree of
the meridian at the equator. In consequence of this local attraction,
the degrees of the meridian in that part of Italy seem to increase
towards the equator through a small space, instead of decreasing, as if
the earth was drawn out at the poles, instead of being flattened.

Many other discrepancies occur, but from the mean of the five principal
measurements of arcs in Peru, India, France, England, and Lapland, Mr.
Ivory has deduced that the figure which most nearly follows this law is
an ellipsoid of revolution whose equatorial radius is 3962·824 miles,
and the polar radius 3949·585 miles. The difference, or 13·239 miles,
divided by the equatorial radius, is 1/299 nearly[3] (N. 128). This
fraction is called the compression of the earth, and does not differ
much from that given by the lunar inequalities. Since the preceding
quantities were determined, arcs of the meridian have been measured in
various parts of the globe, of which the most extensive are the Russian
arc of 25° 20ʹ between the Glacial Sea and the Danube, conducted under
the superintendence of M. Struve, and the Indian arc extended to 21°
21ʹ, by Colonel Everest. The compression deduced by Bessel from the sum
of ten arcs is 298-3/4, the equatorial radius 3962·802, and the polar
3949·554 miles, whilst Mr. Airy arrives at an almost identical result
(3962·824, 3949·585, and 298-83/100) from a consideration of all the
arcs, measured up to 1831, including the great Indian and Russian ones.
If we assume the earth to be a sphere, the length of a degree of the
meridian is 69-14/100 English miles. Therefore 360 degrees, or the whole
equatorial circumference of the globe, is 24,899 English miles.
Eratosthenes, who died 194 years before the Christian era, was the first
to give an approximate value of the earth’s circumference, by the
measurement of an arc between Alexandria and Syene.

There is another method of finding the figure of the earth, totally
different from the preceding, solely depending upon the increase of
gravitation from the equator to the poles. The force of gravitation at
any place is measured by the descent of a heavy body during the first
second of its fall. And the intensity of the centrifugal force is
measured by the deflection of any point from the tangent in a second.
For, since the centrifugal force balances the attraction of the earth,
it is an exact measure of the gravitating force. Were the attraction to
cease, a body on the surface of the earth would fly off in the tangent
by the centrifugal force, instead of bending round in the circle of
rotation. Therefore, the deflection of the circle from the tangent in a
second measures the intensity of the earth’s attraction, and is equal to
the versed sine of the arc described during that time, a quantity easily
determined from the known velocity of the earth’s rotation. Whence it
has been found that at the equator the centrifugal force is equal to the
289th part of gravity. Now, it is proved by analysis that, whatever the
constitution of the earth and planets may be, if the intensity of
gravitation at the equator be taken equal to unity, the sum of the
compression of the ellipsoid, and the whole increase of gravitation from
the equator to the pole, is equal to five halves of the ratio of the
centrifugal force to gravitation at the equator. This quantity with
regard to the earth is 5/2 of 1/289 or 1/115·2. Consequently, the
compression of the earth is equal to 1/115·2 diminished by the whole
increase of gravitation. So that its form will be known, if the whole
increase of gravitation from the equator to the pole can be determined
by experiment. This has been accomplished by a method founded upon the
following considerations:—If the earth were a homogeneous sphere without
rotation, its attraction on bodies at its surface would be everywhere
the same. If it be elliptical and of variable density, the force of
gravity, theoretically, ought to increase from the equator to the pole,
as unity _plus_ a constant quantity multiplied into the square of the
sine of the latitude (N. 127). But for a spheroid in rotation the
centrifugal force varies, by the laws of mechanics, as the square of the
sine of the latitude, from the equator, where it is greatest, to the
pole, where it vanishes. And, as it tends to make bodies fly off the
surface, it diminishes the force of gravity by a small quantity. Hence,
by gravitation, which is the difference of these two forces, the fall of
bodies ought to be accelerated from the equator to the poles
proportionably to the square of the sine of the latitude; and the weight
of the same body ought to increase in that ratio. This is directly
proved by the oscillations of the pendulum (N. 129), which, in fact, is
a falling body; for, if the fall of bodies be accelerated, the
oscillations will be more rapid: in order, therefore, that they may
always be performed in the same time, the length of the pendulum must be
altered. By numerous and careful experiments it is proved that a
pendulum, which oscillates 86,400 times in a mean day at the equator,
will do the same at every point of the earth’s surface, if its length be
increased progressively to the pole, as the square of the sine of the
latitude.

From the mean of these it appears that the whole decrease of gravitation
from the poles to the equator is 0·0051449, which, subtracted from
1/115·2, shows that the compression of the terrestrial spheroid is about
1/285·26. This value has been deduced by the late Mr. Baily, president
of the Astronomical Society, who devoted much attention to this subject;
at the same time, it may be observed that no two sets of pendulum
experiments give the same result, probably from local attractions. The
compression obtained by this method does not differ much from that given
by the lunar inequalities, nor from the arcs in the direction of the
meridian, and those perpendicular to it. The near coincidence of these
three values, deduced by methods so entirely independent of each other,
shows that the mutual tendencies of the centres of the celestial bodies
to one another, and the attraction of the earth for bodies at its
surface, result from the reciprocal attraction of all their particles.
Another proof may be added. The nutation of the earth’s axis and the
precession of the equinoxes (N. 146) are occasioned by the action of the
sun and moon on the protuberant matter at the earth’s equator. And,
although these inequalities do not give the absolute value of the
terrestrial compression, they show that the fraction expressing it is
comprised between the limits 1/279 and 1/573.

It might be expected that the same compression should result from each,
if the different methods of observation could be made without error.
This, however, is not the case; for after allowance has been made for
every cause of error, such discrepancies are found, both in the degrees
of the meridian and in the length of the pendulum, as show that the
figure of the earth is very complicated. But they are so small, when
compared with the general results, that they may be disregarded. The
compression deduced from the mean of the whole appears not to differ
much from 1/300; that given by the lunar theory has the advantage of
being independent of the irregularities of the earth’s surface and of
local attractions. The regularity with which the observed variation in
the length of the pendulum follows the law of the square of the sine of
the latitude proves the strata to be elliptical, and symmetrically
disposed round the centre of gravity of the earth, which affords a
strong presumption in favour of its original fluidity. It is remarkable
how little influence the sea has on the variation of the lengths of the
arcs of the meridian, or on gravitation; neither does it much affect the
lunar inequalities, from its density being only about a fifth of the
mean density of the earth. For, if the earth were to become fluid, after
being stripped of the ocean, it would assume the form of an ellipsoid of
revolution whose compression is 1/304·8, which differs very little from
that determined by observation, and proves, not only that the density of
the ocean is inconsiderable, but that its mean depth is very small.
There are profound cavities in the bottom of the sea, but its mean depth
probably does not much exceed the mean height of the continents and
islands above its level. On this account, immense tracts of land may be
deserted or overwhelmed by the ocean, as appears really to have been the
case, without any great change in the form of the terrestrial spheroid.
The variation in the length of the pendulum was first remarked by
Richter in 1672, while observing transits of the fixed stars across the
meridian at Cayenne, about five degrees north of the equator. He found
that his clock lost at the rate of 2^m 28^s daily, which induced him
to determine the length of a pendulum beating seconds in that latitude;
and, repeating the experiments on his return to Europe, he found the
seconds’ pendulum at Paris to be more than the twelfth of an inch longer
than that at Cayenne. The form and size of the earth being determined, a
standard of measure is furnished with which the dimensions of the solar
system may be compared.




                              SECTION VII.

Parallax—Lunar Parallax found from Direct Observation—Solar Parallax
  deduced from the Transit of Venus—Distance of the Sun from the
  Earth—Annual Parallax—Distance of the Fixed Stars.


THE parallax of a celestial body is the angle under which the radius of
the earth would be seen if viewed from the centre of that body; it
affords the means of ascertaining the distances of the sun, moon, and
planets (N. 130). When the moon is in the horizon at the instant of
rising or setting, suppose lines to be drawn from her centre to the
spectator and to the centre of the earth: these would form a
right-angled triangle with the terrestrial radius, which is of a known
length; and, as the parallax or angle at the moon can be measured, all
the angles and one side are given; whence the distance of the moon from
the centre of the earth may be computed. The parallax of an object may
be found, if two observers under the same meridian, but at a very great
distance from one another, observe its zenith distances on the same day
at the time of its passage over the meridian. By such contemporaneous
observations at the Cape of Good Hope and at Berlin, the mean horizontal
parallax of the moon was found to be 3459ʺ, whence the mean distance of
the moon is about sixty times the greatest terrestrial radius, or
237,608 miles nearly.[4] Since the parallax is equal to the radius of
the earth divided by the distance of the moon, it varies with the
distance of the moon from the earth under the same parallel of latitude,
and proves the ellipticity of the lunar orbit. When the moon is at her
mean distance, it varies with the terrestrial radii, thus showing that
the earth is not a sphere (N. 131).

Although the method described is sufficiently accurate for finding the
parallax of an object as near as the moon, it will not answer for the
sun, which is so remote that the smallest error in observation would
lead to a false result. But that difficulty is obviated by the transits
of Venus. When that planet is in her nodes (N. 132), or within 1-1/4° of
them, that is, in, or nearly in, the plane of the ecliptic, she is
occasionally seen to pass over the sun like a black spot. If we could
imagine that the sun and Venus had no parallax, the line described by
the planet on his disc, and the duration of the transit, would be the
same to all the inhabitants of the earth. But, as the semi-diameter of
the earth has a sensible magnitude when viewed from the centre of the
sun, the line described by the planet in its passage over his disc
appears to be nearer to his centre, or farther from it, according to the
position of the observer; so that the duration of the transit varies
with the different points of the earth’s surface at which it is observed
(N. 133). This difference of time, being entirely the effect of
parallax, furnishes the means of computing it from the known motions of
the earth and Venus, by the same method as for the eclipses of the sun.
In fact, the ratio of the distances of Venus and the sun from the earth
at the time of the transit is known from the theory of their elliptical
motion. Consequently the ratio of the parallaxes of these two bodies,
being inversely as their distances, is given; and as the transit gives
the difference of the parallaxes, that of the sun is obtained. In 1769
the parallax of the sun was determined by observations of a transit of
Venus made at Wardhus in Lapland, and at Tahiti in the South Sea. The
latter observation was the object of Cook’s first voyage. The transit
lasted about six hours at Tahiti, and the difference in duration at
these two stations was eight minutes; whence the sun’s horizontal
parallax was found to be 8ʺ·72. But by other considerations it has been
reduced by Professor Encke to 8ʺ·5776; from which the mean distance of
the sun appears to be about ninety-five millions of miles. This is
confirmed by an inequality in the motion of the moon, which depends upon
the parallax of the sun, and which, when compared with observation,
gives 8ʺ·6 for the sun’s parallax. The transits of Venus in 1874 and
1882 will be unfavourable for ascertaining the accuracy of the solar
parallax, and no other transit of that planet will take place till the
twenty-first century; but in the mean time recourse may be had to the
oppositions of Mars.

The parallax of Venus is determined by her transits; that of Mars by
direct observation, and it is found to be nearly double that of the sun,
when the planet is in opposition. The distance of these two planets from
the earth is therefore known in terrestrial radii, consequently their
mean distances from the sun may be computed; and as the ratios of the
distances of the planets from the sun are known by Kepler’s law, of the
squares of the periodic times of any two planets being as the cubes of
their mean distances from the sun, their absolute distances in miles are
easily found (N. 134). This law is very remarkable, in thus uniting all
the bodies of the system, and extending to the satellites as well as the
planets.

Far as the earth seems to be from the sun, Uranus is no less than
nineteen, and Neptune thirty times farther. Situate on the verge of the
system, the sun must appear from Uranus not much larger than Venus does
to us, and from Neptune as a star of the fifth magnitude. The earth
cannot even be visible as a telescopic object to a body so remote as
either Uranus or Neptune. Yet man, the inhabitant of the earth, soars
beyond the vast dimensions of the system to which his planet belongs,
and assumes the diameter of its orbit as the base of a triangle whose
apex extends to the stars.

Sublime as the idea is, this assumption proves ineffectual, except in a
very few cases; for the apparent places of the fixed stars are not
sensibly changed by the earth’s annual revolution. With the aid derived
from the refinements of modern astronomy, and of the most perfect
instruments, a sensible parallax has been detected only in a very few of
these remote suns. α Centauri has a parallax of one second of space,
therefore it is the nearest known star, and yet it is more than two
hundred thousand times farther from us than the sun is. At such a
distance not only the terrestrial orbit shrinks to a point, but the
whole solar system, seen in the focus of the most powerful telescope,
might be eclipsed by the thickness of a spider’s thread. Light, flying
at the rate of 190,000 miles in a second, would take more than three
years to travel over that space. One of the nearest stars may therefore
have been kindled or extinguished more than three years before we could
have been aware of so mighty an event. But this distance must be small
when compared with that of the most remote of the bodies which are
visible in the heavens. The fixed stars are undoubtedly luminous like
the sun: it is therefore probable that they are not nearer to one
another than the sun is to the nearest of them. In the milky way and the
other starry nebulæ, some of the stars that seem to us to be close to
others may be far behind them in the boundless depth of space; nay, may
be rationally supposed to be situate many thousand times farther off.
Light would therefore require thousands of years to come to the earth
from those myriads of suns of which our own is but “the remote
companion.”




                             SECTION VIII.

Masses of Planets that have no Satellites determined from their
  Perturbations—Masses of the others obtained from the Motions of their
  Satellites—Masses of the Sun, the Earth, of Jupiter and of the Jovial
  System—Mass of the Moon—Real Diameters of Planets, how obtained—Size
  of Sun, Densities of the Heavenly Bodies—Formation of Astronomical
  Tables—Requisite Data and Means of obtaining them.


THE masses of such planets as have no satellites are known by comparing
the inequalities they produce in the motions of the earth and of each
other, determined theoretically, with the same inequalities given by
observation; for the disturbing cause must necessarily be proportional
to the effect it produces. The masses of the satellites themselves may
also be compared with that of the sun by their perturbations. Thus, it
is found, from the comparison of a vast number of observations with La
Place’s theory of Jupiter’s satellites, that the mass of the sun is no
less than 65,000,000 times greater than the least of these moons. But,
as the quantities of matter in any two primary planets are directly as
the cubes of the mean distances at which their satellites revolve, and
inversely as the squares of their periodic times (N. 135), the mass of
the sun and of any planets which have satellites may be compared with
the mass of the earth. In this manner it is computed that the mass of
the sun is 354,936 times that of the earth; whence the great
perturbations of the moon, and the rapid motion of the perigee and nodes
of her orbit (N. 136). Even Jupiter, the largest of the planets, has
been found by Professor Airy to be 1047·871 times less than the sun;
and, indeed, the mass of the whole Jovial system is not more than the
1054·4th part of that of the sun. So that the mass of the satellites
bears a very small proportion to that of their primary. The mass of the
moon is determined from several sources—from her action on the
terrestrial equator, which occasions the nutation in the axis of
rotation; from her horizontal parallax; from an inequality she produces
in the sun’s longitude; and from her action on the tides. The three
first quantities, computed from theory and compared with their observed
values, give her mass respectively equal to the 1/71, 1/74·2, and
1/69·2, part of that of the earth, which do not differ much from each
other. Dr. Brinkley has found it to be 1/80 from the constant of lunar
nutation: but, from the moon’s action in raising the tides, her mass
appears to be about the 1/75 part of that of the earth—a value that
cannot differ much from the truth.

The apparent diameters of the sun, moon, and planets are determined by
measurement; therefore their real diameters may be compared with that of
the earth; for the real diameter of a planet is to the real diameter of
the earth, or 7926 miles, as the apparent diameter of the planet to the
apparent diameter of the earth as seen from the planet, that is, to
twice the parallax of the planet. According to Bessel, the mean apparent
diameter of the sun is 1923ʺ·64, and with the solar parallax 8ʺ·5776, it
will be found that the diameter of the sun is about 886,877 miles.
Therefore, if the centre of the sun were to coincide with the centre of
the earth, his volume would not only include the orbit of the moon, but
would extend nearly as far again; for the moon’s mean distance from the
earth is about sixty times the earth’s equatorial radius, or 238,793
miles: so that twice the distance of the moon is 477,586 miles, which
differs but little from the solar radius; his equatorial radius is
probably not much less than the major axis of the lunar orbit. The
diameter of the moon is only 2160 miles; and Jupiter’s diameter of
88,200 miles is very much less than that of the sun; the diameter of
Pallas does not much exceed 79 miles, so that an inhabitant of that
planet, in one of our steam carriages, might go round his world in a few
hours. The diameters of Lutetia and Atalanta are only 8 and 4 miles
respectively; but the whole of the 55 telescopic planets are so small,
that their united mass is probably not more than the fifth or sixth part
of that of the moon.

The densities of bodies are proportional to their masses, divided by
their volumes. Hence, if the sun and planets be assumed to be spheres,
their volumes will be as the cubes of their diameters. Now, the apparent
diameters of the sun and earth, at their mean distance, are 1923ʺ·6 and
17ʺ·1552, and the mass of the earth is the 354,936th part of that of the
sun taken as the unit. It follows, therefore, that the earth is four
times as dense as the sun. But the sun is so large that his attractive
force would cause bodies to fall through about 334·65 feet in a second.
Consequently, if he were habitable by human beings, they would be unable
to move, since their weight would be thirty times as great as it is
here. A man of moderate size would weigh about two tons at the surface
of the sun; whereas at the surface of some of the new planets he would
be so light that it would be impossible to stand steady, since he would
only weigh a few pounds. The mean density of the earth has been
determined by the following method. Since a comparison of the action of
two planets upon a third gives the ratio of the masses of these two
planets, it is clear that, if we can compare the effect of the whole
earth with the effect of any part of it, a comparison may be instituted
between the mass of the whole earth and the mass of that part of it. Now
a leaden ball was weighed against the earth by comparing the effects of
each upon a pendulum; the nearness of the smaller mass making it produce
a sensible effect as compared with that of the larger: for by the laws
of attraction the whole earth must be considered as collected in its
centre. By this method it has been found that the mean density of the
earth is 5·660 times greater than that of water at the temperature of
62° of Fahrenheit’s thermometer. The late Mr. Baily, whose accuracy as
an experimental philosopher is acknowledged, was unremittingly occupied
nearly four years in accomplishing this very important object. In order
to ascertain the mean density of the earth still more perfectly, Mr.
Airy made a series of experiments to compare the simultaneous
oscillations of two pendulums, one at the bottom of the Harton coal-pit,
1260 feet deep, in Northumberland, and the other on the surface of the
earth immediately above it. The oscillations of the pendulums were
compared with an astronomical clock at each station, and the time was
instantaneously transmitted from one to the other by a telegraphic wire.
The oscillations were observed for more than 100 hours continuously,
when it was found that the lower pendulum made 2-1/2 oscillations more
in 24 hours than the upper one. The experiment was repeated for the same
length of time with the same result; but on this occasion the upper
pendulum was taken to the bottom of the mine and the lower brought to
the surface. From the difference between the oscillations at the two
stations it appears that gravitation at the bottom of the mine exceeds
that at the surface by the 1/19190 part, and that the mean density of
the earth is 6·565, which is greater than that obtained by Mr. Baily by
·89. While employed on the trigonometrical survey of Scotland, Colonel
James determined the mean density of the earth to be 5·316, from a
deviation of the plumb-line amounting to 2ʺ, caused by the attraction of
Arthur’s Seat and the heights east of Edinburgh: it agrees more nearly
with the density found by Mr. Baily than with that deduced from Mr.
Airy’s experiments. All the planets and satellites appear to be of less
density than the earth. The motions of Jupiter’s satellites show that
his density increases towards his centre. Were his mass homogeneous, his
equatorial and polar axes would be in the ratio of 41 to 36, whereas
they are observed to be only as 41 to 38. The singular irregularities in
the form of Saturn, and the great compression of Mars, prove the
internal structure of these two planets to be very far from uniform.

Before entering on the theory of rotation, it may not be foreign to the
subject to give some idea of the methods of computing the places of the
planets, and of forming astronomical tables. Astronomy is now divided
into the three distinct departments of theory, observation, and
computation. Since the problem of the three bodies can only be solved by
approximation, the analytical astronomer determines the position of a
planet in space by a series of corrections. Its place in its circular
orbit is first found, then the addition or subtraction of the equation
of the centre (N. 48) to or from its mean place gives its position in
the ellipse. This again is corrected by the application of the principal
periodic inequalities. But, as these are determined for some particular
position of the three bodies, they require to be corrected to suit other
relative positions. This process is continued till the corrections
become less than the errors of observation, when it is obviously
unnecessary to carry the approximation further. The true latitude and
distance of the planet from the sun are obtained by methods similar to
those employed for the longitude.

As the earth revolves equably about its axis in 24 hours, at the rate of
15° in an hour, time becomes a measure of angular motion, and the
principal element in astronomy, where the object is to determine the
exact state of the heavens and the successive changes it undergoes in
all ages, past, present, and to come. Now, the longitude, latitude, and
distance of a planet from the sun are given in terms of the time, by
general analytical formulæ. These formulæ will consequently give the
exact place of the body in the heavens, for any time assumed at
pleasure, provided they can be reduced to numbers. But before the
calculator begins his task the observer must furnish the necessary data,
which are, obviously, the forms of the orbits, and their positions with
regard to the plane of the ecliptic (N. 57). It is therefore necessary
to determine by observation, for each planet, the length of the major
axis of its orbit, the excentricity, the inclination of the orbit to the
plane of the ecliptic, the longitudes of its perihelion and ascending
node at a given time, the periodic time of the planet, and its longitude
at any instant arbitrarily assumed, as an origin from whence all its
subsequent and antecedent longitudes are estimated. Each of these
quantities is determined from that position of the planet on which it
has most influence. For example, the sum of the greatest and least
distances of the planet from the sun is equal to the major axis of the
orbit, and their difference is equal to twice the excentricity. The
longitude of the planet, when at its least distance from the sun, is the
same with the longitude of the perihelion; the greatest latitude of the
planet is equal to the inclination of the orbit: the longitude of the
planet, when in the plane of the ecliptic in passing towards the north,
is the longitude of the ascending node, and the periodic time is the
interval between two consecutive passages of the planet through the same
node, a small correction being made for the precession of the node
during the revolution of the planet (N. 137). Notwithstanding the
excellence of instruments and the accuracy of modern observers,
unavoidable errors of observation can only be compensated by finding the
value of each element from the mean of a thousand, or even many
thousands of observations. For as it is probable that the errors are not
all in one direction, but that some are in excess and others in defect,
they will compensate each other when combined.

However, the values of the elements determined separately can only be
regarded as approximate, because they are so connected that the
estimation of any one independently will induce errors in the others.
The excentricity depends upon the longitude of the perihelion, the mean
motion depends upon the major axis, the longitude of the node upon the
inclination of the orbit, and _vice versâ_. Consequently, the place of a
planet computed with the approximate data will differ from its observed
place. Then the difficulty is to ascertain what elements are most in
fault, since the difference in question is the error of all; that is
obviated by finding the errors of some thousands of observations, and
combining them, so as to correct the elements simultaneously, and to
make the sum of the squares of the errors a minimum with regard to each
element (N. 138). The method of accomplishing this depends upon the
Theory of Probabilities; a subject fertile in most important results in
the various departments of science and of civil life, and quite
indispensable in the determination of astronomical data. A series of
observations continued for some years will give approximate values of
the secular and periodic inequalities, which must be corrected from time
to time, till theory and observation agree. And these again will give
values of the masses of the bodies forming the solar system, which are
important data in computing their motions. The periodic inequalities
derived from a great number of observations are employed for the
determination of the values of the masses till such time as the secular
inequalities shall be perfectly known, which will then give them with
all the necessary precision. When all these quantities are determined in
numbers, the longitude, latitude, and distance of the planet from the
sun are computed for stated intervals, and formed into tables, arranged
according to the time estimated from a given epoch, so that the place of
the body may be determined from them by inspection alone, at any instant
for perhaps a thousand years before and after that epoch. By this
tedious process, tables have been computed for all the great planets,
and several of the small, besides the moon and the satellites of
Jupiter. In the present state of astronomy the masses and elements of
the orbits are pretty well known, so that the tables only require to be
corrected from time to time as observations become more accurate. Those
containing the motions of Jupiter, Saturn, and Uranus have already been
twice constructed within the last thirty years, and the tables of
Jupiter and Saturn agree almost perfectly with modern observation. The
following prediction will be found in the sixth edition of this book,
published in the year 1842: “Those of Uranus, however, are already
defective, probably because the discovery of that planet in 1781 is too
recent to admit of much precision in the determination of its motions,
or that possibly it may be subject to disturbances from some unseen
planet revolving about the sun beyond the present boundaries of our
system. If, after a lapse of years, the tables formed from a combination
of numerous observations should be still inadequate to represent the
motions of Uranus, the discrepancies may reveal the existence, nay, even
the mass and orbit, of a body placed for ever beyond the sphere of
vision.”[5]

That prediction has been fulfilled since the seventh edition of this
book was published. Not only the existence of Neptune, revolving at the
distance of three thousand millions of miles from the sun, has been
discovered from his disturbing action on Uranus, but his mass, the form
and position of his orbit in space, and his periodic time had been
determined before the planet had been seen, and the planet itself was
discovered in the very point of the heavens which had been assigned to
it. It had been noticed for years that the perturbation of Uranus had
increased in an unaccountable manner (N. 139). After the disturbing
action of all the known planets had been determined, it was found that,
between the years 1833 and 1837, the observed and computed distance of
Uranus from the sun differed by 240,000 miles, which is about the mean
distance of the moon from the earth, while, in 1841, the error in the
geocentric longitude of the planet amounted to 96ʺ. These discrepancies
were therefore attributed to the attraction of some unseen and unknown
planet, consequently they gave rise to a case altogether unprecedented
in the history of astronomy. Heretofore it was required to determine the
disturbing action of one known planet upon another. Whereas the inverse
problem had now to be solved, in which it was required to find the place
of an unknown body in the heavens, at a given time, together with its
mass, and the form and position of its orbit, from the disturbance it
produced on the motions of another. The difficulty was extreme, because
all the elements of the orbit of Uranus were erroneous from the action
of Neptune, and those of Neptune’s orbit were unknown. In this dilemma
it was necessary to form some hypothesis with regard to the unknown
planet; it was therefore assumed, according to Bode’s empirical law on
the mean distances of the planets, that it was revolving at twice the
distance of Uranus from the sun. In fact, the periodic time of Uranus is
about 84 years, and, as the discrepancies in his motions increased
slowly and regularly, it was evident that it would require a planet with
a much longer periodic time to produce them—moreover, it was clear that
the new planet must be exterior to Uranus, otherwise it would have
disturbed the motions of Saturn.

Another circumstance tended to lessen the difficulty; the latitude of
Uranus was not much affected, therefore it was concluded that the
inclination of the orbit of the unknown body must be very small, and, as
that of the orbit of Uranus is only 46ʹ 28ʺ·4, both planets were assumed
to be moving in the plane of the ecliptic, and thus the elements of the
orbit of the unknown planet were reduced from six to four. Having thus
assumed that the unknown body was revolving in a circle in the plane of
the ecliptic, the analytical expression of its action on the motion of
Uranus, when in numerous points of its orbit, was compared with the
observed longitude of Uranus, through a regular series of years, by
means of which the faulty elements of the orbit of Uranus were
eliminated, or got rid of, and there only remained a relation between
the mass of the new planet and three of the elements of its orbit; and
it then was necessary to assume such a value for two of them as would
suit the rest. That was accomplished so dexterously, that the
perturbations of Uranus were perfectly conformable to the motions of
Neptune, moving in the orbit thus found, and the place of the new planet
exactly agreed with observation. Subsequently its orbit and motions have
been determined more accurately.

The honour of this admirable effort of genius is shared by Mr. Adams and
M. Le Verrier, who, independently of each other, arrived at these
wonderful results. Mr. Adams had determined the mass and apparent
diameter of Neptune, with all the circumstances of its motion, eight
months before M. Le Verrier had terminated his results, and had also
pointed out the exact spot where the planet would be found; but the
English observers neglected to look for it till M. Le Verrier made known
his researches, and communicated its position to Dr. Galle, at Berlin,
who found it the very first night he looked for it, and then it was
evident that it would have been seen in the place Mr. Adams had assigned
to it eight months before had it been looked for. So closely did the
results of these two great mathematicians agree.

Neptune has a diameter of 39,793 miles, consequently he is nearly 200
times larger than the earth, and may be seen with a telescope of
moderate power. His motion is retrograde at present, and six times
slower than that of the earth. At so great a distance from the sun it
can only have the 1/1300th part of the light and heat the earth
receives; but having a satellite, the deficiency of light may in some
measure be supplied.

The prediction may now be transferred from Uranus to Neptune, whose
perturbations may reveal the existence of a planet still further
removed, which may for ever remain beyond the reach of telescopic
vision—yet its mass, the form and position of its orbit, and all the
circumstances of its motion may become known, and the limits of the
solar system may still be extended hundreds of millions of miles.

The mean distance of Neptune from the sun has subsequently proved to be
only 2893 millions of miles, and the period of his revolution 166 years,
so that Baron Bode’s law, of the interval between the orbits of any two
planets being twice as great as the inferior interval and half of the
superior, fails in the case of Neptune, though it was useful on the
first approximation to his motions; and since Bode’s time it has led to
the discovery of fifty-five telescopic planets revolving between the
orbits of Mars and Jupiter, some by chance, others by a systematic
search on the faith that these minute planets are fragments of a larger
body that has exploded, because their distances from the sun are nearly
the same; the lines of the nodes of some of their orbits terminate in
the same points of the heavens, and the inclinations of their orbits are
such as might have taken place from their mutual disturbances at the
time of the explosion, and while yet they were near enough for their
forms to affect their motions. The orbits of the more recently
discovered asteroids show that this hypothesis is untenable.

The tables of Mars, Venus, and even those of the sun, have been greatly
improved, and still engage the attention of our Astronomer Royal, Mr.
Airy, and other eminent astronomers. We are chiefly indebted to the
German astronomers for tables of the four older telescopic planets,
Vesta, Juno, Ceres, and Pallas; the others have only been discovered
since the year 1845.

The determination of the path of a planet when disturbed by all the
others, a problem which has employed the talents of the greatest
astronomers, from Newton to the present day, is only successfully
accomplished with regard to the older planets, which revolve in nearly
circular orbits, but little inclined to the plane of the ecliptic. When
the excentricity and inclination of the orbits are great, their analysis
fails, because the series expressing the co-ordinates of the bodies
become extremely complicated, and do not converge when applied to comets
and the telescopic planets. This difficulty has been overcome by Sir
John Lubbock, and other mathematicians, who have the honour of having
completed the theory of planetary motion, which becomes every day of
more importance, from the new planets that have been discovered, and
also with regard to comets, many of which return to the sun at regular
intervals, and from whose perturbations the masses of the planets will
be more accurately determined, and the retarding influence of the
ethereal medium better known.




                              SECTION IX.

Rotation of the Sun and Planets—Saturn’s Rings—Periods of the Rotation
  of the Moon and other Satellites equal to the Periods of their
  Revolutions—Form of Lunar Spheroid—Libration, Aspect, and Constitution
  of the Moon—Rotation of Jupiter’s Satellites.


THE oblate form of several of the planets indicates rotatory motion.
This has been confirmed in most cases by tracing spots on their surface,
by which their poles and times of rotation have been determined. The
rotation of Mercury is unknown, on account of his proximity to the sun;
that of the new planets has not yet been ascertained. The sun revolves
in twenty-five days and ten hours about an axis which is directed
towards a point half-way between the pole-star and α of Lyra, the plane
of rotation being inclined by 7° 30ʹ, or a little more than seven
degrees, to the plane of the ecliptic: it may therefore be concluded
that the sun’s mass is a spheroid, flattened at the poles. From the
rotation of the sun, there was every reason to believe that he has a
progressive motion in space, a circumstance which is confirmed by
observation. But, in consequence of the reaction of the planets, he
describes a small irregular orbit about the centre of gravity of the
system, never deviating from his position by more than twice his own
diameter, or a little more than seven times the distance of the moon
from the earth. The sun and all his attendants rotate from west to east,
on axes that remain nearly parallel to themselves (N. 140) in every
point of their orbit, and with angular velocities that are sensibly
uniform (N. 141). Although the uniformity in the direction of their
rotation is a circumstance hitherto unaccounted for in the economy of
nature, yet, from the design and adaptation of every other part to the
perfection of the whole, a coincidence so remarkable cannot be
accidental. And, as the revolutions of the planets and satellites are
also from west to east, it is evident that both must have arisen from
the primitive cause which determined the planetary motions.[6] Indeed,
La Place has computed the probability to be as four millions to one that
all the motions of the planets, both of rotation and revolution, were at
once imparted by an original common cause, but of which we know neither
the nature nor the epoch.

The larger planets rotate in shorter periods than the smaller planets
and the earth. Their compression is consequently greater, and the action
of the sun and of their satellites occasions a nutation in their axes
and a precession of their equinoxes (N. 147) similar to that which
obtains in the terrestrial spheroid, from the attraction of the sun and
moon on the prominent matter at the equator. Jupiter revolves in less
than ten hours round an axis at right angles to certain dark belts or
bands, which always cross his equator. (See Plate 1.) This rapid
rotation occasions a very great compression in his form. His equatorial
axis exceeds his polar axis by 6000 miles, whereas the difference in the
axes of the earth is only about twenty-six and a half. It is an evident
consequence of Kepler’s law of the squares of the periodic times of the
planets being as the cubes of the major axes of their orbits, that the
heavenly bodies move slower the farther they are from the sun. In
comparing the periods of the revolutions of Jupiter and Saturn with the
times of their rotation, it appears that a year of Jupiter contains
nearly ten thousand of his days, and that of Saturn about thirty
thousand Saturnian days.

The appearance of Saturn is unparalleled in the system of the world. He
is a spheroid nearly 1000 times larger than the earth, surrounded by a
ring even brighter than himself, which always remains suspended in the
plane of his equator: and, viewed with a very good telescope, it is
found to consist of two concentric rings, divided by a dark band. The
exterior ring, as seen through Mr. Lassell’s great equatorial at Malta,
has a dark-striped band through the centre, and is altogether less
bright than the interior ring, one half of which is extremely brilliant;
while the interior half is shaded in rings like the seats in an
amphitheatre. Mr. Lassell made the remarkable discovery of a dark
transparent ring, whose edge coincides with the inner edge of the
interior ring, and which occupies about half the space between it and
Saturn. He compares it to a band of dark-coloured crape drawn across a
portion of the disc of the planet, and the part projected upon the blue
sky is also transparent. At the time these observations were made at
Malta, Captain Jacob discovered the transparent ring at Madras. It is
conjectured to be fluid; even the luminous rings cannot be very dense,
since the density of Saturn himself is known to be less than the eighth
part of that of the earth. A transit of the ring across a star might
reveal something concerning this wonderful object. The ball of Saturn is
striped by belts of different colours. At the time of these observations
the part above the ring was bright white; at his equator there was a
ruddy belt divided in two, above which were belts of a bluish green
alternately dark and light, while at the pole there was a circular space
of a pale colour. (See Plate 2.) The mean distance of the interior part
of the double ring from the surface of the planet is about 22,240 miles,
it is no less than 33,360 miles broad, but, by the estimation of Sir
John Herschel, its thickness does not much exceed 100 miles, so that it
appears like a plane. By the laws of mechanics, it is impossible that
this body can retain its position by the adhesion of its particles
alone. It must necessarily revolve with a velocity that will generate a
centrifugal force sufficient to balance the attraction of Saturn.
Observation confirms the truth of these principles, showing that the
rings rotate from west to east about the planet in ten hours and a half,
which is nearly the time a satellite would take to revolve about Saturn
at the same distance. Their plane is inclined to the ecliptic, at an
angle of 28° 10ʹ 44ʺ·5; in consequence of this obliquity of position,
they always appear elliptical to us, but with an excentricity so
variable as even to be occasionally like a straight line drawn across
the planet. In the beginning of October, 1832, the plane of the rings
passed through the centre of the earth; in that position they are only
visible with very superior instruments, and appear like a fine line
across the disc of Saturn. About the middle of December, in the same
year, the rings became invisible, with ordinary instruments, on account
of their plane passing through the sun. In the end of April, 1833, the
rings vanished a second time, and reappeared in June of that year.
Similar phenomena will occur as often as Saturn has the same longitude
with either node of his rings. Each side of these rings has alternately
fifteen years of sunshine and fifteen years of darkness.

It is a singular result of theory, that the rings could not maintain
their stability of rotation if they were everywhere of uniform
thickness; for the smallest disturbance would destroy the equilibrium,
which would become more and more deranged, till, at last, they would be
precipitated on the surface of the planet. The rings of Saturn must
therefore be irregular solids, of unequal breadth in different parts of
the circumference, so that their centres of gravity do not coincide with
the centres of their figures. Professor Struve has also discovered that
the centre of the rings is not concentric with the centre of Saturn. The
interval between the outer edge of the globe of the planet and the outer
edge of the rings on one side is 11ʺ·272, and, on the other side, the
interval is 11ʺ·390, consequently there is an excentricity of the globe
in the rings of 0ʺ·215. If the rings obeyed different forces, they would
not remain in the same plane, but the powerful attraction of Saturn
always maintains them and his satellites in the plane of his equator.
The rings, by their mutual action, and that of the sun and satellites,
must oscillate about the centre of Saturn, and produce phenomena of
light and shadow whose periods extend to many years. According to M.
Bessel the mass of Saturn’s ring is equal to the 1/118 part of that of
the planet.

The periods of rotation of the moon and the other satellites are equal
to the times of their revolutions, consequently these bodies always turn
the same face to their primaries. However, as the mean motion of the
moon is subject to a secular inequality, which will ultimately amount to
many circumferences (N. 108), if the rotation of the moon were perfectly
uniform and not affected by the same inequalities, it would cease
exactly to counterbalance the motion of revolution; and the moon, in the
course of ages, would successively and gradually discover every point of
her surface to the earth. But theory proves that this never can happen;
for the rotation of the moon, though it does not partake of the periodic
inequalities of her revolution, is affected by the same secular
variations, so that her motions of rotation and revolution round the
earth will always balance each other, and remain equal. This
circumstance arises from the form of the lunar spheroid, which has three
principal axes of different lengths at right angles to each other.

The moon is flattened at her poles from her centrifugal force, therefore
her polar axis is the least. The other two are in the plane of her
equator, but that directed towards the earth is the greatest (N. 142).
The attraction of the earth, as if it had drawn out that part of the
moon’s equator, constantly brings the greatest axis, and consequently
the same hemisphere, towards us, which makes her rotation participate in
the secular variations of her mean motion of revolution. Even if the
angular velocities of rotation and revolution had not been nicely
balanced in the beginning of the moon’s motion, the attraction of the
earth would have recalled the greatest axis to the direction of the line
joining the centres of the moon and earth; so that it would have
vibrated on each side of that line in the same manner as a pendulum
oscillates on each side of the vertical from the influence of
gravitation. No such libration is perceptible; and, as the smallest
disturbance would make it evident, it is clear that, if the moon has
ever been touched by a comet, the mass of the latter must have been
extremely small. If it had been only the hundred thousandth part of that
of the earth, it would have rendered the libration sensible. According
to analysis, a similar libration exists in the motions of Jupiter’s
satellites, which still remains insensible to observation, and yet the
comet of 1770 passed twice through the midst of them.

The moon, it is true, is liable to librations depending upon the
position of the spectator. At her rising, part of the western edge of
her disc is visible, which is invisible at her setting, and the contrary
takes place with regard to her eastern edge. There are also librations
arising from the relative positions of the earth and moon in their
respective orbits; but, as they are only optical appearances, one
hemisphere will be eternally concealed from the earth. For the same
reason the earth, which must be so splendid an object to one lunar
hemisphere, will be for ever veiled from the other. On account of these
circumstances, the remoter hemisphere of the moon has its day a
fortnight long, and a night of the same duration, not even enlightened
by a moon, while the favoured side is illuminated by the reflection of
the earth during its long night. A planet exhibiting a surface thirteen
times larger than that of the moon, with all the varieties of clouds,
land, and water, coming successively into view, must be a splendid
object to a lunar traveller in a journey to his antipodes. The great
height of the lunar mountains probably has a considerable influence on
the phenomena of her motion, the more so as her compression is small,
and her mass considerable. In the curve passing through the poles, and
that diameter of the moon which always points to the earth, nature has
furnished a permanent meridian, to which the different spots on her
surface have been referred, and their positions are determined with as
much accuracy as those of many of the most remarkable places on the
surface of our globe. According to the observations of Professor Secchi
at Rome, the mountains of the moon are mostly volcanic and of three
kinds. The first and oldest have their borders obliterated, so that they
look like deep wells; the second, which are of an intermediate class,
have elevated, and, for the most part, regular unbroken edges, with the
ground around them raised to a prodigious extent in proportion to the
size of the volcano, with generally an insulated rock in the centre of
the crater. The third, and most recent class, are very small, and seem
to be the last effort of the expiring volcanic force, which is probably
now extinct.

The distance and minuteness of Jupiter’s satellites render it extremely
difficult to ascertain their rotation. It was, however, accomplished by
Sir William Herschel from their relative brightness. He observed that
they alternately exceed each other in brilliancy, and, by comparing the
maxima and minima of their illumination with their positions relatively
to the sun and to their primary, he found that, like the moon, the time
of their rotation is equal to the period of their revolution about
Jupiter. Miraldi was led to the same conclusion with regard to the
fourth satellite, from the motion of a spot on its surface.




                               SECTION X.

Rotation of the Earth invariable—Decrease in the Earth’s mean
  Temperature—Earth originally in a state of Fusion—Length of Day
  constant—Decrease of Temperature ascribed by Sir John Herschel to the
  variation in the Excentricity of the Terrestrial Orbit—Difference in
  the Temperature of the two Hemispheres erroneously ascribed to the
  Excess in the Length of Spring and Summer in the Southern Hemisphere;
  attributed by Sir Charles Lyell to the Operation of existing
  Causes—Three principal Axes of Rotation—Position of the Axis of
  Rotation on the Surface of the Earth invariable—Ocean not sufficient
  to restore the Equilibrium of the Earth if deranged—Its Density and
  mean Depth—Internal Structure of the Earth.


The rotation of the earth, which determines the length of the day, may
be regarded as one of the most important elements in the system of the
world. It serves as a measure of time, and forms the standard of
comparison for the revolutions of the celestial bodies, which, by their
proportional increase or decrease, would soon disclose any changes it
might sustain. Theory and observation concur in proving that, among the
innumerable vicissitudes which prevail throughout creation, the period
of the earth’s diurnal rotation is immutable. The water of rivers,
falling from a higher to a lower level, carries with it the velocity due
to its revolution with the earth at a greater distance from the centre;
it will therefore accelerate, although to an almost infinitesimal
extent, the earth’s daily rotation. The sum of all these increments of
velocity, arising from the descent of all the rivers on the earth’s
surface, would in time become perceptible, did not nature, by the
process of evaporation, raise the waters back to their sources, and
thus, by again removing matter to a greater distance from the centre,
destroy the velocity generated by its previous approach; so that the
descent of rivers does not affect the earth’s rotation. Enormous masses
projected by volcanoes from the equator to the poles, and the contrary,
would indeed affect it, but there is no evidence of such convulsions.
The disturbing action of the moon and planets, which has so powerful an
effect on the revolution of the earth, in no way influences its
rotation. The constant friction of the trade winds on the mountains and
continents between the tropics does not impede its velocity, which
theory even proves to be the same as if the sea, together with the
earth, formed one solid mass. But, although these circumstances be
insufficient, a variation in the mean temperature would certainly
occasion a corresponding change in the velocity of rotation. In the
science of dynamics it is a principle in a system of bodies or of
particles revolving about a fixed centre, that the momentum or sum of
the products of the mass of each into its angular velocity and distance
from the centre is a constant quantity, if the system be not deranged by
a foreign cause. Now, since the number of particles in the system is the
same whatever its temperature may be, when their distances from the
centre are diminished, their angular velocity must be increased, in
order that the preceding quantity may still remain constant. It follows,
then, that, as the primitive momentum of rotation with which the earth
was projected into space must necessarily remain the same, the smallest
decrease in heat, by contracting the terrestrial spheroid, would
accelerate its rotation, and consequently diminish the length of the
day. Notwithstanding the constant accession of heat from the sun’s rays,
geologists have been induced to believe, from the fossil remains, that
the mean temperature of the globe is decreasing.

The high temperature of mines, hot springs, and above all the internal
fires which have produced, and do still occasion, such devastation on
our planet, indicate an augmentation of heat towards its centre. The
increase of density corresponding to the depth and the form of the
spheroid, being what theory assigns to a fluid mass in rotation, concurs
to induce the idea that the temperature of the earth was originally so
high as to reduce all the substances of which it is composed to a state
of fusion or of vapour, and that in the course of ages it has cooled
down to its present state; that it is still becoming colder; and that it
will continue to do so till the whole mass arrives at the temperature of
the medium in which it is placed, or rather at a state of equilibrium
between this temperature, the cooling power of its own radiation, and
the heating effect of the sun’s rays.

Previous to the formation of ice at the poles, the ancient lands of
northern latitudes might, no doubt, have been capable of producing those
tropical plants preserved in the coal-measures, if indeed such plants
could flourish without the intense light of a tropical sun. But, even if
the decreasing temperature of the earth be sufficient to produce the
observed effects, it must be extremely slow in its operation; for, in
consequence of the rotation of the earth being a measure of the periods
of the celestial motions, it has been proved that, if the length of the
day had decreased by the three-thousandth part of a second since the
observations of Hipparchus two thousand years ago, it would have
diminished the secular equation of the moon by 44ʺ·4. It is, therefore,
beyond a doubt that the mean temperature of the earth cannot have
sensibly varied during that time. If, then, the appearances exhibited by
the strata are really owing to a decrease of internal temperature, it
either shows the immense periods requisite to produce geological
changes, to which two thousand years are as nothing, or that the mean
temperature of the earth had arrived at a state of equilibrium before
these observations.

However strong the indications of the primitive fluidity of the earth,
as there is no direct proof of it, the hypothesis can only be regarded
as very probable. But one of the most profound philosophers and elegant
writers of modern times has found in the secular variation of the
excentricity of the terrestrial orbit an evident cause of decreasing
temperature. That accomplished author, in pointing out the mutual
dependencies of phenomena, says, “It is evident that the mean
temperature of the whole surface of the globe, in so far as it is
maintained by the action of the sun at a higher degree than it would
have were the sun extinguished, must depend on the mean quantity of the
sun’s rays which it receives, or—which comes to the same thing—on the
total quantity received in a given invariable time; and, the length of
the year being unchangeable in all the fluctuations of the planetary
system, it follows that the total amount of solar radiation will
determine, _cæteris paribus_, the general climate of the earth. Now, it
is not difficult to show that this amount is inversely proportional to
the minor axis of the ellipse described by the earth about the sun
(N. 143), regarded as slowly variable; and that, therefore, the major
axis remaining, as we know it to be, constant, and the orbit being
actually in a state of approach to a circle, and consequently the minor
axis being on the increase, the mean annual amount of solar radiation
received by the whole earth must be actually on the decrease. We have,
therefore, an evident real cause to account for the phenomenon.” The
limits of the variation in the excentricity of the earth’s orbit are
unknown. But, if its ellipticity has ever been as great as that of the
orbit of Mercury or Pallas, the mean temperature of the earth must have
been sensibly higher than it is at present. Whether it was great enough
to render our northern climates fit for the production of tropical
plants, and for the residence of the elephant and other animals now
inhabitants of the torrid zone, it is impossible to say.

Of the decrease in temperature of the northern hemisphere there is
abundant evidence in the fossil plants discovered in very high
latitudes, which could only have existed in a tropical climate, and
which must have grown near the spot where they are found, from the
delicacy of their structure and the perfect state of their preservation.
This change of temperature has been erroneously ascribed to an excess in
the duration of spring and summer in the northern hemisphere, in
consequence of the excentricity of the solar ellipse. The length of the
seasons varies with the position of the perihelion (N. 64) of the
earth’s orbit for two reasons. On account of the excentricity, small as
it is, any line passing through the centre of the sun divides the
terrestrial ellipse into two unequal parts, and by the laws of
elliptical motion the earth moves through these two portions with
unequal velocities. The perihelion always lies in the smaller portion,
and there the earth’s motion is the most rapid. In the present position
of the perihelion, spring and summer north of the equator exceed by
about eight days the duration of the same seasons south of it. And
10,492 years ago the southern hemisphere enjoyed the advantage we now
possess from the secular variation of the perihelion. Yet Sir John
Herschel has shown that by this alternation neither hemisphere acquires
any excess of light or heat above the other; for, although the earth is
nearer to the sun while moving through that part of its orbit in which
the perihelion lies than in the other part, and consequently receives a
greater quantity of light and heat, yet as it moves faster it is exposed
to the heat for a shorter time. In the other part of the orbit, on the
contrary, the earth, being farther from the sun, receives fewer of his
rays; but because its motion is slower, it is exposed to them for a
longer time; and, as in both cases the quantity of heat and the angular
velocity vary exactly in the same proportion, a perfect compensation
takes place (N. 144). So that the excentricity of the earth’s orbit has
little or no effect on the temperature corresponding to the difference
of the seasons.

Sir Charles Lyell, in his excellent works on Geology, refers the
increased cold of the northern hemisphere to the operation of existing
causes with more probability than most theories that have been advanced
in solution of this difficult subject. The loftiest mountains would be
represented by a grain of sand on a globe six feet in diameter, and the
depth of the ocean by a scratch on its surface. Consequently the gradual
elevation of a continent or chain of mountains above the surface of the
ocean, or their depression below it, is no very great event compared
with the magnitude of the earth, and the energy of its subterranean
fires, if the same periods of time be admitted in the progress of
geological as in astronomical phenomena, which the successive and
various races of extinct beings show to have been immense. Climate is
always more intense in the interior of continents than in islands or
sea-coasts. An increase of land within the tropics would therefore
augment the general heat, and an increase in the temperate and frigid
zones would render the cold more severe. Now it appears that most of the
European, North Asiatic, and North American continents and islands were
raised from the deep after the coal-measures were formed in which the
fossil tropical plants are found; and a variety of geological facts
indicate the existence of an ancient and extensive archipelago
throughout the greater part of the northern hemisphere. Sir Charles
Lyell is therefore of opinion that the climate of these islands must
have been sufficiently mild, in consequence of the surrounding ocean, to
clothe them with tropical plants, and render them a fit abode for the
huge animals whose fossil remains are so often found; that the
arborescent ferns and the palms of these regions, carried by streams to
the bottom of the ocean, were imbedded in the strata which were by
degrees heaved up by the subterranean fires during a long succession of
ages, till the greater part of the northern hemisphere became dry land
as it now is, and that the consequence has been a continual decrease of
temperature.

It is evident, from the marine shells found on the tops of the highest
mountains and in almost every part of the globe, that immense continents
have been elevated above the ocean which must have engulfed others. Such
a catastrophe would be occasioned by a variation in the position of the
axis of rotation on the surface of the earth; for the seas tending to a
new equator would leave some portions of the globe and overwhelm others.
Now, it is found by the laws of mechanics that in every body, be its
form or density what it may, there are at least three axes at right
angles to each other, round any one of which, if the solid begins to
rotate, it will continue to revolve for ever, provided it be not
disturbed by a foreign cause, but that the rotation about any other axis
will only be for an instant, and consequently the poles or extremities
of the instantaneous axis of rotation would perpetually change their
position on the surface of the body. In an ellipsoid of revolution the
polar diameter and every diameter in the plane of the equator are the
only permanent axes of rotation (N. 145). Hence, if the ellipsoid were
to begin to revolve about any diameter between the pole and the equator,
the motion would be so unstable that the axis of rotation and the
position of the poles would change every instant. Therefore, as the
earth does not differ much from this figure, if it did not turn round
one of its principal axes, the position of the poles would change daily;
the equator, which is 90° distant, would undergo corresponding
variations; and the geographical latitudes of all places, being
estimated from the equator, assumed to be fixed, would be perpetually
changing. A displacement in the position of the poles of only two
hundred miles would be sufficient to produce these effects, and would
immediately be detected. But, as the latitudes are found to be
invariable, it may be concluded that the terrestrial spheroid must have
revolved about the same axis for ages. The earth and planets differ so
little from ellipsoids of revolution, that in all probability any
libration from one axis to another, produced by the primitive impulse
which put them in motion, must have ceased soon after their creation
from the friction of the fluids at their surface.

Theory also proves that neither nutation, precession, nor any of the
disturbing forces that affect the system, have the smallest influence on
the axis of rotation, which maintains a permanent position on the
surface, if the earth be not disturbed in its rotation by a foreign
cause, as the collision of a comet, which might have happened in the
immensity of time. But, had that been the case, its effects would still
have been perceptible in the variations of the geographical latitudes.
If we suppose that such an event had taken place, and that the
disturbance had been very great, equilibrium could then only have been
restored with regard to a new axis of rotation by the rushing of the
seas to the new equator, which they must have continued to do till the
surface was everywhere perpendicular to the direction of gravity. But it
is probable that such an accumulation of the waters would not be
sufficient to restore equilibrium if the derangement had been great, for
the mean density of the sea is only about a fifth part of the mean
density of the earth, and the mean depth of the Pacific Ocean is
supposed not to be more than four or five miles, whereas the equatorial
diameter of the earth exceeds the polar diameter by about 26-1/2 miles.
Consequently the influence of the sea on the direction of gravity is
very small. And, as it thus appears that a great change in the position
of the axis is incompatible with the law of equilibrium, the geological
phenomena in question must be ascribed to an internal cause. Indeed it
is now demonstrated that the strata containing marine diluvia, which are
in lofty situations, must have been formed at the bottom of the ocean,
and afterwards upheaved by the action of subterraneous fires. Besides,
it is clear, from the mensuration of the arcs of the meridian and the
length of the seconds’ pendulum, as well as from the lunar theory, that
the internal strata and also the external outline of the globe are
elliptical, their centres being coincident and their axes identical with
that of the surface—a state of things which, according to the
distinguished author lately quoted, is incompatible with a subsequent
accommodation of the surface to a new and different state of rotation
from that which determined the original distribution of the component
matter. Thus, amidst the mighty revolutions which have swept innumerable
races of organized beings from the earth, which have elevated plains and
buried mountains in the ocean, the rotation of the earth and the
position of the axes on its surface have undergone but slight
variations.

The strata of the terrestrial spheroid are not only concentric and
elliptical, but the lunar inequalities show that they increase in
density from the surface of the earth to its centre. This would
certainly have happened if the earth had originally been fluid, for the
denser parts must have subsided towards the centre as it approached a
state of equilibrium. But the enormous pressure of the superincumbent
mass is a sufficient cause for the phenomenon. Professor Leslie observes
that air compressed into the fiftieth part of its volume has its
elasticity fifty times augmented. If it continues to contract at that
rate, it would, from its own incumbent weight, acquire the density of
water at the depth of thirty-four miles. But water itself would have its
density doubled at the depth of ninety-three miles, and would even
attain the density of quicksilver at a depth of 362 miles. Descending
therefore towards the centre through nearly 4000 miles, the condensation
of ordinary substances would surpass the utmost powers of conception.
Dr. Young says that steel would be compressed into one-fourth and stone
into one-eighth of its bulk at the earth’s centre. However, we are yet
ignorant of the laws of compression of solid bodies beyond a certain
limit; from the experiments of Mr. Perkins they appear to be capable of
a greater degree of compression than has generally been imagined.

But a density so extreme is not borne out by astronomical observation.
It might seem to follow therefore that our planet must have a widely
cavernous structure, and that we tread on a crust or shell whose
thickness bears a very small proportion to the diameter of its sphere.
Possibly, too, this great condensation at the central regions may be
counterbalanced by the increased elasticity due to a very elevated
temperature.




                              SECTION XI.

Precession and Nutation—Their Effects on the Apparent Places of the
  Fixed Stars.


IT has been shown that the axis of rotation is invariable on the surface
of the earth; and observation as well as theory prove that, were it not
for the action of the sun and moon on the matter at the equator, it
would remain exactly parallel to itself in every point of its orbit.

The attraction of an external body not only draws a spheroid towards it,
but, as the force varies inversely as the square of the distance, it
gives it a motion about its centre of gravity, unless when the
attracting body is situated in the prolongation of one of the axes of
the spheroid. The plane of the equator is inclined to the plane of the
ecliptic at an angle of 23° 27ʹ 28ʺ·29; and the inclination of the lunar
orbit to the same is 5° 8ʹ 47ʺ·9. Consequently, from the oblate figure
of the earth, the sun and moon, acting obliquely and unequally on the
different parts of the terrestrial spheroid, urge the plane of the
equator from its direction, and force it to move from east to west, so
that the equinoctial points have a slow retrograde motion on the plane
of the ecliptic of 50ʺ·41 annually. The direct tendency of this action
is to make the planes of the equator and ecliptic coincide, but it is
balanced by the tendency of the earth to return to stable rotation about
the polar diameter, which is one of its principal axes of rotation.
Therefore the inclination of the two planes remains constant, as a top
spinning preserves the same inclination to the plane of the horizon.
Were the earth spherical, this effect would not be produced, and the
equinoxes would always correspond with the same points of the ecliptic,
at least as far as this kind of motion is concerned. But another and
totally different cause which operates on this motion has already been
mentioned. The action of the planets on one another and on the sun
occasions a very slow variation in the position of the plane of the
ecliptic, which affects its inclination to the plane of the equator, and
gives the equinoctial points a slow but direct motion on the ecliptic of
0ʺ·31 annually, which is entirely independent of the figure of the
earth, and would be the same if it were a sphere. Thus the sun and moon
by moving the plane of the equator cause the equinoctial points to
retrograde on the ecliptic: and the planets by moving the plane of the
ecliptic give them a direct motion, though much less than the former.
Consequently the difference of the two is the mean precession, which is
proved both by theory and observation to be about 50ʺ·1 annually
(N. 146).

As the longitudes of all the fixed stars are increased by this quantity,
the effects of precession are soon detected. It was accordingly
discovered by Hipparchus in the year 128 before Christ, from a
comparison of his own observations with those of Timocharis 155 years
before. In the time of Hipparchus the entrance of the sun into the
constellation Aries was the beginning of spring; but since that time the
equinoctial points have receded 30°, so that the constellations called
the signs of the zodiac are now at a considerable distance from those
divisions of the ecliptic which bear their names. Moving at the rate of
50ʺ·1 annually, the equinoctial points will accomplish a revolution in
25,868 years. But, as the precession varies in different centuries, the
extent of this period will be slightly modified. Since the motion of the
sun is direct, and that of the equinoctial points retrograde, he takes a
shorter time to return to the equator than to arrive at the same stars;
so that the tropical year of 365^d 5^h 48^m 49^s·7 must be increased
by the time he takes to move through an arc of 50ʺ·1, in order to have
the length of the sidereal year. The time required is 20^m 19^s·6, so
that the sidereal year contains 365^d 6^h 9^m 9^s·6 mean solar days.

The mean annual precession is subject to a secular variation; for,
although the change in the plane of the ecliptic in which the orbit of
the sun lies be independent of the form of the earth, yet, by bringing
the sun, moon, and earth into different relative positions from age to
age, it alters the direct action of the two first on the prominent
matter at the equator: on this account the motion of the equinox is
greater by 0ʺ·455 now than it was in the time of Hipparchus.
Consequently the actual length of the tropical year is about 4^s·21
shorter than it was at that time. The utmost change that it can
experience from this cause amounts to 43 seconds.

Such is the secular motion of the equinoxes. But it is sometimes
increased and sometimes diminished by periodic variations, whose periods
depend upon the relative positions of the sun and moon with regard to
the earth, and which are occasioned by the direct action of these bodies
on the equator. Dr. Bradley discovered that by this action the moon
causes the pole of the equator to describe a small ellipse in the
heavens, the axes of which are 18ʺ·5 and 13ʺ·674, the longer being
directed towards the pole of the ecliptic. The period of this inequality
is about 19 years, the time employed by the nodes of the lunar orbit to
accomplish a revolution. The sun causes a small variation in the
description of this ellipse; it runs through its period in half a year.
Since the whole earth obeys these motions, they affect the position of
its axis of rotation with regard to the starry heavens, though not with
regard to the surface of the earth; for in consequence of precession
alone the pole of the equator moves in a circle round the pole of the
ecliptic in 25,868 years, and by nutation alone it describes a small
ellipse in the heavens every 19 years, on each side of which it deviates
every half-year from the action of the sun. The real curve traced in the
starry heavens by the imaginary prolongation of the earth’s axis is
compounded of these three motions (N. 147). This nutation in the earth’s
axis affects both the precession and obliquity with small periodic
variations. But in consequence of the secular variation in the position
of the terrestrial orbit, which is chiefly owing to the disturbing
energy of Jupiter on the earth, the obliquity of the ecliptic is
annually diminished, according to M. Bessel, by 0ʺ·457. This variation
in the course of ages may amount to 10 or 11 degrees; but the obliquity
of the ecliptic to the equator can never vary more than 2° 42ʹ or 3°,
since the equator will follow in some measure the motion of the
ecliptic.

It is evident that the places of all the celestial bodies are affected
by precession and nutation. Their longitudes estimated from the equinox
are augmented by precession; but, as it affects all the bodies equally,
it makes no change in their relative positions. Both the celestial
latitudes and longitudes are altered to a small degree by nutation;
hence all observations must be corrected for these inequalities. In
consequence of this real motion in the earth’s axis, the pole-star,
forming part of the constellation of the Little Bear, which was formerly
12° from the celestial pole, is now within 1° 24ʹ of it, and will
continue to approach it till it is within 1/2°, after which it will
retreat from the pole for ages; and 12,934 years hence the star α Lyræ
will come within 5° of the celestial pole, and become the polar star of
the northern hemisphere.




                              SECTION XII.

Mean and Apparent Sidereal Time—Mean and Apparent Solar Time—Equation of
  Time—English and French Subdivisions of Time—Leap Year—Christian
  Era—Equinoctial Time—Remarkable Eras depending upon the Position of
  the Solar Perigee—Inequality of the Lengths of the Seasons in the two
  Hemispheres—Application of Astronomy to Chronology—English and French
  Standards of Weights and Measures.


ASTRONOMY has been of immediate and essential use in affording
invariable standards for measuring duration, distance, magnitude, and
velocity. The mean sidereal day measured by the time elapsed between two
consecutive transits of any star at the same meridian (N. 148), and the
mean sidereal year which is the time included between two consecutive
returns of the sun to the same star, are immutable units with which all
great periods of time are compared; the oscillations of the isochronous
pendulum measure its smaller portions. By these invariable standards
alone we can judge of the slow changes that other elements of the system
may have undergone. Apparent sidereal time, which is measured by the
transit of the equinoctial point at the meridian of any place, is a
variable quantity, from the effects of precession and nutation. Clocks
showing apparent sidereal time are employed for observation, and are so
regulated that they indicate 0^h 0^m 0^s at the instant the
equinoctial point passes the meridian of the observatory. And as time is
a measure of angular motion, the clock gives the distances of the
heavenly bodies from the equinox by observing the instant at which each
passes the meridian, and converting the interval into arcs at the rate
of 15° to an hour.

The returns of the sun to the meridian and to the same equinox or
solstice have been universally adopted as the measure of our civil days
and years. The solar or astronomical day is the time that elapses
between two consecutive noons or midnights. It is consequently longer
than the sidereal day, on account of the proper motion of the sun during
a revolution of the celestial sphere. But, as the sun moves with greater
rapidity at the winter than at the summer solstice, the astronomical day
is more nearly equal to the sidereal day in summer than in winter. The
obliquity of the ecliptic also affects its duration; for near the
equinoxes the arc of the equator is less than the corresponding arc of
the ecliptic, and in the solstices it is greater (N. 149). The
astronomical day is therefore diminished in the first case, and
increased in the second. If the sun moved uniformly in the equator at
the rate of 59ʹ 8ʺ·33 every day, the solar days would be all equal. The
time therefore which is reckoned by the arrival of an imaginary sun at
the meridian, or of one which is supposed to move uniformly in the
equator, is denominated mean solar time, and is given by clocks and
watches in common life. When it is reckoned by the arrival of the real
sun at the meridian, it is true or apparent time, and is given by dials.
The difference between the time shown by a clock and a dial is the
equation of time given in the Nautical Almanac, sometimes amounting to
as much as sixteen minutes. The apparent and mean time coincide four
times in the year; when the sun’s daily motion in right ascension is
equal to 59ʹ 8ʺ·33 in a mean solar day, which happens about the 16th of
April, the 16th of June, the 1st of September, and the 25th of December.

The astronomical day begins at noon, but in common reckoning the day
begins at midnight. In England it is divided into twenty-four hours,
which are counted by twelve and twelve; but in France astronomers,
adopting the decimal division, divide the day into ten hours, the hour
into one hundred minutes, and the minute into a hundred seconds, because
of the facility in computation, and in conformity with their decimal
system of weights and measures. This subdivision is not now used in
common life, nor has it been adopted in any other country; and although
some scientific writers in France still employ that division of time,
the custom is beginning to wear out. At one period during the French
Revolution, the clock in the gardens of the Tuileries was regulated to
show decimal time. The mean length of the day, though accurately
determined, is not sufficient for the purposes either of astronomy or
civil life. The tropical or civil year of 365^d 5^h 48^m 49^s·7,
which is the time elapsed between the consecutive returns of the sun to
the mean equinoxes or solstices, including all the changes of the
seasons, is a natural cycle peculiarly suited for a measure of duration.
It is estimated from the winter solstice, the middle of the long annual
night under the north pole. But although the length of the civil year is
pointed out by nature as a measure of long periods, the
incommensurability that exists between the length of the day and the
revolution of the sun renders it difficult to adjust the estimation of
both in whole numbers. If the revolution of the sun were accomplished in
365 days, all the years would be of precisely the same number of days,
and would begin and end with the sun at the same point of the ecliptic.
But as the sun’s revolution includes the fraction of a day, a civil year
and a revolution of the sun have not the same duration. Since the
fraction is nearly the fourth of a day, in four years it is nearly equal
to a revolution of the sun, so that the addition of a supernumerary day
every fourth year nearly compensates the difference. But in process of
time further correction will be necessary, because the fraction is less
than the fourth of a day. In fact, if a bissextile be suppressed at the
end of three out of four centuries, the year so determined will only
exceed the true year by an extremely small fraction of a day; and if in
addition to this a bissextile be suppressed every 4000 years, the length
of the year will be nearly equal to that given by observation. Were the
fraction neglected, the beginning of the year would precede that of the
tropical year, so that it would retrograde through the different seasons
in a period of about 1507 years. The Egyptian year began with the
heliacal rising of Sirius (N. 150), and contained only 365 days, by
which they lost one year in every 1461 years, their Sothaic period, or
that cycle in which the heliacal rising of Sirius passes through the
whole year and takes place again on the same day. The division of the
year into months is very old and almost universal. But the period of
seven days, by far the most permanent division of time, and the most
ancient monument of astronomical knowledge, was used by the Brahmins in
India with the same denominations employed by us, and was alike found in
the calendars of the Jews, Egyptians, Arabs, and Assyrians. It has
survived the fall of empires, and has existed among all successive
generations, a proof of their common origin.

The day of the new moon immediately following the winter solstice in the
707th year of Rome was made the 1st of January of the first year of
Julius Cæsar. The 25th of December of his forty-fifth year is considered
as the date of Christ’s nativity; and the forty-sixth year of the Julian
Calendar is assumed to be the first of our era. The preceding year is
called the first year before Christ by chronologists, but by astronomers
it is called the year 0. The astronomical year begins on the 31st of
December at noon; and the date of an observation expresses the days and
hours which have actually elapsed since that time.

Since solar and sidereal time are estimated from the passage of the sun
and the equinoctial point across the meridian of each place, the hours
are different at different places: while it is one o’clock at one place,
it is two at another, three at another, &c.; for it is obvious that it
is noon at one part of the globe at the same moment that it is midnight
at another diametrically opposite to it: consequently an event which
happens at one and the same instant of absolute time is recorded at
different places as having happened at different times. Therefore, when
observations made at different places are to be compared, they must be
reduced by computation to what they would have been had they been made
under the same meridian. To obviate this it was proposed by Sir John
Herschel to employ mean equinoctial time, which is the same for all the
world, and independent alike of local circumstances and inequalities in
the sun’s motion. It is the time elapsed from the instant the mean sun
enters the mean vernal equinox, and is reckoned in mean solar days and
parts of a day.

Some remarkable astronomical eras are determined by the position of the
major axis of the solar ellipse, which depends upon the direct motion of
the perigee (N. 102) and the precession of the equinoxes conjointly, the
annual motion of the one being 11ʺ·8, and that of the other 50ʺ·1. Hence
the axis, moving at the rate of 61ʺ·9 annually, accomplishes a tropical
revolution in 209·84 years. It coincided with the line of the equinoxes
4000 or 4089 years before the Christian era, much about the time
chronologists assign for the creation of man. In 6483 the major axis
will again coincide with the line of the equinoxes; but then the solar
perigee will coincide with the equinox of autumn, whereas at the
creation of man it coincided with the vernal equinox. In the year 1246
the major axis was perpendicular to the line of the equinoxes; then the
solar perigee coincided with the solstice of summer, and the apogee with
the solstice of winter. According to La Place, who computed these
periods from different data, the last coincidence happened in the year
1250 of our era, which induced him to propose that year as a universal
epoch, the vernal equinox of the year 1250 to be the first day of the
first year. These eras can only be regarded as approximate, since
ancient observations are too inaccurate, and modern observations too
recent, to afford data for their precise determination.

The variation in the position of the solar ellipse occasions
corresponding changes in the length of the seasons. In its present
position spring is shorter than summer, and autumn longer than winter;
and while the solar perigee continues as it now is, between the solstice
of winter and the equinox of spring, the period including spring and
summer will be longer than that including autumn and winter. In this
century the difference is between seven and eight days. The intervals
will be equal towards the year 6483, when the perigee will coincide with
the equinox of spring; but, when it passes that point, the spring and
summer taken together will be shorter than the period including the
autumn and winter (N. 151). These changes will be accomplished in a
tropical revolution of the major axis of the earth’s orbit, which
includes an interval of 20,984 years. Were the orbit circular, the
seasons would be equal; their difference arises from the excentricity of
the orbit, small as it is; but the changes are so trifling as to be
imperceptible in the short span of human life.

No circumstance in the whole science of astronomy excites a deeper
interest than its application to chronology. “Whole nations,” says La
Place, “have been swept from the earth, with their languages, arts, and
sciences, leaving but confused masses of ruins to mark the place where
mighty cities stood; their history, with the exception of a few doubtful
traditions, has perished; but the perfection of their astronomical
observations marks their high antiquity, fixes the periods of their
existence, and proves that, even at that early time, they must have made
considerable progress in science.” The ancient state of the heavens may
now be computed with great accuracy; and, by comparing the results of
calculation with ancient observations, the exact period at which they
were made may be verified if true, or, if false, their error may be
detected. If the date be accurate and the observation good, it will
verify the accuracy of modern tables, and will show to how many
centuries they may be extended without the fear of error. A few examples
will show the importance of the subject.

At the solstices the sun is at his greatest distance from the equator;
consequently his declination at these times is equal to the obliquity of
the ecliptic (N. 152), which was formerly determined from the meridian
length of the shadow of the stile of a dial on the day of a solstice.
The lengths of the meridian shadow at the summer and winter solstices
are recorded to have been observed at the city of Layang, in China, 1100
years before the Christian era. From these the distances of the sun from
the zenith (N. 153) of the city of Layang are known. Half the sum of
these zenith distances determines the latitude, and half their
difference gives the obliquity of the ecliptic at the period of the
observation; and, as the law of the variation of the obliquity is known,
both the time and place of the observations have been verified by
computations from modern tables. Thus the Chinese had made some advances
in the science of astronomy at that early period. Their whole chronology
is founded on the observations of eclipses, which prove the existence of
that empire for more than 4700 years. The epoch of the lunar tables of
the Indians, supposed by Bailly to be 3000 years before the Christian
era, was proved by La Place, from the acceleration of the moon, not to
be more ancient than the time of Ptolemy, who lived in the second
century after it. The great inequality of Jupiter and Saturn, whose
cycle embraces 918 years, is peculiarly fitted for marking the
civilization of a people. The Indians had determined the mean motions of
these two planets in that part of their periods when the apparent mean
motion of Saturn was at the slowest, and that of Jupiter the most rapid.
The periods in which that happened were 3102 years before the Christian
era, and the year 1491 after it. The returns of comets to their
perihelia may possibly mark the present state of astronomy to future
ages.

The places of the fixed stars are affected by the precession of the
equinoxes; and, as the law of that variation is known, their positions
at any time may be computed. Now Eudoxus, a contemporary of Plato,
mentions a star situate in the pole of the equator, and it appears from
computation that χ Draconis was not very far from that place about 3000
years ago; but, as it is only about 2150 years since Eudoxus lived, he
must have described an anterior state of the heavens, supposed to be the
same that was mentioned by Chiron about the time of the siege of Troy.
Thus every circumstance concurs in showing that astronomy was cultivated
in the highest ages of antiquity.

It is possible that a knowledge of astronomy may lead to the
interpretation of hieroglyphical characters. Astronomical signs are
often found on the ancient Egyptian monuments, probably employed by the
priests to record dates. The author had occasion to witness an instance
of this most interesting application of astronomy, in ascertaining the
date of a papyrus, sent from Egypt by Mr. Salt, in the hieroglyphical
researches of the late Dr. Thomas Young, whose profound and varied
acquirements do honour to his country, and to the age in which he lived.
The manuscript was found in a mummy case; it proved to be a horoscope of
the age of Ptolemy, and its date was determined from the configuration
of the heavens at the time of its construction.

The form of the earth furnishes a standard of weights and measures for
the ordinary purposes of life, as well as for the determination of the
masses and distances of the heavenly bodies. The length of the pendulum
vibrating seconds of mean solar time, in the latitude of London, forms
the standard of the British measure of extension. Its approximate length
oscillating in vacuo at the temperature of 62° of Fahrenheit, and
reduced to the level of the sea (N. 154), was determined by Captain
Kater to be 39·1393 inches. The weight of a cubic inch of water at the
temperature of 62° of Fahrenheit, barometer 30 inches, was also
determined in parts of the imperial troy pound, whence a standard both
of weight and capacity was deduced. The French have adopted the mètre,
equal to 3·2808992 English feet, for their unit of linear measure, which
is the ten-millionth part of the arc of the meridian which extends from
the equator to the pole, as deduced from the measures of the separate
arc extending from Formentera, the most southern of the Balearic
Islands, to Dunkirk. Should the national standards of the two countries
ever be lost, both may be recovered, since they are derived from natural
and invariable ones. The length of the measure deduced from that of the
pendulum would be found again with more facility than the mètre. But, as
no measure is mathematically exact, an error in the original standard
may at length become sensible in measuring a great extent, whereas the
error that must necessarily arise in measuring the quadrant of the
meridian (N. 155) is rendered totally insensible by subdivision in
taking its ten-millionth part. The French have adopted the decimal
division, not only in time, but also in their degrees, weights, and
measures, on account of the very great facility it affords in
computation. It has not been adopted by any other country, though
nothing is more desirable than that all nations should concur in using
the same standards, not only on account of convenience, but as affording
a more definite idea of quantity. It is singular that the decimal
division of the day, of space, weights, and measures, was employed in
China 4000 years ago; and that at the time Ibn Junis made his
observations at Cairo, about the year 1000 of the Christian era, the
Arabs were in the habit of employing the vibrations of the pendulum in
their astronomical observations as a measure of time.




                             SECTION XIII.

Tides—Forces that produce them—Origin and Course of Tidal Wave—Its
  Speed—Three kinds of Oscillations in the Ocean—The Semidiurnal
  Tides—Equinoctial Tides—Effects of the Declination of the Sun and
  Moon—Theory insufficient without Observation—Direction of the Tidal
  Wave—Height of Tides—Mass of Moon obtained from her Action on the
  Tides—Interference of Undulations—Impossibility of a Universal
  Inundation—Currents.


ONE of the most immediate and remarkable effects of a gravitating force
external to the earth is the alternate rise and fall of the surface of
the sea twice in the course of a lunar day, or 24^h 50^m 28^s of mean
solar time. As it depends upon the action of the sun and moon, it is
classed among astronomical problems, of which it is by far the most
difficult and its explanation the least satisfactory. The form of the
surface of the ocean in equilibrio, when revolving with the earth round
its axis, is an ellipsoid flattened at the poles; but the action of the
sun and moon, especially of the moon, disturbs the equilibrium of the
ocean. If the moon attracted the centre of gravity of the earth and all
its particles with equal and parallel forces, the whole system of the
earth and the waters that cover it would yield to these forces with a
common motion, and the equilibrium of the seas would remain undisturbed.
The difference of the forces and the inequality of their directions
alone disturb the equilibrium.

The particles of water under the moon are more attracted than the centre
of gravity of the earth, in the inverse ratio of the square of the
distance. Hence they have a tendency to leave the earth, but are
retained by their gravitation, which is diminished by this tendency. On
the contrary, the moon attracts the centre of the earth more powerfully
than she attracts the particles of water in the hemisphere opposite to
her; so that the earth has a tendency to leave the waters, but is
retained by gravitation, which is again diminished by this tendency.
Thus the waters immediately under the moon are drawn from the earth, at
the same time that the earth is drawn from those which are diametrically
opposite to her, in both instances producing an elevation of the ocean
of nearly the same height above the surface of equilibrium; for the
diminution of the gravitation of the particles in each position is
almost the same, on account of the distance of the moon being great in
comparison of the radius of the earth. Were the earth entirely covered
by the sea, the waters thus attracted by the moon would assume the form
of an oblong spheroid whose greater axis would point towards the moon;
since the columns of water under the moon, and in the direction
diametrically opposite to her, are rendered lighter in consequence of
the diminution of their gravitation; and, in order to preserve the
equilibrium, the axes 90° distant would be shortened. The elevation, on
account of the smaller space to which it is confined, is twice as great
as the depression, because the contents of the spheroid always remain
the same. If the waters were capable of assuming the form of equilibrium
instantaneously, that is, the form of the spheroid, its summit would
always point to the moon notwithstanding the earth’s rotation. But, on
account of their resistance, the rapid motion produced in them by
rotation prevents them from assuming at every instant the form which the
equilibrium of the forces acting upon them requires. Hence, on account
of the inertia of the waters, if the tides be considered relatively to
the whole earth and open seas, there is a meridian about 30° eastward of
the moon, where it is always high water both in the hemisphere where the
moon is and in that which is opposite. On the west side of this circle
the tide is flowing, on the east it is ebbing, and on every part of the
meridian at 90° distant it is low water. This great wave, which follows
all the motions of the moon as far as the rotation of the earth will
permit, is modified by the action of the sun, the effects of whose
attraction are in every respect like those produced by the moon, though
greatly less in degree. Consequently a similar wave, but much smaller,
raised by the sun, tends to follow his motions, which at times combines
with the lunar wave, and at others opposes it, according to the relative
positions of the two luminaries; but as the lunar wave is only modified
a little by the solar, the tides must necessarily happen twice in a day,
since the rotation of the earth brings the same point twice under the
meridian of the moon in that time, once under the superior and once
under the inferior meridian.

The periodic motions of the waters of the ocean, on the hypothesis of an
ellipsoid of revolution, entirely covered by the sea, are, however, very
far from according with observation. This arises from the great
irregularities in the surface of the earth, which is but partially
covered by the sea, from the variety in the depths of the ocean, the
manner in which it is spread out on the earth, the position and
inclination of the shores, the currents, and the resistance which the
waters meet with: causes impossible to estimate generally, but which
modify the oscillations of the great mass of the ocean. However, amidst
all these irregularities, the ebb and flow of the sea maintain a ratio
to the forces producing them sufficient to indicate their nature, and to
verify the law of the attraction of the sun and moon on the sea. La
Place observes, that the investigation of such relations between cause
and effect is no less useful in natural philosophy than the direct
solution of problems, either to prove the existence of the causes or to
trace the laws of their effects. Like the theory of probabilities, it is
a happy supplement to the ignorance and weakness of the human mind.

Since the disturbing action of the sun and moon can only become sensible
in a very great extent of deep water, the Antarctic Ocean is the origin
and birthplace of our tides. A succession of tidal waves from that
source follow one another in a north-westerly direction down the Pacific
and Atlantic Oceans, modified as they proceed by the depth of the water
and the form of the coasts. For when the sun and moon are in the same
meridian, and pass over the mass of waters lying east from Van Diemen’s
Land, New Zealand, and the South Pole, the resulting force of their
combined attraction, penetrating to the abyss of the deep and boundless
circuit of the Southern Ocean, raises a vast wave or ridge of water,
which tends to follow the luminaries to the north and west, and
continues to flow in that direction long after the bodies cease to act
upon it; but it is so retarded by the rotation of the earth and by the
inertia of the water, that it does not arrive at the different parts of
the coasts till after the moon’s southing (N. 156). When this tidal wave
leaves the Antarctic Ocean and enters the Pacific, it rushes along the
western coast of America to its farthest end, but it is so much
obstructed by the number of islands in the middle of that ocean that it
is hardly perceptible among them; while on the east it enters the Indian
Ocean, strikes with violence on the coasts of Hindostan and the shores
at the mouths of the Ganges, and causes the terrific bore in the Hoogly.
The part of this tidal wave that enters the Atlantic passes impetuously
along the coasts of Africa and America, arriving later and later at each
place. It is modified, however, by a tide raised in the Atlantic, which
is deep and free from islands; and this combined tidal wave, still
coming northward, pours its surge into the Gulf of Fundy to the height
of fifty feet; then being deflected by the coast of America at right
angles, it rushes eastward, bringing high water to the western coasts of
Ireland and England. It then goes round Scotland, brings high water to
Aberdeen and the opposite coasts of Norway and Denmark, and, continuing
its course to the south, arrives at the mouth of the Thames and fills
the channels of that river on the morning of the third day after leaving
the Antarctic Ocean.

Thus the tides in our ports are owing to an impulse from the waters of
the Antarctic seas raised by the action of the sun and moon. No doubt a
similar action raised that tide in the North Polar Ocean which Dr. Kane
saw rolling on the northern coast of Greenland in 82° N. latitude, but
which, in the present state of the globe, is imprisoned by bars of ice
and ice-bound lands.

The tidal wave extends to the bottom of the ocean, and moves uniformly
and with great speed in very deep water, variably and slow in shallow
water; the time of propagation depends upon the depth of the sea, as
well as on the nature and form of the coasts. It varies inversely as the
square of the depth—a law which theoretically affords the means of
ascertaining the proportionate depth of the sea in different parts. It
is one of the great constants of nature, and is to fluids what the
pendulum is to solids—a connecting link between time and force.

For example: the tidal wave moves across the Southern Ocean with the
velocity of 1000 miles an hour, and in the Atlantic it is scarcely less
on account of the deep trough which runs through the centre of that
ocean; but the sea is so shallow on the British coast that it takes more
time to come from Aberdeen to London than to travel over an arc of 120°,
between 60° S. lat. and 60° N. lat.

In deep water the tidal wave is merely a rise and fall of the surface;
the water does not advance, though the wave does. Indeed, if so heavy a
body as water were to move at the rate of 1000 miles an hour, it would
cause universal destruction, since in the most violent hurricanes the
velocity of the wind is little more than 100 miles an hour. Besides, it
is evident that no ship could either sail or steam against it. When the
water is shallow, however, there is a motion of translation in the water
along with the tide.

In the deep ocean the undulating motion consists of two distinct
things—an advancing form and a molecular movement. The motion of each
particle of water is in an ellipse lying wholly in the vertical plane;
so that, after the momentary displacement during the passage of the
wave, they return to their places again. The resistance of the sea-bed
is insensible in deep water; but when the tidal wave, which extends to
the very bottom of the ocean, comes into shallow water with diminished
velocity, the particles of water moving in vertical ellipses strike the
bottom, and by reaction the wave rises higher; and that being
continually repeated, as the form moves on the wave rises higher and
higher, bends more and more forward, till at last it loses its
equilibrium, and then both form and water roll to the shore, and the
elliptical trajectories of the particles, which in deep water were
vertical, incline more and more, till at length they become horizontal.
The distance from the shore at which the water begins to be translated
depends upon the depth, the nature of the coast, and the form of the
shore. Mr. Scott Russell has demonstrated that in shallow water the
velocity of the wave is equal to that which a heavy body falling freely
by its gravity would acquire in descending through half the depth of the
fluid.

It is proved by daily experience, as well as by strict mathematical
reasoning, that, if a number of waves or oscillations be excited in a
fluid by different forces, each pursues its course and has its effect
independently of the rest. Now, in the tides there are three kinds of
oscillations, depending on different causes, and producing their effects
independently of each other, which may therefore be estimated
separately. The oscillations of the first kind, which are very small,
are independent of the rotation of the earth, and, as they depend upon
the motion of the disturbing body in its orbit, they are of long
periods. The second kind of oscillations depend upon the rotation of the
earth, therefore their period is nearly a day. The oscillations of the
third kind vary with an angle equal to twice the angular rotation of the
earth, and consequently happen twice in twenty-four hours (N. 157). The
first afford no particular interest, and are extremely small; but the
difference of two consecutive tides depends upon the second. At the time
of the solstices this difference, which ought to be very great according
to Newton’s theory, is hardly sensible on our shores. La Place has shown
that the discrepancy arises from the depth of the sea, and that if the
depth were uniform there would be no difference in the consecutive tides
but that which is occasioned by local circumstances. It follows,
therefore, that, as this difference is extremely small, the sea,
considered in a large extent, must be nearly of uniform depth, that is
to say, there is a certain mean depth from which the deviation is not
great. The mean depth of the Pacific Ocean is supposed to be about four
or five miles, that of the Atlantic only three or four, which, however,
is mere conjecture. Possibly the great extent and uniformly small depth
of the Atlantic over the telegraphic platform may prevent the difference
of the oscillations in question from being perceptible on our shores.
From the formulæ which determine the difference of these consecutive
tides it is proved that the precession of the equinoxes and the nutation
of the earth’s axis are the same as if the sea formed one solid mass
with the earth.

The oscillations of the third kind are the semi-diurnal tides so
remarkable on our coasts. In these there are two phenomena particularly
to be distinguished, one occurring twice in a month, the other twice in
a year.

The first phenomenon is, that the tides are much increased in the
syzygies (N. 158), or at the time of new and full moon: in both cases
the sun and moon are in the same meridian; for when the moon is new they
are in conjunction, and when she is full they are in opposition. In each
of these positions their action is combined to produce the highest or
spring tides under that meridian, and the lowest in those points that
are 90° distant. It is observed that the higher the sea rises in full
tide, the lower it is in the ebb. The neap tides take place when the
moon is in quadrature. They neither rise so high nor sink so low as the
spring tides. It is evident that the spring tides must happen twice in a
month, since in that time the moon is once new and once full. Theory
proves that each partial tide increases as the cube of the parallax or
apparent diameter of the body producing it, for the greater the apparent
diameter the nearer the body and the more intense its action upon the
sea; hence the spring tides are much increased when the moon is in
perigee, for then she is nearest to the earth.

The second phenomenon in the tides is the augmentation occurring at the
time of the equinoxes, when the sun’s declination is zero (N. 159),
which happens twice in every year. The spring tides which take place at
that time are often much increased by the equinoctial gales, and, on the
hypothesis of the whole earth covered by the ocean, would be the
greatest possible if the line of the moon’s nodes coincided with that of
her perigee, for then the whole action of the luminaries would be in the
plane of the equator. But since the Antarctic Ocean is the source of the
tides, it is evident that the spring tide must be greatest when the moon
is in perigee, and when both luminaries have their highest southern
declination, for then they act most directly upon the great circuit of
the south polar seas.

The sun and moon are continually making the circuit of the heavens at
different distances from the plane of the equator, on account of the
obliquity of the ecliptic and the inclination of the lunar orbit. The
moon takes about 29-1/2 days to vary through all her declinations, which
sometimes extend 28-3/4° on each side of the equator, while the sun
requires nearly 365-1/4 days to accomplish his motions through 23-1/2°
on each side of the same plane, so that their combined action causes
great variations in the tides. Both the height and time of high water
are perpetually changing, and, although the problem does not admit of a
general solution, it is necessary to analyse the phenomena which ought
to arise from the attraction of the sun and moon, but the result must be
corrected in each particular case for local circumstances, so that the
theory of the tides in each port becomes really a matter of experiment,
and can only be determined by means of a vast number of observations,
including many revolutions of the moon’s nodes.

The mean height of the tides will be increased by a very small quantity
for ages to come, in consequence of the decrease in the mean distance of
the moon from the earth; the contrary effect will take place after that
period has elapsed, and the moon’s mean distance begins to increase
again, which it will continue to do for many ages. Thus the mean
distance of the moon and the consequent minute increase in the height of
the tides will oscillate between fixed limits for ever.

The height to which the tides rise is much greater in narrow channels
than in the open sea, on account of the obstructions they meet with. The
sea is so pent up in the British Channel that the tides sometimes rise
as much as fifty feet at St. Malo, on the coast of France; whereas on
the shores of some of the South Sea islands, near the centre of the
Pacific, they do not exceed one or two feet. The winds have great
influence on the height of the tides, according as they conspire with or
oppose them. But the actual effect of the wind in exciting the waves of
the ocean extends very little below the surface. Even in the most
violent storms the water is probably calm at the depth of ninety or a
hundred fathoms. The tidal wave of the ocean does not reach the
Mediterranean nor the Baltic, partly from their position and partly from
the narrowness of the Straits of Gibraltar and of the Categat, but it is
very perceptible in the Red Sea and in Hudson’s Bay. The ebb and flow of
the sea are perceptible in rivers to a very great distance from their
estuaries. In the Narrows of Pauxis, in the river of the Amazons, more
than five hundred miles from the sea, the tides are evident. It requires
so many days for the tide to ascend this mighty stream, that the
returning tides meet a succession of those which are coming up; so that
every possible variety occurs at some part or other of its shores, both
as to magnitude and time. It requires a very wide expanse of water to
accumulate the impulse of the sun and moon, so as to render their
influence sensible; on that account the tides in the Mediterranean and
Black Sea are scarcely perceptible.

These perpetual commotions in the waters are occasioned by forces that
bear a very small proportion to terrestrial gravitation: the sun’s
action in raising the ocean is only the 1/38448000 of gravitation at the
earth’s surface, and the action of the moon is little more than twice as
much; these forces being in the ratio of 1 to 2.35333, when the sun and
moon are at their mean distances from the earth. From this ratio the
mass of the moon is found to be only the 1/75 part of that of the earth.
Had the action of the sun on the ocean been exactly equal to that of the
moon, there would have been no neap tides, and the spring tides would
have been of twice the height which the action of either the sun or moon
would have produced separately—a phenomenon depending upon the
interference of the waves or undulations.

A stone plunged into a pool of still water occasions a series of waves
to advance along the surface, though the water itself is not carried
forward, but only rises into heights and sinks into hollows, each
portion of the surface being elevated and depressed in its turn. Another
stone of the same size, thrown into the water near the first, will
occasion a similar set of undulations. Then, if an equal and similar
wave from each stone arrive at the same spot at the same time, so that
the elevation of the one exactly coincides with the elevation of the
other, their united effect will produce a wave twice the size of either.
But, if one wave precede the other by exactly half an undulation, the
elevation of the one will coincide with the hollow of the other, and the
hollow of the one with the elevation of the other; and the waves will so
entirely obliterate one another, that the surface of the water will
remain smooth and level. Hence, if the length of each wave be
represented by 1, they will destroy one another at intervals of 1/2,
3/2, 5/2, &c., and will combine their effects at the intervals 1, 2, 3,
&c. It will be found according to this principle, when still water is
disturbed by the fall of two equal stones, that there are certain lines
on its surface of a hyperbolic form, where the water is smooth in
consequence of the waves obliterating each other, and that the elevation
of the water in the adjacent parts corresponds to both the waves united
(N. 160). Now, in the spring and neap tides arising from the combination
of the simple solilunar waves, the spring tide is the joint result of
the combination when they coincide in time and place; and the neap tide
happens when they succeed each other by half an interval, so as to leave
only the effect of their difference sensible. It is, therefore, evident
that, if the solar and lunar tides were of the same height, there would
be no difference, consequently no neap tides, and the spring tides would
be twice as high as either separately. In the port of Batsha, in
Tonquin, where the tides arrive by two channels of lengths corresponding
to half an interval, there is neither high nor low water on account of
the interference of the waves.

The initial state of the ocean has no influence on the tides; for,
whatever its primitive conditions may have been, they must soon have
vanished by the friction and mobility of the fluid. One of the most
remarkable circumstances in the theory of the tides is the assurance
that, in consequence of the density of the sea being only one-fifth of
the mean density of the earth, and the earth itself increasing in
density towards the centre, the stability of the equilibrium of the
ocean never can be subverted by any physical cause. A general inundation
arising from the mere instability of the ocean is therefore impossible.
A variety of circumstances, however, tend to produce partial variations
in the equilibrium of the seas, which is restored by means of currents.
Winds and the periodical melting of the ice at the poles occasion
temporary watercourses; but by far the most important causes are the
centrifugal force induced by the velocity of the earth’s rotation, and
variations in the density of the sea.

The centrifugal force may be resolved into two forces—one perpendicular,
and another tangent to the earth’s surface (N. 161). The tangential
force, though small, is sufficient to make the fluid particles within
the polar circles tend towards the equator, and the tendency is much
increased by the immense evaporation in the equatorial regions from the
heat of the sun, which disturbs the equilibrium of the ocean. To this
may also be added the superior density of the waters near the poles,
from their low temperature. In consequence of the combination of all
these circumstances, two great currents perpetually set from each pole
towards the equator. But, as they come from latitudes where the rotatory
motion of the surface of the earth is very much less than it is between
the tropics, on account of their inertia, they do not immediately
acquire the velocity with which the solid part of the earth’s surface is
revolving at the equatorial regions; from whence it follows that, within
twenty-five or thirty degrees on each side of the line, the ocean has a
general motion from east to west, which is much increased by the action
of the trade winds. Both in the Pacific and Atlantic currents of
enormous magnitude are deflected by the continents and islands to the
north and south from this mighty mass of rushing waters, which convey
the warmth of the equator to temper the severity of the polar regions,
while to maintain the equilibrium of the seas counter currents of cold
water are poured from the polar oceans to mingle with the warm waters at
the line, so that a perpetual circulation is maintained.

Icebergs are sometimes drifted as far as the Azores from the Polar seas,
and from the south pole they have come even to the Cape of Good Hope.
But the ice which encircles the south pole extends to lower latitudes by
10° than that which surrounds the north. In consequence of the polar
current Sir Edward Parry was obliged to give up his attempt to reach the
north pole in the year 1827, because the fields of ice were drifting to
the south faster than his party could travel over them to the north.

Kotzebue and Sir James Ross found a stratum of constant temperature in
the ocean at a depth depending upon the latitude: at the equator it is
at the depth of 7200 feet, from whence it gradually rises till it comes
to the surface in both hemispheres about the latitude of 56° 26ʹ, where
the water has the same temperature at all depths; it then descends to
4500 feet below the surface about the 70th parallel both in the Arctic
and Antarctic Seas. The temperature of that aqueous zone is about 39°·5
of Fahrenheit.[7] It divides the surface of the ocean into five great
zones of temperature, namely, a medial region, in which the highest mean
temperature is 82° Fahr., two temperate zones each of 39°·5 Fahr., and
two polar basins at the freezing point of salt water.




                              SECTION XIV.

Molecular Forces—Permanency of the ultimate Particles of
  Matter—Interstices—Mossotti’s Theory—Rankin’s Theory of Molecular
  Vortices—Gases reduced to Liquids by Pressure—Gravitation of
  Particles—Cohesion—Crystallization—Cleavage—Isomorphism—Minuteness of
  the Particles—Height of Atmosphere—Chemical Affinity—Definite
  Proportions and Relative Weights of Atoms—Faraday’s Discovery with
  regard to Affinity—Capillary Attraction.


THE oscillations of the atmosphere, and its action upon the rays of
light coming from the heavenly bodies, connect the science of astronomy
with the equilibrium and movements of fluids and the laws of molecular
attraction. Hitherto that force has been under consideration which acts
upon masses of matter at sensible distances; but now the effects of such
forces are to be considered as act at inappreciable distances upon the
ultimate molecules of material bodies.

All substances consist of an assemblage of material particles, or
molecules, which are far too small to be visible by any means human
ingenuity has yet been able to devise, and which are much beyond the
limits of our perceptions. They neither can be created nor destroyed;
bodies may be burned, but their particles are not consumed—they are
merely liberated from one combination to enter into another, nor are
their peculiar properties ever changed; whatever combinations they may
enter into, they are ever and invariably the same.

Since every known substance may be reduced in bulk by pressure, it
follows that the particles of matter are not in actual contact, but are
separated by interstices; and it is evident that the smaller the
interstitial spaces the greater the density. These spaces appear to be
filled with air in some cases, as may be inferred from certain
semi-opaque minerals and other substances becoming transparent when
plunged into water. Sometimes they may possibly contain some unknown and
highly elastic fluid, such as Sir David Brewster has discovered in the
minute cavities of various minerals, which occasionally causes them to
explode under the hands of the lapidary; but as it is inconceivable that
the particles of matter should act upon one another without some means
of communication, it is presumed that the interstices of material
substances contain a portion of the ethereal medium with which the
regions of space are filled.

The various hypotheses that have been formed as to the nature and action
of the forces which unite the particles of matter, have been
successively given up as science advanced, and now nothing decisive has
been attained, although Professor Mossotti, of Pisa, by a very able
analysis, has endeavoured to prove the identity of the cohesive force
with gravitation. As the particles of material bodies are not in actual
contact, he supposes that each is surrounded by an atmosphere of the
ethereal medium, which he conceives to be electricity; moreover he
assumes that the atoms of the medium repel one another, that the
particles of matter also repel one another, but with less intensity, and
that there is a mutual attraction between the particles of matter and
the atoms of the medium, forces which are assumed to vary inversely as
the square of the distance.

Hence, when the material molecules of a body are inappreciably near to
one another, they mutually repel each other with a force which
diminishes rapidly as the infinitely small distance between the material
molecules augments, and at last vanishes. When the molecules are still
farther apart, the force becomes attractive. At that particular point
where the change takes place the forces of repulsion and attraction
balance each other, so that the molecules of a body are neither disposed
to approach nor recede, but remain in equilibrio. If we try to press
them nearer, the repulsive force resists the attempt; and if we
endeavour to break the body so as to tear the particles asunder, the
attractive force predominates and keeps them together. This is what
constitutes the cohesive force, or force of aggregation, by which the
molecules of all substances are united. The limits of the distance at
which the negative action becomes positive vary according to the
temperature and nature of the molecules, and determine whether the body
which they form be solid, liquid, or aëriform.

Beyond this neutral point the attractive force increases as the distance
between the molecules augments till it attains a maximum; when the
particles are more apart, it diminishes; and, as soon as they are
separated by finite or sensible distances, it varies directly as their
mass and inversely as the square of the distance, which is precisely the
law of universal gravitation.

Thus, on the hypothesis that the mutual repulsion between the electric
atoms is a little more powerful than the mutual repulsion between the
particles of matter, the ether and the matter attract each other with
unequal intensities, which leaves an excess of attractive force
constituting gravitation. As the gravitating force is in operation
wherever there is matter, the ethereal electric medium must encompass
all the bodies in the universe; and, as it is utterly incomprehensible
that the celestial bodies should exert a reciprocal attraction through a
void, the Professor concludes that the ethereal electrical medium fills
all space.

It is true that this connexion between the molecular forces and
gravitation depends upon hypothesis; but in the greater number of
physical investigations some hypothesis is requisite in the first
instance to aid the imperfection of our senses; and when the phenomena
of nature accord with the assumption, we are justified in believing it
to be a general law.

Mr. Rankin’s theory of molecular vortices, or the molecular structure of
matter, is independent of electricity. According to his hypothesis, each
atom of matter consists of an inappreciably small nucleus, encompassed
by an elastic ethereal atmosphere which is retained in its position by
attractive forces directed towards the molecule, whilst the molecules
attract each other in the direction of straight lines joining their
centres. The nuclei may either be solid, or a high condensation of the
atmospheres which surround each with decreasing density. When the
attraction between the molecules is such that the elasticity of the
atmospheres is insensible, the body is a perfect solid, the rigidity of
which bears a certain definite proportion to the elasticity of the
volume. When the atmospheres are less condensed and the attraction of
the molecules merely produces a cohesive force sufficient to balance the
atomic elasticity of the atmosphere, the body is a perfect liquid; and
when the attraction of the molecules is very small compared with the
elasticity of their ethereal atmospheres, the body is a perfect gas.
These atmospheres are supposed to be portions of the ethereal medium
which penetrates into the interstices of every substance, and their
elasticity to be due to the heat generated by the centrifugal force or
oscillations among their atoms, for motion is the cause of heat, the
force producing the motions varying simply as the density of the ether.

In aëriform fluids, although the particles are more remote from each
other than in liquids and solids, yet the pressure may be so great as to
reduce an aëriform fluid to a liquid, and a liquid to a solid. Dr.
Faraday has reduced some of the gases to a liquid state by very great
compression; but although atmospheric air is capable of a diminution of
volume to which we do not know a limit, it has hitherto always retained
its gaseous qualities, and resumes its primitive volume the instant the
pressure is removed. Substances are said to be more or less elastic,
according to the facility with which they regain their bulk or volume
when the pressure is removed; thus liquids resist compression on account
of their elasticity, and in solids the resistance is much greater but
variable, and the effort required to break a substance is a measure of
the cohesive force exerted by its particles. In stone, iron, steel, and
all brittle and hard substances, the cohesion of the particles is
powerful but of small extent; in elastic bodies, on the contrary, its
action is weak, but more extensive. An infinite variety of conditions
may be observed in the fusion of metals and other substances passing
from hardness to toughness, viscidity, and through all the other stages
to perfect fluidity and even to vapour. Since all bodies expand by heat,
the cohesive force is weakened by increase of temperature. The cohesion
of matter or the strength of substances forms an important branch of
study in engineering.

Every particle of matter, whether it forms a constituent part of a
solid, liquid, or aëriform fluid, is subject to the law of gravitation.
The weight of the atmosphere, of gases and vapour, shows that they
consist of gravitating particles. In liquids the cohesive force is not
sufficiently powerful to resist the action of gravitation. Therefore,
although their component particles still maintain their connexion, the
liquid is scattered by their weight, unless when it is confined in a
vessel or has already descended to the lowest point possible, and
assumed a level surface from the mobility of its particles and the
influence of the gravitating forces, as in the ocean, or a lake. Solids
would also fall to pieces by the weight of their particles, if the force
of cohesion were not powerful enough to resist the efforts of
gravitation.

The phenomena arising from the force of cohesion are innumerable. The
spherical form of rain-drops; the difficulty of detaching a plate of
glass from the surface of water; the force with which two plane surfaces
adhere when pressed together; the drops that cling to the window-glass
in a shower of rain—are all effects of cohesion entirely independent of
atmospheric pressure, and are included in the same analytical formula
(N. 162) which expresses all the circumstances accurately, although the
laws according to which the forces of cohesion and repulsion vary are
unknown. It is more than probable that the spherical form of the sun and
planets is due to the force of cohesion, as they have every appearance
of having been at one period in a state of fusion.

A very remarkable instance has occasionally been observed in plate-glass
manufactories. After the large plates of glass of which mirrors are to
be made have received their last polish, they are carefully wiped and
laid on their edges with their surfaces resting on one another. In the
course of time the cohesion has sometimes been so powerful, that they
could not be separated without breaking. Instances have occurred where
two or three have been so perfectly united, that they have been cut and
their edges polished as if they had been fused together; and so great
was the force required to make the surfaces slide that one tore off a
portion of the surface of the other.

In liquids and gases the forms of the particles have no influence, they
are so far apart; but the structure of solids varies according to the
sides which the particles present to one another during their
aggregation. Nothing is known of their form further than the
dissimilarity of their different sides in certain cases, which appears
from their reciprocal attractions during crystallisation being more or
less powerful according to the sides they present to one another.
Crystallisation is an effect of molecular attraction regulated by
certain laws, according to which atoms of the same kind of matter unite
in regular forms—a fact easily proved by dissolving a piece of alum in
pure water. The mutual attraction of the particles is destroyed by the
water; but, if it be evaporated, they unite, and form in uniting
eight-sided figures called octahedrons (N. 163). These however are not
all the same. Some have their angles cut off, others their edges, and
some both, while the remainder take the regular form. It is quite clear
that the same circumstances which cause the aggregation of a few
particles would, if continued, cause the addition of more; and the
process would go on as long as any particles remain free round the
primitive nucleus, which would increase in size, but would remain
unchanged in form, the figure of the particles being such as to maintain
the regularity and smoothness of the surfaces of the solid and their
mutual inclinations. A broken crystal will by degrees resume its regular
figure when put back again into the solution of alum, which shows that
the internal and external particles are similar, and have a similar
attraction for the particles held in solution. The original conditions
of aggregation which make the molecules of the same substance unite in
different forms must be very numerous, since of carbonate of lime alone
there are many hundred varieties; and certain it is, from the motion of
polarised light through rock crystal, that a very different arrangement
of particles is requisite to produce an extremely small change in
external form. A variety of substances in crystallising combine
chemically with a certain portion of water which in a dry state forms an
essential part of their crystals, and, according to the experiments of
MM. Haidinger and Mitscherlich, seems in some cases to give the peculiar
determination to their constituent molecules. These gentlemen have
observed that the same substance crystallising at different temperatures
unites with different quantities of water and assumes a corresponding
variety of forms. Seleniate of zinc, for example, unites with three
different portions of water, and assumes three different forms,
according as its temperature in the act of crystallising is hot,
lukewarm, or cold. Sulphate of soda also, which crystallises at 90° of
Fahrenheit without water of crystallisation, combines with water at the
ordinary temperature, and takes a different form. Heat appears to have a
great influence on the phenomena of crystallisation, not only when the
particles of matter are free, but even when firmly united, for it
dissolves their union, and gives them another determination. Professor
Mitscherlich found that prismatic crystals of sulphate of nickel
(N. 164), exposed to a summer’s sun in a close vessel, had their
internal structure so completely altered without any exterior change,
that when broken open they were composed internally of octahedrons with
square bases. The original aggregation of the internal particles had
been dissolved, and a disposition given to arrange themselves in a
crystalline form. Crystals of sulphate of magnesia and of sulphate of
zinc, gradually heated in alcohol till it boils, lose their transparency
by degrees, and when opened are found to consist of innumerable minute
crystals totally different in form from the whole crystals; and
prismatic crystals of zinc (N. 165) are changed in a few seconds into
octahedrons by the heat of the sun: other instances might be given of
the influence of even moderate degrees of temperature on molecular
attraction in the interior of substances. It must be observed that these
experiments give entirely new views with regard to the constitution of
solid bodies. We are led from the mobility of fluids to expect great
changes in the relative positions of their molecules, which must be in
perpetual motion even in the stillest water or calmest air; but we were
not prepared to find motion to such an extent in the interior of solids.
That their particles are brought nearer by cold and pressure, or removed
farther from one another by heat, might be expected; but it could not
have been anticipated that their relative positions could be so entirely
changed as to alter their mode of aggregation. It follows, from the low
temperature at which these changes are effected, that there is probably
no portion of inorganic matter that is not in a state of relative
motion.

Professor Mitscherlich’s discoveries with regard to the forms of
crystallised substances, as connected with their chemical character,
have thrown additional light on the constitution of material bodies.
There is a certain set of crystalline forms which are not susceptible of
variation, as the die or cube (N. 166), which may be small or large, but
is invariably a solid bounded by six square surfaces or planes. Such
also is the tetrahedron (N. 167) or four-sided solid contained by four
equal-sided triangles. Several other solids belong to this class, which
is called the Tessular system of crystallisation. There are other
crystals which, though bounded by the same number of sides, and having
the same form, are yet susceptible of variation; for instance, the
eight-sided figure with a square base, called an octahedron (N. 168),
which is sometimes flat and low, and sometimes acute and high. It was
formerly believed that identity of form in all crystals not belonging to
the Tessular system indicated identity of chemical composition.
Professor Mitscherlich, however, has shown that substances differing to
a certain degree in chemical composition have the property of assuming
the same crystalline form. For example, the neutral phosphate of soda
and the arseniate of soda crystallise in the very same form, contain the
same quantities of acid, alkali, and water of crystallisation; yet they
differ so far, that one contains arsenic and the other an equivalent
quantity of phosphorus. Substances having such properties are said to be
isomorphous, that is, equal in form. Of these there are many groups,
each group having the same form, and similarity though not identity of
chemical composition. For instance, one of the isomorphous groups is
that consisting of certain chemical substances called the protoxides of
iron, copper, zinc, nickel, and manganese, all of which are identical in
form and contain the same quantity of oxygen, but differ in the
respective metals they contain, which are, however, nearly in the same
proportion in each. All these circumstances tend to prove that
substances having the same crystalline form must consist of ultimate
atoms having the same figure and arranged in the very same order; so
that the form of crystals is dependent on their atomic constitution.

All crystallised bodies have joints called cleavages, at which they
split more easily than in other directions; on this property the whole
art of cutting diamonds depends. Each substance splits in a manner and
in forms peculiar to itself. For example, all the hundreds of forms of
carbonate of lime split into six-sided figures, called rhombohedrons
(N. 169), whose alternate angles measure 105·55° and 75·05°, however far
the division may be carried; therefore the ultimate particle of
carbonate of lime is presumed to have that form. However this may be, it
is certain that all the various crystals of that mineral may be formed
by building up six-sided solids of the form described, in the same
manner as children build houses with miniature bricks. It may be
imagined that a wide difference may exist between the particles of an
unformed mass and a crystal of the same substance—between the common
shapeless limestone and the pure and limpid crystal of Iceland spar; yet
chemical analysis detects none; their ultimate atoms are identical, and
crystallisation shows that the difference arises only from the mode of
aggregation. Besides, all substances either crystallise naturally, or
may be made to do so by art. Liquids crystallise in freezing, vapours by
sublimation (N. 170); and hard bodies, when fused, crystallise in
cooling. Hence it may be inferred that all substances are composed of
atoms, on whose magnitude, density, and form, their nature and qualities
depend; and, as these qualities are unchangeable, the ultimate particles
of matter must be incapable of wear—the same now as when created.

The size of the ultimate particles of matter must be small in the
extreme. Organised beings, possessing life and all its functions, have
been discovered so small, that a million of them would occupy less space
than a grain of sand. The malleability of gold, the perfume of musk, the
odour of flowers, and many other instances might be given of the
excessive minuteness of the atoms of matter. Supposing the density of
the air at the surface of the earth to be represented by unity, Sir John
Herschel has shown that, under any hypothesis as to its atoms, it would
require a fraction having at least 1370 figures in its denominator to
express its tenuity in the interplanetary space; yet the definite
proportions of chemical compounds afford a proof that divisibility of
matter has a limit. The cohesive force, which has been the subject of
the preceding considerations, only unites particles of the same kind of
matter; whereas affinity, which is the cause of chemical compounds, is
the mutual attraction between particles of different kinds of matter,
generally producing a compound which has no sensible property in common
with its component parts except that of their combined gravity, as, for
example, water, which is a compound of oxygen and hydrogen gases. It is
merely a result of the electrical state of the particles, chemical
affinity and electricity being only forms of the same power. In most
cases it produces electricity, as in the oxidation of metals and
combustion, and in every case without exception heat is evolved by
bodies while combining chemically; and as heat is an expansive force,
chemical action is changed into mechanical expansion, but it is not
known in this case why heat is produced, nor the manner in which the
particles act.

It is a permanent and universal law in vast numbers of unorganised
bodies that their composition is definite and invariable, the same
compound always consisting of the same elements united together in the
same proportions. Two substances may indeed be mixed; but they will not
combine to form a third substance different from both, unless their
component particles unite in definite proportions; that is to say, one
part by weight of one of the substances will unite with one part by
weight of the other, or with two parts, or three, or four, &c., so as to
form a new substance; but in any other proportions they will only be
mechanically mixed. For example, one part by weight of hydrogen gas will
combine with eight parts by weight of oxygen gas, and form water; or it
will unite with sixteen parts by weight of oxygen, and form a substance
called deutoxide of hydrogen; but, added to any other weight of oxygen,
it will produce one or both of these compounds mingled with the portion
of oxygen or hydrogen in excess. The law of definite proportion
established by Dr. Dalton, on the principle that every compound body
consists of a combination of the atoms of its constituent parts, is of
universal application, and is in fact one of the most important
discoveries in physical science, furnishing information previously
unhoped for with regard to the most secret and minute operations of
nature, in disclosing the relative weights of the ultimate atoms of
matter. Thus an atom of oxygen uniting with an atom of hydrogen forms
the compound water; but, as every drop of water however small consists
of eight parts by weight of oxygen and one part by weight of hydrogen,
it follows that an atom of oxygen is eight times heavier than an atom of
hydrogen. In the same manner sulphuretted hydrogen gas consists of
sixteen parts by weight of sulphur and one of hydrogen; therefore an
atom of sulphur is sixteen times heavier than an atom of hydrogen. Also
carbonic oxide is constituted of six parts by weight of carbon and eight
of oxygen; and, as an atom of oxygen has eight times the weight of an
atom of hydrogen, it follows that an atom of carbon is six times heavier
than one of hydrogen. Since the same definite proportion holds in the
composition of a vast number of substances that have been examined, it
has been concluded that there are great differences in the weights of
the ultimate particles of matter. Although Dalton’s law is fully
established, yet instances have occurred from which it appears that the
atomic theory deduced from it is not always maintained. M. Gay Lussac
discovered that gases unite together by their bulk or volumes, in such
simple and definite proportions as one to one, one to two, one to three,
&c. For example, one volume or measure of oxygen unites with two volumes
or measures of hydrogen in the formation of water.

Dr. Faraday has proved, by experiments on bodies both in solution and
fusion, that chemical affinity is merely a result of the electrical
state of the particles of matter. Now it must be observed that the
composition of bodies, as well as their decomposition, may be
accomplished by means of electricity; and Dr. Faraday has found that
this chemical composition and decomposition, by a given current of
electricity, is always accomplished according to the laws of definite
proportions; and that the quantity of electricity requisite for the
decomposition of a substance is exactly the quantity necessary for its
composition. Thus the quantity of electricity which can decompose a
grain weight of water is exactly equal to the quantity of electricity
which unites the elements of that grain of water together, and is
equivalent to the quantity of atmospheric electricity which is active in
a very powerful flash of lightning. This law is universal, and of that
high and general order which characterises all great discoveries.
Chemical force is extremely powerful. A pound of the best coal gives
when burnt sufficient heat to raise the temperature of 8086 pounds of
water one Centigrade degree, whence Professor Helmholtz of Bonn has
computed that the magnitude of the chemical force of attraction between
the particles of a pound of coal and the quantity of oxygen that
corresponds to it, is capable of lifting a weight of 100 pounds to the
height of 20 miles.

Dr. Faraday has given a singular instance of cohesive force inducing
chemical combination, by the following experiment, which seems to be
nearly allied to the discovery made by M. Dœbereiner, in 1823, of the
spontaneous combustion of spongy platinum (N. 171) exposed to a stream
of hydrogen gas mixed with common air. A plate of platinum with
extremely clean surfaces, when plunged into oxygen and hydrogen gas
mixed in the proportions which are found in the constitution of water,
causes the gases to combine and water to be formed, the platinum to
become red-hot, and at last an explosion to take place; the only
conditions necessary for this curious experiment being excessive purity
in the gases and in the surface of the plate. A sufficiently pure
metallic surface can only be obtained by immersing the platinum in very
strong hot sulphuric acid and then washing it in distilled water, or by
making it the positive pole of a galvanic pile in dilute sulphuric acid.
It appears that the force of cohesion, as well as the force of affinity,
exerted by particles of matter, extends to all the particles within a
very minute distance. Hence the platinum, while drawing the particles of
the two gases towards its surface by its great cohesive attraction,
brings them so near to one another that they come within the sphere of
their mutual affinity, and a chemical combination takes place. Dr.
Faraday attributes the effect in part also to a diminution in the
elasticity of the gaseous particles on their sides adjacent to the
platinum, and to their perfect mixture or association, as well as to the
positive action of the metal in condensing them against its surface by
its attractive force. The particles when chemically united run off the
surface of the metal in the form of water by their gravitation, or pass
away as aqueous vapour and make way for others.

The oscillations of the atmosphere, and the changes in its temperature,
are measured by variations in the heights of the barometer and
thermometer. But the actual length of the liquid columns depends not
only upon the force of gravitation, but upon the cohesive force or
reciprocal attraction between the molecules of the liquid and those of
the tube containing it. This peculiar action of the cohesive force is
called capillary attraction or capillarity. If a glass tube of extremely
fine bore, such as a small thermometer tube, be plunged into a cup of
water or spirit of wine, the liquid will immediately rise in the tube
above the level of that in the cup; and the surface of the little column
thus suspended will be a hollow hemisphere, whose diameter is the
interior diameter of the tube. If the same tube be plunged into a cupful
of mercury, the liquid will also rise in the tube, but it will never
attain the level of that in the cup, and its surface will be a
hemisphere whose diameter is also the diameter of the tube (N. 172). The
elevation or depression of the same liquid in different tubes of the
same matter is in the inverse ratio of their internal diameters
(N. 173), and altogether independent of their thickness; whence it
follows that the molecular action is insensible at sensible distances,
and that it is only the thinnest possible film of the interior surface
of the tubes that exerts a sensible action on the liquid. So much indeed
is this the case, that, when tubes of the same bore are completely
wetted with water throughout their whole extent, mercury will rise to
the same height in all of them, whatever be their thickness or density,
because the minute coating of moisture is sufficient to remove the
internal column of mercury beyond the sphere of attraction of the tube,
and to supply the place of a tube by its own capillary attraction. The
forces which produce the capillary phenomena are the reciprocal
attraction of the tube and the liquid, and of the liquid particles on
one another; and, in order that the capillary column may be in
equilibrio, the weight of that part of it which rises above or sinks
below the level of the liquid in the cup must balance these forces.

The estimation of the action of the liquid is a difficult part of this
problem. La Place, Dr. Young, and other mathematicians, have considered
the liquid within the tube to be of uniform density; but M. Poisson, in
one of those masterly productions in which he elucidates the most
abstruse subjects, has proved that the phenomena of capillary attraction
depend upon a rapid decrease in the density of the liquid column
throughout an extremely small space at its surface. Every indefinitely
thin layer of a liquid is compressed by the liquid above it, and
supported by that below. Its degree of condensation depends upon the
magnitude of the compressive force; and, as this force decreases rapidly
towards the surface, where it vanishes the density of the liquid
decreases also. M. Poisson has shown that, when this force is omitted,
the capillary surface becomes plane, and that the liquid in the tube
will neither rise above nor sink below the level of that in the cup. In
estimating the forces, it is also necessary to include the variation in
the density of the capillary surface round the edges from the attraction
of the tube.

The direction of the resulting force determines the curvature of the
surface of the capillary column. In order that a liquid may be in
equilibrio, the force resulting from all the forces acting upon it must
be perpendicular to the surface. Now it appears that, as glass is more
dense than water or alcohol, the resulting force will be inclined
towards the interior side of the tube; therefore the surface of the
liquid must be more elevated at the sides of the tube than in the centre
in order to be perpendicular to it, so that it will be concave as in the
thermometer. But, as glass is less dense than mercury, the resulting
force will be inclined from the interior side of the tube (N. 174), so
that the surface of the capillary column must be more depressed at the
sides of the tube than in the centre, in order to be perpendicular to
the resulting force, and is consequently convex, as may be perceived in
the mercury of the barometer when rising. The absorption of moisture by
sponges, sugar, salt, &c., are familiar examples of capillary
attraction. Indeed the pores of sugar are so minute, that there seems to
be no limit to the ascent of the liquid. Wine is drawn up in a curve on
the interior surface of a glass; tea rises above its level on the side
of a cup; but, if the glass or cup be too full, the edges attract the
liquid downwards, and give it a rounded form. A column of liquid will
rise above or sink below its level between two plane parallel surfaces
when near to one another, according to the relative densities of the
plates and the liquid (N. 175); and the phenomena will be exactly the
same as in a cylindrical tube whose diameter is double the distance of
the plates from each other. If the two surfaces be very near to one
another, and touch each other at one of their upright edges, the liquid
will rise highest at the edges that are in contact, and will gradually
diminish in height as the surfaces become more separated. The whole
outline of the liquid column will have the form of a hyperbola. Indeed,
so universal is the action of capillarity, that solids and liquids
cannot touch one another without producing a change in the form of the
surface of the liquid.

The attractions and repulsions arising from capillarity present many
curious phenomena. If two plates of glass or metal, both of which are
either dry or wet, be partly immersed in a liquid parallel to one
another, the liquid will be raised or depressed close to their surfaces,
but will maintain its level through the rest of the space that separates
them. At such a distance they neither attract nor repel one another; but
the instant they are brought so near as to make the level part of the
liquid disappear, and the two curved parts of it meet, the two plates
will rush towards each other and remain pressed together (N. 176). If
one of the surfaces be wet and the other dry, they will repel one
another when so near as to have a curved surface of liquid between them;
but, if forced to approach a little nearer, the repulsion will be
overcome, and they will attract each other as if they were both wet or
both dry. Two balls of pith or wood floating in water, or two balls of
tin floating in mercury, attract one another as soon as they are so near
that the surface of the liquid is curved between them. Two ships in the
ocean may be brought into collision by this principle. But two balls,
one of which is wet and the other dry, repel one another as soon as the
liquid which separates them is curved at its surface. A bit of tea-leaf
is attracted by the edge of the cup if wet, and repelled when dry,
provided it be not too far from the edge and the cup moderately full; if
too full, the contrary takes place. It is probable that the rise of the
sap in vegetables is in some degree owing to capillarity.




                              SECTION XV.

Analysis of the Atmosphere—Its Pressure—Law of Decrease in
  Density—Law of Decrease in Temperature—Measurement of Heights
  by the Barometer—Extent of the Atmosphere—Barometrical
  Variations—Oscillations—Trade-Winds—Cloud-Ring—Monsoons—Rotation of
  Winds—Laws of Hurricanes.


THE atmosphere is not homogeneous. It appears from analysis that, of 100
parts, 99·5 consist of nitrogen and oxygen gases mixed in the
proportions of 79 to 21 of volume, the remainder consists of 0·05 parts
of carbonic acid and on an average 0·45 of aqueous vapour. These
proportions are found to be the same at all heights hitherto attained by
man. The air is an elastic fluid, resisting pressure in every direction,
and is subject to the law of gravitation. As the space in the top of the
tube of a barometer is a vacuum, the column of mercury suspended by the
pressure of the atmosphere on the surface of that in the cistern is a
measure of its weight. Consequently every variation in the density
occasions a corresponding rise or fall in the barometrical column. At
the level of the sea in latitude 42°, and at the temperature of melting
ice, the mean height of the barometer is 29·922 or 30 inches nearly. The
pressure of the atmosphere is about fifteen pounds on every square inch;
so that the surface of the whole globe sustains a weight of
11,671,000,000 hundreds of millions of pounds. Shell-fish, which have
the power of producing a vacuum, adhere to the rocks by a pressure of
fifteen pounds upon every square inch of contact.

The atmosphere when in equilibrio is an ellipsoid flattened at the poles
from its rotation with the earth. In that state its strata are of
uniform density at equal heights above the level of the sea; but since
the air is both heavy and elastic, its density necessarily diminishes in
ascending above the surface of the earth; for each stratum of air is
compressed only by the weight above it. Therefore the upper strata are
less dense because they are less compressed than those below them.
Whence it is easy to show, supposing the temperature to be constant,
that if the heights above the earth be taken in increasing arithmetical
progression, that is, if they increase by equal quantities, as by a foot
or a mile, the densities of the strata of air, or the heights of the
barometer which are proportionate to them, will decrease in geometrical
progression. For example, at the level of the sea if the mean height of
the barometer be 29·922 inches, at the height of 18,000 feet it will be
14·961 inches, or one half as great; at the height of 36,000 feet it
will be one-fourth as great; at 54,000 feet it will be one-eighth, and
so on. Sir John Herschel has shown that the actual decrease is much more
rapid, and that, in any hypothesis that has been formed with regard to
the divisibility of the aërial atoms, a vacuum exists at the height of
80 or 90 miles above the earth’s surface, inconceivably more perfect
than any that can be produced in the best air-pumps. Indeed the decrease
in density is so rapid that three-fourths of all the air contained in
the atmosphere is within four miles of the earth; and, as its
superficial extent is 200 millions of square miles, its relative
thickness is less than that of a sheet of paper when compared with its
breadth. The air even on mountain tops is sufficiently rare to diminish
the intensity of sound, to affect respiration, and to occasion a loss of
muscular strength. The blood burst from the lips and ears of M. de
Humboldt as he ascended the Andes; and he experienced the same
difficulty in kindling and maintaining a fire at great heights which
Marco Polo, the Venetian, felt on the mountains of Central Asia. M.
Gay-Lussac ascended in a balloon to the height of 4·36 miles, and he
suffered greatly from the rarity of the air. It is true that at the
height of thirty-seven miles the atmosphere is still dense enough to
reflect the rays of the sun when 18° below the horizon; but the tails of
comets show that extremely attenuated matter is capable of reflecting
light. And although, at the height of fifty miles, the bursting of the
meteor of 1783 was heard on earth like the report of a cannon, it only
proves the immensity of the explosion of a mass half a mile in diameter,
which could produce a sound capable of penetrating air three thousand
times more rare than that we breathe. But even these heights are
extremely small when compared with the radius of the earth.

The density of the air is modified by various circumstances, chiefly by
changes of temperature, because heat dilates the air and cold contracts
it, varying 1/480 of the whole bulk when at 32° for every degree of
Fahrenheit’s thermometer. Experience shows that the heat of the air
decreases as the height above the surface of the earth increases. It
appears that the mean temperature of space is 226° below the zero point
of Fahrenheit by the theories of Fourier and Pouillet, but Sir John
Herschel has computed it to be -239° Fahr. from observations made during
the ascent in balloons. Such would probably be the temperature of the
surface of the earth also, were it not for the non-conducting power of
the air, whence it is enabled to retain the heat of the sun’s rays,
which the earth imbibes and radiates in all directions. The decrease in
heat is very irregular; each authority gives a different estimate,
because it varies with latitude and local circumstances, but from the
mean of five different statements it seems to be about one degree for
every 334 feet; the mean of observations made in balloons is 400 feet,
which is probably nearer the truth. This is the cause of the severe cold
and perpetual snow on the summits of the alpine chains. In the year 1852
four ascents in a balloon took place from the meteorological observatory
at Kew, in which the greatest height attained was 22,370 feet. The
observations then made by Mr. Welsh furnished Sir John Herschel with
data for computing that the temperature of space is minus 239°, that is
239° below the zero point of Fahrenheit, that the limiting temperature
of the atmosphere is probably 77-1/2 degrees below that point at the
equator, and 119-1/2 below it at the poles, with a range of temperature
from the surface of 161-1/2° in the former case, and 119-1/2° in the
latter. During these ascents it was found that the temperature of the
air decreases uniformly up to a certain point, where it is arrested and
remains constant, or increases through a depth of 2000 or 3000 feet,
after which it decreases again according to the same law as before.
Throughout this zone of constant temperature it either rains, or there
is a great fall in the dew point; in short, it is the region of clouds,
and the increase of temperature is owing to the latent or absorbed heat
set free by the condensation of the aqueous vapour. In the latitude of
Kew the cloud region begins at altitudes varying between 2000 and 6500
feet, according to the state of the weather.

Were it not for the effects of temperature on the density of the air,
the heights of mountains might be determined by the barometer alone; but
as the thermometer must also be consulted, the determination becomes
more complicated. Mr. Ivory’s method of computing heights from
barometrical measurements has the advantage of combining accuracy with
the greatest simplicity. Indeed the accuracy with which the heights of
mountains can be obtained by this method is very remarkable. Admiral
Smyth, R.N., and Sir John Herschel measured the height of Etna by the
barometer, without any communication and in different years; Admiral
Smyth made it 10,874 feet, and Sir John Herschel 10,873, the difference
being only one foot. In consequence of the diminished pressure of the
atmosphere water boils at a lower temperature on mountain tops than in
the valleys, which induced Fahrenheit to propose this mode of
observation as a method of ascertaining their heights. It is very
simple, as Professor Forbes ascertained that the temperature of the
boiling point varies in arithmetical proportion with the height, or 5495
feet for every degree of Fahrenheit, so that the calculation of height
becomes one of arithmetic only, without the use of any table.

The mean pressure of the atmosphere is not the same all over the globe.
It is less by 0·24 of an inch at the equator than at the tropics or in
the higher latitudes, in consequence of the ascent of heated air and
vapour from the surface of the ocean. It is less also on the shores of
the Baltic Sea than it is in France, and it was observed by Sir James C.
Ross that throughout the whole of the Antarctic Ocean, from 68° to 74°
S. latitude, and from 8° to 7° W. longitude, there is a depression of
the barometer amounting to an inch and upwards, which is equivalent to
an elevation above the sea level of 800 feet. A similar depression was
observed by M. Erman in the sea of Ochotzk, and in the adjacent
continent of eastern Siberia. Sir John Herschel assigns as the cause of
these singular anomalies the great system of circulation of the trade
and antetrade winds, in both hemispheres, reacting upon the general mass
of the continents as obstacles in their path, which is modified by the
configuration of the land.

There are various periodic oscillations in the atmosphere, which, rising
and falling like waves in the sea, occasion corresponding changes in the
height of the barometer, but they differ as much from the trade-winds,
monsoons, and other currents, as the tides of the sea do from the
Gulf-stream and other oceanic rivers. The sun and moon disturb the
equilibrium of the atmosphere by their attraction, and produce annual
undulations which have their maximum altitudes at the equinoxes, and
their minima at the solstices. There are also lunar tides, which ebb and
flow twice in the course of a lunation. The diurnal tides, which
accomplish their rise and fall in six hours, are greatly modified by the
heat of the sun. Between the tropics the barometer attains its maximum
height about nine in the morning, then sinks till three or four in the
afternoon; it again rises and attains a second maximum about nine in the
evening, and then it begins to fall, and reaches a second minimum at
three in the morning, again to pursue the same course. According to M.
Bouvard, the amount of the oscillations at the equator is proportional
to the temperature, and in other parallels it varies as the temperature
and the square of the cosine of the latitude conjointly; consequently it
decreases from the equator to the poles, but it is somewhat greater in
the day than in the night.

Besides these small undulations, there are vast waves perpetually moving
over the continents and oceans in separate and independent systems,
being confined to local, yet very extensive districts, probably
occasioned by long-continued rains or dry weather over large tracts of
country. By numerous barometrical observations made simultaneously in
both hemispheres, the courses of several have been traced, some of which
occupy twenty-four, and others thirty-six, hours to accomplish their
rise and fall. One especially of these vast barometric waves, many
hundreds of miles in breadth, has been traced over the greater part of
Europe; and not its breadth only, but also the direction of its front
and its velocity, have been clearly ascertained. Although, like all
other waves, these are but moving forms, yet winds arise dependent on
them like tide streams in the ocean. Mr. Birt has determined the periods
of other waves of still greater extent and duration, two of which
required seventeen days to rise and fall; and another which takes
fourteen days to complete its undulation, called by Mr. Birt the
November wave, passes annually over the British Islands, probably over
the whole of Europe and the seas on its northern coasts. Its crest,
which appears to be 6000 miles in extent, moves from N.W. to S.E. at the
rate of about 19 miles an hour; while the extent of its barometrical
elevation from its trough to its crest is seldom less than an inch,
sometimes double that quantity. The great crest is preceded and followed
at about five days’ interval by two lower ones, and the beginning and
end are marked by deep depressions. The researches of M. Leverrier leave
no doubt that the great Crimean storm of the 14th November, 1854, was
part of this phenomenon,[8] for even a very small difference of
atmospheric pressure is sufficient to raise a considerable wind. Since
each oscillation has its perfect effect independently of the others,
each one is marked by a change in the barometer, and this is beautifully
illustrated by curves constructed from a series of observations. The
general form of the curve shows the course of the principal wave, while
small undulations in its outline mark the maxima and minima of the minor
oscillations.

The trade-winds, which are the principal currents in the atmosphere, are
only a particular case of those very general laws which regulate the
motion of the winds depending on the rarefaction of the air combined
with the rotation of the earth on its axis. They are permanent currents
of wind between the tropics, blowing to the N.E. on the N. side of the
equator, and to the S.E. on the S. side.

If currents of air come from the poles, it is clear that equilibrium
must be restored by counter-currents from the equator; moreover, winds
coming from the poles, where there is no rotation, to the equator, which
revolves from W. to E. at the rate of 1000 miles an hour, must of
necessity move in a direction resulting from their own progressive
motion and that of rotation; hence, in blowing towards the equator the
bias is to the E., and in blowing from it the bias is to the W. Thus as
N. and S. winds from the poles blow along the surface from the tropics
to the equator, in consequence of this composition of motions that from
the N. becomes the N.E. trade-wind, and that from the S. the S.E.
trade-wind. Now these winds being in contrary directions cross at the
equator, balance each other through about 6 degrees of latitude, and
produce a belt of calms of that breadth encircling the globe, known as
the calms of the equator, or the Variables of seamen. The heat of the
sun rarefies the air so much, that the trade-winds, after crossing at
the equator, ascend into the higher regions of the atmosphere, where
that from the N. goes to the tropic of Capricorn, and that from the S.
to the tropic of Cancer. But while travelling in these lofty regions
they become cold and heavy, and, sinking to the surface at the tropics,
each proceeds to the opposite pole from which it set out. Now, however,
they have a greater rotatory motion than the places they successively
arrive at, so the bias is to the W., and they become the N.W. and S.W.
extra-tropical winds.

If on arriving at the poles the air were to accumulate there, the
circulation of the winds would cease; but currents rise into the upper
regions, and flow back again to the tropics, where they sink down to
fill the vacuum caused by the great precipitation of vapour in these
regions, and then flow to the equator as trade-winds (N. 177). So the
currents of air cross again at the tropics and produce two belts of
calms which surround the globe, named by Lieutenant Maury the Calms of
Cancer and the Calms of Capricorn, but generally known to sailors as the
Doldrums. Thus the winds go from pole to pole and back again,
alternately as under and upper currents. In their circuits the winds
cross each other five times, producing regions of calms at the poles,
the tropics, and equator. The trade-winds generally extend for about 28°
on each side of the equator, but, on account of the greater quantity of
land in the northern hemisphere, the N.E. trade-wind is narrower than
the S.E.

The sun is perpetually raising enormous quantities of vapour from the
ocean which the trade-winds carry to the equator: it is condensed when
it rises with the air into the higher strata, and forms a ring of clouds
along the southern side of the belt of equatorial calms that surrounds
the earth, which, during the day, is perpetually pouring down torrents
of rain, while the sun continually beating upon its upper surface
dissolves the clouds into invisible vapour which is carried by the winds
and condensed into rain on the extra-tropical regions. The whole system
of trade-winds, equatorial and tropical calms, with the cloud ring,
follow the sun in declination; consequently in its journeys back and
forwards it annually travels over 1000 miles of latitude, and regulates
the dry and rainy season in the tropical parts of the earth.

The monsoons, which are periodic winds in the Indian Ocean, in part
depend upon this movement. For when the sun is in the northern
hemisphere the trade-winds come northward with him; and when his intense
heat expands the air over the Great Gobi and other arid Asiatic deserts,
it ascends; the N.E. trade-wind is drawn in to fill the vacuum and
ascends with it; then the S.E. trade-wind, being no longer met and
balanced by the N.E. trade, passes into the northern hemisphere, and as
it proceeds northward from the equator it is deflected to the west by
the rotation of the earth, combined with the indraught over the heated
deserts, and becomes the S.W. monsoon, which blows while the sun is
north of the equator, but as soon as he goes south, and no longer
rarefies the air over the Indian deserts, the S.E. trade-wind resumes
its usual course, and is then known as the S.E. monsoon. The influence
of the heated deserts is perceptible to the distance of 1000 miles from
the shore; the monsoons prevail with great steadiness over the Arabian
Gulf, the Indian Ocean, and part of the China Sea. At the change,
torrents of rain and violent thunderstorms accompany the conflict
between the contending winds.

The Sahara desert in North Africa, and those of Utah, Texas, and New
Mexico, occasion the monsoons which prevail in the North Atlantic and on
both sides of Central America, and the monsoons which blow to the north
of Australia show the sterility of the interior, even if other proofs
were wanting. From the powerful effect of the land in drawing off the
winds from their course, it may be seen why the N.E. trade-winds are
narrower than the S.E. trades.

In the extra-tropical winds in the North Atlantic, which blow from the
40th parallel to the pole, the north-westerly are to the easterly as 2
to 1: hence there would be an accumulation of air at the pole at the
expense of the equator, did not a current rise at the pole and return to
the equator through the high regions of the atmosphere, which confirms
the theory of the rotation of the wind.

There are many proofs of the existence of the counter-currents above the
trade-winds. On the Peak of Teneriffe the prevailing winds are from the
west. Light clouds have frequently been seen moving rapidly from west to
east at a very great height above the trade-winds, which were sweeping
along the surface of the ocean in a contrary direction. Rains, clouds,
and nearly all the other atmospheric phenomena, occur below the height
of 18,000 feet, and generally much nearer to the surface of the earth.
They are owing to currents of air running upon each other in horizontal
strata, differing in their electric state, in temperature and moisture,
as well as in velocity and direction.

When north and south winds blow alternately, the wind at any place will
veer in one uniform direction through every point of the compass,
provided the one begins before the other has ceased. In the northern
hemisphere a north wind sets out with a smaller degree of rotatory
motion than the places have at which it successively arrives,
consequently it passes through all the points of the compass from N. to
N.E. and E. A current from the south, on the contrary, sets out with a
greater rotatory velocity than the places have at which it successively
arrives, so by the rotation of the earth it is deflected from S. to S.W.
and W. Now, if the vane at any place should have veered from the N.
through N.E. to E., and a south wind should spring up, it would combine
its motion with the former and cause the vane to turn successively from
the E. to S.E. and S. But by the earth’s rotation this south wind will
veer to the S.W. and W., and, if a north wind should now arise, it would
combine its motion with that of the west, and cause it to veer to the
N.W. and N. Thus two alternations of north and south wind will cause the
vane at any place to go completely round the compass, from N. to E., S.,
W., and N. again. At the Royal Observatory at Greenwich the wind
accomplishes five circuits in that direction in the course of a year.
When circumstances combine to produce alternate north and south winds in
the southern hemisphere, the gyration is in the contrary direction.
Although the general tendency of the wind may be rotatory, and is so in
many instances, at least for part of the year, yet it is so often
counteracted by local circumstances, that the winds are in general very
irregular, every disturbance in atmospheric equilibrium from heat or any
other cause producing a corresponding wind. The most prevalent winds in
Europe are the N.E. and S.W.; the former arises from the north polar
current, and the latter from causes already mentioned. The law of the
wind’s rotation was first described by Dr. Dalton, but has been
developed by Professor Dove, of Berlin.

Hurricanes are those storms of wind in which the portion of the
atmosphere that forms them revolves in a horizontal circuit round a
vertical or somewhat inclined axis of rotation, while the axis itself,
and consequently the whole storm, is carried forward along the surface
of the globe, so that the direction in which the storm is advancing is
quite different from the direction in which the rotatory current may be
blowing at any point. In the West Indies, where hurricanes are frequent
and destructive, they generally originate in the tropical regions near
the inner boundary of the trade-winds, and are caused by the vertical
ascent of a column of rarefied air, whose place is supplied by a rush of
wind from the surrounding regions, set into gyration by the rotation of
the earth. By far the greater number of Atlantic hurricanes have begun
eastward of the lesser Antilles or Caribbean Islands.

In every case the axis of the storm moves in an elliptical or parabolic
curve, having its vertex in or near the tropic of Cancer, which marks
the external limit of the trade-winds north of the equator. As the
motion before it reaches the tropic is in a straight line from S.E. to
N.W., and after it has passed it from S.W. to N.E., the bend of the
curve is turned towards Florida and the Carolinas. In the southern
hemisphere the body of the storm moves in exactly the opposite
direction. The hurricanes which originate south of the equator, and
whose initial path is from N.E. to S.W., bend round at the tropic of
Capricorn, and then move from N.W. to S.E.

The extent and velocity of these storms are great; for instance, the
hurricane that took place on the 12th of August, 1830, was traced from
eastward of the Caribbee Islands, along the Gulf Stream, to the bank of
Newfoundland, a distance of more than 3000 miles, which it passed over
in six days. Although the hurricane of the 1st of September, 1821, was
not so extensive, its velocity was greater, as it moved at the rate of
30 miles an hour: small storms are generally more rapid than those of
greater dimensions.

The action of these storms seems to be at first confined to the stratum
of air nearest the earth, and then they seldom appear to be more than a
mile high, though sometimes they are raised higher; or even divided by a
mountain into two separate storms, each of which continues its new path
and gyrations with increased violence. This occurred in the gale of the
25th of December, 1821, in the Mediterranean, when the Spanish mountains
and the Maritime Alps became new centres of motion.

By the friction of the earth the axis of the storm bends a little
forward. This causes a continual intermixture of the lower and warmer
strata of air with those that are higher and colder, producing torrents
of rain and violent electric explosions.

The breadth of the whirlwind is greatly augmented when the path of the
storm changes on crossing the tropic. The vortex of a storm has covered
an extent of the surface of the globe 500 miles in diameter.

The revolving motion accounts for the sudden and violent changes
observed during hurricanes. In consequence of the rotation of the air,
the wind blows in opposite directions on each side of the axis of the
storm, and the violence of the blast increases from the circumference
towards the centre of gyration, but in the centre itself the air is in
repose: hence, when the body of the storm passes over a place, the wind
begins to blow moderately, and increases to a hurricane as the centre of
the whirlwind approaches; then, in a moment, a dead and awful calm
succeeds, suddenly followed by a renewal of the storm in all its
violence, but now blowing in a direction diametrically opposite to its
former course. This happened at the Island of St. Thomas on the 2nd of
August, 1837, where the hurricane increased in violence till half-past
seven in the morning, when perfect stillness took place for forty
minutes, after which the storm recommenced in a contrary direction.

The sudden fall of the mercury in the barometer in the regions
habitually visited by hurricanes is a certain indication of a coming
tempest. In consequence of the centrifugal force of these rotatory
storms the air becomes rarefied, and, as the atmosphere is disturbed to
some distance beyond the actual circle of gyration or limits of the
storm, the barometer often sinks some hours before its arrival, from the
original cause of the rotatory disturbance. It continues sinking under
the first half of the hurricane, is at a maximum sometimes of two inches
in the centre of gyration, and again rises during the passage of the
latter half, though it does not attain its greatest height till the
storm is over. The diminution of atmospheric pressure is greater and
extends over a wider area in the temperate zones than in the torrid, on
account of the sudden expansion of the circle of rotation when the gale
crosses the tropic.

As the fall of the barometer gives warning of the approach of a
hurricane, so the laws of the storm’s motion afford the seaman knowledge
to guide him in avoiding it. In the northern temperate zone, if the gale
begins from the S.E. and veers by S. to W., the ship should steer to the
S.E.; but, if the gale begins from the N.E., and changes through N. to
N.W., the vessel should go to the N.W. In the northern part of the
torrid zone, if the storm begin from the N.E., and veer through E. to
S.E., the ship should steer to the N.E.; but, if it begin from the N.W.,
and veer by W. to S.W., the ship should steer to the S.W., because she
is in the south-western side of the storm. Since the laws of storms are
reversed in the southern hemisphere, the rules for steering vessels are
necessarily reversed also. A heavy swell is peculiarly characteristic of
these storms. In the open sea the swell often extends many leagues
beyond the range of the gale which produced it.

Waterspouts are occasioned by small whirlwinds, which always have their
origin at a great distance from that part of the sea from which the
spout begins to rise, where it is generally calm. The whirl is produced
by two currents of air, which, running in opposite directions, compress
one another by their impetus, so that they rise in spiral eddies to the
clouds. They move slowly along the surface of the sea, sometimes in
vertical, and sometimes in twisted spirals, putting the sea into violent
agitation as they pass, and carrying the water aloft by the force of
gyration. Occasionally the eddies begin in the clouds and dip down to
the sea.




                              SECTION XVI.

Sound—Propagation of Sound illustrated by a Field of Standing
  Corn—Nature of Waves—Propagation of Sound through the
  Atmosphere—Intensity—Noises—A Musical Sound—Quality—Pitch—Extent of
  Human Hearing—Velocity of Sound in Air, Water, and Solids—Causes of
  the Obstruction of Sound—Law of its Intensity—Reflection of
  Sound—Echoes—Thunder—Refraction of Sound—Interference of Sounds.


ONE of the most important uses of the atmosphere is the conveyance of
sound. Without the air, deathlike silence would prevail through nature,
for in common with all substances it has a tendency to impart vibrations
to bodies in contact with it. Therefore undulations received by the air,
whether it be from a sudden impulse, such as an explosion or the
vibrations of a musical chord, are propagated in every direction, and
produce the sensation of sound upon the auditory nerves. A bell rung
under the exhausted receiver of an air-pump is inaudible, which shows
that the atmosphere is really the medium of sound. In the small
undulations of deep water in a calm, the vibrations of the liquid
particles are made in the vertical plane, that is, up and down, or at
right angles to the direction of the transmission of the waves. But the
vibrations of the particles of air which produce sound differ from
these, being performed in the same direction in which the waves of sound
travel. The propagation of sound has been illustrated by a field of corn
agitated by the wind. However irregular the motion of the corn may seem
on a superficial view, it will be found, if the velocity of the wind be
constant, that the waves are all precisely similar and equal, and that
all are separated by equal intervals and move in equal times.

A sudden blast depresses each ear equally and successively in the
direction of the wind, but, in consequence of the elasticity of the
stalks and the force of the impulse, each ear not only rises again as
soon as the pressure is removed, but bends back nearly as much in the
contrary direction, and then continues to oscillate backwards and
forwards in equal times, like a pendulum, to a less and less extent,
till the resistance of the air puts a stop to the motion. These
vibrations are the same for every individual ear of corn. Yet, as their
oscillations do not all commence at the same time, but successively, the
ears will have a variety of positions at any one instant. Some of the
advancing ears will meet others in their returning vibrations, and, as
the times of oscillation are equal for all, they will be crowded
together at regular intervals. Between these there will occur equal
spaces where the ears will be few, in consequence of being bent in
opposite directions; and at other equal intervals they will be in their
natural upright positions. So that over the whole field there will be a
regular series of condensations and rarefactions among the ears of corn,
separated by equal intervals, where they will be in their natural state
of density. In consequence of these changes the field will be marked by
an alternation of bright and dark bands. Thus the successive waves which
fly over the corn with the speed of the wind are totally distinct from,
and entirely independent of the extent of the oscillations of each
individual ear, though both take place in the same direction. The length
of a wave is equal to the space between two ears precisely in the same
state of motion, or which are moving similarly, and the time of the
vibration of each ear is equal to that which elapses between the arrival
of two successive waves at the same point. The only difference between
the undulations of a corn-field and those of the air which produce sound
is, that each ear of corn is set in motion by an external cause, and is
uninfluenced by the motion of the rest; whereas in air, which is a
compressible and elastic fluid, when one particle begins to oscillate,
it communicates its vibrations to the surrounding particles, which
transmit them to those adjacent, and so on continually. Hence from the
successive vibrations of the particles of air the same regular
condensations and rarefactions take place as in the field of corn,
producing waves throughout the whole mass of air, though each molecule
like each individual ear of corn never moves far from its state of rest.
The small waves of a liquid, and the undulations of the air, like waves
in the corn, are evidently not real masses moving in the direction in
which they are advancing, but merely outlines, motions, or forms passing
along, and comprehending all the particles of an undulating fluid which
are at once in a vibratory state. It is thus that an impulse given to
any one point of the atmosphere is successively propagated in all
directions, in a wave diverging as from the centre of a sphere to
greater and greater distances, but with decreasing intensity, in
consequence of the increasing number of particles of inert matter which
the force has to move; like the waves formed in still water by a falling
stone, which are propagated circularly all around the centre of
disturbance (N. 160).

The intensity of sound depends upon the violence and extent of the
initial vibrations of air; but, whatever they may be, each undulation
when once formed can only be transmitted straight forwards, and never
returns back again unless when reflected by an opposing obstacle. The
vibrations of the aërial molecules are always extremely small, whereas
the waves of sound vary from a few inches to several feet. The various
musical instruments, the human voice and that of animals, the singing of
birds, the hum of insects, the roar of the cataract, the whistling of
the wind, and the other nameless peculiarities of sound, show at once an
infinite variety in the modes of aërial vibration, and the astonishing
acuteness and delicacy of the ear, thus capable of appreciating the
minutest differences in the laws of molecular oscillation.

All mere noises are occasioned by irregular impulses communicated to the
ear; and, if they be short, sudden, and repeated beyond a certain degree
of quickness, the ear loses the intervals of silence, and the sound
appears continuous. Still such sounds will be mere noise: in order to
produce a musical sound, the impulses, and consequently the undulations
of the air, must be all exactly similar in duration and intensity, and
must recur after exactly equal intervals of time. If a blow be given to
the nearest of a series of broad, flat, and equidistant palisades, set
edgewise in a line direct from the ear, each palisade will repeat or
echo the sound; and these echoes, returning to the ear at successive
equal intervals of time, will produce a musical note. The quality of a
musical note depends upon the abruptness, and its intensity upon the
violence and extent of the original impulse. In the theory of harmony
the only property of sound taken into consideration is the pitch, which
varies with the rapidity of the vibrations. The grave or low tones are
produced by very slow vibrations, which increase in frequency as the
note becomes more acute. The lowest man’s voice makes 396 vibrations in
a second, whilst the highest woman’s voice makes 2112. Very deep tones
are not heard by all alike, and Dr. Wollaston, who made a variety of
experiments on the sense of hearing, found that many people, though not
at all deaf, are quite insensible to the cry of the bat or the cricket,
while to others it is painfully shrill. From his experiments he
concluded that human hearing is limited to about nine octaves, extending
from the lowest note of the organ to the highest known cry of insects;
and he observes with his usual originality that, “as there is nothing in
the nature of the atmosphere to prevent the existence of vibrations
incomparably more frequent than any of which we are conscious, we may
imagine that animals like the Grylli, whose powers appear to commence
nearly where ours terminate, may have the faculty of hearing still
sharper sounds which we do not know to exist, and that there may be
other insects hearing nothing in common with us, but endowed with a
power of exciting, and a sense which perceives vibrations, of the same
nature indeed as those which constitute our ordinary sounds, but so
remote that the animals which perceive them may be said to possess
another sense, agreeing with our own solely in the medium by which it is
excited.”

M. Savart, so well known for the number and beauty of his researches in
acoustics, has proved that a high note of a given intensity, being heard
by some ears and not by others, must not be attributed to its pitch, but
to its feebleness. His experiments, and those more recently made by
Professor Wheatstone, show that, if the pulses could be rendered
sufficiently powerful, it would be difficult to fix a limit to human
hearing at either end of the scale. M. Savart had a wheel made about
nine inches in diameter with 360 teeth set at equal distances round its
rim, so that while in motion each tooth successively hit on a piece of
card. The tone increased in pitch with the rapidity of the rotation, and
was very pure when the number of strokes did not exceed three or four
thousand in a second, but beyond that it became feeble and indistinct.
With a wheel of a larger size a much higher tone could be obtained,
because, the teeth being wider apart, the blows were more intense and
more separated from one another. With 720 teeth on a wheel thirty-two
inches in diameter, the sound produced by 12,000 strokes in a second was
audible, which corresponds to 24,000 vibrations of a musical chord. So
that the human ear can appreciate a sound which only lasts the 24,000th
part of a second. This note was distinctly heard by M. Savart and by
several people who were present, which convinced him that with another
apparatus still more acute sounds might be rendered audible.

For the deep tones M. Savart employed a bar of iron, two feet eight
inches long, about two inches broad, and half an inch in thickness,
which revolved about its centre as if its arms were the spokes of a
wheel. When such a machine rotates, it impresses a motion on the air
similar to its own, and, when a thin board or card is brought close to
its extremities, the current of air is momentarily interrupted at the
instant each arm of the bar passes before the card; it is compressed
above the card and dilated below; but the instant the spoke has passed a
rush of air to restore equilibrium makes a kind of explosion, and, when
these succeed each other rapidly, a musical note is produced of a pitch
proportional to the velocity of the revolution. When M. Savart turned
this bar slowly, a succession of single beats was heard; as the velocity
became greater, the sound was only a rattle; but, as soon as it was
sufficient to give eight beats in a second, a very deep musical note was
distinctly audible corresponding to sixteen single vibrations in a
second, which is the lowest that has hitherto been produced. When the
velocity of the bar was much increased, the intensity of the sound was
hardly bearable. The spokes of a revolving wheel produce the sensation
of sound, on the very same principle that a burning stick whirled round
gives the impression of a luminous circle. The vibrations excited in the
organ of hearing by one beat have not ceased before another impulse is
given. Indeed it is indispensable that the impressions made upon the
auditory nerves should encroach upon each other in order to produce a
full and continued note. On the whole, M. Savart has come to the
conclusion, that the most acute sounds would be heard with as much ease
as those of a lower pitch, if the duration of the sensation produced by
each pulse could be diminished proportionally to the augmentation of the
number of pulses in a given time: and on the contrary, if the duration
of the sensation produced by each pulse could be increased in proportion
to their number in a given time, that the deepest tones would be as
audible as any of the others.

The velocity of sound is uniform and independent of the nature, extent,
and intensity of the primitive disturbance. Consequently sounds of every
quality and pitch travel with equal speed. The smallest difference in
their velocity is incompatible either with harmony or melody, for notes
of different pitches and intensities, sounded together at a little
distance, would arrive at the ear in different times. A rapid succession
of notes would in this case produce confusion and discord. But, as the
rapidity with which sound is transmitted depends upon the elasticity of
the medium through which it has to pass, whatever tends to increase the
elasticity of the air must also accelerate the motion of sound. On that
account its velocity is greater in warm than in cold weather, supposing
the pressure of the atmosphere constant. In dry air, at the freezing
temperature, sound travels at the rate of 1090 feet in a second, and for
any higher temperature one foot must be added for every degree of the
thermometer above 32°: hence at 62° of Fahrenheit its speed in a second
is 1120 feet, or 765 miles an hour, which is about three-fourths of the
diurnal velocity of the earth’s equator. Since all the phenomena of the
transmission of sound are simple consequences of the physical properties
of the air, they have been predicted and computed rigorously by the laws
of mechanics. It was found, however, that the velocity of sound,
determined by observation, exceeded what it ought to have been
theoretically by 173 feet, or about one-sixth of the whole amount. La
Place suggested that this discrepancy might arise from the increased
elasticity of the air in consequence of a development of latent or
absorbed heat (N. 178) during the undulations of sound, and calculation
confirmed the accuracy of his views. The aërial molecules being suddenly
compressed give out their absorbed heat; and, as air is too bad a
conductor to carry it rapidly off, it occasions a momentary and local
rise of temperature, which, increasing the elasticity of the air without
at the same time increasing its inertia, causes the movement to be
propagated more rapidly. Analysis gives the true velocity of sound in
terms of the elevation of temperature that a mass of air is capable of
communicating to itself, by the disengagement of its own absorbed heat
when suddenly compressed in a given ratio. This change of temperature
however could not be obtained _directly_ by any experiments which had
been made at that epoch; but by inverting the problem, and assuming the
velocity of sound as given by experiment, it was computed that the
temperature of a mass of air is raised nine-tenths of a degree when the
compression is equal to 1/116 of its volume.

Probably all liquids are elastic, though considerable force is required
to compress them. Water suffers a condensation of nearly 0·0000496 for
every atmosphere of pressure, and is consequently capable of conveying
sound even more rapidly than air, the velocity in the former being 4708
feet in a second. A person under water hears sounds made in air feebly,
but those produced in water very distinctly. According to the
experiments of M. Colladon, the sound of a bell was conveyed under water
through the Lake of Geneva to the distance of about nine miles. He also
perceived that the progress of sound through water is greatly impeded by
the interposition of any object, such as a projecting wall; consequently
sound under water resembles light in having a distinct shadow. It has
much less in air, being transmitted all round buildings or other
obstacles, so as to be heard in every direction, though often with a
considerable diminution of intensity, as when a carriage turns the
corner of a street.

The velocity of sound in passing through solids is in proportion to
their hardness, and is much greater than in air or water. A sound which
takes some time in travelling through the air passes almost
instantaneously along a wire six hundred feet long; consequently it is
heard twice—first as communicated by the wire, and afterwards through
the medium of the air. The facility with which the vibrations of sound
are transmitted along the grain of a log of wood is well known. Indeed
they pass through iron, glass, and some kinds of wood, at the rate of
18,530 feet in a second. The velocity of sound is obstructed by a
variety of circumstances, such as falling snow, fog, rain, or any other
cause which disturbs the homogeneity of the medium through which it has
to pass. M. de Humboldt says that it is on account of the greater
homogeneity of the atmosphere during the night that sounds are then
better heard than during the day, when its density is perpetually
changing from partial variations of temperature. His attention was
called to this subject on the plain surrounding the Mission of the
Apures by the rushing noise of the great cataracts of the Orinoco, which
seemed to be three times as loud by night as by day. This he illustrated
by experiment. A tall glass half full of champagne cannot be made to
ring as long as the effervescence lasts. In order to produce a musical
note, the glass together with the liquid it contains must vibrate in
unison as a system, which it cannot do in consequence of the fixed air
rising through the wine and disturbing its homogeneity, because, the
vibrations of the gas being much slower than those of the liquid, the
velocity of the sound is perpetually interrupted. For the same reason
the transmission of sound as well as light is impeded in passing through
an atmosphere of variable density. Sir John Herschel, in his admirable
Treatise on Sound, thus explains the phenomenon:—“It is obvious,” he
says, “that sound as well as light must be obstructed, stifled, and
dissipated from its original direction by the mixture of air of
different temperatures, and consequently elasticities; and thus the same
cause which produces that extreme transparency of the air at night,
which astronomers alone fully appreciate, renders it also more
favourable to sound. There is no doubt, however, that the universal and
dead silence generally prevalent at night renders our auditory nerves
sensible to impressions which would otherwise escape notice. The analogy
between sound and light is perfect in this as in so many other respects.
In the general light of day the stars disappear. In the continual hum of
voices, which is always going on by day, and which reach us from all
quarters, and never leave the ear time to attain complete tranquillity,
those feeble sounds which catch our attention at night make no
impression. The ear, like the eye, requires long and perfect repose to
attain its utmost sensibility.”

Many instances may be brought in proof of the strength and clearness
with which sound passes over the surface of water or ice. Lieutenant
Forster was able to carry on a conversation across Port Bowen Harbour,
when frozen, a distance of a mile and a half.

The intensity of sound depends upon the extent of the excursions of the
fluid molecules, on the energy of the transient condensations and
dilatations, and on the greater or less number of particles which
experience these effects. We estimate that intensity by the impetus of
these fluid molecules on our organs, which is consequently as the square
of the velocity, and not by their inertia, which is as the simple
velocity. Were the latter the case, there would be no sound, because the
inertia of the receding waves of air would destroy the equal and
opposite inertia of those advancing; whence it may be concluded that the
intensity of sound diminishes inversely as the square of the distance
from its origin. In a tube, however, the force of sound does not decay
as in open air, unless perhaps by friction against the sides. M. Biot
found, from a number of highly-interesting experiments made on the pipes
of the aqueducts in Paris, that a continued conversation could be
carried on in the lowest possible whisper through a cylindrical tube
about 3120 feet long, the time of transmission through that space being
2·79 seconds. In most cases sound diverges in all directions so as to
occupy at any one time a spherical surface; but Dr. Young has shown that
there are exceptions, as, for example, when a flat surface vibrates only
in one direction. The sound is then most intense when the ear is at
right angles to the surface, whereas it is scarcely audible in a
direction precisely perpendicular to its edge. In this case it is
impossible that the whole of the surrounding air can be affected in the
same manner, since the particles behind the sounding surface must be
moving towards it whenever the particles before it are retreating. Hence
in one half of the surrounding sphere of air its motions are retrograde,
while in the other half they are direct; consequently, at the edges
where these two portions meet, the motions of the air will neither be
retrograde nor direct, and therefore it must be at rest.

It appears, from theory as well as daily experience, that sound is
capable of reflection from surfaces (N. 179) according to the same laws
as light. Indeed any one who has observed the reflection of the waves
from a wall on the side of a river, after the passage of a steam-boat,
will have a perfect idea of the reflection of sound and of light. As
every substance in nature is more or less elastic, it may be agitated
according to its own law by the impulse of a mass of undulating air; and
reciprocally the surface by its reaction will communicate its
undulations back again into the air. Such reflections produce echoes;
and as a series of them may take place between two or more obstacles,
each will cause an echo of the original sound, growing fainter and
fainter till it dies away; because sound, like light, is weakened by
reflection. Should the reflecting surface be concave towards a person,
the sound will converge towards him with increased intensity, which will
be greater still if the surface be spherical and concentric with him.
Undulations of sound diverging from one focus of an elliptical shell
(N. 180) converge in the other after reflection. Consequently a sound
from the one will be heard in the other as if it were close to the ear.
The rolling noise of thunder has been attributed to reverberation
between different clouds, which may possibly be the case to a certain
extent. Sir John Herschel is of opinion that an intensely prolonged peal
is probably owing to a combination of sounds, because, the velocity of
electricity being incomparably greater than that of sound, the thunder
may be regarded as originating in every point of a flash of lightning at
the same instant. The sound from the nearest point will arrive first;
and if the flash run in a direct line from a person, the noise will come
later and later from the remote points of its path in a continued roar.
Should the direction of the flash be inclined, the succession of sounds
will be more rapid and intense: and if the lightning describe a circular
curve round a person, the sound will arrive from every point at the same
instant with a stunning crash. In like manner the subterranean noises
heard during earthquakes like distant thunder may arise from the
consecutive arrival at the ear of undulations propagated at the same
instant from nearer and more remote points; or if they originate in the
same point, the sound may come by different routes through strata of
different densities.

Sounds under water are heard very distinctly in the air immediately
above; but the intensity decays with great rapidity as the observer goes
farther off, and is altogether inaudible at the distance of two or three
hundred yards. So that waves of sound, like those of light, in passing
from a dense to a rare medium, are not only refracted, but suffer total
reflection at very oblique incidences (N. 189).

The laws of interference extend also to sound. It is clear that two
equal and similar musical strings will be in unison if they communicate
the same number of vibrations to the air in the same time. But if two
such strings be so nearly in unison that one performs a hundred
vibrations in a second, and the other a hundred and one in the same
period—during the first few vibrations the two resulting sounds will
combine to form one of double the intensity of either, because the
aërial waves will sensibly coincide in time and place; but one will
gradually gain on the other till at the fiftieth vibration it will be
half an oscillation in advance. Then the waves of air which produce the
sound being sensibly equal, but the receding part of the one coinciding
with the advancing part of the other, they will destroy one another, and
occasion an instant of silence. The sound will be renewed immediately
after, and will gradually increase till the hundredth vibration, when
the two waves will combine to produce a sound double the intensity of
either. These intervals of silence and greatest intensity, called beats,
will recur every second; but if the notes differ much from one another,
the alternations will resemble a rattle; and if the strings be in
perfect unison, there will be no beats, since there will be no
interference. Thus by interference is meant the co-existence of two
undulations in which the lengths of the waves are the same. And as the
magnitude of an undulation may be diminished by the addition of another
transmitted in the same direction, it follows that one undulation may be
absolutely destroyed by another when waves of the same length are
transmitted in the same direction, provided that the maxima of the
undulations are equal, and that one follows the other by half the length
of a wave. A tuning-fork affords a good example of interference. When
that instrument vibrates, its two branches alternately recede from and
approach one another; each communicates its vibrations to the air, and a
musical note is the consequence. If the fork be held upright about a
foot from the ear, and turned round its axis while vibrating, at every
quarter revolution the sound will scarcely be heard, while at the
intermediate points it will be strong and clear. This phenomenon arises
from the interference of the undulations of air coming from the two
branches of the fork. When the two branches coincide, or when they are
at equal distances from the ear, the waves of air combine to reinforce
each other; but at the quadrants, where the two branches are at unequal
distances from the ear, the lengths of the waves differ by half an
undulation, and consequently destroy one another.




                             SECTION XVII.

Vibration of Musical Strings—Harmonic Sounds—Nodes—Vibration of Air in
  Wind-Instruments—Vibration of Solids—Vibrating
  Plates—Bells—Harmony—Sounding Boards—Forced
  Vibrations—Resonance—Speaking Machines.


WHEN the particles of elastic bodies are suddenly disturbed by an
impulse, they return to their natural position by a series of
isochronous vibrations, whose rapidity, force, and permanency depend
upon the elasticity, the form, and the mode of aggregation which unites
the particles of the body. These oscillations are communicated to the
air, and on account of its elasticity they excite alternate
condensations and dilatations in the strata of the fluid nearest to the
vibrating body; from thence they are propagated to a distance. A string
or wire stretched between two pins, when drawn aside and suddenly let
go, will vibrate till its own rigidity and the resistance of the air
reduce it to rest. These oscillations may be rotatory, in every plane,
or confined to one plane according as the motion is communicated. In the
piano-forte, where the strings are struck by a hammer at one extremity,
the vibrations probably consist of a bulge running to and fro from end
to end. Different modes of vibration may be obtained from the same
sonorous body. Suppose a vibrating string to give the lowest C of the
pianoforte which is the fundamental note of the string; if it be lightly
touched exactly in the middle, so as to retain that point at rest, each
half will then vibrate twice as fast as the whole, but in opposite
directions; the ventral or bulging segments will be alternately above
and below the natural position of the string, and the resulting note
will be the octave above C. When a point at a third of the length of the
string is kept at rest, the vibrations will be three times as fast as
those of the whole string, and will give the twelfth above C. When the
point of rest is one-fourth of the whole, the oscillations will be four
times as fast as those of the fundamental note, and will give the double
octave; and so on. These acute sounds are called the harmonics of the
fundamental note. It is clear, from what has been stated, that the
string thus vibrating could not give these harmonics spontaneously
unless it divided itself at its aliquot parts into two, three, four, or
more segments in opposite states of vibration separated by points
actually at rest. In proof of this, pieces of paper placed on the string
at the half, third, fourth, or other aliquot points, according to the
corresponding harmonic sound, will remain on it during its vibration,
but will instantly fly off from any of the intermediate points. The
points of rest, called the nodal points of the string, are a mere
consequence of the law of interferences; for, if a rope fastened at one
end be moved to and fro at the other extremity so as to transmit a
succession of equal waves along it, they will be successively reflected
when they arrive at the other end of the rope by the fixed point, and in
returning they will occasionally interfere with the advancing waves;
and, as these opposite undulations will at certain points destroy one
another, the point of the rope in which this happens will remain at
rest. Thus a series of nodes and ventral segments will be produced whose
number will depend upon the tension and the frequency of the alternate
motions communicated to the moveable end. So, when a string fixed at
both ends is put in motion by a sudden blow at any point of it, the
primitive impulse divides itself into two pulses running opposite ways,
which are each totally reflected at the extremities, and, running back
again along the whole length, are again reflected at the other ends. And
thus they will continue to run backwards and forwards, crossing one
another at each traverse, and occasionally interfering, so as to produce
nodes; so that the motion of a string fastened at both ends consists of
a wave or pulse continually doubled back on itself by reflection at the
fixed extremities.

Harmonics generally co-exist with the fundamental sound in the same
vibrating body. If one of the lowest strings of the pianoforte be
struck, an attentive ear will not only hear the fundamental note, but
will detect all the others sounding along with it, though with less and
less intensity as their pitch becomes higher. According to the law of
co-existing undulations, the whole string and each of its aliquot parts
are in different and independent states of vibration at the same time;
and as all the resulting notes are heard simultaneously, not only the
air, but the ear also, vibrates in unison with each at the same instant
(N. 181).

Harmony consists in an agreeable combination of sounds. When two chords
perform their vibrations in the same time, they are in unison; but, when
their vibrations are so related as to have a common period, after a few
oscillations they produce concord. Thus, when the vibrations of two
strings bear a very simple relation to each other, as where one of them
makes two, three, four, &c., vibrations in the time the other makes one;
or, if it accomplishes three, four, &c., vibrations while the other
makes two, the result is a concord which is the more perfect the shorter
the common period. In discords, on the contrary, the beats are
distinctly audible, which produces a disagreeable and harsh effect,
because the vibrations do not bear a simple relation to one another, as
where one of two strings makes eight vibrations while the other
accomplishes fifteen. The pleasure afforded by harmony is attributed by
Dr. Young to the love of order, and to a predilection for a regular
repetition of sensations natural to the human mind, which is gratified
by the perfect regularity and rapid recurrence of the vibrations. The
love of poetry and dancing he conceives to arise in some degree from the
rhythm of the one and the regularity of the motions in the other.

A blast of air passing over the open end of a tube, as over the reeds in
Pan’s pipes; over a hole in one side, as in the flute; or through the
aperture called a reed, with a flexible tongue, as in the clarinet, puts
the internal column of air into longitudinal vibrations by the alternate
condensations and rarefactions of its particles. At the same time the
column spontaneously divides itself into nodes, between which the air
also vibrates longitudinally, but with a rapidity inversely proportional
to the length of the divisions, giving the fundamental note or one of
its harmonics. The nodes are produced on the principle of interferences
by the reflection of the longitudinal undulations of the air at the ends
of the pipe, as in the musical string, only that in one case the
undulations are longitudinal, and in the other transverse.

A pipe, either open or shut at both ends, when sounded, vibrates entire,
or divides itself spontaneously into two, three, four, &c., segments
separated by nodes. The whole column gives the fundamental note by waves
or vibrations of the same length with the pipe. The first harmonic is
produced by waves half as long as the tube, the second harmonic by waves
a third as long, and so on. The harmonic segments in an open and shut
pipe are the same in number, but differently placed. In a shut pipe the
two ends are nodes, but in an open pipe there is half a segment at each
extremity, because the air at these points is neither rarefied nor
condensed, being in contact with that which is external. If one of the
ends of the open pipe be closed, its fundamental note will be an octave
lower: the air will now divide itself into three, five, seven, &c.,
segments; and the wave producing its fundamental note will be twice as
long as the pipe, so that it will be doubled back (N. 182). All these
notes may be produced separately by varying the intensity of the blast.
Blowing steadily and gently, the fundamental note will sound; when the
force of the blast is increased the note will all at once start up an
octave; when the intensity of the wind is augmented the twelfth will be
heard; and, by continuing to increase the force of the blast, the other
harmonics may be obtained, but no force of wind will produce a note
intermediate between these. The harmonics of a flute may be obtained in
this manner, from the lowest C or D upwards, without altering the
fingering, merely by increasing the intensity of the blast and altering
the form of the lips. Pipes of the same dimensions, whether of lead,
glass, or wood, give the same tone as to pitch under the same
circumstances, which shows that the air alone produces the sound.

Metal springs fastened at one end, when forcibly bent, endeavour to
return to rest by a series of vibrations, which give very pleasing
tones, as in musical boxes. Various musical instruments have been
constructed, consisting of metallic springs thrown into vibration by a
current of air. Among the most perfect of these are Mr. Wheatstone’s
Symphonion, Concertina, and Æolian Organ, instruments of different
effects and capabilities, but all possessing considerable execution and
expression.

The Syren is an ingenious instrument, devised by M. Cagniard de la Tour,
for ascertaining the number of pulsations in a second, corresponding to
each pitch: the notes are produced by jets of air passing through small
apertures, arranged at regular distances in a circle on the side of a
box, before which a disc revolves pierced with the same number of holes.
During a revolution of the disc the currents are alternately intercepted
and allowed to pass as many times as there are apertures in it, and a
sound is produced whose pitch depends on the velocity of rotation.

A glass or metallic rod, when struck at one end, or rubbed in the
direction of its length with a wet finger, vibrates longitudinally, like
a column of air, by the alternate condensation and expansion of its
constituent particles, producing a clear and beautiful musical note of a
high pitch, on account of the rapidity with which these substances
transmit sound. Rods, surfaces, and, in general, all undulating bodies,
resolve themselves into nodes. But in surfaces the parts which remain at
rest during their vibrations are lines which are curved or plane
according to the substance, its form, and the mode of vibration. If a
little fine dry sand be strewed over the surface of a plate of glass or
metal, and if undulations be excited by drawing the bow of a violin
across its edge, it will emit a musical sound, and the sand will
immediately arrange itself in the nodal lines, where alone it will
accumulate and remain at rest, because the segments of the surface on
each side will be in different states of vibration, the one being
elevated while the other is depressed; and, as these two motions meet in
the nodal lines, they neutralise one another. These lines vary in form
and position with the part where the bow is drawn across, and the point
by which the plate is held. The motion of the sand shows in what
direction the vibrations take place. If they be perpendicular to the
surface, the sand will be violently tossed up and down till it finds the
points of rest. If they be tangential, the sand will only creep along
the surface to the nodal lines. Sometimes the undulations are oblique,
or compounded of both the preceding. If a bow be drawn across one of the
angles of a square plate of glass or metal held firmly by the centre,
the sand will arrange itself in two straight lines parallel to the sides
of the plate, and crossing in the centre so as to divide it into four
equal squares, whose motions will be contrary to each other. Two of the
diagonal squares will make their excursions on one side of the plate,
while the other two make their vibrations on the other side of it. This
mode of vibration produces the lowest tone of the plate (N. 183). If the
plate be still held by the centre, and the bow applied to the middle of
one of the sides, the vibrations will be more rapid, and the tone will
be a fifth higher than in the preceding case: now the sand will arrange
itself from corner to corner, and will divide the plate into four equal
triangles, each pair of which will make their excursions on opposite
sides of the plate. The nodal lines and pitch vary not only with the
point where the bow is applied, but with the point by which the plate is
held, which being at rest necessarily determines the direction of one of
the quiescent lines. The forms assumed by the sand in square plates are
very numerous, corresponding to all the various modes of vibration. The
lines in circular plates are even more remarkable for their symmetry,
and upon them the forms assumed by the sand may be classed in three
systems. The first is the diametrical system, in which the figures
consist of diameters dividing the circumference of the plate into equal
parts, each of which is in a different state of vibration from those
adjacent. Two diameters, for example, crossing at right angles, divide
the circumference into four equal parts; three diameters divide it into
six equal parts; four divide it into eight, and so on. In a metallic
plate, these divisions may amount to thirty-six or forty. The next is
the concentric system, where the sand arranges itself in circles, having
the same centre with the plate; and the third is the compound system,
where the figures assumed by the sand are compounded of the other two,
producing very complicated and beautiful forms. Galileo seems to have
been the first to notice the points of rest and motion in the
sounding-board of a musical instrument; but to Chladni is due the whole
discovery of the symmetrical forms of the nodal lines in vibrating
plates (N. 184). Professor Wheatstone has shown, in a paper read before
the Royal Society in 1833, that all Chladni’s figures, and indeed all
the nodal figures of vibrating surfaces, result from very simple modes
of vibration oscillating isochronously, and superposed upon each other;
the resulting figure varying with the component modes of vibration, the
number of the superpositions, and the angles at which they are
superposed. For example, if a square plate be vibrating so as to make
the sand arrange itself in straight lines parallel to one side of the
plate, and if, in addition to this, such vibrations be excited as would
have caused the sand to form in lines perpendicular to the first had the
plate been at rest, the combined vibrations will make the sand form in
lines from corner to corner (N. 185).

M. Savart’s experiments on the vibrations of flat glass rulers are
highly interesting. Let a lamina of glass 27^{in}·56 long, 0·59 of an
inch broad, and 0·06 of an inch in thickness, be held by the edges in
the middle, with its flat surface horizontal. If this surface be strewed
with sand, and set in longitudinal vibration by rubbing its under
surface with a wet cloth, the sand on the upper surface will arrange
itself in lines parallel to the ends of the lamina, always in one or
other of two systems (N. 186). Although the same one of the two systems
will always be produced by the same plate of glass, yet among different
plates of the preceding dimensions, even though cut from the same sheet
side by side, one will invariably exhibit one system, and the other the
other, without any visible reason for the difference. Now, if the
positions of these quiescent lines be marked on the upper surface, and
if the plate be turned so that the lower surface becomes the upper one,
the sand being strewed, and vibrations excited as before, the nodal
lines will still be parallel to the ends of the lamina, but their
positions will be intermediate between those of the upper surface
(N. 187). Thus it appears that all the motions of one half of the
thickness of the lamina, or ruler, are exactly contrary to those of the
corresponding points of the other half. If the thickness of the lamina
be increased, the other dimensions remaining the same, the sound will
not vary, but the number of nodal lines will be less. When the breadth
of the lamina exceeds the 0·6 of an inch, the nodal lines become curved,
and are different on the two surfaces. A great variety of forms are
produced by increasing the breadth and changing the form of the surface;
but in all it appears that the motions in one half of the thickness are
opposed to those in the other half.

M. Savart also found, by placing small paper rings round a cylindrical
tube or rod, so as to rest upon it at one point only, that, when the
tube or rod is continually turned on its axis in the same direction, the
rings slide along during the vibrations, till they come to a quiescent
point, where they rest. By tracing these nodal lines he discovered that
they twist in a spiral or corkscrew round rods and cylinders, making one
or more turns according to the length; but at certain points, varying in
number according to the mode of vibration of the rod, the screw stops,
and recommences on the other side, though it is turned in a contrary
direction; that is, on one side it is a right-handed screw, on the other
a left (N. 188). The nodal lines in the interior surface of the tube are
perfectly similar to those in the exterior, but they occupy intermediate
positions. If a small ivory ball be put within the tube, it will follow
these nodal lines when the tube is made to revolve on its axis.

All solids which ring when struck, such as bells, drinking glasses,
gongs, &c., have their shape momentarily and forcibly changed by the
blow, and from their elasticity, or tendency to resume their natural
form, a series of undulations take place, owing to the alternate
condensations and rarefactions of the particles of solid matter. These
have also their harmonic tones, and consequently nodes. Indeed,
generally, when a rigid system of any form whatever vibrates either
transversely or longitudinally, it divides itself into a certain number
of parts which perform their vibrations without disturbing one another.
These parts are at every instant in alternate states of undulation; and,
as the points or lines where they join partake of both, they remain at
rest, because the opposing motions destroy one another.

The air, notwithstanding its rarity, is capable of transmitting its
undulations when in contact with a body susceptible of admitting and
exciting them. It is thus that sympathetic undulations are excited by a
body vibrating near insulated tended strings, capable of following its
undulations, either by vibrating entire, or by separating themselves
into their harmonic divisions. If two chords equally stretched, of which
one is twice or three times longer than the other, be placed side by
side, and if the shorter be sounded, its vibrations will be communicated
by the air to the other, which will be thrown into such a state of
vibration that it will be spontaneously divided into segments equal in
length to the shorter string. When a tuning-fork receives a blow and is
made to rest upon a piano-forte during its vibration, every string
which, either by its natural length or by its spontaneous subdivisions,
is capable of executing corresponding vibrations, responds in a
sympathetic note. The same effect will be produced by the stroke of a
bell near a piano or harp. Some one or other of the notes of an organ
are generally in unison with one of the panes or with the whole sash of
a window, which consequently resounds when those notes are sounded. A
peal of thunder has frequently the same effect. The sound of very large
organ-pipes is generally inaudible till the air be set in motion by the
undulations of some of the superior accords, and then the sound becomes
extremely energetic. Recurring vibrations occasionally influence each
other’s periods. For example, two adjacent organ-pipes nearly in unison
may force themselves into concord; and two clocks, whose rates differed
considerably when separate, have been known to beat together when fixed
to the same wall, and one clock has forced the pendulum of another into
motion, when merely standing on the same stone pavement. These forced
oscillations, which correspond in their periods with those of the
exciting cause, are to be traced in every department of physical
science. Several instances of them have already occurred in this work.
Such are the tides, which follow the sun and moon in all their motions
and periods. The nutation of the earth’s axis also, which corresponds
with the period, and represents the motion of the nodes of the moon, is
again reflected back to the moon, and may be traced in the nutation of
the lunar orbit. And, lastly, the acceleration of the moon’s mean motion
represents the action of the planets on the earth reflected by the sun
to the moon.

In consequence of the facility with which the air communicates
undulations, all the phenomena of vibrating plates may be exhibited by
sand strewed on paper or parchment, stretched over a harmonica glass or
large bell-shaped tumbler. In order to give due tension to the paper or
vellum, it must be wetted, stretched over the glass, gummed round the
edges, allowed to dry, and varnished over, to prevent changes in its
tension from the humidity of the atmosphere. If a circular disc of glass
be held concentrically over this apparatus, with its plane parallel to
the surface of the paper, and set in vibration by drawing a bow across
its edge, so as to make sand on its surface take any of Chladni’s
figures, the sand on the paper will assume the very same form, in
consequence of the vibrations of the disc being communicated to the
paper by the air. When the disc is removed slowly in a horizontal
direction, the forms on the paper will correspond with those on the
disc, till the distance is too great for the air to convey the
vibrations. If the disc while vibrating be gradually more and more
inclined to the horizon, the figures on the paper will vary by degrees;
and, when the vibrating disc is perpendicular to the horizon, the sand
on the paper will form into straight lines parallel to the surface of
the disc, by creeping along it instead of dancing up and down. If the
disc be made to turn round its vertical diameter while vibrating, the
nodal lines on the paper will revolve, and exactly follow the motion of
the disc. It appears, from this experiment, that the motions of the
aërial molecules in every part of a spherical wave, propagated from a
vibrating body as a centre, are parallel to each other, and not
divergent like the radii of a circle. When a slow air is played on a
flute near this apparatus, each note calls up a particular form in the
sand, which the next note effaces, to establish its own. The motion of
the sand will even detect sounds that are inaudible. By the vibrations
of sand on a drum-head the besieged have discovered the direction in
which a counter-mine was working. M. Savart, who made these beautiful
experiments, employed this apparatus to discover nodal lines in masses
of air. He found that the air of a room, when thrown into undulations by
the continued sound of an organ-pipe, or by any other means, divides
itself into masses separated by nodal curves of double curvature, such
as spirals, on each side of which the air is in opposite states of
vibration. He even traced these quiescent lines going out at an open
window, and for a considerable distance in the open air. The sand is
violently agitated where the undulations of the air are greatest, and
remains at rest in the nodal lines. M. Savart observed, that when he
moved his head away from a quiescent line towards the right the sound
appeared to come from the right, and when he moved it towards the left
the sound seemed to come from the left, because the molecules of air are
in different states of motion on each side of the quiescent line.

A musical string gives a very feeble sound when vibrating alone, on
account of the small quantity of air set in motion; but when attached to
a sounding-board, as in the harp and piano-forte, it communicates its
undulations to that surface, and from thence to every part of the
instrument; so that the whole system vibrates isochronously, and by
exposing an extensive undulating surface, which transmits its
undulations to a great mass of air, the sound is much reinforced. The
intensity is greatest when the vibrations of the string or sounding body
are perpendicular to the sounding-board, and least when they are in the
same plane with it. The sounding-board of the piano-forte is better
disposed than that of any other stringed instrument, because the hammers
strike the strings so as to make them vibrate at right angles to it. In
the guitar, on the contrary, they are struck obliquely, which renders
the tone feeble, unless when the sides, which also act as a
sounding-board, are deep. It is evident that the sounding-board and the
whole instrument are agitated at once by all the superposed vibrations
excited by the simultaneous or consecutive notes that are sounded, each
having its perfect effect independently of the rest. A sounding-board
not only reciprocates the different degrees of pitch, but all the
nameless qualities of tone. This has been beautifully illustrated by
Professor Wheatstone in a series of experiments on the transmission
through solid conductors of musical performances, from the harp, piano,
violin, clarinet, &c. He found that all the varieties of pitch, quality,
and intensity are perfectly transmitted with their relative gradations,
and may be communicated, through conducting wires or rods of very
considerable length, to a properly disposed sounding-board in a distant
apartment. The sounds of an entire orchestra may be transmitted and
reciprocated by connecting one end of a metallic rod with a
sounding-board near the orchestra, so placed as to resound to all the
instruments, and the other end with the sounding-board of a harp, piano,
or guitar, in a remote apartment. Professor Wheatstone observes, “The
effect of this experiment is very pleasing; the sounds, indeed, have so
little intensity as scarcely to be heard at a distance from the
reciprocating instrument; but, on placing the ear close to it, a
diminutive band is heard in which all the instruments preserve their
distinctive qualities, and the pianos and fortes, the crescendos and
diminuendos, their relative contrasts. Compared with an ordinary band
heard at a distance through the air, the effect is as a landscape seen
in miniature beauty through a concave lens, compared with the same scene
viewed by ordinary vision through a murky atmosphere.”

Every one is aware of the reinforcement of sound by the resonance of
cavities. When singing or speaking near the aperture of a wide-mouthed
vessel, the intensity of some one note in unison with the air in the
cavity is often augmented to a great degree. Any vessel will resound if
a body vibrating the natural note of the cavity be placed opposite to
its orifice, and be large enough to cover it, or at least to set a large
portion of the adjacent air in motion. For the sound will be alternately
reflected by the bottom of the cavity and the undulating body at its
mouth. The first impulse of the undulating substance will be reflected
by the bottom of the cavity, and then by the undulating body, in time to
combine with the second new impulse. This reinforced sound will also be
twice reflected in time to conspire with the third new impulse; and, as
the same process will be repeated on every new impulse, each will
combine with all its echoes to reinforce the sound prodigiously.
Professor Wheatstone, to whose ingenuity we are indebted for so much new
and valuable information on the theory of sound, has given some very
striking instances of resonance. If one of the branches of a vibrating
tuning-fork be brought near the embouchure of a flute, the lateral
apertures of which are stopped so as to render it capable of producing
the same sound as the fork, the feeble and scarcely audible sound of the
fork will be augmented by the rich resonance of the column of air within
the flute, and the tone will be full and clear. The sound will be found
greatly to decrease by closing or opening another aperture; for the
alteration in the length of the column of air renders it no longer fit
perfectly to reciprocate the sound of the fork. This experiment may be
made on a concert flute with a C tuning-fork. But Professor Wheatstone
observes, that in this case it is generally necessary to finger the
flute for B, because, when blown into with the mouth, the under-lip
partly covers the embouchure, which renders the sound about a semitone
flatter than it would be were the embouchure entirely uncovered. He has
also shown, by the following experiment, that any one among several
simultaneous sounds may be rendered separately audible. If two bottles
be selected, and tuned by filling them with such a quantity of water as
will render them unisonant with two tuning-forks which differ in pitch,
on bringing both of the vibrating tuning-forks to the mouth of each
bottle alternately, in each case that sound only will be heard which is
reciprocated by the unisonant bottle.

Several attempts have been made to imitate the articulation of the
letters of the alphabet. About the year 1779, MM. Kratzenstein of St.
Petersburg, and Kempelen of Vienna, constructed instruments which
articulated many letters, words, and even sentences. Mr. Willis of
Cambridge has adapted cylindrical tubes to a reed, whose length can be
varied at pleasure by sliding joints. Upon drawing out a tube while a
column of air from the bellows of an organ is passing through it, the
vowels are pronounced in the order, _i_, _e_, _a_, _o_, _u_. On
extending the tube, they are repeated after a certain interval, in the
inverted order, _u_, _o_, _a_, _e_, _i_. After another interval they are
again obtained in the direct order, and so on. When the pitch of the
reed is very high, it is impossible to sound some of the vowels, which
is in perfect correspondence with the human voice, female singers being
unable to pronounce _u_ and _o_ in their high notes. From the singular
discoveries of M. Savart on the nature of the human voice, and the
investigations of Mr. Willis on the mechanism of the larynx, it may be
presumed that ultimately the utterance or pronunciation of modern
languages will be conveyed, not only to the eye, but also to the ear of
posterity. Had the ancients possessed the means of transmitting such
definite sounds, the civilised world would still have responded in
sympathetic notes at the distance of many ages.




                             SECTION XVIII.

Refraction—Astronomical Refraction and its Laws—Formation of Tables of
  Refraction—Terrestrial Refraction—Its Quantity—Instances of
  extraordinary Refraction—Reflection—Instances of extraordinary
  Reflection—Loss of Light by the Absorbing Power of the
  Atmosphere—Apparent Magnitude of Sun and Moon in the Horizon.


NOT only everything we hear but all we see is through the medium of the
atmosphere. Without some knowledge of its action upon light, it would be
impossible to ascertain the position of the heavenly bodies, or even to
determine the exact place of very distant objects upon the surface of
the earth; for, in consequence of the refractive power of the air, no
distant object is seen in its true position.

All the celestial bodies appear to be more elevated than they really
are; because the rays of light, instead of moving through the atmosphere
in straight lines, are continually inflected towards the earth. Light
passing obliquely out of a rare into a denser medium, as from vacuum
into air, or from air into water, is bent or refracted from its course
towards a perpendicular to that point of the denser surface where the
light enters it (N. 189). In the same medium, the sine of the angle
contained between the incident ray and the perpendicular is in a
constant ratio to the sine of the angle contained by the refracted ray
and the same perpendicular; but this ratio varies with the refracting
medium. The denser the medium, the more the ray is bent. The barometer
shows that the density of the atmosphere decreases as the height above
the earth increases. Direct experiments prove that the refractive power
of the air increases with its density. It follows therefore that, if the
temperature be uniform, the refractive power of the air is greatest at
the earth’s surface, and diminishes upwards.

A ray of light from a celestial object falling obliquely on this
variable atmosphere, instead of being refracted at once from its course,
is gradually more and more bent during its passage through it so as to
move in a vertical curved line, in the same manner as if the atmosphere
consisted of an infinite number of strata of different densities. The
object is seen in the direction of a tangent to that part of the curve
which meets the eye; consequently the apparent altitude (N. 190) of the
heavenly bodies is always greater than their true altitude. Owing to
this circumstance, the stars are seen above the horizon after they are
set, and the day is lengthened from a part of the sun being visible,
though he really is behind the rotundity of the earth. It would be easy
to determine the direction of a ray of light through the atmosphere if
the law of the density were known; but, as this law is perpetually
varying with the temperature, the case is very complicated. When rays
pass perpendicularly from one medium into another, they are not bent;
and experience shows, that in the same surface, though the sines of the
angles of incidence and refraction retain the same ratio, the refraction
increases with the obliquity of incidence (N. 189). Hence it appears
that the refraction is greatest at the horizon, and at the zenith there
is none. But it is proved that, at all heights above ten degrees,
refraction varies nearly as the tangent of the angular distance of the
object from the zenith, and wholly depends upon the heights of the
barometer and thermometer. For the quantity of refraction at the same
distance from the zenith varies nearly as the height of the barometer,
the temperature being constant; and the effect of the variation of
temperature is to diminish the quantity of refraction by about its 480th
part for every degree in the rise of Fahrenheit’s thermometer. Not much
reliance can be placed on celestial observations, within less than ten
or twelve degrees of the horizon, on account of irregular variations in
the density of the air near the surface of the earth, which are
sometimes the cause of very singular phenomena. The humidity of the air
produces no sensible effect on its refractive power; and it has been
proved that the amount of refraction is the same whatever be the
velocity of the incident light, that is whether the light comes from a
star in that part of the heavens towards which the earth is going, or
from one in that part of the sky whence it is receding.

Bodies, whether luminous or not, are only visible by the rays which
proceed from them. As the rays must pass through strata of different
densities in coming to us, it follows that, with the exception of stars
in the zenith, no object either in or beyond our atmosphere is seen in
its true place. But the deviation is so small in ordinary cases that it
causes no inconvenience, though in astronomical and trigonometrical
observations due allowance must be made for the effects of refraction.
Dr. Bradley’s tables of refraction were formed by observing the zenith
distances of the sun at his greatest declinations, and the zenith
distances of the pole-star above and below the pole. The sum of these
four quantities is equal to 180°, diminished by the sum of the four
refractions, whence the sum of the four refractions was obtained; and,
from the law of the variation of refraction determined by theory, he
assigned the quantity due to each altitude (N. 191). The mean horizontal
refraction is about 35ʹ 6ʺ, and at the height of forty-five degrees it
is 58ʺ·36. The effect of refraction upon the same star above and below
the pole was noticed by Alhazen, a Saracen astronomer of Spain, in the
ninth century; but its existence was known to Ptolemy in the second,
though he was ignorant of its quantity.

The refraction of a terrestrial object is estimated differently from
that of a celestial body. It is measured by the angle contained between
the tangent to the curvilineal path of the ray where it meets the eye,
and the straight line joining the eye and the object (N. 192). Near the
earth’s surface the path of the ray may be supposed to be circular; and
the angle at the centre of the earth corresponding to this path is
called the horizontal angle. The quantity of terrestrial refraction is
obtained by measuring contemporaneously the elevation of the top of a
mountain above a point in the plain at its base, and the depression of
that point below the top of the mountain. The distance between these two
stations is the chord of the horizontal angle; and it is easy to prove
that double the refraction is equal to the horizontal angle, increased
by the difference between the apparent elevation and the apparent
depression. Whence it appears that, in the mean state of the atmosphere,
the refraction is about the fourteenth part of the horizontal angle.

Some very singular appearances occur from the accidental expansion or
condensation of the strata of the atmosphere contiguous to the surface
of the earth, by which distant objects, instead of being elevated, are
depressed. Sometimes, being at once both elevated and depressed, they
appear double, one of the images being direct, and the other inverted.
In consequence of the upper edges of the sun and moon being less
refracted than the lower, they often appear to be oval when near the
horizon. The looming also or elevation of coasts, mountains, and ships,
when viewed across the sea, arises from unusual refraction. A friend of
the author’s, while standing on the plains of Hindostan, saw the whole
upper chain of the Himalaya Mountains start into view, from a sudden
change in the density of the air, occasioned by a heavy shower after a
very long course of dry and hot weather. Single and double images of
objects at sea, arising from sudden changes of temperature which are not
so soon communicated to the water on account of its density as to the
air, occur more rarely and are of shorter duration than similar
appearances on land. In 1818 Captain Scoresby, whose observations on the
phenomena of the polar seas are so valuable, recognised his father’s
ship by its inverted image in the air, although the vessel itself was
below the horizon. He afterwards found that she was seventeen miles
beyond the horizon, and thirty miles distant. Two images are sometimes
seen suspended in the air over a ship, one direct and the other
inverted, with their topmasts or their hulls meeting, according as the
inverted image is above or below the direct image (N. 193). Dr.
Wollaston has proved that these appearances are owing to the refraction
of the rays through media of different densities, by the very simple
experiment of looking along a red-hot poker at a distant object. Two
images are seen, one direct and another inverted, in consequence of the
change induced by the heat in the density of the adjacent air. He
produced the same effect by a saline or saccharine solution with water
and spirit of wine floating upon it (N. 194).

Many of the phenomena that have been ascribed to extraordinary
refraction seem to be occasioned by a partial or total reflection of the
rays of light at the surfaces of strata of different densities (N. 189).
It is well known that, when light falls obliquely upon the external
surface of a transparent medium, as on a plate of glass or a stratum of
air, one portion is reflected and the other transmitted. But, when light
falls very obliquely upon the internal surface, the whole is reflected,
and not a ray is transmitted. In all cases the angles made by the
incident and reflected rays with a perpendicular to the surface being
equal, as the brightness of the reflected image depends on the quantity
of light, those arising from total reflection must be by far the most
vivid. The delusive appearance of water, so well known to African
travellers and to the Arab of the desert as the Lake of the Gazelles, is
ascribed to the reflection which takes place between strata of air of
different densities, owing to radiation of heat from the arid sandy
plains. The mirage described by Captain Mundy in his Journal of a Tour
in India probably arises from this cause. “A deep precipitous valley
below us, at the bottom of which I had seen one or two miserable
villages in the morning, bore in the evening a complete resemblance to a
beautiful lake; the vapour which played the part of water ascending
nearly half way up the sides of the vale, and on its bright surface
trees and rocks being distinctly reflected. I had not been long
contemplating this phenomenon, before a sudden storm came on and dropped
a curtain of clouds over the scene.”

An occurrence which happened on the 18th of November, 1804, was probably
produced by reflection. Dr. Buchan, while watching the rising sun from
the cliff about a mile to the east of Brighton, at the instant the solar
disc emerged from the surface of the ocean, saw the cliff on which he
was standing, a windmill, his own figure and that of a friend, depicted
immediately opposite to him on the sea. This appearance lasted about ten
minutes, till the sun had risen nearly his own diameter above the
surface of the waves. The whole then seemed to be elevated into the air,
and successively vanished. The rays of the sun fell upon the cliff at an
incidence of 73° from the perpendicular, and the sea was covered with a
dense fog many yards in height, which gradually receded before the
rising sun. When extraordinary refraction takes place laterally, the
strata of variable density are perpendicular to the horizon, and, if
combined with vertical refraction, the objects are magnified as when
seen through a telescope. From this cause, on the 26th of July, 1798,
the cliffs of France, fifty miles off, were seen as distinctly from
Hastings as if they had been close at hand; and even Dieppe was said to
have been visible in the afternoon.

The stratum of air in the horizon is so much thicker and more dense than
the stratum in the vertical, that the sun’s light is diminished 1300
times in passing through it, which enables us to look at him when
setting without being dazzled. The loss of light, and consequently of
heat, by the absorbing power of the atmosphere, increases with the
obliquity of incidence. Of ten thousand rays falling on its surface,
8123 arrive at a given point of the earth if they fall perpendicularly;
7024 arrive if the angle of direction be fifty degrees; 2831, if it be
seven degrees; and only five rays will arrive through a horizontal
stratum. Since so great a quantity of light is lost in passing through
the atmosphere, many celestial objects are altogether invisible from the
plain, which may be seen from elevated situations. Diminished splendour,
and the false estimate we make of distance from the number of
intervening objects, lead us to suppose the sun and moon to be much
larger when in the horizon than at any other altitude, though their
apparent diameters are then somewhat less. Instead of the sudden
transitions of light and darkness, the reflective power of the air
adorns nature with the rosy and golden hues of the Aurora and twilight.
Even when the sun is eighteen degrees below the horizon, a sufficient
portion of light remains to show that at the height of thirty miles it
is still dense enough to reflect light. The atmosphere scatters the
sun’s rays, and gives all the beautiful tints and cheerfulness of day.
It transmits the blue light in greatest abundance; the higher we ascend,
the sky assumes a deeper hue; but, in the expanse of space, the sun and
stars must appear like brilliant specks in profound blackness.




                              SECTION XIX.

Constitution of Light according to Sir Isaac Newton—Absorption of
  Light—Colours of Bodies—Constitution of Light according to Sir David
  Brewster—New Colours—Fraunhofer’s Dark Lines—Dispersion of Light—The
  Achromatic Telescope—Homogeneous Light—Accidental and Complementary
  Colours—M. Plateau’s Experiments and Theory of Accidental Colours.


IT is impossible thus to trace the path of a sunbeam through our
atmosphere without feeling a desire to know its nature, by what power it
traverses the immensity of space, and the various modifications it
undergoes at the surfaces and in the interior of terrestrial substances.

Sir Isaac Newton proved the compound nature of white light, as emitted
from the sun, by passing a sunbeam through a glass prism (N. 195),
which, separating the rays by refraction, formed a spectrum or oblong
image of the sun, consisting of seven colours, red, orange, yellow,
green, blue, indigo, and violet—of which the red is the least
refrangible, and the violet the most. But, when he reunited these seven
rays by means of a lens, the compound beam became pure white as before.
He insulated each coloured ray, and, finding that it was no longer
capable of decomposition by refraction, concluded that white light
consists of seven kinds of homogeneous light, and that to the same
colour the same refrangibility ever belongs, and to the same
refrangibility the same colour. Since the discovery of absorbent media,
however, it appears that this is not the constitution of the solar
spectrum.

We know of no substance that is either perfectly opaque or perfectly
transparent. Even gold may be beaten so thin as to be pervious to light.
On the contrary, the clearest crystal, the purest air or water, stops or
absorbs its rays when transmitted, and gradually extinguishes them as
they penetrate to greater depths. On this account objects cannot be seen
at the bottom of very deep water, and many more stars are visible to the
naked eye from the tops of mountains than from the valleys. The quantity
of light that is incident on any transparent substance is always greater
than the sum of the reflected and refracted rays. A small quantity is
irregularly reflected in all directions by the imperfections of the
polish by which we are enabled to see the surface; but a much greater
portion is absorbed by the body. Bodies that reflect all the rays appear
white, those that absorb them all seem black; but most substances, after
decomposing the white light which falls upon them, reflect some colours
and absorb the rest. A violet reflects the violet rays alone and absorbs
the others. Scarlet cloth absorbs almost all the colours except red.
Yellow cloth reflects the yellow rays most abundantly, and blue cloth
those that are blue. Consequently colour is not a property of matter,
but arises from the action of matter upon light. In fact, the law of
action and reaction obtains in light as in every other department of
nature, so that light cannot be reflected, refracted, much less
absorbed, by any medium without being reacted upon by it. Thus a white
riband reflects all the rays, but, when dyed red, the particles of the
silk acquire the property of reflecting the red rays most abundantly and
of absorbing the others. Upon this property of unequal absorption the
colours of transparent media depend; for they also receive their colour
from their power of stopping or absorbing some of the colours of white
light, and transmitting others. As, for example, black and red inks,
though equally homogeneous, absorb different kinds of rays; and, when
exposed to the sun, they become heated in different degrees; while pure
water seems to transmit all rays equally, and is not sensibly heated by
the passing light of the sun. The rich dark light transmitted by a
smalt-blue finger-glass is not a homogeneous colour like the blue or
indigo of the spectrum, but is a mixture of all the colours of white
light which the glass has not absorbed. The colours absorbed are such as
mixed with the blue tint would form white light. When the spectrum of
seven colours is viewed through a thin plate of this glass, they are all
visible; and, when the plate is very thick, every colour is absorbed
between the extreme red and the extreme violet, the interval being
perfectly black; but, if the spectrum be viewed through a certain
thickness of the glass intermediate between the two, it will be found
that the middle of the red space, the whole of the orange, a great part
of the green, a considerable part of the blue, a little of the indigo,
and a very little of the violet, vanish, being absorbed by the blue
glass; and that the yellow rays occupy a larger space, covering part of
that formerly occupied by the orange on one side and by the green on the
other: so that the blue glass absorbs the red light, which when mixed
with the yellow constitutes orange; and also absorbs the blue light,
which when mixed with the yellow forms the part of the green space next
to the yellow. Hence, by absorption, green light is decomposed into
yellow and blue, and orange light into yellow and red: consequently the
orange and green rays, though incapable of decomposition by refraction,
can be resolved by absorption, and actually consist of two different
colours possessing the same degree of refrangibility. Difference of
colour, therefore, is not a test of difference of refrangibility, and
the conclusion deduced by Newton is no longer admissible as a general
truth. By this analysis of the spectrum, not only with blue glass but
with a variety of coloured media, Sir David Brewster, so justly
celebrated for his optical discoveries, is of opinion that the solar
spectrum consists of three primary colours, red, yellow, and blue, each
of which exists throughout its whole extent, but with different degrees
of intensity in different parts; and that the superposition of these
three produces all the seven hues according as each primary colour is in
excess or defect. That since a certain portion of red, yellow, and blue
rays constitute white light, the colour of any point of the spectrum may
be considered as consisting of the predominating colour at that point
mixed with white light. Consequently, “by absorbing the excess of any
colour at any point of the spectrum above what is necessary to form
white light, such white light will appear at that point as never mortal
eye looked upon before this experiment, since it possesses the
remarkable property of remaining the same after any number of
refractions, and of being capable of decomposition by absorption alone.”
This analysis of light has been called in question by Professor Challis,
of Cambridge, who does not admit of any resolution by absorbing media
different from that by the prism, though he admits that a mixture of
blue and yellow solar light produces green. Professor Stokes, on the
contrary, does not allow that a mixture of blue and yellow solar light
produces green, although that mixture produces green when the light is
from other sources, for he found the gradation from sunlight to pass
from yellow through diluted yellow, white, diluted blue to blue; so he
does not admit of Sir David Brewster’s analysis of the spectrum;
however, there appears to be still a doubt as to the real character of
the phenomena presented by certain absorbing substances.

In addition to the seven colours of the Newtonian spectrum, Sir John
Herschel has discovered a set of very dark red rays beyond the red
extremity of the spectrum which can only be seen when the eye is
defended from the glare of the other colours by a dark blue cobalt
glass. He has also found that beyond the extreme violet there are
visible rays of a lavender gray colour, which may be seen by throwing
the spectrum on a sheet of paper moistened by the carbonate of soda. The
illuminating power of the different rays of the spectrum varies with the
colour. The most intense light is in the mean yellow ray, or, according
to M. Fraunhofer, at the boundary of the orange and yellow.

When the prism is very perfect and the sunbeam small, so that the
spectrum may be received on a sheet of white paper in its utmost state
of purity, it presents the appearance of a riband shaded with all the
prismatic colours, having its breadth irregularly striped or subdivided
by an indefinite number of dark, and sometimes black lines. The greater
number of these rayless lines are so extremely narrow that it is
impossible to see them in ordinary circumstances. The best method is to
receive the spectrum on the object-glass of a telescope, so as to
magnify them sufficiently to render them visible. This experiment may
also be made, but in an imperfect manner, by viewing a narrow slit
between two nearly closed window-shutters through a very excellent glass
prism held close to the eye, with its refracting angle parallel to the
line of light. The rayless lines in the red portion of the spectrum
become most visible as the sun approaches the horizon, while those in
the blue extremity are most obvious in the middle of the day. When the
spectrum is formed by the sun’s rays, either direct or indirect—as from
the sky, clouds, rainbow, moon, or planets—the black bands are always
found to be in the same parts of the spectrum, and under all
circumstances to maintain the same relative positions. Similar dark
lines are also seen in the light of the stars, in the electric light,
and in the flame of combustible substances, though differently arranged,
each star and each flame having a system of dark lines peculiar to
itself. Dr. Wollaston and M. Fraunhofer, of Munich, discovered these
lines deficient of rays independently of each other. M. Fraunhofer found
that their number extends to nearly six hundred, but they are much more
numerous. There are bright lines in the solar spectrum which also
maintain a fixed position. Among the dark lines, M. Fraunhofer selected
seven of the most remarkable, and determined their distances so
accurately, that they now form standard and invariable points of
reference for measuring the refractive powers of different media on the
rays of light, which renders this department of optics as exact as any
of the physical sciences. These lines are designated by the letters of
the alphabet, beginning with B, which is in the red near the end of the
spectrum; C is farther advanced in the red; D is in the orange; E in the
green; F in the blue; G in the indigo; and H in the violet. By means of
these fixed points, M. Fraunhofer has ascertained from prismatic
observation the refrangibility of seven of the principal rays in each of
ten different substances solid and liquid. The refraction increased in
all from the red to the violet end of the spectrum. The rays that are
wanting in the solar spectrum, which occasion the dark lines, were
supposed to be absorbed by the atmosphere of the sun. But the annular
eclipse which happened on the 15th of May, 1836, afforded Professor
Forbes the means of proving that the dark lines in question cannot be
attributed to the absorption of the solar atmosphere; they were neither
broader nor more numerous in the spectrum formed during that phenomenon
than at any other time, though the rays came only from the circumference
of the sun’s disc, and consequently had to traverse a greater depth of
his atmosphere.

Sir David Brewster found that in certain states of the atmosphere the
obscure lines become much broader, and some of them deeply black; and he
observed also, that, at the time the sun was setting in a veil of red
light, part of the luminous spectrum was absorbed, whence he concluded
that the earth’s atmosphere had absorbed the rays of light which
occupied the dark bands. By direct experiments also the atmosphere was
observed to act powerfully upon the rayless lines.

When a lens is used along with a prism, longitudinal dark lines of
different breadths are seen to cross the bands, already described, at
right angles; these M. Ragona-Scina and M. Babinet believe to be lines
of interference which exist in light that has passed through a convex
lens.

The lines are different both in kind and number in the spectra of gases
and flames. In a highly-magnified spectrum from light passed through
nitrous acid gas, Sir David Brewster counted 2000 dark bands. In the
spectrum of a lamp, and generally of all white flames, none of the
defective lines are found; so all such flames contain rays which do not
exist in the light of the sun or stars. Brilliant red lines appear in
the spectrum produced by the combustion of nitre upon charcoal; and in
all artificial flames dark and bright bands exist, sometimes
corresponding in position with those in the solar spectrum, and
sometimes not.

A sunbeam received on a screen, after passing through a small round hole
in a window-shutter, appears like a round white spot; but when a prism
is interposed, the beam no longer occupies the same space. It is
separated into the prismatic colours, and spread over a line of
considerable length, while its breadth remains the same with that of the
white spot. The act of spreading or separation is called the dispersion
of the coloured rays. Dispersion always takes place in the plane of
refraction, and is greater as the angle of incidence is greater. It
varies inversely as the length of a wave of light, and directly as its
velocity: hence towards the blue end of the spectrum, where the
undulations of the rays are least, the dispersion is greatest.
Substances have very different dispersive powers; that is to say, the
spectra formed by two equal prisms of different substances, under
precisely the same circumstances, are of different lengths. Thus, if a
prism of flint-glass and one of crown-glass of equal refracting angles
be presented to two rays of white light at equal angles, it will be
found that the space over which the coloured rays are dispersed by the
flint-glass is much greater than the space occupied by that produced by
the crown-glass: and as the quantity of dispersion depends upon the
refracting angle of the prism, the angles of the two prisms may be made
such that, when the prisms are placed close together with their edges
turned opposite ways, they will exactly oppose each other’s action, and
will refract the coloured rays equally, but in contrary directions, so
that an exact compensation will be effected, and the light will be
refracted without colour (N. 195). The achromatic telescope is
constructed on this principle. It consists of a tube with an
object-glass or lens at one end to bring the rays to a focus, and form
an image of the distant object, and a magnifying-glass at the other end
to view the image thus formed. Now it is found that the object-glass,
instead of making the rays converge to one point, disperses them, and
gives a confused and coloured image: but by constructing it of two
lenses in contact, one of flint and the other of crown-glass of certain
forms and proportions, the dispersion is counteracted, and a perfectly
well-defined and colourless image of the object is formed (N. 196). It
was thought to be impossible to produce refraction without colour, till
Mr. Hall, a gentleman of Worcestershire, constructed a telescope on this
principle in the year 1733; and twenty-five years afterwards the
achromatic telescope was brought to perfection by Mr. Dollond, a
celebrated optician in London.

By means of Mr. Fraunhofer’s determination of the refraction of the
principal rays in substances, their dispersive powers may be found
(N. 197).

A perfectly homogeneous colour is very rarely to be found; but the tints
of all substances are most brilliant when viewed in light of their own
colour. The red of a wafer is much more vivid in red than in white
light; whereas, if placed in homogeneous yellow light, it can no longer
appear red, because there is not a ray of red in the yellow light. Were
it not that the wafer, like all other bodies, whether coloured or not,
reflects white light at its outer surface, it would appear absolutely
black when placed in yellow light.

After looking steadily for a short time at a coloured object, such as a
red wafer, on turning the eyes to a white substance, a green image of
the wafer appears, which is called the accidental colour of red. All
tints have their accidental colours: thus the accidental colour of
orange is blue; that of yellow is indigo; of green, reddish white; of
blue, orange-red; of violet, yellow; and of white, black; and _vice
versâ_. When the direct and accidental colours are of the same
intensity, the accidental is then called the complementary colour,
because any two colours are said to be complementary to one another
which produce white when combined.

From experiments by M. Plateau of Brussels, it appears that two
complementary colours from direct impression, which would produce white
when combined, produce black, or extinguish one another, by their union,
when accidental; and also that the combination of all the tints of the
solar spectrum produces white light if they be from a direct impression
on the eye, whereas blackness results from a union of the same tints if
they be accidental; and in every case where the real colours produce
white by their combination, the accidental colours of the same tints
produce black. When the image of an object is impressed on the retina
only for a few moments, the picture left is exactly of the same colour
with the object, but in an extremely short time the picture is succeeded
by the accidental image. M. Plateau attributes this phenomenon to a
reaction of the retina after being excited by direct vision, so that the
accidental impression is of an opposite nature to the corresponding
direct impression. He conceives that when the eye is excited by being
fixed for a time on a coloured object, and then withdrawn from the
excitement, it endeavours to return to its state of repose; but in so
doing, that it passes this point, and spontaneously assumes an opposite
condition, like a spring which, bent in one direction, in returning to
its state of rest bends as much the contrary way. The accidental image
thus results from a particular modification of the organ of sight, in
virtue of which it spontaneously gives us a new sensation after it has
been excited by direct vision. If the prevailing impression be a very
strong white light, its accidental image is not black, but a variety of
colours in succession. According to M. Plateau, the retina offers a
resistance to the action of light, which increases with the duration of
this action; whence, after looking intently at an object for a long
time, it appears to decrease in brilliancy. The imagination has a
powerful influence on our optical impressions, and has been known to
revive the images of highly luminous objects months, and even years,
afterwards.




                              SECTION XX.

Interference of Light—Undulatory Theory of Light—Propagation of
  Light—Newton’s Rings—Measurement of the Length of the Waves of Light,
  and of the Frequency of the Vibrations of Ether for each
  Colour—Newton’s Scale of Colours—Diffraction of Light—Sir John
  Herschel’s Theory of the Absorption of Light—Refraction and Reflection
  of Light.


NEWTON and most of his immediate successors imagined light to be a
material substance, emitted by all self-luminous bodies in extremely
minute particles, moving in straight lines with prodigious velocity,
which, by impinging upon the optic nerves, produce the sensation of
light. Many of the observed phenomena have been explained by this
theory; it is, however, totally inadequate to account for the following
circumstances.

When two equal rays of red light, proceeding from two luminous points,
fall upon a sheet of white paper in a dark room, they produce a red spot
on it which will be twice as bright as either ray would produce singly,
provided the difference in the lengths of the two beams, from the
luminous points to the red spot on the paper, be exactly the 0·0000258th
part of an inch. The same effect will take place if the difference in
the lengths be twice, three times, four times, &c., that quantity. But
if the difference in the lengths of the two rays be equal to one-half of
the 0·0000258th part of an inch, or to its 1-1/2, 2-1/2, 3-1/2, &c.,
part, the one light will entirely extinguish the other, and will produce
absolute darkness on the paper where the united beams fall. If the
difference in the lengths of their paths be equal to the 1-1/4, 2-1/4,
3-1/4, &c., of the 0·0000258th part of an inch, the red spot arising
from the combined beams will be of the same intensity which one alone
would produce. If violet light be employed, the difference in the
lengths of the two beams must be equal to the 0·0000157th part of an
inch, in order to produce the same phenomena; and for the other colours,
the difference must be intermediate between the 0·0000258th and the
0·0000157th part of an inch. Similar phenomena may be seen by viewing
the flame of a candle through two very fine slits in a card extremely
near to one another (N. 198); or by admitting the sun’s light into a
dark room through a pin-hole about the fortieth of an inch in diameter,
receiving the image on a sheet of white paper, and holding a slender
wire in the light. Its shadow will be found to consist of a bright white
bar or stripe in the middle, with a series of alternate black and
brightly-coloured stripes on each side. The rays which bend round the
wire in two streams are of equal lengths in the middle stripe; it is
consequently doubly bright from their combined effect; but the rays
which fall on the paper on each side of the bright stripe, being of such
unequal lengths as to destroy one another, form black lines. On each
side of these black lines the rays are again of such lengths as to
combine to form bright stripes, and so on alternately till the light is
too faint to be visible. When any homogeneous light is used, such as
red, the alternations are only black and red; but on account of the
heterogeneous nature of white light, the black lines alternate with
vivid stripes or fringes of prismatic colours, arising from the
superposition of systems of alternate black lines and lines of each
homogeneous colour. That the alternation of black lines and coloured
fringes actually does arise from the mixture of the two streams of light
which flow round the wire, is proved by their vanishing the instant one
of the streams is interrupted. It may therefore be concluded, as often
as these stripes of light and darkness occur, that they are owing to the
rays combining at certain intervals to produce a joint effect, and at
others to extinguish one another. Now it is contrary to all our ideas of
matter to suppose that two particles of it should annihilate one another
under any circumstances whatever; while, on the contrary, two opposing
motions may; and it is impossible not to be struck with the perfect
similarity between the interferences of small undulations of air or of
water and the preceding phenomena. The analogy is indeed so perfect,
that philosophers of the highest authority concur in the belief that the
celestial regions are filled with an extremely rare and highly elastic
medium or ether, whose particles are capable of receiving the vibrations
communicated to them by self-luminous bodies, and of transmitting them
to the optic nerves, so as to produce the sensation of light. The
acceleration in the mean motion of Encke’s comet, as well as of the
comet discovered by M. Biela, renders the existence of such a medium
certain. It is clear that, in this hypothesis, the alternate stripes of
light and darkness are entirely the effect of the interference of the
undulations; for, by actual measurement, the length of a wave of the
mean red rays of the solar spectrum is equal to the 0·0000258th part of
an inch; consequently, when the elevations of the waves combine, they
produce double the intensity of light that each would do singly; and
when half a wave combines with a whole—that is, when the hollow of one
wave is filled up by the elevation of another—darkness is the result. At
intermediate points between these extremes, the intensity of the light
corresponds to intermediate differences in the lengths of the rays.

The theory of interferences is a particular case of the general
mechanical law of the superposition of small motions; whence it appears
that the disturbance of a particle of an elastic medium, produced by two
co-existent undulations, is the sum of the disturbances which each
undulation would produce separately; consequently, the particle will
move in the diagonal of a parallelogram, whose sides are the two
undulations. If, therefore, the two undulations agree in direction, or
nearly so, the resulting motion will be very nearly equal to their sum,
and in the same direction; if they nearly oppose one another, the
resulting motion will be nearly equal to their difference; and, if the
undulations be equal and opposite, the resultant will be zero, and the
particle will remain at rest.

The preceding experiments, and the inferences deduced from them, which
have led to the establishment of the doctrine of the undulations of
light, are the most splendid memorials of our illustrious countryman Dr.
Thomas Young, though Huygens was the first to originate the idea.

It is supposed that the particles of luminous bodies are in a state of
perpetual agitation, and that they possess the property of exciting
regular vibrations in the molecules of the ethereal medium,
corresponding to the vibrations of their own molecules; and that, on
account of its elastic nature, one particle of the ether when set in
motion communicates its vibrations to those adjacent, which in
succession transmit them to those farther off; so that the primitive
impulse is transferred from particle to particle, and the undulating
motion darts through ether like a wave in water; so that light is
motion, and therefore subject to the laws of dynamics and mathematical
analysis. Although the progressive motion of light is known by
experience to be uniform and in a straight line, the vibrations of the
particles are always at right angles to the direction of the ray. The
propagation of light is like the spreading of waves in water; but, if
one ray alone be considered, its motion may be conceived by supposing a
rope of indefinite length stretched horizontally, one end of which is
held in the hand. If it be agitated to and fro at regular intervals,
with a motion perpendicular to its length, a series of similar and equal
tremors or waves will be propagated along it; and if the regular
impulses be given in a variety of planes, as up and down, from right to
left, and also in oblique directions, the successive undulations will
take place in every possible plane. An analogous motion in the ether,
when communicated to the optic nerves, would produce the sensation of
common light. It is evident that the waves which flow from end to end of
the cord in a serpentine form are altogether different from the
perpendicular vibratory motion of each particle of the rope, which never
deviates far from a state of rest. So, in ether, each particle vibrates
perpendicularly to the direction of the ray; but these vibrations are
totally different from and independent of the undulations which are
transmitted through it, in the same manner as the vibrations of each
particular ear of corn are independent of the waves that rush from end
to end of a harvest-field when agitated by the wind.

The intensity of light depends upon the amplitude or extent of the
vibrations of the particles of ether, while its colour depends upon
their frequency. The time of the vibration of a particle of ether is, by
theory, as the length of a wave directly, and inversely as its velocity.
Now, as the velocity of light is known to be 190,000 miles in a second,
if the lengths of the waves of the different coloured rays could be
measured, the number of vibrations in a second corresponding to each
could be computed. That has been accomplished as follows:—All
transparent substances of a certain thickness, with parallel surfaces,
reflect and transmit white light; but, if they be extremely thin, both
the reflected and transmitted light is coloured. The vivid hues on
soap-bubbles, the iridescent colours produced by heat on polished steel
and copper, the fringes of colour between the laminæ of Iceland spar and
sulphate of lime, all consist of a succession of hues disposed in the
same order, totally independent of the colour of the substance, and
determined solely by its greater or less thickness—a circumstance which
affords the means of ascertaining the length of the waves of each
coloured ray, and the frequency of the vibrations of the particles
producing them. If a plate of glass be laid upon a lens of almost
imperceptible curvature, before an open window, when they are pressed
together a black spot will be seen in the point of contact, surrounded
by seven rings of vivid colours, all differing from one another
(N. 199). In the first ring, estimated from the black spot, the colours
succeed each other in the following order:—black, very faint blue,
brilliant white, yellow, orange, and red. They are quite different in
the other rings, and in the seventh the only colours are pale bluish
green and very pale pink. That these rings are formed between the two
surfaces in apparent contact may be proved by laying a prism on the lens
instead of the plate of glass, and viewing the rings through the
inclined side of it that is next to the eye, which arrangement prevents
the light reflected from the upper surface mixing with that from the
surfaces in contact, so that the intervals between the rings appear
perfectly black—one of the strongest circumstances in favour of the
undulatory theory; for, although the phenomena of the rings can be
explained by either hypothesis, there is this material difference, that,
according to the undulatory theory, the intervals between the rings
ought to be absolutely black, which is confirmed by experiment; whereas,
by the doctrine of emanation, they ought to be half illuminated, which
is not found to be the case. M. Fresnel, whose opinion is of the first
authority, thought this test conclusive. It may therefore be concluded
that the rings arise entirely from the interference of the rays: the
light reflected from each of the surfaces in apparent contact reaches
the eye by paths of different lengths, and produces coloured and dark
rings alternately, according as the reflected waves coincide or destroy
one another. The breadths of the rings are unequal; they decrease in
width, and the colours become more crowded, as they recede from the
centre. Coloured rings are also produced by transmitting light through
the same apparatus; but the colours are less vivid, and are
complementary to those reflected, consequently the central spot is
white.

The size of the rings increases with the obliquity of the incident
light, the same colour requiring a greater thickness or space between
the glasses to produce it than when the light falls perpendicularly upon
them. Now, if the apparatus be placed in homogeneous instead of white
light, the rings will all be of the same colour with that of the light
employed, that is to say, if the light be red, the rings will be red,
divided by black intervals. The size of the rings varies with the colour
of the light. They are largest in red, and decrease in magnitude with
the succeeding prismatic colours, being smallest in violet light.

Since one of the glasses is plane and the other spherical, it is evident
that from the point of contact the space between them gradually
increases in thickness all round, so that a certain thickness of air
corresponds to each colour, which in the undulatory system measures the
length of the wave producing it (N. 200). By actual measurement Sir
Isaac Newton found that the squares of the diameters of the brightest
part of each ring are as the odd numbers, 1, 3, 5, 7, &c.; and that the
squares of the diameters of the darkest parts are as the even numbers,
0, 2, 4, 6, &c. Consequently, the intervals between the glasses at these
points are in the same proportion. If, then, the thickness of the air
corresponding to any one colour could be found, its thickness for all
the others would be known. Now, as Sir Isaac Newton knew the radius of
curvature of the lens, and the actual breadth of the rings in parts of
an inch, it was easy to compute that the thickness of air at the darkest
part of the first ring is the 1/89000 part of an inch, whence all the
others have been deduced. As these intervals determine the length of the
waves on the undulatory hypothesis, it appears that the length of a wave
of the extreme red of the solar spectrum is equal to the 0·0000266th
part of an inch; that the length of a wave of the extreme violet is
equal to the 0·0000167th part of an inch; and, as the time of a
vibration of a particle of ether producing any particular colour is
directly as the length of a wave of that colour, and inversely as the
velocity of light, it follows that the molecules of ether producing the
extreme red of the solar spectrum perform 458 millions of millions of
vibrations in a second; and that those producing the extreme violet
accomplish 727 millions of millions of vibrations in the same time. The
lengths of the waves of the intermediate colours, and the number of
their vibrations, being intermediate between these two, white light,
which consists of all the colours, is consequently a mixture of waves of
all lengths between the limits of the extreme red and violet. The
determination of these minute portions of time and space, both of which
have a real existence, being the actual results of measurement, do as
much honour to the genius of Newton as that of the law of gravitation.

The number of advancing waves of light in an inch is known to be from
37,600 to 59,880, and the number of lateral vibrations is from 458 to
727 billions in a second, but the _extent_ of these lateral vibrations
of the particles of the ethereal medium is not known, though both their
extent and velocity are probably very small compared with the length of
the advancing waves and the velocity of propagation. Colour is
identified with the number of vibrations; but whether reflection,
refraction, absorption, &c., have any relations to the lateral
vibrations, or whether they are dependent in part upon some physical
action of the ethereal medium unknown and unsuspected, are points as yet
undetermined. To ascertain these circumstances, Dr. Faraday instituted a
series of the most refined experiments upon the relation of the minute
particles of metals to the vibrations of light.

Gold acts powerfully on light, and possesses a real transparency,
transmitting green rays when very thin; and being capable of extreme
division by solvents without losing its metallic character, its
particles transmit rays of various colours according to their size;
those that transmit the rose-colour in Bohemian glass are of
inconceivable minuteness. The progressive waves of the ether are so long
compared with the dimensions of the molecules to which gold can be
reduced, that it seemed probable to Dr. Faraday when the latter were
placed in a sunbeam that some effective relation might be discovered
between them and the smaller vibrations of the ethereal medium; in which
case, if reflection, refraction, &c., depended upon such relations,
there was reason to expect that these functions would change sensibly by
the substitution of different sized particles of the gold for one
another. At one time Dr. Faraday hoped he had changed one colour into
another by means of gold, which would have been equivalent to a change
in the number of vibrations; but although he has not yet confirmed that
result, his researches are of the greatest interest.[9]

The phenomenon of the coloured rings takes place _in vacuo_ as well as
in air, which proves that it is the distance between the lenses alone,
and not the air, which produces the colours. However, if water or oil be
put between them, the rings contract, but no other change ensues; and
Newton found that the thickness of different media at which a given tint
is seen is in the inverse ratio of their refractive indices, so that the
thickness of laminæ which could not otherwise be measured may be known
by their colour; and, as the position of the colours in the rings is
invariable, they form a fixed standard of comparison, well known as
Newton’s scale of colours; each tint being estimated according to the
ring to which it belongs from the central spot inclusively. Not only the
periodical colours which have been described, but the colours seen in
thick plates of transparent substances, the variable hues of feathers,
of insects’ wings, mother-of-pearl, and of striated substances, all
depend upon the same principle. To these may be added the coloured
fringes surrounding the shadows of all bodies held in an extremely small
beam of light, and the coloured rings surrounding the small beam itself
when received on a screen.

When a very slender sunbeam, passing through a small pin-hole into a
dark room, is received on a white screen, or plate of ground-glass, at
the distance of a little more than six feet, the spot of light on the
screen is larger than the pin-hole: and, instead of being bounded by
shadow, it is surrounded by a series of coloured rings separated by
obscure intervals. The rings are more distinct in proportion to the
smallness of the beam (N. 201). When the light is white there are seven
rings, which dilate or contract with the distance of the screen from the
hole. As the distance of the screen diminishes, the white central spot
contracts to a point and vanishes; and, on approaching still nearer, the
rings gradually close in upon it, so that the centre assumes
successively the most intense and vivid hues. When the light is
homogeneous—red, for example—the rings are alternately red and black,
and more numerous; and their breadth varies with the colour, being
broadest in red light and narrowest in violet. The tints of the coloured
fringes from white light, and their obliteration after the seventh ring,
arise from the superposition of the different sets of fringes of all the
coloured rays. The shadows of objects are also bordered by coloured
fringes when held in this slender beam of light. If the edge of a knife
or hair, for example, be held in it, the rays, instead of proceeding in
straight lines past its edge, are bent when quite close to it, and
proceed from thence to the screen in curved lines called hyperbolas; so
that the shadow of the object is enlarged, and, instead of being at once
bounded by light, is surrounded or edged with coloured fringes
alternating with black bands, which are more distinct the smaller the
pin-hole (N. 202). The fringes are altogether independent of the form or
density of the object, being the same when it is round or pointed, when
of glass or platinum. When the rays which form the fringes arrive at the
screen, they are of different lengths, in consequence of the curved path
they follow after passing the edge of the object. The waves are
therefore in different phases or states of vibration, and either
conspire to form coloured fringes or destroy one another in the obscure
intervals. The coloured fringes bordering the shadows of objects were
first described by Grimaldi in 1665; but, besides these, he noticed that
there are others within the shadows of slender bodies exposed to a small
sunbeam, a phenomenon which has already been mentioned to have afforded
Dr. Young the means of proving, beyond all controversy, that coloured
rings are produced by the interference of light.

It may be concluded that material substances derive their colours from
two different causes: some from the law of interference, such as
iridescent metals, peacocks’ feathers, &c.; others from the unequal
absorption of the rays of white light, such as vermilion, ultramarine,
blue, or green cloth, flowers, and the greater number of coloured
bodies. The latter phenomena have been considered extremely difficult to
reconcile with the undulatory theory of light, and much discussion has
arisen as to what becomes of the absorbed rays. But that embarrassing
question has been ably answered by Sir John Herschel in a most profound
paper on the Absorption of Light by coloured Media, and cannot be better
given than in his own words. It must, however, be premised, that, as all
transparent bodies are traversed by light, they are presumed to be
permeable to the ether. He says,—“Now, as regards only the general fact
of the obstruction and ultimate extinction of light in its passage
through gross media, if we compare the corpuscular and undulatory
theories, we shall find that the former appeals to our ignorance, the
latter to our knowledge, for its explanation of the absorptive
phenomena. In attempting to explain the extinction of light on the
corpuscular doctrine, we have to account for the light so extinguished
as a material body, which we must not suppose annihilated. It may,
however, be transformed; and among the imponderable agents, heat,
electricity, &c., it may be that we are to search for the light which
has become thus comparatively stagnant. The heating power of the solar
rays gives a _primâ facie_ plausibility to the idea of the
transformation of light into heat by absorption. But, when we come to
examine the matter more nearly, we find it encumbered on all sides with
difficulties. How is it, for instance, that the most luminous rays are
not the most calorific, but that, on the contrary, the calorific energy
accompanies, in its greatest intensity, rays which possess comparatively
feeble illuminating powers? These and other questions of a similar
nature may perhaps admit of answer in a more advanced state of our
knowledge; but at present there is none obvious. It is not without
reason, therefore, that the question, ‘What becomes of light?’ which
appears to have been agitated among the photologists of the last
century, has been regarded as one of considerable importance as well as
obscurity by the corpuscular philosophers. On the other hand, the answer
to this question, afforded by the undulatory theory of light, is simple
and distinct. The question, ‘What becomes of light?’ merges in the more
general one, ‘What becomes of motion?’ And the answer, on dynamical
principles, is, that it continues for ever. No motion is, strictly
speaking, annihilated; but it may be divided, and the divided parts made
to oppose and _in effect_ destroy one another. A body struck, however
perfectly elastic, vibrates for a time, and then appears to sink into
its original repose. But this apparent rest (even abstracting from the
inquiry that part of the motion which may be conveyed away by the
ambient air) is nothing else than a state of subdivided and mutually
destroying motion, in which every molecule continues to be agitated by
an indefinite multitude of internally reflected waves, propagated
through it in every possible direction, from every point in its surface
on which they successively impinge. The superposition of such waves
will, it is easily seen, at length operate their mutual destruction,
which will be the more complete the more irregular the figure of the
body, and the greater the number of internal reflections.” Thus Sir John
Herschel, by referring the absorption of light to the subdivision and
mutual destruction of the vibrations of ether in the interior of bodies,
brings another class of phenomena under the laws of the undulatory
theory.

According to Mr. Rankin’s hypothesis of Molecular Vortices[10] the
absorption of light and radiant heat consists in the transference of
motion from the molecules to their atmospheres, and conversely the
emission of light and radiant heat is the transmission of motion from
the atmospheres to the molecules. The great velocity of light and heat
is a natural consequence of this hypothesis, according to which the
vibratory masses must be extremely small compared with the forces
exerted by them.

The ethereal medium pervading space is supposed to penetrate all
material substances, occupying the interstices between their molecules;
but in the interior of refracting media it exists in a state of less
elasticity compared with its density _in vacuo_; and, the more
refractive the medium, the less the elasticity of the ether within it.
Hence the waves of light are transmitted with less velocity in such
media as glass and water than in the external ether. As soon as a ray of
light reaches the surface of a diaphanous reflecting substance, for
example a plate of glass, it communicates its undulations to the ether
next in contact with the surface, which thus becomes a new centre of
motion, and two hemispherical waves are propagated from each point of
this surface; one of which proceeds forward into the interior of the
glass, with a less velocity than the incident waves; and the other is
transmitted back into the air, with a velocity equal to that with which
it came (N. 203). Thus, when refracted, the light moves with a different
velocity without and within the glass; when reflected, the ray comes and
goes with the same velocity. The particles of ether without the glass,
which communicate their motions to the particles of the dense and less
elastic ether within it, are analogous to small elastic balls striking
large ones; for some of the motion will be communicated to the large
balls, and the small ones will be reflected. The first would cause the
refracted wave, and the last the reflected. Conversely, when the light
passes from glass to air, the action is similar to large balls striking
small ones. The small balls receive a motion which would cause the
refracted ray, and the part of the motion retained by the large ones
would occasion the reflected wave; so that, when light passes through a
plate of glass or of any other medium differing in density from the air,
there is a reflection at both surfaces; but this difference exists
between the two reflections, that one is caused by a vibration in the
same direction with that of the incident ray, and the other by a
vibration in the opposite direction.

A single wave of air or ether would not produce the sensation of sound
or light. In order to excite vision, the vibrations of the molecules of
ether must be regular, periodical, and very often repeated: and, as the
ear continues to be agitated for a short time after the impulse by which
alone a sound becomes continuous, so also the fibres of the retina,
according to M. d’Arcet, continue to vibrate for about the eighth part
of a second after the exciting cause has ceased. The interval of time
during which the impression lasts is longer for the blue than for red or
white light: it must not be less than 0ʺ·34. Every one must have
observed, when a strong impression is made by a bright light, that an
object remains visible for a short time after shutting the eyes, which
is supposed to be in consequence of the continued vibrations of the
fibres of the retina. Occasionally the retina becomes insensible to
feebly illuminated objects when continuously presented. If the eye be
turned aside for a moment, the object becomes again visible. It is
probably on this account that the owl makes so peculiar a motion with
its head when looking at objects in the twilight. It is quite possible
that many vibrations may be excited in the ethereal medium incapable of
producing undulations in the fibres of the human retina, which yet have
a powerful effect on those of other animals or of insects. Such may
receive luminous impressions of which we are totally unconscious, and at
the same time they may be insensible to the light and colours which
affect our eyes, their perceptions beginning where ours end.




                              SECTION XXI.

Polarization of Light—Defined—Polarization by Refraction—Properties of
  the Tourmaline—Double Refraction—All doubly Refracted Light is
  Polarized—Properties of Iceland Spar—Tourmaline absorbs one of the two
  Refracted Rays—Undulations of Natural Light—Undulations of Polarized
  Light—The Optic Axes of Crystals—M. Fresnel’s Discoveries on the Rays
  passing along the Optic Axis—Polarization by Reflection.


IN giving a sketch of the constitution of light, it is impossible to
omit the extraordinary property of its polarization, “the phenomena of
which,” Sir John Herschel says, “are so singular and various, that to
one who has only studied the common branches of physical optics it is
like entering into a new world, so splendid as to render it one of the
most delightful branches of experimental inquiry, and so fertile in the
views it lays open of the constitution of natural bodies, and the
minuter mechanism of the universe, as to place it in the very first rank
of the physico-mathematical sciences, which it maintains by the rigorous
application of geometrical reasoning its nature admits and requires.”

Light is said to be polarized, which, by being once reflected or
refracted, is rendered incapable of being again reflected or refracted
at certain angles. In general, when a ray of light is reflected from a
pane of plate-glass, or any other substance, it may be reflected a
second time from another surface, and it will also pass freely through
transparent bodies. But, if a ray of light be reflected from a pane of
plate-glass at an angle of 57°, it is rendered totally incapable of
reflection at the surface of another pane of glass in certain definite
positions, but it will be completely reflected by the second pane in
other positions. It likewise loses the property of penetrating
transparent bodies in particular positions, whilst it is freely
transmitted by them in others. Light, so modified as to be incapable of
reflection and transmission in certain directions, is said to be
polarized.

Light may be polarized by reflection from any polished surface, and the
same property is also imparted by refraction. It is proposed to explain
these methods of polarizing light, to give a short account of its most
remarkable properties, and to endeavour to describe a few of the
splendid phenomena it exhibits.

If a brown tourmaline, which is a mineral generally crystallized in the
form of a long prism, be cut longitudinally, that is, parallel to the
axis of the prism, into plates about the thirtieth of an inch in
thickness, and the surfaces polished, luminous objects may be seen
through them, as through plates of coloured glass. The axis of each
plate is in its longitudinal section parallel to the axis of the prism
whence it was cut (N. 204). If one of these plates be held
perpendicularly between the eye and a candle, and turned slowly round in
its own plane, no change will take place in the image of the candle. But
if the plate be held in a fixed position, with its axis or longitudinal
section vertical, when a second plate of tourmaline is interposed
between it and the eye, parallel to the first, and turned slowly round
in its own plane, a remarkable change will be found to have taken place
in the nature of the light. For the image of the candle will vanish and
appear alternately at every quarter revolution of the plate, varying
through all degrees of brightness down to total or almost total
evanescence, and then increasing again by the same degrees as it had
before decreased. These changes depend upon the relative positions of
the plates. When the longitudinal sections of the two plates are
parallel, the brightness of the image is at its maximum; and, when the
axes of the sections cross at right angles, the image of the candle
vanishes. Thus the light, in passing through the first plate of
tourmaline, has acquired a property totally different from the direct
light of the candle. The direct light would have penetrated the second
plate equally well in all directions, whereas the refracted ray will
only pass through it in particular positions, and is altogether
incapable of penetrating it in others. The refracted ray is polarized in
its passage through the first tourmaline, and experience shows that it
never loses that property, unless when acted upon by a new substance.
Thus, one of the properties of polarized light is the incapability of
passing through a plate of tourmaline perpendicular to it, in certain
positions, and its ready transmission in other positions at right angles
to the former.

Many other substances have the property of polarizing light. If a ray of
light falls upon a transparent medium, which has the same temperature,
density, and structure throughout every part, as fluids, gases, glass,
&c., and a few regularly crystallized minerals, it is refracted into a
single pencil of light by the laws of ordinary refraction, according to
which the ray, passing through the refracting surface from the object to
the eye, never quits a plane perpendicular to that surface. Almost all
other bodies, such as the greater number of crystallized minerals,
animal and vegetable substances, gums, resins, jellies, and all solid
bodies having unequal tensions, whether from unequal temperature or
pressure, possess the property of doubling the image or appearance of an
object seen through them in certain directions; because a ray of natural
light falling upon them is refracted into two pencils which move with
different velocities, and are more or less separated, according to the
nature of the body and the direction of the incident ray. Whenever a ray
of natural light is thus divided into two pencils in its passage through
a substance, both of the transmitted rays are polarized. Iceland spar, a
carbonate of lime, which by its natural cleavage may be split into the
form of a rhombohedron, possesses the property of double refraction in
an eminent degree, as may be seen by pasting a piece of paper, with a
large pin-hole in it, on the side of the spar farthest from the eye. The
hole will appear double when held to the light (N. 205). One of these
pencils is refracted according to the same law as in glass or water,
never quitting the plane perpendicular to the refracting surface, and is
therefore called the ordinary ray. But the other does quit the plane,
being refracted according to a different and much more complicated law,
and on that account is called the extraordinary ray. For the same reason
one image is called the ordinary, and the other the extraordinary image.
When the spar is turned round in the same plane, the extraordinary image
of the hole revolves about the ordinary image, which remains fixed, both
being equally bright. But if the spar be kept in one position, and
viewed through a plate of tourmaline, it will be found that, as the
tourmaline revolves, the images vary in their relative brightness—one
increases in intensity till it arrives at a maximum, at the same time
that the other diminishes till it vanishes, and so on alternately at
each quarter revolution, proving both rays to be polarized. For in one
position the tourmaline transmits the ordinary ray, and reflects the
extraordinary; and, after revolving 90°, the extraordinary ray is
transmitted, and the ordinary ray is reflected. Thus another property of
polarized light is, that it cannot be divided into two equal pencils by
double refraction, in positions of the doubly refracting bodies in which
a ray of common light would be so divided.

Were tourmaline like other doubly refracting bodies, each of the
transmitted rays would be double; but that mineral, when of a certain
thickness, after separating the light into two polarized pencils,
absorbs that which undergoes ordinary refraction, and consequently shows
only one image of an object. On this account tourmaline is peculiarly
fitted for analyzing polarized light, which shows nothing remarkable
till viewed through it or something equivalent.

The pencils of light, on leaving a double refracting substance, are
parallel; and it is clear, from the preceding experiments, that they are
polarized in planes at right angles to each other (N. 206). But that
will be better understood by considering the change produced in common
light by the action of the polarizing body. It has been shown that the
undulations of ether, which produce the sensation of common light, are
performed in every possible plane, at right angles to the direction in
which the ray is moving. But the case is very different after the ray
has passed through a doubly refracting substance, like Iceland spar. The
light then proceeds in two parallel pencils, whose undulations are still
indeed transverse to the direction of the rays, but they are
accomplished in planes at right angles to one another, analogous to two
parallel stretched cords, one of which performs its undulations only in
a horizontal plane, and the other in a vertical or upright plane
(N. 206). Thus the polarizing action of Iceland spar and of all doubly
refracting substances is to separate a ray of common light, whose waves
or undulations are in every plane, into two parallel rays, whose waves
or undulations lie in planes at right angles to each other. By a simple
mechanical law each vibratory motion of the first is resolved into two
vibratory motions at right angles to one another. The ray of common
light may be assimilated to a round rod, whereas the two polarized rays
are like two parallel long flat rulers, one of which is laid
horizontally on its broad surface, and the other horizontally on its
edge. The alternate transmission and obstruction of one of these
flattened beams by the tourmaline is similar to the facility with which
a card may be passed between the bars of a grating or wires of a cage,
if presented edgeways, and the impossibility of its passing in a
transverse direction.

Although it generally happens that a ray of light, in passing through
Iceland spar, is separated into two polarized rays, yet there is one
direction along which it is refracted in one ray only, and that
according to the ordinary law. This direction is called the optic axis
(N. 207). Many crystals and other substances have two optic axes,
inclined to each other, along which a ray of light is transmitted in one
pencil by the law of ordinary refraction. The extraordinary ray is
sometimes refracted towards the optic axis, as in quartz, zircon, ice,
&c., which are therefore said to be positive crystals; but when it is
bent from the optic axis, as in Iceland spar, tourmaline, emerald,
beryl, &c., the crystals are negative, which is the most numerous class.
The ordinary ray moves with uniform velocity within a doubly refracting
substance, but the velocity of the extraordinary ray varies with the
position of the ray relatively to the optic axis, being a maximum when
its motion within the crystal is at right angles to the optic axis, and
a minimum when parallel to it. Between these extremes its velocity
varies according to a determinate law.

It had been inferred, from the action of Iceland spar on light, that in
all doubly refracting substances one only of two rays is turned aside
from the plane of ordinary refraction, while the other follows the
ordinary law; and the great difficulty of observing the phenomena tended
to confirm that opinion. M. Fresnel, however, proved by a most profound
mathematical inquiry, _à priori_, that the extraordinary ray must be
wanting in glass and other uncrystallized substances, and that it must
necessarily exist in carbonate of lime, quartz, and other bodies having
one optic axis, but that in a numerous class of substances, which
possess two optic axes, both rays must undergo extraordinary refraction,
and consequently that both must deviate from their original plane; and
these results have been perfectly confirmed by subsequent experiments.
This theory of refraction, which for generalization is perhaps only
inferior to the law of gravitation, has enrolled the name of Fresnel
among those which pass not away, and makes his early loss a subject of
deep regret to all who take an interest in the higher paths of
scientific research.

When a beam of common light is partly reflected at, and partly
transmitted through a transparent surface, the reflected and refracted
pencils contain equal quantities of polarized light, and their planes of
polarization are at right angles to one another: hence, a pile of panes
of glass will give a polarized beam by refraction. For, if a ray of
common light pass through them, part of it will be polarized by the
first plate, the second plate will polarize a part of what passes
through it, and the rest will do the same in succession, till the whole
beam is polarized, except what is lost by reflection at the different
surfaces, or by absorption. This beam is polarized in a plane at right
angles to the plane of reflection, that is, at right angles to the plane
passing through the incident and reflected ray (N. 208).

By far the most convenient way of polarizing light is by reflection. A
plane of plate-glass laid upon a piece of black cloth, on a table at an
open window, will appear of a uniform brightness from the reflection of
the sky or clouds. But if it be viewed through a plate of tourmaline,
having its axis vertical, instead of being illuminated as before, it
will be obscured by a large cloudy spot, having its centre quite dark,
which will readily be found by elevating or depressing the eye, and will
only be visible when the angle of incidence is 57°, that is, when the
line from the eye to the centre of the black spot makes an angle of 33°
with the surface of the reflector (N. 209). When the tourmaline is
turned round in its own plane, the dark cloud will diminish, and
entirely vanish when the axis of the tourmaline is horizontal, and then
every part of the surface of the glass will be equally illuminated. As
the tourmaline revolves, the cloudy spot will appear and vanish
alternately at every quarter revolution. Thus, when a ray of light is
incident on a pane of plate-glass at an angle of 57°, the reflected ray
is rendered incapable of penetrating a plate of tourmaline whose axis is
in the plane of incidence. Consequently it has acquired the same
character as if it had been polarized by transmission through a plate of
tourmaline, with its axis at right angles to the plane of reflection. It
is found by experience that this polarized ray is incapable of a second
reflection at certain angles and in certain positions of the incident
plane. For if another pane of plate-glass, having one surface blackened,
be so placed as to make an angle of 33° with the reflected ray, the
image of the first pane will be reflected in its surface, and will be
alternately illuminated and obscured at every quarter revolution of the
blackened pane, according as the plane of reflection is parallel or
perpendicular to the plane of polarization. Since this happens by
whatever means the light has been polarized, it evinces another general
property of polarized light, which is, that it is incapable of
reflection in a plane at right angles to the plane of polarization.

All reflecting surfaces are capable of polarizing light, but the angle
of incidence at which it is completely polarized is different in each
substance (N. 210). It appears that the angle for plate-glass is 57°; in
crown-glass it is 56° 55ʹ, and no ray will be completely polarized by
water unless the angle of incidence be 53° 11ʹ. The angles at which
different substances polarize light are determined by a very simple and
elegant law, discovered by Sir David Brewster, “That the tangent of the
polarizing angle for any medium is equal to the sine of the angle of
incidence divided by the sine of the angle of refraction of that
medium.” Whence also the refractive power even of an opaque body is
known when its polarizing angle has been determined.

If a ray, polarized by refraction or by reflection from any substance
not metallic, be viewed through a piece of Iceland spar, each image will
alternately vanish and reappear at every quarter revolution of the spar,
whether it revolves from right to left or from left to right; which
shows that the properties of the polarized ray are symmetrical on each
side of the plane of polarization.

Although there be only one angle in each substance at which light is
completely polarized by one reflection, yet it may be polarized at any
angle of incidence by a sufficient number of reflections. For, if a ray
falls upon the upper surface of a pile of plates of glass at an angle
greater or less than a polarizing angle, a part only of the reflected
ray will be polarized, but a part of what is transmitted will be
polarized by reflection at the surface of the second plate, part at the
third, and so on till the whole is polarized. This is the best
apparatus; but one plate of glass having its inferior surface blackened,
or even a polished table, will answer the purpose.




                             SECTION XXII.

Phenomena exhibited by the Passage of Polarized Light through Mica and
  Sulphate of Lime—The Coloured Images produced by Polarized Light
  passing through Crystals having one and two Optic Axes—Circular
  Polarization—Elliptical Polarization—Discoveries of MM. Biot, Fresnel,
  and Professor Airy—Coloured Images produced by the Interference of
  Polarized Rays—Fluorescence.


SUCH is the nature of polarized light and of the laws it follows. But it
is hardly possible to convey an idea of the splendour of the phenomena
it exhibits under circumstances which an attempt will now be made to
describe.

If light polarized by reflection from a pane of glass be viewed through
a plate of tourmaline, with its longitudinal section vertical, an
obscure cloud, with its centre totally dark, will be seen on the glass.
Now, let a plate of mica, uniformly about the thirtieth of an inch in
thickness, be interposed between the tourmaline and the glass; the dark
spot will instantly vanish, and, instead of it, a succession of the most
gorgeous colours will appear, varying with every inclination of the
mica, from the richest reds, to the most vivid greens, blues, and
purples (N. 211). That they may be seen in perfection, the mica must
revolve at right angles to its own plane. When the mica is turned round
in a plane perpendicular to the polarized ray, it will be found that
there are two lines in it where the colours entirely vanish. These are
the optic axes of the mica, which is a doubly refracting substance, with
two optic axes, along which light is refracted in one pencil.

No colours are visible in the mica, whatever its position may be with
regard to the polarized light, without the aid of the tourmaline, which
separates the transmitted ray into two pencils of coloured light
complementary to one another, that is, which taken together would make
white light. One of these it absorbs, and transmits the other; it is
therefore called the analyzing plate. The truth of this will appear more
readily if a film of sulphate of lime, between the twentieth and
sixtieth of an inch thick, be used instead of the mica. When the film is
of uniform thickness, only one colour will be seen when it is placed
between the analyzing plate and the reflecting glass; as, for example,
red. But, when the tourmaline revolves, the red will vanish by degrees
till the film is colourless; then it will assume a green hue, which will
increase and arrive at its maximum when the tourmaline has turned
through ninety degrees; after that, the green will vanish and the red
will reappear, alternating at each quadrant. Thus the tourmaline
separates the light which has passed through the film into a red and a
green pencil; in one position it absorbs the green and lets the red
pass, and in another it absorbs the red and transmits the green. This is
proved by analyzing the ray with Iceland spar instead of tourmaline;
for, since the spar does not absorb the light, two images of the
sulphate of lime will be seen, one red and the other green; and these
exchange colours every quarter revolution of the spar, the red becoming
green, and the green red; and, where the images overlap, the colour is
white, proving the red and green to be complementary to each other. The
tint depends on the thickness of the film. Films of sulphate of lime,
the 0·00124 and 0·01818 of an inch respectively, give white light in
whatever position they may be held, provided they be perpendicular to
the polarized ray; but films of intermediate thickness will give all
colours. Consequently, a wedge of sulphate of lime, varying in thickness
between the 0·00124 and the 0·01818 of an inch, will appear to be
striped with all colours when polarized light is transmitted through it.
A change in the inclination of the film, whether of mica or sulphate of
lime, is evidently equivalent to a variation in thickness.

When a plate of mica, held as close to the eye as possible, at such an
inclination as to transmit the polarized ray along one of its optic
axes, is viewed through the tourmaline with its axis vertical, a most
splendid appearance is presented. The cloudy spot in the direction of
the optic axis is seen surrounded by a set of vividly coloured rings of
an oval form, divided into two unequal parts by a black curved band
passing through the cloudy spot about which the rings are formed. The
other optic axis of the mica exhibits a similar image (N. 212).

When the two optic axes of a crystal make a small angle with one
another, as in nitre, the two sets of rings touch externally; and, if
the plate of nitre be turned round in its own plane, the black
transverse bands undergo a variety of changes, till, at last, the whole
richly coloured image assumes the form of the figure 8, traversed by a
black cross (N. 213). Substances with one optic axis have but one set of
coloured circular rings, with a broad black cross passing through its
centre, dividing the rings into four equal parts. When the analyzing
plate revolves, this figure recurs at every quarter revolution; but in
the intermediate positions it assumes the complementary colours, the
black cross becoming white.

It is in vain to attempt to describe the beautiful phenomena exhibited
by innumerable bodies which undergo periodic changes in form and colour
when the analyzing plate revolves, but not one of them shows a trace of
colour without the aid of tourmaline, or something equivalent, to
analyze the light, and as it were to call these beautiful phantoms into
existence. Tourmaline has the disadvantage of being itself a coloured
substance; but that inconvenience may be obviated by employing a
reflecting surface as an analyzing plate. When polarized light is
reflected by a plate of glass at the polarizing angle, it will be
separated into two coloured pencils; and, when the analyzing plate is
turned round in its own plane, it will alternately reflect each ray at
every quarter revolution, so that all the phenomena that have been
described will be seen by reflection on its surface.

Coloured rings are produced by analyzing polarized light transmitted
through glass melted and suddenly or unequally cooled; also through thin
plates of glass bent with the hand, jelly indurated or compressed, &c.
&c. In short, all the phenomena of coloured rings may be produced,
either permanently or transiently, in a variety of substances, by heat
and cold, rapid cooling, compression, dilatation, and induration; and so
little apparatus is necessary for performing the experiments, that, as
Sir John Herschel says, a piece of window glass or a polished table to
polarize the light, a sheet of clear ice to produce the rings, and a
broken fragment of plate-glass placed near the eye to analyze the light,
are alone requisite to produce one of the most splendid of optical
exhibitions.

Pressure produces remarkable changes in the optical properties of
crystals. Compression, perpendicular to the axis, transforms a crystal
with one optic axis into one with two. A slice of quartz and one of
beryl, both cut perpendicularly to their axis, were compressed thus by
MM. Moignot and Soleil. They found that the single system in the quartz,
which is a positive crystal, was doubled in the direction of the
compression, while in the beryl, which is a negative crystal, the
duplication was perpendicular to the compression. In the quartz the axis
of the double system coincided with the line of pressure, but in the
tourmaline, which is a negative crystal, the line which joins the
centres of the rings was perpendicular to the pressure.

If a positive crystal be compressed in the direction of its axis the
tint of the rings descends, and that of a negative crystal rises. But if
the crystals be dilated in the direction of their optic axis, the tints
in positive crystals rise, and negative descend.

It has been observed, that when a ray of light, polarized by reflection
from any surface not metallic, is analyzed by a doubly refracting
substance, it exhibits properties which are symmetrical both to the
right and left of the plane of reflection, and the ray is then said to
be polarized according to that plane. This symmetry is not destroyed
when the ray, before being analyzed, traverses the optic axis of a
crystal having but one optic axis, as evidently appears from the
circular forms of the coloured rings already described. Regularly
crystallized quartz, however, forms an exception. In it, even though the
rays should pass through the optic axis itself, where there is no double
refraction, the primitive symmetry of the ray is destroyed, and the
plane of primitive polarization deviates either to the right or left of
the observer, by an angle proportional to the thickness of the plate of
quartz. This angular motion, or true rotation of the plane of
polarization, which is called circular polarization, is clearly proved
by the phenomena. The coloured rings produced by all crystals having but
one optic axis are circular, and traversed by a black cross concentric
with the rings; so that the light entirely vanishes throughout the space
enclosed by the interior ring, because there is neither double
refraction nor polarization along the optic axis. But in the system of
rings produced by a plate of quartz, whose surfaces are perpendicular to
the axis of the crystal, the part within the interior ring, instead of
being void of light, is occupied by a uniform tint of red, green, or
blue, according to the thickness of the plate (N. 214). Suppose the
plate of quartz to be 1/25 of an inch thick, which will give the red
tint to the space within the interior ring; when the analyzing plate is
turned, in its own plane through an angle of 17-1/2°, the red hue
vanishes. If a plate of rock crystal 2/25 of an inch thick be used, the
analyzing plate must revolve through 35° before the red tint vanishes,
and so on, every additional 25th of an inch in thickness requiring an
additional rotation of 17-1/2°; whence it is manifest that the plane of
polarization revolves in the direction of a spiral within the rock
crystal. It is remarkable that, in some crystals of quartz, the plane of
polarization revolves from right to left, and in others from left to
right, although the crystals themselves differ apparently only by a very
slight, almost imperceptible, variety in form. In these phenomena the
rotation to the right is accomplished according to the same laws, and
with the same energy, as that to the left. But if two plates of quartz
be interposed, which possess different affections, the second plate
undoes, either wholly or partly, the rotatory motion which the first had
produced, according as the plates are of equal or unequal thickness.
When the plates are of unequal thickness, the deviation is in the
direction of the strongest, and exactly the same with that which a third
plate would produce equal in thickness to the difference of the two.

M. Biot has discovered the same properties in a variety of liquids. Oil
of turpentine, and an essential oil of laurel, cause the plane of
polarization to turn to the left, whereas the syrup of sugar-cane, and a
solution of natural camphor, by alcohol, turn it to the right. A
compensation is effected by the superposition or mixture of two liquids
which possess these opposite properties, provided no chemical action
takes place. A remarkable difference was also observed by M. Biot
between the action of the particles of the same substances when in a
liquid or solid state. The syrup of grapes, for example, turns the plane
of polarization to the left as long as it remains liquid; but, as soon
as it acquires the solid form of sugar, it causes the plane of
polarization to revolve towards the right, a property which it retains
even when again dissolved. Instances occur also in which these
circumstances are reversed.

A ray of light passing through a liquid possessing the power of circular
polarization is not affected by mixing other fluids with the liquid—such
as water, ether, alcohol, &c.—which do not possess circular polarization
themselves, the angle of deviation remaining exactly the same as before
the mixture. Whence M. Biot infers that the action exercised by the
liquids in question does not depend upon their mass, but that it is a
molecular action exercised by the ultimate particles of matter, which
depends solely upon the individual constitution, and is entirely
independent of the positions and mutual distances of the particles with
regard to each other. These important discoveries show that circular
polarization surpasses the power of chemical analysis in giving certain
and direct evidence of the similarity or difference existing in the
molecular constitution of bodies, as well as of the permanency of that
constitution, or of the fluctuations to which it may be liable. For
example, no chemical difference has been discovered between syrup from
the sugar-cane and syrup from grapes. Yet the first causes the plane of
polarization to revolve to the right, and the other to the left;
therefore some essential difference must exist in the nature of their
ultimate molecules. The same difference is to be traced between the
juices of such plants as give sugar similar to that from the cane, and
those which give sugar like that obtained from grapes.

If chlorate of soda be dissolved in water, the liquid has no circular
polarization; but if the solution be allowed to crystallize, some of the
crystals turn the light to the right and others to the left. Now, if all
those of one kind be gathered together and dissolved a second time, the
liquid will have no circular polarization; but if crystals be allowed to
form, some will turn the light to the right and others to the left,
although only one kind was dissolved.[11]

It is a fact established by M. Biot, that in circular polarization the
laws of rotation followed by the different simple rays of light are
dissimilar in different substances. Whence he infers that the deviation
of the simple rays from one another ought not to result from a special
property of the luminous principle only, but that the proper action of
the molecules must also concur in modifying the deviations of the simple
rays differently in different substances.

One of the many brilliant discoveries of M. Fresnel is the production of
circular and elliptical polarization by the internal reflection of light
from plate-glass. He has shown that, if light polarized by any of the
usual methods be twice reflected within a glass rhomb (N. 169) of a
given form, the vibrations of the ether that are perpendicular to the
plane of incidence will be retarded a quarter of a vibration, which
causes the vibrating particles to describe circles, and the succession
of such vibrating particles throughout the extent of a wave to form
altogether a circular helix, or curve like a corkscrew. However, that
only happens when the plane of polarization is inclined at an angle of
45° to the plane of incidence. When these two planes form an angle
either greater or less, the succession of vibrating particles forms an
elliptical helix, which curve may be represented by twisting a thread in
a spiral about an oval rod. These curves will turn to the right or left,
according to the position of the incident plane.

The motion of the ethereal medium in elliptical and circular
polarization may be represented by the analogy of a stretched cord; for,
if the extremity of such a cord be agitated at equal and regular
intervals by a vibratory motion entirely confined to one plane, the cord
will be thrown into an undulating curve lying wholly in that plane. If
to this motion there be superadded another similar and equal, but
perpendicular to the first, the cord will assume the form of an
elliptical helix; its extremity will describe an ellipse, and every
molecule throughout its length will successively do the same. But, if
the second system of vibrations commence exactly a quarter of an
undulation later than the first, the cord will take the form of a
circular helix or corkscrew, the extremity will move uniformly in a
circle, and every molecule throughout the cord will do the same in
succession. It appears, therefore, that both circular and elliptical
polarization may be produced by the composition of the motions of two
rays in which the particles of ether vibrate in planes at right angles
to one another.

Professor Airy, in a very profound and able paper published in the
Cambridge Transactions, has proved that all the different kinds of
polarized light are obtained from rock crystal. When polarized light is
transmitted through the axis of a crystal of quartz, in the emergent ray
the particles of ether move in a circular helix; and when it is
transmitted obliquely so as to form an angle with the axis of the prism,
the particles of ether move in an elliptical helix, the ellipticity
increasing with the obliquity of the incident ray; so that, when the
incident ray falls perpendicularly to the axis, the particles of ether
move in a straight line. Thus quartz exhibits every variety of
elliptical polarization, even including the extreme cases where the
excentricity is zero, or equal to the greater axis of the ellipse
(N. 215). In many crystals the two rays are so little separated, that it
is only from the nature of the transmitted light that they are known to
have the property of double refraction. M. Fresnel discovered, by
experiments on the properties of light passing through the axis of
quartz, that it consists of two superposed rays, moving with different
velocities; and Professor Airy has shown that in these two rays the
molecules of ether vibrate in similar ellipses at right angles to each
other, but in different directions; that their ellipticity varies with
the angle which the incident ray makes with the axis; and that, by the
composition of their motions, they produce all the phenomena of
polarized light observed in quartz.

It appears, from what has been said, that the molecules of ether always
perform their vibrations at right angles to the direction of the ray,
but very differently in the various kinds of light. In natural light the
vibrations are rectilinear, and in every plane. In ordinary polarized
light they are rectilinear, but confined to one plane; in circular
polarization the vibrations are circular; and in elliptical polarization
the molecules vibrate in ellipses. These vibrations are communicated
from molecule to molecule, in straight lines when they are rectilinear,
in a circular helix when they are circular, and in an oval or elliptical
helix when elliptical.

Some fluids possess the property of circular polarization naturally, as
oil of turpentine, the essential oils of laurel and lemon, sugar of
grapes, and various liquids.

Elliptical polarization is produced by reflection from metallic
surfaces. Mr. Baden Powell discovered it also in the light reflected
from China ink, chromate of lead, plumbago, &c. Mr. Airy observed that
the light reflected from the diamond is elliptically polarized; and Mr.
Jamin has shown that this kind of polarization is generally produced by
reflection from almost all transparent bodies, whatever their refractive
power may be, especially from glass at angles very little different from
the law of the tangents.

Water polarizes light circularly when between the points of maximum
density and solidification; hence it becomes crystalline.

The coloured images from polarized light arise from the interference of
the rays (N. 216). MM. Fresnel and Arago found that two rays of
polarized light interfere and produce coloured fringes if they be
polarized in the same plane, but that they do not interfere when
polarized in different planes. In all intermediate positions, fringes of
intermediate brightness are produced. The analogy of a stretched cord
will show how this happens. Suppose the cord to be moved backwards and
forwards horizontally at equal intervals; it will be thrown into an
undulating curve lying all in one plane. If to this motion there be
superadded another similar and equal, commencing exactly half an
undulation later than the first, it is evident that the direct motion
every molecule will assume, in consequence of the first system of waves,
will at every instant be exactly neutralized by the retrograde motion it
would take in virtue of the second; and the cord itself will be
quiescent in consequence of the interference. But, if the second system
of waves be in a plane perpendicular to the first, the effect would only
be to twist the rope, so that no interference would take place. Rays
polarized at right angles to each other may subsequently be brought into
the same plane without acquiring the property of producing coloured
fringes; but, if they belong to a pencil the whole of which was
originally polarized in the same plane, they will interfere.

The manner in which the coloured images are formed may be conceived by
considering that, when polarized light passes through the optic axis of
a doubly refracting substance,—as mica, for example,—it is divided into
two pencils by the analyzing tourmaline; and, as one ray is absorbed,
there can be no interference. But, when polarized light passes through
the mica in any other direction, it is separated into two white rays,
and these are again divided into four pencils by the tourmaline, which
absorbs two of them; and the other two, being transmitted in the same
plane with different velocities, interfere and produce the coloured
phenomena. If the analysis be made with Iceland spar, the single ray
passing through the optic axis of the mica will be refracted into two
rays, polarized in different planes, and no interference will happen.
But, when two rays are transmitted by the mica, they will be separated
into four by the spar, two of which will interfere to form one image,
and the other two, by their interference, will produce the complementary
colours of the other image when the spar has revolved through 90°;
because, in such positions of the spar as produce the coloured images,
only two rays are visible at a time, the other two being reflected. When
the analysis is accomplished by reflection, if two rays are transmitted
by the mica, they are polarized in planes at right angles to each other.
And, if the plane of reflection of either of these rays be at right
angles to the plane of polarization, only one of them will be reflected,
and therefore no interference can take place; but in all other positions
of the analyzing plate both rays will be reflected in the same plane,
and consequently will produce coloured rings by their interference.

It is evident that a great deal of the light we see must be polarized,
since most bodies which have the power of reflecting or refracting light
also have the power of polarizing it. The blue light of the sky is
completely polarized at an angle of 74° from the sun in a plane passing
through his centre.

A constellation of talent almost unrivalled at any period in the history
of science has contributed to the theory of polarization, though the
original discovery of that property of light was accidental, and arose
from an occurrence which, like thousands of others, would have passed
unnoticed had it not happened to one of those rare minds capable of
drawing the most important inferences from circumstances apparently
trifling. In 1808, while M. Malus was accidentally viewing with a
doubly-refracting prism a brilliant sunset reflected from the windows of
the Luxembourg Palace in Paris, on turning the prism slowly round, he
was surprised to see a very great difference in the intensity of the two
images, the most refracted alternately changing from brightness to
obscurity at each quadrant of revolution. A phenomenon so unlooked for
induced him to investigate its cause, whence sprung one of the most
elegant and refined branches of physical optics.

Fluorescence, or the internal dispersion of light, though far from
possessing the beauty or extensive consequences of polarized light, is
scarcely less wonderful. A variety of substances, such as canary-glass,
a solution of sulphate of quinine, fluor-spar, and a great number of
organic substances, have the property of diminishing the refrangibility
of light by internal dispersion, consequently of increasing the length
of the waves, and lowering the colour in the prismatic scale; it is
therefore called degraded light, or fluorescence, because first
discovered in fluor-spar.

If a piece of glass coloured by cobalt be fixed in a hole in a
window-shutter of a dark room, a slab of white porcelain placed near it
will appear blue; but if the slab be viewed through a yellow glass
coloured by silver, it will appear to be almost quite black, because the
yellow glass absorbs all the rays transmitted by the blue glass. If,
however, a piece of canary-glass be laid on the slab while it is dark,
every part of the canary-glass will shine as if it were self-luminous,
and with so bright a light that anything written on the slab that was
invisible before may now be distinctly read. Such is the singular
phenomenon of internal dispersion, degraded light, or fluorescence. The
brightness is by no means due to phosphorescence, because the
canary-glass only shines when under the influence of the active or blue
rays, whereas phosphorescent bodies shine by their own light—the latter
has independent, the former dependent, emission; it is possible,
however, that a connexion may hereafter be traced between them.

It appears from the analytical investigation of this phenomenon that the
vibrations of the fluorescent substance are analogous to those of a
sonorous body, as a bell or musical cord, which give the fundamental
note and its harmonics. Now since there is a reciprocal action between
the molecules of matter and light, when the light of the sun is absorbed
by a substance capable of fluorescence, it puts the whole of its
molecules into vibrations the same as its own, analogous to the
fundamental note, while at the same time a certain number of molecules
take more rapid vibrations exactly like the harmonics. The latter form
new centres of light throughout the substance, which impart their
vibrations to the ethereal medium around, and constitute fluorescence or
degraded light. For example, in the experiment that has been described,
the blue light imparted its own vibrations to _all_ the molecules of the
canary-glass, and also more rapid vibrations to a certain number of
them. All of the blue rays were excluded by the yellow glass held before
the eye; but it was pervious to the rays emanating in more rapid
vibrations from the smaller number of molecules, which thus became
really new centres of light, different from the sun’s light, though
owing to it; the one celestial, the other terrestrial; and the latter
vibrations being more rapid than those of the blue light, their
refrangibility was less, and therefore their colour lower in the
prismatic scale. Mr. Power computed from his formulæ, that fluorescent
light is produced by undulations which are a major or minor third below
the pitch of the general vibration of the medium—that is to say, below
the vibrations which the whole molecules of the body most readily
assume.

Professor Stokes, of Cambridge, who made the preceding experiment, found
that the chemical rays from a point in the solar spectrum produced, in a
solution of the sulphate of quinine, light of a sky-blue colour, which
emanates in all directions from the liquid, and that this blue
fluorescent light contains, when analysed, all the rays of the spectrum;
hence he inferred that the dispersive power or fluorescence had lowered
the refrangibility of the chemical rays, so as to make them visible: and
Sir David Brewster observes that the new spectrum, of all colours into
which they were transformed, must possess the extraordinary property of
being a luminous spectrum, either without chemical rays or full of them.
The dispersion in the quinine solution is greatest near the surface, but
the blue emanation proceeds from every part of the liquid; and Sir John
Herschel, who discovered the fluorescent property in this liquid, and
gave it the name of epipolic light, found that the remainder of the
beam, when it issued from the solution, though not apparently different
from the incident white light, is yet so much changed in passing through
the liquid, that it is no longer capable of producing fluorescence,
though still capable of common dispersion. The blue light from the
solution of quinine, when examined, consisted of rays extending over a
great part of the spectrum.

By passing a sunbeam through a bluish kind of fluor-spar, Sir David
Brewster perceived that the blue colour is not superficial, as it
appears to be, but that some veins in the interior of the crystal
disperse blue light, others pink, and even white light; in short, he met
with fluorescence in such a variety of substances, that he concludes it
may prevail more or less in the greater number of solids and liquids.

Professor Draper, of New York, proved that the result is the same
whether the incident light be polarized or not, and that the dispersed
or degraded light is never polarized, but that it emanates in all
directions, as if the substance were self-luminous; he made experiments
with light from all parts of the solar spectrum, and with various
substances, and always found that the refrangibility of the incident ray
was diminished by internal dispersion, and that the colour was changed
to suit the new refrangibility. Professor Draper has also shown that the
law of action and reaction prevails in all the phenomena of the sunbeam,
as in every other department of nature; so that a beam cannot be
reflected, refracted, much less absorbed, without producing some change
upon the recipient medium; and Mr. Power proved analytically that the
solar rays can exercise no action upon any medium through which they are
transmitted, without being accompanied by a diminution of refraction. He
says, “The new light emanating from the fluorescent media is just like
any other light of the same prismatic composition. In its physical
properties it retains no trace of its parentage; it is of terrestrial
origin, and its colour depends simply on its new refrangibility, having
nothing to do with that of the producing rays, nor to the circumstance
of their belonging to the visible or invisible part of the spectrum.”
These phenomena can only be explained by the undulatory theory of light.




                             SECTION XXIII.

Objections to the Undulatory Theory, from a difference in the Action of
  Sound and Light under the same circumstances, removed—The Dispersion
  of Light according to the Undulatory Theory—Arago’s final proof that
  the Undulatory Theory is the Law of Nature.


THE numerous phenomena of periodical colours arising from the
interference of light, which do not admit of satisfactory explanation on
any other principle than the undulatory theory, are the strongest
arguments in favour of that hypothesis; and even cases which at one time
seemed unfavourable to that doctrine have proved upon investigation to
proceed from it alone. Such is the erroneous objection which has been
made, in consequence of a difference in the mode of action of light and
sound, under the same circumstances, in one particular instance. When a
ray of light from a luminous point, and a diverging sound, are both
transmitted through a very small hole into a dark room, the light goes
straight forward and illuminates a small spot on the opposite wall,
leaving the rest in darkness; whereas the sound on entering diverges in
all directions, and is heard in every part of the room. These phenomena,
however, instead of being at variance with the undulatory theory, are
direct consequences of it, arising from the very great difference
between the magnitude of the undulations of sound and those of light.
The undulations of light are incomparably less than the minute aperture,
while those of sound are much greater. Therefore when light, diverging
from a luminous point, enters the hole, the rays round its edges are
oblique, and consequently of different lengths, while those in the
centre are direct, and nearly or altogether of the same lengths. So that
the small undulations between the centre and the edges are in different
phases, that is, in different states of undulation. Therefore the
greater number of them interfere, and by destroying one another produce
darkness all around the edges of the aperture; whereas the central rays,
having the same phases, combine, and produce a spot of bright light on a
wall or screen directly opposite the hole. The waves of air producing
sound, on the contrary, being very large compared with the hole, do not
sensibly diverge in passing through it, and are therefore all so nearly
of the same length, and consequently in the same phase or state of
undulation, that none of them interfere sufficiently to destroy one
another. Hence all the particles of air in the room are set into a state
of vibration, so that the intensity of the sound is very nearly
everywhere the same. Strong as the preceding cases may be, the following
experiment, made by M. Arago, seems to be decisive in favour of the
undulatory doctrine. Suppose a plano-convex lens of very great radius to
be placed upon a plate of very highly polished metal. When a ray of
polarized light falls upon this apparatus at a very great angle of
incidence, Newton’s rings are seen at the point of contact. But as the
polarizing angle of glass differs from that of metal, when the light
falls on the lens at the polarizing angle of glass, the black spot and
the system of rings vanish. For although light in abundance continues to
be reflected from the surface of the metal, not a ray is reflected from
the surface of the glass that is in contact with it, consequently no
interference can take place; which proves beyond a doubt that Newton’s
rings result from the interference of the light reflected from both the
surfaces apparently in contact (N. 199).

Notwithstanding the successful adaptation of the undulatory system to
phenomena, the dispersion of light for a long time offered a formidable
objection to that theory, which has been removed by Professor Powell of
Oxford.

A sunbeam falling on a prism, instead of being refracted to a single
point of white light, is separated into its component colours, which are
dispersed or scattered unequally over a considerable space, of which the
portion occupied by the red rays is the least, and that over which the
violet rays are dispersed is the greatest. Thus the rays of the coloured
spectrum, whose waves are of different lengths, have different degrees
of refrangibility, and consequently move with different velocities,
either in the medium which conveys the light from the sun, or in the
refracting medium, or in both; whereas rays of all colours come from the
sun to the earth with the same velocity. If, indeed, the velocities of
the various rays were different in space, the aberration of the fixed
stars, which is inversely as the velocity, would be different for
different colours, and every star would appear as a spectrum whose
length would be parallel to the direction of the earth’s motion, which
is not found to agree with observation. Besides, there is no such
difference in the velocities of the long and short waves of air in the
analogous case of sound, since notes of the lowest and highest pitch are
heard in the order in which they are struck. In fact, when the sunbeam
passes from air into the prism, its velocity is diminished; and, as its
refraction, and consequently its dispersion, depend solely upon the
diminished velocity of the transmission of its waves, they ought to be
the same for waves of all lengths, unless a connexion exists between the
length of a wave and the velocity with which it is propagated. Now, this
connexion between the length of a wave of any colour, and its velocity
or refrangibility in a given medium, has been deduced by Professor
Powell from M. Cauchy’s investigations of the properties of light on a
peculiar modification of the undulatory hypothesis. Hence the
refrangibility of the various coloured rays, computed from this relation
for any given medium, when compared with their refrangibility in the
same medium determined by actual observation, will show whether the
dispersion of light comes under the laws of that theory. But, in order
to accomplish this, it is clear that the length of the waves should be
found independently of refraction, and a very beautiful discovery of M.
Fraunhofer furnishes the means of doing so.

That philosopher obtained a perfectly pure and complete coloured
spectrum, with all its dark and bright lines, by the interference of
light alone, from a sunbeam passing through a series of fine parallel
wires covering the object glass of a telescope. In this spectrum, formed
independently of prismatic refraction, the positions of the coloured
rays depend only on the lengths of their waves, and M. Fraunhofer found
that the intervals between them are precisely proportional to the
differences of these lengths. He measured the lengths of the waves of
the different colours at seven fixed points, determined by seven of the
principal dark and bright lines. Professor Powell, availing himself of
these measures, has made the requisite computations, and has found that
the coincidence of theory with observation is perfect for ten substances
whose refrangibility had been previously determined by the direct
measurements of M. Fraunhofer, and for ten others whose refrangibility
has more recently been ascertained by M. Rudberg. Thus, in the case of
seven rays in each of twenty different substances, solid and fluid, the
dispersion of light takes place according to the laws of the undulatory
theory: and there can hardly be a doubt that dispersion in all other
bodies will be found to follow the same law. It is, however, an express
condition of the connexion between the velocity of light and the length
of its undulations, that the intervals between the vibrating molecules
of the ethereal fluid should bear a sensible relation to the length of
an undulation. The coincidence of the computed with the observed
refractions shows that this condition is fulfilled within the refracting
media; but the aberration of the fixed stars leads to the inference that
it does not hold in the ethereal regions, where the velocities of the
rays of all colours are the same. Strong as all that precedes is in
favour of the undulatory theory, the relative velocity of light in air
and water is the final and decisive proof. By the Newtonian theory the
velocity is greater in water than in air, by the undulatory theory it is
less; hence if a comparison could be made it would decide which is the
law of nature. The difficulty consisted in comparing the velocity of
light passing through a small extent of water with the velocity of light
in air, which is 10,000 times greater than the velocity of the earth in
its orbit. This delicate and difficult experiment was made by means of
an instrument invented by Professor Wheatstone for measuring the
velocity of electricity. It consists of a small mirror which revolves in
its own plane like a coin spinning on its edge. When it revolves very
rapidly the reflected image of an object changes its place perceptibly
in an inconceivably small fraction of a second. The mirrors used in the
experiment were made to revolve more than 1000 times in a second, by
which means the places of the two images—one from light passing through
air, and the other from light passing through an equal length of
water—were found to be such as to prove that the velocity of light in
air and in water is as 4 to 3, while by the Newtonian theory it is as 3
to 4. By this final and decisive proof the undulatory theory may from
henceforth be regarded as the law of nature. This experiment was
accomplished by M. Fizeau and M. Léon-Faucault, at the suggestion of M.
Arago, whose eyesight did not permit him to undertake it himself.




                             SECTION XXIV.

Chemical or Photographic Rays of Solar Spectrum—Scheele, Ritter, and
  Wollaston’s Discoveries—Wedgwood’s and Sir Humphry Davy’s Photographic
  Pictures—The Calotype—The Daguerreotype—The Chromatype—The
  Cyanotype—Collodion—Sir John Herschel’s Discoveries in the Chemical
  Spectrum—M. Becquerel’s Discoveries of Inactive Lines in ditto—Thermic
  Spectrum—Phosphoric Spectrum—Electrical Properties—Parathermic
  Rays—Moser and Hunt’s Experiments—General Structure and antagonist
  Properties of Solar Spectrum—Defracted Spectrum.


THE Solar Spectrum exercises an energetic action on matter, producing
the most wonderful and mysterious changes on the organised and
unorganised creation.

All bodies are probably affected by light, but it acts with greatest
energy on such as are of weak chemical affinity, imparting properties to
them which they did not possess before. Collodion and metallic salts,
especially those of silver, whose molecules are held together by an
unstable equilibrium, are of all bodies the most susceptible of its
influence; the effects, however, vary with the substances employed, and
with the different rays of the solar spectrum, the chemical properties
of which are by no means alike. As early as 1772 M. Scheele showed that
the pure white colour of chloride of silver was rapidly darkened by the
blue rays of the solar spectrum, while the red rays had no effect upon
it: and in 1801 M. Ritter discovered that invisible rays beyond the
violet extremity have the property of blackening argentine salts, that
this property diminishes towards the less refrangible part of the
spectrum, and that the red rays have an opposite quality, that of
restoring the blackened salt of silver to its original purity; from
which he inferred that the most refrangible extremity of the spectrum
has an oxygenising power, and the other that of deoxygenating. Dr.
Wollaston found that gum guaiacum acquires a green colour in the violet
and blue rays, and resumes its original tint in the red. No attempt had
been made to trace natural objects by means of light reflected from
them, till Mr. Wedgwood, together with Sir Humphry Davy, took up the
subject: they produced profiles and tracings of objects on surfaces
prepared with nitrate and chloride of silver, but they did not succeed
in rendering their pictures permanent. This difficulty was overcome in
1814 by M. Niepcé, who produced a permanent picture of surrounding
objects by placing in the focus of a camera-obscura a metallic plate
covered with a film of asphalt dissolved in oil of lavender.

Mr. Fox Talbot, without any knowledge of M. Niepcé’s experiments, had
been engaged in the same pursuit, and must be regarded as an independent
inventor of photography, one of the most beautiful arts of modern times:
he was the first who succeeded in using paper chemically prepared for
receiving impressions from natural objects; and he also discovered a
method of fixing permanently the impressions—that is, of rendering the
paper insensible to any further action of light. In the calotype, one of
Mr. Talbot’s applications of the art, the photographic surface is
prepared by washing smooth writing-paper, first with a solution of
nitrate of silver, then with bromide of potassium, and again with
nitrate of silver, drying it at a fire after each washing; the paper is
thus rendered so sensitive to light that even the passage of a thin
cloud is perceptible on it, consequently it must be prepared by
candle-light. Portraits, buildings, insects, leaves of plants—in short,
every object is accurately delineated in a few seconds; and in the focus
of a camera-obscura the most minute objects are so exactly depicted that
the microscope reveals new beauties.

Since the effect of the chemical agency of light is to destroy the
affinity between the salt and the silver, Mr. Talbot found that, in
order to render these impressions permanent on paper, it was only
necessary to wash it with salt and water, or with a solution of iodide
of potassium. For these liquids the liquid hyposulphites have been
advantageously substituted, which are the most efficacious in dissolving
and removing the unchanged salt, leaving the reduced silver on the
paper. The calotype picture is negative, that is, the lights and shadows
are the reverse of what they are in nature, and the right-hand side in
nature is the left in the picture; but if it be placed with its face
pressed against photographic paper, between a board and a plate of
glass, and exposed to the sun a short time, a positive and direct
picture, as it is in nature, is formed: engravings may be exactly copied
by this simple process, and a direct picture may be produced at once by
using photographic paper already made brown by exposure to light.

While Mr. Fox Talbot was engaged in these very elegant discoveries in
England, M. Daguerre had brought to perfection and made public that
admirable process by which he has compelled Nature permanently to
engrave her own works; and thus the talents of France and England have
been combined in bringing to perfection this useful art. Copper, plated
with silver, was successfully employed by M. Daguerre for copying nature
by the agency of light. The surface of the plate is converted into an
iodide of silver, by placing it horizontally with its face downwards in
a covered box, in the bottom of which there is a small quantity of
iodine which evaporates spontaneously. In three or four minutes the
surface acquires a yellow tint, and then, screening it carefully from
light, it must be placed in the focus of a camera obscura, where an
invisible image of external objects will be impressed on it in a few
minutes. When taken out, the plate must be exposed in another box to the
action of mercurial vapour, which attaches itself to those parts of the
plate which had been exposed to light, but does not adhere to such parts
as had been in shadow; and as the quantity of mercury over the other
parts is in exact proportion to the degree of illumination, the shading
of the picture is perfect. The image is fixed, first by removing the
iodine from the plate by plunging it into hyposulphite of soda, and then
washing it in distilled water; by this process the yellow colour is
destroyed, and in order to render the mercury permanent, the plate must
be exposed a few minutes to nitric vapour, then placed in nitric acid
containing copper or silver in solution at a temperature of 61-1/4° of
Fahrenheit for a short time, and lastly polished with chalk. This final
part of the process is due to Dr. Berre, of Vienna.

Nothing can be more beautiful than the shading of these chiaroscuro
pictures when objects are at rest, but the least motion destroys the
effect; the method therefore is more applicable to buildings than
landscape. Colour is wanting; but the researches of Sir John Herschel
give reason to believe that even this will ultimately be attained.

The most perfect impressions of seaweeds, leaves of plants, feathers,
&c., may be formed by bringing the object into close contact with a
sheet of photographic paper, between a board and plate of glass; then
exposing the whole to the sun for a short time, and afterwards fixing it
by the process described. The colours of the pictures vary with the
preparation of the paper, by which almost any tint may be produced.

In the chromatype, a peculiar photograph discovered by Mr. Hunt,
chromate of copper is used, on which a dark brown negative image is
first formed, but by the continued action of light it is changed to a
positive yellow picture on a white ground; the farther effect of light
is checked by washing the picture in pure water.

In cyanotypes, a class of photographs discovered by Sir John Herschel,
in which cyanogen in its combinations with iron forms the ground, the
pictures are Prussian blue and white. In the chrysotype of the same
eminent philosopher, the image is first received on paper prepared with
the ammonia-citrate of iron, and afterwards washed with a neutral
solution of gold. It is fixed by water acidulated with sulphuric acid,
and lastly by hydriodate of potash, from which a white and purple
photograph results. It is vain to attempt to describe the various
beautiful effects which Sir John Herschel obtained from chemical
compounds, and from the juices of plants; the juice of the red poppy
gives a positive bluish purple image, that of the ten-week stock a fine
rose colour on a pale straw-coloured ground.

Pictures may be made by exposure to sunshine, on all compound substances
having a weak chemical affinity; but the image is often invisible, as in
the Daguerreotype, till brought out by washing in some chemical
preparation. Water is frequently sufficient; indeed Sir John Herschel
brought out dormant photographs by breathing on them, and some
substances are insensible to the action of light till moistened, as for
example, gum guaiacum. Argentine papers, however, are little subject to
the influence of moisture. The power of the solar rays is augmented in
certain cases by placing a plate of glass in close contact over the
sensitive surface.

All these various experiments, though highly interesting, have now been
superseded. It was found that paper did not always answer for
photography, on account of imperfections in its structure; silver plates
were too expensive; and glass was found to be unimpressable.
Nevertheless, M. Niepcé de Victor obtained beautiful results upon glass
coated with albumen mixed with sensitive substances, which suggested the
medium by means of which the art has been brought to its present
perfection, and that final step is due to Mr. Scott Archer. He coated a
plate of glass thinly with collodion, that is, gun-cotton dissolved in
ether and alcohol, which dries into a delicate transparent film of
extreme adhesiveness, and of such intense sensibility that the action of
light upon it is so instantaneous that it arrests a stormy sea or a
fleeting cloud before they have time to change. Now landscapes in
chiaroscuro are produced of great beauty, which by the slower methods
were mere masses of deep shade and broad light. Architecture is even
more perfectly obtained, but it fails to give a pleasing representation
of the human countenance.

Chemical action always accompanies the sun’s light, but the analysis of
the solar spectrum has partly disclosed the wonderful nature of the
emanation. In the research, properties most important and unexpected
have been discovered by Sir John Herschel, who imprints the stamp of
genius on all he touches—his eloquent papers can alone convey an
adequate idea of their value in opening a field of inquiry vast and
untrodden. The following brief and imperfect account of his experiments
is all that can be attempted here:—

A certain degree of chemical energy is distributed through every part of
the solar spectrum, and also to a considerable extent through the dark
spaces at each extremity. This distribution does not depend on the
refrangibility of the rays alone, but also on the nature of the rays
themselves, and on the physical properties of the analyzing medium on
which the rays are received, whose changes indicate and measure their
action. The length of the photographic image of the _same_ solar
spectrum varies with the physical qualities of the surface on which it
is impressed. When the solar spectrum is received on paper prepared with
bromide of silver, the chemical spectrum, as indicated merely by the
length of the darkened part, includes within its limits the whole
luminous spectrum, extending in one direction far beyond the extreme
violet and lavender rays, and in the other down to the extremest red:
with tartrate of silver the darkening occupies not only all the space
under the most refrangible rays, but reaches much beyond the extreme
red. On paper prepared with formobenzoate of silver the chemical
spectrum is cut off at the orange rays, with phosphate of silver in the
yellow, and with chloride of gold it terminates with the green, with
carbonate of mercury it ends in the blue, and on paper prepared with the
percyanide of gold, ammonia, and nitrate of silver, the darkening lies
entirely beyond the visible spectrum at its most refrangible extremity,
and is only half its length, whereas in some cases chemical action
occupies a space more than twice the length of the luminous image.

The point of maximum energy of chemical action varies as much for
different preparations as the scale of action. In the greater number of
cases the point of deepest blackening lies about the lower edge of the
indigo rays, though in no two cases is it exactly the same, and in many
substances it is widely different. On paper prepared with the juice of
the ten-week stock (Mathiola annua) there are two maxima, one in the
mean yellow and a weaker in the violet; and on a preparation of tartrate
of silver Sir John Herschel found three, one in the least refrangible
blue, one in the indigo, and a third beyond the visible violet. The
decrease in photographic energy is seldom perfectly alike on both sides
of the maximum. Thus at the most refrangible end of the solar spectrum
the greatest chemical power is exerted in most instances where there is
least light and heat, and even in the space where both sensibly cease.

Not only the intensity but the kind of action is different in the
different points of the solar spectrum, as evidently appears from the
various colours that are frequently impressed on the same analyzing
surface, each ray having a tendency to impart its own colour. Sir John
Herschel obtained a coloured image of the solar spectrum on paper
prepared according to Mr. Talbot’s principle, from a sunbeam refracted
by a glass prism and then highly condensed by a lens. The photographic
image was rapidly formed and very intense, and, when withdrawn from the
spectrum and viewed in common daylight, it was found to be coloured with
sombre but unequivocal tints imitating the prismatic colours, which
varied gradually from red through green and blue to a purplish black.
After washing the surface in water, the tints became more decided by
being kept a few days in the dark—a phenomenon, Sir John observes, of
constant occurrence, whatever be the preparation of the paper, provided
colours are produced at all. He also obtained a coloured image on
nitrate of silver, the part under the blue rays becoming a blue brown,
while that under the violet had a pinkish shade, and sometimes green
appeared at the point corresponding to the least refrangible blue. Mr.
Hunt found on a paper prepared with fluoride of silver that a yellow
line was impressed on the space occupied by the yellow rays, a green
band on the space under the green rays, an intense blue throughout the
space on which the blue and indigo rays fell, and under the violet rays
a ruddy brown appeared; these colours remained clear and distinct after
being kept two months.

Notwithstanding the great variety in the scale of action of the solar
spectrum, the darkening or deoxydizing principle that prevails in the
more refrangible part rarely surpasses or even attains the mean yellow
ray which is the point of maximum illumination; it is generally cut off
abruptly at that point which seems to form a limit between the opposing
powers which prevail at the two ends of the spectrum. The bleaching or
oxydizing effect of the red rays on blackened muriate of silver
discovered by M. Ritter of Jena, and the restoration by the same rays of
discoloured gum guaiacum to its original tint by Dr. Wollaston, have
already been mentioned as giving the first indications of that
difference in the mode of action of the chemical rays at the two ends of
the visible spectrum, now placed beyond a doubt.

The action exerted by the less refrangible rays beyond and at the red
extremity of the solar spectrum, in most instances, so far from
blackening metallic salts, protects them from the action of the diffused
daylight: but, if the prepared surface has already been blackened by
exposure to the sun, they possess the remarkable property of bleaching
it in some cases, and under other circumstances of changing the black
surface into a fiery red.

Sir John Herschel, to whom we owe most of our knowledge of the
properties of the chemical spectrum, prepared a sheet of paper by
washing it with muriate of ammonia, and then with two coats of nitrate
of silver; on this surface he obtained an impression of the solar
spectrum exhibiting a range of colours very nearly corresponding with
its natural hues. But a very remarkable phenomenon occurred at the end
of least refrangibility; the red rays exerted a protecting influence
which preserved the paper from the change which it would otherwise have
undergone from the deoxydizing influence of the dispersed light which
always surrounds the solar spectrum, and this maintained its whiteness.
Sir John met with another instance on paper prepared with bromide of
silver, on which the whole of the space occupied by the visible spectrum
was darkened down to the very extremity of the red rays, but an
oxydizing action commenced beyond the extreme red, which maintained the
whiteness of the paper to a considerable distance beyond the last
traceable limit of the visible rays, thus evincing decidedly the
existence of some chemical power over a considerable space beyond the
least refrangible end of the spectrum. Mr. Hunt also found that on the
Daguerreotype plate a powerful protecting influence is exercised by the
extreme red rays. In these cases the red and those dark rays beyond them
exert an action of an opposite nature to that of the violet and lavender
rays.

The least refrangible part of the solar spectrum possesses also, under
certain circumstances, a bleaching property, by which the metallic salts
are restored to their original whiteness after being blackened by
exposure to common daylight, or to the most refrangible rays of the
solar spectrum.

Paper prepared with iodide of silver, when washed over with ferrocyanite
of potash, blackens rapidly when exposed to the solar spectrum. It
begins in the violet rays and extends over all the space occupied by the
dark chemical rays, and over the whole visible spectrum down to the
extreme red rays. This image is coloured, the red rays giving a reddish
tint and the blue a blueish. In a short time a bleaching process begins
under the red rays, and extends upwards to the green, but the space
occupied by the extreme red is maintained perfectly dark. Mr. Hunt found
that a similar bleaching power is exerted by the red rays on paper
prepared with protocyanide of potassium and gold with a wash of nitrate
of silver.

The application of a moderately strong hydriodate of potash to darkened
photographic paper renders it peculiarly susceptible of being whitened
by further exposure to light. If paper prepared with bromide of silver
be washed with ferrocyanate of potash while under the influence of the
solar spectrum, it is immediately darkened throughout the part exposed
to the visible rays down to the end of the red, some slight interference
being perceptible about the region of the orange and yellow. After this
a bleaching action begins over the part occupied by the red rays, which
extends to the green. By longer exposure an oval spot begins again to
darken about the centre of the bleached space; but, if the paper receive
another wash of the hydriodate of potash, the bleaching action extends
up from the green, over the region occupied by the most refrangible rays
and considerably beyond them, thus inducing a negative action in the
most refrangible part of the spectrum.

In certain circumstances the red rays, instead of restoring darkened
photographic paper to its original whiteness, produce a deep red colour.
When Sir John Herschel received the spectrum on paper somewhat
discoloured by exposure to direct sunshine, instead of whiteness, a red
border was formed extending from the space occupied by the orange, and
nearly covering that on which the red fell. When, instead of exposing
the paper in the first instance to direct sunshine, it was blackened by
the violet rays of a prismatic spectrum, or by a sunbeam that had
undergone the absorptive action of a solution of ammonia-sulphate of
copper, the red rays of the condensed spectrum produced on it, not
whiteness, but a full and fiery red, which occupied the whole space on
which any of the visible red rays had fallen; and this red remained
unchanged, however long the paper remained exposed to the least
refrangible rays.

Sunlight transmitted through red glass produces the same effect as the
red rays of the spectrum in the foregoing experiment. Sir John Herschel
placed an engraving over a paper blackened by exposure to sunshine,
covering the whole with a dark red-brown glass previously ascertained to
absorb every ray beyond the orange: in this way a photographic copy was
obtained in which the shades were black, as in the original engraving;
but the lights, instead of being white, were of the red colour of venous
blood, and no other colour could be obtained by exposure to light,
however long. Sir John ascertained that every part of the spectrum
impressed by the more refrangible rays is equally reddened, or nearly
so, by the subsequent action of the less refrangible; thus the red rays
have the very remarkable property of assimilating to their own colour
the blackness already impressed on photographic paper.

That there is a deoxydating property in the more refrangible rays, and
an oxydating action in the less refrangible part of the spectrum, is
manifest from the blackening of one and the bleaching effect of the
other; but the peculiar action of the red rays in the experiments
mentioned shows that some other principle exists different from
contrariety of action. These opposite qualities are balanced or
neutralized in the region of the mean yellow ray. But, although this is
the general character of the photographic spectrum, under certain
circumstances even the red rays have a deoxydating power, while the blue
and violet exert a contrary influence; but these are rare exceptions.

The photographic action of the two portions of the solar spectrum being
so different, Sir John Herschel tried the effect of their united action
by superposing the less refrangible part of the spectrum over the more
refrangible portion by means of two prisms; and he thus discovered that
two rays of different refrangibility, and therefore of different lengths
of undulation, acting simultaneously, produce an effect which neither,
acting separately, can do.

Some circumstances that occurred during the analysis of the chemical
spectrum seem to indicate an absorptive action in the sun’s atmosphere.
The spectral image impressed on paper prepared with nitrate of silver
and Rochelle salt commenced at, or very little below, the mean yellow
ray, of a delicate lead colour; and when the action was arrested, such
was the character of the whole photographic spectrum. But, when the
light of the solar spectrum was allowed to continue its action, there
was observed to come on suddenly a new and much more intense impression
of darkness, confined in length to the blue and violet rays; and, what
is most remarkable, confined also in breadth to the middle of the sun’s
image, so far at least as to leave a border of the lead-coloured
spectrum traceable, not only round the clear and well-defined convexity
of the dark interior spectrum at the less refrangible end, but also
laterally along both its edges; and this border was the more easily
traced, and less liable to be mistaken, from its striking contrast of
colour with the interior spectrum, the former being lead gray, the
latter an extremely rich deep velvety brown. The less refrangible end of
this interior brown spectrum presented a sharply terminated and
regularly elliptical contour, the more refrangible a less decided one.
“It may seem too hazardous,” Sir John continues, “to look for the cause
of this very singular phenomenon in a real difference between the
chemical agencies of those rays which issue from the central portion of
the sun’s disc, and those which, emanating from its borders, have
undergone the absorptive action of a much greater depth of its
atmosphere; and yet I confess myself somewhat at a loss what other cause
to assign for it. It must suffice, however, to have thrown out the hint,
remarking only, that I have other, and I am disposed to think decisive,
evidence of the existence of an absorptive solar atmosphere extending
beyond the luminous one.” M. Arago observed that the rays from the
centre of the sun have a greater photographic power than those from the
edges, and the photographic images of the sun, taken on glass by M.
Niepcé, were blood-red, much deeper in the centre, and on one occasion
the image was surrounded by an auriol. Several circumstances concur in
showing that there are influences also concerned in the transmission of
the photographic action which have not yet been explained, as, for
example, the influence which the time of the day exercises on the
rapidity with which photographic impressions are made, the sun being
much less effective two hours after passing the meridian than two hours
before. There is also reason to suspect that the effect in some way
depends on the latitude, since a much longer time is required to obtain
an image under the bright skies of the tropics than in England; and it
is even probable that there is a difference in the sun’s light in high
and low latitudes, because an image of the solar spectrum, obtained on a
Daguerreotype plate in Virginia, by Dr. Draper, differed from a spectral
image obtained by Mr. Hunt on a similar plate in England. The inactive
spaces discovered in the photographic spectrum by M. E. Becquerel,
similar to those in the luminous spectrum, and coinciding with them, is
also a phenomenon of which no explanation has yet been given; possibly
the chemical rays may be absorbed by the atmosphere with those of light.
Although chemical action extends over the whole luminous spectrum, and
much beyond it, in gradations of more or less intensity, it is found by
careful investigation to be by no means continuous; numerous inactive
lines cross it, coinciding with those in the luminous image as far as it
extends; besides, a very great number exist in the portions that are
obscure, and which overlap the visible part. There are three
extraspectral lines beyond the red, and some strongly marked groups on
the obscure part beyond the violet; but the whole number of those
inactive lines, especially in the dark spaces, is so great that it is
impossible to count them.

Notwithstanding this coincidence in the inactive lines of the two
spectra, photographic energy is independent of both light and heat,
since it exerts the most powerful influence in those rays where they are
least, and also in spaces where neither sensibly exist; but the
transmission of the sun’s light through coloured media makes that
independence quite evident. Heat and light pass abundantly through
yellow glass, or a solution of chromate of potash; but the greater part
of the chemical rays are excluded, and chlorine gas diluted with common
air, though highly pervious to the luminous and calorific principles,
has the same effect. Sir John Herschel found that a slight degree of
yellow London fog had a similar effect with that of pale yellow media:
he also remarked that a weak solution of azolitmine in potash, which
admits a great quantity of green light, excludes chemical action; and
some years ago the author, while making experiments on the transmission
of chemical rays, observed that green glass, coloured by oxide of copper
about the 20th of an inch thick, excludes the photographic rays; and, as
M. Melloni has shown that substance to be impervious to the most
refrangible calorific rays, it has the property of excluding the whole
of the most refrangible part of the solar spectrum, visible and
invisible. Green mica, if not too thin, has also the same effect,
whereas amethyst, deep blue, and violet-coloured glasses, though they
transmit a very little light, allow the chemical rays to pass freely.
Thus light and photographic energy may be regarded as distinct parts of
the solar beam, and both being propagated by vibrations of the etherial
medium they are merely motion. Excellent images have been obtained of
the moon in its different phases by Professor Secchi, at Rome;
candlelight is nearly deficient of the chemical rays. How far they may
influence crystallization and other molecular arrangements is unknown,
but their power is universal wherever the solar beam falls, although
their effect only becomes evident in cases of unstable molecular
equilibrium.

It is not by vision alone that a knowledge of the sun’s rays is
acquired: touch proves that they have the power of raising the
temperature of substances exposed to their action. Sir William Herschel
discovered that rays which produce the sensation of heat exist in the
solar spectrum independent of those of light; when he used a prism of
flint glass, he found that the warm rays are most abundant in the dark
space a little beyond the red extremity of the spectrum, that from
thence they decrease towards the violet, beyond which they are
insensible. It may be concluded therefore, that the calorific rays vary
in refrangibility, and that those beyond the extreme red are less
refrangible than any rays of light. Since Sir William Herschel’s time it
has been discovered that the calorific spectrum exceeds the luminous one
in length in the ratio of 42 to 25, but the most singular phenomenon is
its want of continuity. Sir John Herschel blackened the under side of a
sheet of very thin white paper by the smoke of a lamp, and, having
exposed the white side to the solar spectrum, he drew a brush dipped in
spirit of wine over it, by which the paper assumed a black hue when
sufficiently saturated. The heat in the spectrum evaporated the spirit
first on those parts of the paper where it fell with greatest intensity,
thereby restoring their white colour, and he thus discovered that the
heat increases uniformly and gradually throughout the luminous spectrum,
and that it comes to a maximum and forms a spot at a considerable
distance beyond the extreme red. It then decreases, but again increasing
it forms a second maximum spot, after which it ceases altogether through
a short space, but is again renewed and forms two more insulated spots,
and even a fifth may be traced at a little distance from the latter.
These circumstances are probably owing to the absorbing action of the
atmospheres of the sun and earth. “The effect of the former,” says Sir
John, “is beyond our control, unless we could carry our experiments to
such a point of delicacy as to operate separately on rays emanating from
the centre and borders of the sun’s disc; that of the earth’s, though it
cannot be eliminated any more than in the case of the sun’s, may yet be
varied to a considerable extent by experiments made at great elevations,
under a vertical sun, and compared with others where the sun is more
oblique, the situation lower, and the atmospheric pressure of a
temporarily high amount. Should it be found that this cause is in
reality concerned in the production of the spots, we should see reason
to believe that a large portion of solar heat never reaches the earth’s
surface, and that what is incident on the summits of lofty mountains
differs not only in quantity but also in quality from what the plains
receive.”

A remarkable phosphorescent property was discovered by M. E. Becquerel
in the solar spectrum. Two luminous bands separated by a dark one are
excited by the solar spectrum on paper covered with a solution of gum
arabic, and strewed with powdered sulphuret of calcium or Canton’s
phosphorus. One of the luminous bands occupies the space under the least
refrangible violet rays, and the other that beyond the lavender rays, so
that the dark band lies under the extreme violet and lavender rays. When
the action of the light is continued, the whole surface beyond the least
refrangible violet shines, the luminous bands already mentioned
brightest; but all the space from the least refrangible violet to the
extreme red remains dark. If the surface, prepared either with the
sulphuret of calcium or Bologna stone, be exposed to the sun’s light for
a little time, it becomes luminous all over; but when, in this state, a
solar spectrum is thrown upon it, the whole remains luminous except the
part from the least refrangible violet to the extreme red, on which
space the light is extinguished; and when the temperature of the surface
is raised by a lamp, the bright parts become more luminous and the dark
parts remain dark. Glass stained by the protoxide of copper, which
transmits only the red and orange rays, has the same effect with the
less refrangible part of the spectrum; hence there can be no doubt that
the most refrangible and obscure rays of the spectrum excite
phosphorescence, while all the less refrangible rays of light and heat
extinguish it.

Paper prepared with the sulphuret of barium, when under the solar
spectrum, shows only one space of maximum luminous intensity, and the
destroying rays are the same as in the sulphuret of calcium. Thus the
obscure rays beyond the extreme violet produce light, while the luminous
rays extinguish it.

The phosphoric spectrum has inactive lines which coincide with those in
the luminous and chemical spectra, at least as far as it extends; but in
order to be seen the spectrum must be received for a few seconds upon
the prepared surface through an aperture in a dark room, then the
aperture must be closed, and the temperature of the surface raised two
or three hundred degrees; the phosphorescent parts then shine
brilliantly and the dark lines appear black. Since the parts of similar
refrangibility in different spectra are traversed by the same dark
lines, rays of the same refrangibility are probably absorbed at the same
time by the different media through which they pass.

It appears from the experiments of MM. Becquerel and Biot, that
electrical disturbances produce these phosphorescent effects. There is
thus a mysterious connexion between the most refrangible rays and
electricity which the experiments of M. E. Becquerel confirm, showing
that electricity is developed during chemical action by the violet rays,
that it is feebly developed by the blue and indigo, but that none is
excited by the less refrangible part of the spectrum.

A series of experiments by Sir John Herschel have disclosed a new set of
obscure rays in the solar spectrum, which seem to bear the same relation
to those of heat that the photographic or chemical rays bear to the
luminous. They are situate in that part of the spectrum which is
occupied by the less refrangible visible colours, and have been named by
their discoverer Parathermic rays. It must be held in remembrance that
the region of greatest heat in the solar spectrum lies in the dark space
beyond the visible red. Now, Sir John Herschel found that in experiments
with a solution of gum guaiacum in soda, which gives the paper a green
colour, the green, yellow, orange, and red rays of the spectrum
invariably discharged the colour, while no effect was produced by the
extra-spectral rays of heat, which ought to have had the greatest effect
had heat been the cause of the phenomenon. When an aqueous solution of
chlorine was poured over a slip of paper prepared with gum guaiacum
dissolved in soda, a colour varying from a deep somewhat greenish hue to
a fine celestial blue was given to it; and, when the solar spectrum was
thrown on the paper while moist, the colour was discharged from all the
space under the less refrangible luminous rays, at the same time that
the more distant thermic rays beyond the spectrum evaporated the
moisture from the space on which they fell; so that the heat spots
became apparent. But the spots disappeared as the paper dried, leaving
the surface unchanged; while the photographic impression within the
visible spectrum increased in intensity; the non-luminous thermic rays,
though evidently active _as to heat_, were yet incapable of effecting
that peculiar chemical change which other rays of much less heating
power were all the time producing. Sir John having ascertained that an
artificial heat from 180° to 280° of Fahrenheit changed the green tint
of gum guaiacum to its original yellow hue when moist, but that it had
no effect when dry, he therefore tried whether heat from a hot iron
applied to the back of the paper used in the last-mentioned experiment
while under the influence of the solar spectrum might not assist the
action of the calorific rays; but, instead of doing so, it greatly
accelerated the discoloration over the spaces occupied by the less
refrangible rays, but had no effect on the extra-spectral region of
maximum heat. Obscure terrestrial heat, therefore, is capable of
assisting and being assisted in effecting this peculiar change by those
rays of the spectrum, whether luminous or thermic, which occupy its red,
yellow, and green regions; while, on the other hand, it receives no such
assistance from the purely thermic rays beyond the spectrum acting under
similar circumstances and in an equal state of condensation.

The conclusions drawn from these experiments are confirmed by that which
follows: a photographic picture formed on paper prepared with a mixture
of the solutions of ammonia-citrate of iron and ferro-sesquicyanite of
potash in equal parts, then thrown into water and afterwards dried, will
be blue and negative, that is to say, the lights and shadows will be the
reverse of what they are in nature. If in this state the paper be washed
with a solution of proto-nitrate of mercury, the picture will be
discharged; but if it be well washed and dried, and a hot smoothing-iron
passed over it, the picture instantly reappears, not blue, but brown; if
kept some weeks in this state in perfect darkness between the leaves of
a portfolio, it fades, and almost entirely vanishes, but a fresh
application of heat restores it to its full original intensity. This
curious change is not the effect of light, at least not of light alone.
A certain temperature must be attained, and that suffices in total
darkness; yet, on exposing to a very concentrated spectrum a slip of the
paper used in the last experiment, after the uniform blue colour has
been discharged and a white ground left, this whiteness is changed to
brown over the whole region of the red and orange rays, _but not beyond_
the luminous spectrum.

Sir John thence concludes:—1st. That it is the heat of these rays, not
their light, which operates the change; 2ndly. That this heat possesses
a peculiar chemical quality which is not possessed by the purely
calorific rays outside of the visible spectrum, though far more intense;
and, 3rdly. That the heat radiated from obscurely hot iron abounds
especially in rays analogous to those of the region of the spectrum
above indicated.

Another instance of these singular transformations may be noticed. The
pictures formed on cyanotype paper rendered more sensitive by the
addition of corrosive sublimate are blue on a white ground and positive,
that is, the lights and shadows are the same as in nature, but, by the
application of heat, the colour is changed from blue to brown, from
positive to negative; even by keeping in darkness the blue colour is
restored, as well as the _positive character_. Sir John attributes this,
as in the former instance, to certain rays, which, regarded as rays of
heat or light, or of some influence _sui generis_ accompanying the red
and orange rays of the spectrum, are also copiously emitted by bodies
heated short of redness. He thinks it probable that these invisible
parathermic rays are the rays which radiate from molecule to molecule in
the interior of bodies, that they determine the discharge of vegetable
colours at the boiling temperature, and also the innumerable atomic
transformations of organic bodies which take place at the temperature
below redness, that they are distinct from those of pure heat, and that
they are sufficiently identified by these characters to become
legitimate objects of scientific discussion.

The calorific and parathermic rays appear to be intimately connected
with the discoveries of Messrs. Draper and Moser. Daguerre has shown
that the action of light on the iodide of silver renders it capable of
condensing the vapour of mercury which adheres to the parts affected by
it. Professor Moser of Königsberg has proved that the same effect is
produced by the simple contact of bodies, and even by their very near
juxtaposition, and that in total darkness as well as in light. This
discovery he announced in the following words:—“If a surface has been
touched in any particular parts by any body, it acquires the property of
precipitating all vapours, and these adhere to it or combine chemically
with it on these spots differently from what they do on the untouched
parts.” If we write on a plate of glass or any smooth surface whatever
with blotting-paper, a brush, or anything else, and then clean it, the
characters always reappear if the plate or surface be breathed upon, and
the same effect may be produced even on the surface of mercury; nor is
absolute contact necessary. If a screen cut in a pattern be held over a
polished metallic surface at a small distance, and the whole breathed
on, after the vapour has evaporated so that no trace is left on the
surface, the pattern comes out when it is breathed on again.

Professor Moser proved that bodies exert a very decided influence upon
each other, by placing coins, cut stones, pieces of horn, and other
substances, for a short time on a warm metallic plate: when the
substance was removed, no impression appeared on the plate till it was
breathed upon or exposed to the vapour of mercury, and then these
vapours adhered only to the parts where the substance had been placed,
making distinct images, which in some cases were permanent after the
vapour was removed. Similar impressions were obtained on glass and other
substances even when the bodies were not in contact, and the results
were the same whether the experiments were performed in light or in
darkness.

Mr. Grove found, when plates of zinc and copper were closely
approximated, but not in contact, and suddenly separated, that one was
positively and the other negatively electric; whence he inferred that
the intervening medium was either polarised, or that a radiation
analogous, if not identical, with that which produces Moser’s images
takes place from plate to plate.

Mr. Hunt has shown that many of these phenomena depend on difference of
temperature, and that, in order to obtain good impressions, dissimilar
metals must be used. For example, gold, silver, bronze, and copper coins
were placed on a plate of copper too hot to be touched, and allowed to
remain till the plate cooled: all the coins had made an impression, the
distinctness and intensity of which were in the order of the metals
named. When the plate was exposed to the vapour of mercury the result
was the same, but, when the vapour was wiped off, the gold and silver
coins only had left permanent images on the copper. These impressions
are often minutely perfect, whether the coins are in actual contact with
the plate or one-eighth of an inch above it. The mass of the metal has a
material influence on the result; a large copper coin makes a better
impression on a copper plate than a small silver coin. When coins of
different metals are placed on the same plate they interfere with each
other.

When, instead of being heated, the copper plate was cooled by a freezing
mixture, and bad conductors of heat laid upon it, as wood, paper, glass,
&c., the result was similar.

Mr. Hunt, observing that a black substance leaves a stronger impression
on a metallic surface than a white, applied the property to the art of
copying prints, woodcuts, writing, and printing, on copper amalgamated
on one surface and highly polished, merely by placing the object to be
copied smoothly on the metal, and pressing it into close contact by a
plate of glass: after some hours the plate is subjected to the vapour of
mercury, and afterwards to that of iodine, when a black and accurate
impression of the object comes out on a grey ground. Effects similar to
those attributed to heat may also be produced by electricity. Mr.
Karsten, by placing a glass plate upon one of metal, and on the glass
plate a medal subjected to discharges of electricity, found a perfect
image of the medal impressed on the glass, which could be brought into
evidence by either mercury or iodine; and, when several plates of glass
were interposed between the medal and the metallic plate, each plate of
glass received an image on its upper surface after the passage of
electrical discharges. These discharges have the remarkable power of
restoring impressions that have been long obliterated from plates by
polishing—a proof that the disturbances upon which these phenomena
depend are not confined to the surface of the metals, but that a very
decided molecular change has taken place to a considerable depth. Mr.
Hunt’s experiments prove that the electro-negative metals make the most
decided images upon electro-negative plates, and _vice versâ_. M.
Matteucci has shown that a discharge of electricity does not visibly
affect a polished silver plate, but that it produces an alteration which
renders it capable of condensing vapour.

The impression of an engraving was made by laying it face downwards on a
silver plate iodized, and placing an amalgamated copper plate upon it;
it was left in darkness fifteen hours, during which time an impression
of the engraving had been made on the amalgamated plate _through the
paper_.

An iodized silver plate was placed in darkness with a coil of string
laid on it, and with a polished silver plate suspended one-eighth of an
inch above it: after four hours they were exposed to the vapours of
mercury, which became uniformly deposited on the iodized plate, but on
the silver one there was a sharp image of the string, so that this image
was formed in the dark, and even without contact. Coins or other objects
leave their impressions in the same manner with perfect sharpness and
accuracy, when brought out by vapour without contact, in darkness, and
on simple metals.

Red and orange coloured media, smoked glass, and all bodies that
transmit or absorb the hot rays freely, leave strong impressions on a
plate of copper, whether they be in contact or one-eighth of an inch
above it. Heat must be concerned in this, for a solar spectrum
concentrated by a lens was thrown on a polished plate of copper, and
kept on the same spot by a heliostat for two or three hours: when
exposed to mercurial vapour, a film of the vapour covered the plate
where the diffused light which always accompanies the solar spectrum had
fallen. On the obscure space occupied by the maximum heating power of
Sir William Herschel, and also on the great heat spot in the thermic
spectrum of Sir John Herschel, the condensation of the mercury was so
thick that it stood out a distinct white spot on the plate, while over
the whole space that had been under the visible spectrum the quantity of
vapour was much less than that which covered the other parts, affording
distinct evidence of a negative effect in the luminous spectrum and of
the power of the hot rays, which is not always confined to the surface
of the metal, since in many instances the impressions penetrated to a
considerable depth below it, and consequently were permanent.

Several of these singular effects appear to be owing to the mutual
action of molecules in contact while in a different state, whether of
electricity or temperature: others clearly point at some unknown
influence exerted between surfaces at a distance, and affecting their
molecular structure: possibly it may be the parathermic rays, which have
a peculiar chemical action even in total darkness. In the last
experiment the effect is certainly produced by the positive portion of
one of those remarkable antagonist principles which characterise the
solar spectrum.

Thus it appears that the prism resolves the pure white sunbeam into
three superposed spectra, each varying in refrangibility and intensity
throughout its whole length; the visible part is overlapped at one end
by the chemical or photographic rays, and at the other by the thermic,
but the two latter so much exceed the visible part, that the linear
dimensions of the three—the luminous, thermic, and photographic—are in
proportion to the numbers 25, 42·10, and 55·10, so that the whole solar
spectrum is twice as long as its visible part. The two extremities exert
a decided antagonist energy. The least refrangible luminous rays
obliterate the action of the photographic rays, while the latter produce
phosphorescent light, which is extinguished by the least refrangible
luminous rays. According to Mr. Hunt’s experiment, the hot rays condense
mercurial vapour on a polished metallic plate, while the luminous rays
prevent its formation. Electricity is excited by the chemical rays,
while the parathermic are found in the less refrangible rays alone. Each
of the spectra is crossed by coloured and rayless lines peculiar to
itself, and these are traversed at right angles by innumerable dark
lines of various breadths, the whole forming an inexpressibly wonderful
and glorious creation.

The arrangement varies a little according to the material of the prism
and the manner of producing the spectrum, as in that obtained by
Professor Draper from diffracted light. It was formed by a beam
diffracted by passing through a netting of fine wire, or by reflection
from a polished surface of steel, having fine parallel lines drawn on
it. This diffracted spectrum is divided into two equal parts in the
centre of the yellow; and as in the prismatic spectrum, one half is
antagonist to the other half, the red or negative end undoing what the
positive or violet end has done. The centre of the yellow is the hottest
part, and the heat decreases to both extremities. A line of cold is
supposed to exist on this spectrum answering to Fraunhofer’s dark line
H.

The undulations of the ethereal medium which constitute a sunbeam must
be infinitely varied, each influence having a vibration peculiar to
itself. Those of light are certainly transverse to the direction of the
ray; while Professor Draper believes that those of heat are normal, that
is, in the direction of the ray, like those of sound. A doubt exists
whether the vibrations of polarised light are perpendicular to the plane
of polarisation or in that plane. Professor Stokes of Cambridge has come
to the conclusion, both from the diffracted spectrum and theory, that
they are perpendicular to the plane of polarisation, but M. Holtzmann is
of opinion that they are in that plane, so the subject is still open to
discussion.




                              SECTION XXV.

Size and Constitution of the Sun—The Solar Spots—Intensity of the
  Sun’s Light and Heat—The Sun’s Atmosphere—His influence on the
  Planets—Atmospheres of the Planets—The Moon has none—Lunar
  heat—The Differential Telescope—Temperature of Space—Internal
  Heat of the Earth—Zone of constant Temperature—Increase of Heat
  With the Depth—Central Heat—Volcanic Action—Quantity of Heat
  received from the Sun—Isogeothermal Lines—Line of perpetual
  Congelation—Climate—Isothermal Lines—Same quantity of Heat
  annually received and radiated by the Earth.


THE sun is a globe 880,000 miles in diameter: what his body may be it is
impossible to conjecture, but it seems to be a dark mass surrounded by
an extensive atmosphere at a certain height in which there is a stratum
of luminous clouds which constitutes the photosphere of the sun. Above
it rises the true solar atmosphere, visible as an aureola or corona
during annular and total eclipses, and probably the cause of the
peculiar phenomena in the photographic image of the sun already
mentioned. Through occasional openings in the photosphere or mottled
ocean of flame, the dark nucleus appears like black spots, often of
enormous size. These spots are almost always comprised within a zone of
the sun’s surface, whose breadth measured on a solar meridian does not
extend beyond 30-1/2° on each side of his equator, though they have been
seen at a distance of 39-1/2°. The dark central part of the spots is
surrounded by a succession of obscure cloudy envelopes increasing in
brightness up to a penumbra, sometimes there are three or more shades,
but it requires a good telescope to distinguish the intermediate ones.
The spots gradually increase in size and number from year to year to a
maximum, and then as gradually decrease to a minimum, accomplishing
regular vicissitudes in periods of about eleven years, and are
singularly connected with the cycles of terrestrial magnetism. From
their extensive and rapid changes, there is every reason to believe that
the exterior and incandescent part of the sun is gaseous.

Doubts have arisen as to the uniformity of the quantity of heat emitted
by the sun. Sir William Herschel was the first to suspect that it was
affected by the quantity and magnitude of the spots on his surface;
Professor Secchi has observed that the spots are less hot than the
luminous part; and now Professor Wolf has perceived that the amount of
heat emitted by the sun varies periodically with the spots every 11·11
years, or nearly nine times in a century, beginning at the commencement
of the present one. He has discovered a sub-period in that of the spots,
which no doubt has an effect on the quantity of solar heat. So the
unaccountable vicissitudes in the temperature of different years may
ultimately be found to depend upon the constitution of the sun himself.

The intensity of the sun’s light diminishes from the centre to the
circumference of the solar disc. His direct light has been estimated to
be equal to that of 5563 wax candles of moderate size placed at the
distance of one foot from an object; that of the moon is probably only
equal to the light of one candle at the distance of 12 feet:
consequently the light of the sun is more than three hundred thousand
times greater than that of the moon. According to Professor Secchi’s
experiments at Rome, the heat of the solar image is almost twice as
great at the centre as at the edge. The maximum heat, however, is not in
the centre, but in the solar equator, and the spots are less hot than
the rest of the surface.

The oceans of light and heat probably arising from electric or chemical
processes of immense energy that continually take place at the sun’s
surface (N. 217) are transmitted in undulations by the ethereal medium
in all directions; but notwithstanding the sun’s magnitude and the
inconceivable intensity of light and heat that must exist at his
surface, as the intensity of both diminishes as the square of the
distance increases, his kindly influence can hardly be felt at the
boundaries of our system. In Uranus the sun must be seen like a small
brilliant star not above the hundred and fiftieth part as bright as he
appears to us, but that is 2000 times brighter than our moon, so that he
is really a sun to Uranus, and may impart some degree of warmth. But if
we consider that water would not remain fluid in any part of Mars, even
at his equator, and that, in the temperate zones of the same planet,
even alcohol and quicksilver would freeze, we may form some idea of the
cold that must reign in Uranus and Neptune. The climate of Venus more
nearly resembles that of the earth, though, excepting at her poles, much
too hot for animal and vegetable life such as they exist here, for she
receives seven times as much light and heat as the earth does; but in
Mercury the mean heat from the intensity of the sun’s rays must be above
that of boiling quicksilver, and water would boil even at his poles.
Thus the planets, though kindred with the earth in motion and form, are,
according to our experience, totally unfit for the habitation of such a
being as man, unless indeed their temperature should be modified by
circumstances of which we are not aware, and which may increase or
diminish the sensible heat so as to render them habitable. In our utter
ignorance it may be observed, that the earth, if visible at all from
Neptune, can only be a minute telescopic object; that from the nearest
fixed star the sun must dwindle to a mere point of light; that the whole
solar system would there be hid by a spider’s thread; and that the
starry firmament itself is only the first series of starry systems, the
numbers of which are bounded alone by the imperfection of our
space-penetrating instruments. In this overwhelming majesty of creation,
it seems rash to affirm that the earth alone is inhabited by intelligent
beings, and thus to limit the Omnipotent, who has made nothing in vain.

Several of the planets have extensive and dense atmospheres: according
to Schroëter the atmosphere of Ceres is more than 668 miles high, and
that of Pallas has an elevation of 465 miles, but not a trace of an
atmosphere can be perceived round Vesta. The attraction of the earth has
probably deprived the moon of hers, for the refractive power of the air
at the surface of the earth is at least a thousand times as great as at
the surface of the moon: the lunar atmosphere must therefore be of a
greater degree of rarity than can be produced by our best air-pumps.
This is confirmed by Arago’s observations during a solar eclipse, when
no trace of a lunar atmosphere could be seen. Since then, however, some
indications of air have been perceived in the lunar valleys. In taking
photographic images of the moon and Jupiter at Rome, Professor Secchi
found that the light of the full moon is to that of the quarter moon as
3 to 1. Jupiter gives a photographic image as bright and vigorous as the
brightest part of the moon; but although the light of Jupiter is less
than that of the moon, he is nearly five times farther from the sun; and
as light diminishes as the square of the distance increases, the light
of Jupiter is proportionally greater than that of the moon, consequently
Jupiter’s atmosphere reflects more light than the dark volcanic soil of
the moon; thus Professor Secchi observes photography may in time reveal
the quality of the materials of which the celestial bodies are formed.

The effect of the earth’s atmosphere on lunar heat is remarkable.
Professor Forbes proved that the direct light of the full moon is
incapable of raising a thermometer the one three thousandth part of a
Centigrade degree, at least in England; but at an elevation of 8870 feet
on the Peak of Teneriffe, Mr. Piazzi Smyth found a very sensible heat
from the moon, although she was then 19° south of the equator; so it is
no doubt absorbed by our atmosphere at lower levels.

Some exceedingly interesting experiments might be made by means of a
telescope having a prism attached to its objective extremity, and
furnished with a micrometer, because by it the difference of the
illumination of objects might be determined with extreme accuracy—as for
example, the comparative intensity between the bright and dark parts of
the moon, the comparative intensity of the solar light reflected by the
moon, and the lumière cendré, or the light of the earth reflected on the
moon, whence a comparison might be made between the light of the sun and
that of the earth. Hence also it might be known whether the terrestrial
hemispheres successively visible from the moon are more or less
luminous, according as they contain more land or water, and at the same
time it might be possible to appreciate the more or less cloudy or clear
state of our atmosphere, so that in time we might ultimately find in the
lumière cendré of the moon data upon the mean diaphaneity of different
terrestrial hemispheres which are of different temperatures.

It is found by experience that heat is developed in opaque and
translucent substances by their absorption of solar light, but that the
sun’s rays do not sensibly alter the temperature of perfectly
transparent bodies through which they pass. As the temperature of the
pellucid planetary space can be but little affected by the passage of
the sun’s light and heat, neither can it be sensibly raised by the heat
now radiated from the earth.

Doubtless the radiation of all the bodies in the universe maintains the
ethereal medium at a higher temperature than it would otherwise have,
and must eventually increase it, but by a quantity so evanescent that it
is hardly possible to conceive a time when a change will become
perceptible.

The temperature of space being so low as -239° Fahrenheit, it becomes a
matter of no small interest to ascertain whether the earth may not be
ultimately reduced by radiation to the temperature of the surrounding
medium; what the sources of heat are; and whether they be sufficient to
compensate the loss, and to maintain the earth in a state fit for the
support of animal and vegetable life in time to come. All observations
that have been made under the surface of the ground concur in proving
that there is a stratum at the depth of from 40 to 100 feet throughout
the whole earth where the temperature is invariable at all times and
seasons, and which differs but little from the mean annual temperature
of the country above. According to M. Boussingault, that stratum at the
equator is at the depth of little more than a foot in places sheltered
from the direct rays of the sun; but in our climates it is at a much
greater depth. In the course of more than half a century the temperature
of the earth at the depth of 90 feet, in the cellars of the Observatory
at Paris, has never been above or below 53° of Fahrenheit’s thermometer,
which is only 2° above the mean annual temperature at Paris. This zone,
unaffected by the sun’s rays from above, or by the internal heat from
below, serves as an origin whence the effects of the external heat are
estimated on one side, and the internal temperature of the globe on the
other.

As early as the year 1740 M. Gensanne discovered in the lead-mines of
Giromagny, in the Vosges mountains, three leagues from Béfort, that the
heat of the ground increases with the depth below the zone of constant
temperature. A vast number of observations have been made since that
time, in the mines of Europe and America, by MM. Saussure, Daubuisson,
Humboldt, Cordier, Fox, Reich, and others, which agree, without an
exception, in proving that the temperature of the earth becomes higher
in descending towards its centre. The greatest depth that has been
attained is in the silver-mine of Guanaxato, in Mexico, where M. de
Humboldt found a temperature of 98° at the depth of 285 fathoms, the
mean annual temperature of the country being only 61°. Next to that is
the Dalcoath copper-mine, in Cornwall, where Mr. Fox’s thermometer stood
at 68° in a hole in the rock at the depth of 230 fathoms, and at 82° in
water at the depth of 240 fathoms, the mean annual temperature at the
surface being about 50°. But it is needless to multiply examples, all of
which concur in showing that there is a very great difference between
the temperature in the interior of the earth and at its surface. Mr.
Fox’s observations on the temperature of springs which rise at profound
depths in mines afford the strongest testimony. He found considerable
streams flowing into some of the Cornish mines at the temperature of 80°
or 90°, which is about 30° or 40° above that of the surface, and also
ascertained that nearly 2,000,000 gallons of water are daily pumped from
the bottom of the Poldice mine, which is 176 fathoms deep at 90° or
100°. As this is higher than the warmth of the human body, Mr. Fox
justly observes that it amounts to a proof that the increased
temperature cannot proceed from the persons of the workmen employed in
the mines. Neither can the warmth of mines be attributed to the
condensation of the currents of air which ventilate them. Mr. Fox, whose
opinion is of high authority in these matters, states that, even in the
deepest mines, the condensation of the air would not raise the
temperature more than 5° or 6°; and that, if the heat could be
attributed to this cause, the seasons would sensibly affect the
temperature of mines, which it appears they do not where the depth is
great. Besides, the Cornish mines are generally ventilated by numerous
shafts opening into the galleries from the surface or from a higher
level. The air circulates freely in these, descending in some shafts and
ascending in others. In all cases Mr. Fox found that the upward currents
are of a higher temperature than the descending currents; so much so,
that in winter the moisture is often frozen in the latter to a
considerable depth; the circulation of air, therefore, tends to cool the
mine instead of increasing the heat. Mr. Fox has also removed the
objections arising from the comparatively low temperature of the water
in the shafts of abandoned mines, by showing that observations in them,
from a variety of circumstances which he enumerates, are too discordant
to furnish any conclusion as to the actual heat of the earth. The high
temperature of mines might be attributed to the effects of the fires,
candles, and gunpowder used by the miners, did not a similar increase
obtain in deep wells, and in borings to great depths in search of water,
where no such causes of disturbance occur. In a well dug with a view to
discover salt in the canton of Berne, and long deserted, M. de Saussure
had the most complete evidence of increasing heat. The same has been
confirmed by the temperature of many wells, both in France and England,
especially by the Artesian wells, so named from a peculiar method of
raising water first resorted to in Artois, and since become very
general. An Artesian well consists of a shaft a few inches in diameter,
bored into the earth till a spring is found. To prevent the water being
carried off by the adjacent strata, a tube is let down which exactly
fills the bore from top to bottom, in which the water rises pure to the
surface. It is clear the water could not rise unless it had previously
descended from high ground through the interior of the earth to the
bottom of the well. It partakes of the temperature of the strata through
which it passes, and in every instance has been warmer in proportion to
the depth of the well; but it is evident that the law of increase cannot
be obtained in this manner. Perhaps the most satisfactory experiments on
record are those made by MM. Auguste de la Rive and F. Marcet during the
year 1833, in a boring for water about a league from Geneva, at a place
318 feet above the level of the lake. The depth of the bore was 727
feet, and the diameter only between four and five inches. No spring was
ever found; but the shaft filled with mud, from the moisture of the
ground mixing with the earth displaced in boring, which was peculiarly
favourable for the experiments, as the temperature at each depth may be
considered to be that of the particular stratum. In this case, where
none of the ordinary causes of disturbance could exist, and where every
precaution was employed by scientific and experienced observers, the
temperature was found to increase regularly and uniformly with the depth
at the rate of about 1° of Fahrenheit for every 52 feet. Professor Reich
of Freyberg has found that the mean of a great number of observations
both in mines and wells is 1° of Fahrenheit for every 55 feet of depth;
and from M. Arago’s observations in the Grenelle Artesian well at Paris,
the increase is 1° of Fahrenheit for every 45 feet. Though there can be
no doubt as to the increase of temperature in penetrating the crust of
the earth, there is still much uncertainty as to the law of increase,
which varies with the nature of the soil and other local circumstances;
but, on an average, it has been estimated at the rate of 1° for every 50
or 60 feet, which corresponds with the observations of MM. Marcet and De
la Rive. In consequence of the rapid increase of internal heat, thermal
springs, or such as are independent of volcanic action, rising from a
great depth, must necessarily be very rare and of a high temperature;
and it is actually found that none are so low as 68° of Fahrenheit; that
of Chaudes Aigues, in Auvergne, is about 136°. In many places warm water
from Artesian wells will probably come into use for domestic purposes,
and it is even now employed in manufactories near Stutgardt, in Alsace,
&c.

It is hardly to be expected that at present any information with regard
to the actual internal temperature of the earth should be obtained from
that of the ocean, on account of the mobility of fluids, by which the
colder masses sink downwards, while those that are warmer rise to the
surface. Nevertheless, it may be stated that the temperature of the sea
decreases with the depth between the tropics; while, on the contrary,
all our northern navigators found that the temperature increases with
the depth in the polar seas. The change takes place about the 70th
parallel of latitude. Some ages hence, however, it may be known whether
the earth has arrived at a permanent state as to heat, by comparing
secular observations of the temperature of the ocean if made at a great
distance from the land.

Should the earth’s temperature increase at the rate of 1° for every 50
feet, it is clear that at the depth of 200 miles the hardest substances
must be in a state of fusion, and our globe must in that case either be
encompassed by a stratum of melted lava at that depth, or it must be a
ball of liquid fire 7600 miles in diameter, enclosed in a thin coating
of solid matter; for 200 miles are nothing when compared with the size
of the earth. No doubt the form of the earth, as determined by the
pendulum and arcs of the meridian, as well as by the motions of the
moon, indicates original fluidity and subsequent consolidation and
reduction of temperature by radiation; but whether the law of increasing
temperature is uniform at still greater depths than those already
attained by man, it is impossible to say. At all events, internal
fluidity is not inconsistent with the present state of the earth’s
surface, since earthy matter is as bad a conductor of heat as lava,
which often retains its heat at a very little depth for years after its
surface is cool. Whatever the radiation of the earth might have been in
former times, certain it is that it goes on very slowly in our days; for
M. Fourier has computed that the central heat is decreasing from
radiation by only about the 1/30000th part of a degree in a century. If
so, there can be no doubt that it will ultimately be dissipated; but as
far as regards animal and vegetable life, it is of very little
consequence whether the centre of our planet be liquid fire or ice,
since its condition in either case could have no sensible effect on the
climate at its surface. The internal fire does not even impart heat
enough to melt the snow at the poles, though nearer to the centre than
any other part of the globe.

The immense extent of active volcanic fire is one of the causes of heat
which must not be overlooked.

The range of the Andes from Chile to the north of Mexico, probably from
Cape Horn to Behring Straits, is one vast district of igneous action,
including the Caribbean and the West Indian Islands on one hand; and
stretching quite across the Pacific Ocean, through the Polynesian
Archipelago, the New Hebrides, the Georgian and Friendly Islands, on the
other. Another chain begins with the Aleutian Islands, extends to
Kamtschatka, and from thence passes through the Kurile, Japanese, and
Philippine Islands, to the Moluccas, whence it spreads with terrific
violence through the Indian Archipelago, even to the Bay of Bengal.
Volcanic action may again be followed from the entrance of the Persian
Gulf to Madagascar, Bourbon, the Canaries, and Azores. Thence a
continuous igneous region extends through about 1000 geographical miles
to the Caspian Sea, including the Mediterranean, and extending north and
south between the 35th and 40th parallels of latitude; and in central
Asia a volcanic region occupies 2500 square geographical miles. The
volcanic fires are developed in Iceland in tremendous force; and the
antarctic land discovered by Sir James Ross is an igneous formation of
the boldest structure, where a volcano in high activity rises 12,000
feet above the perpetual ice of these polar deserts, and within 19-1/2°
of the south pole. Throughout this vast portion of the world the
subterraneous fire is often intensely active, producing such violent
earthquakes and eruptions that their effects, accumulated during
millions of years, may account for many of the great geological changes
of igneous origin that have already taken place in the earth, and may
occasion others not less remarkable, should time—that essential element
in the vicissitudes of the globe—be granted, and their energy last.

Sir Charles Lyell, who has shown the power of existing causes with great
ingenuity, estimates that on an average twenty eruptions take place
annually in different parts of the world; and many must occur or have
happened, even on the most extensive and awful scale, among people
equally incapable of estimating their effects and of recording them. We
should never have known the extent of the fearful eruption which took
place in the island of Sumbawa, in 1815, but for the accident of Sir
Stamford Raffles having been governor of Java at the time. It began on
the 5th of April, and did not entirely cease till July. The ground was
shaken through an area of 1000 miles in circumference; the tremors were
felt in Java, the Moluccas, a great part of Celebes, Sumatra, and
Borneo. The detonations were heard in Sumatra, at the distance of 970
geographical miles in a straight line; and at Ternate, 720 miles in the
opposite direction. The most dreadful whirlwinds carried men and cattle
into the air; and with the exception of 26 persons, the whole population
of the island perished to the amount of 12,000. Ashes were carried 300
miles to Java in such quantities that the darkness during the day was
more profound than ever had been witnessed in the most obscure night.
The face of the country was changed by the streams of lava, and by the
upheaving and sinking of the soil. The town of Tomboro was submerged,
and water stood to the depth of 18 feet in places which had been dry
land. Ships grounded where they had previously anchored, and others
could hardly penetrate the mass of cinders which floated on the surface
of the sea for several miles to the depth of two feet. A catastrophe
similar to this, though of less magnitude, took place in the island of
Bali in 1808, which was not heard of in Europe till years afterwards.
The eruption of Coseguina in the Bay of Fonseca, which began on the 19th
of January, 1835, and lasted many days, was even more dreadful and
extensive in its effects than that of Sumbawa. The ashes during this
eruption were carried by the upper current of the atmosphere as far
north as Chiassa, which is upwards of 400 leagues to the windward of
that volcano. Many volcanoes supposed to be extinct have all at once
burst out with inconceivable violence. Witness Vesuvius, on historical
record; and the volcano in the island of St. Vincent in our own days,
whose crater was lined with large trees, and which had not been active
in the memory of man. Vast tracts are of volcanic origin where volcanoes
have ceased to exist for ages. Whence it may be inferred that in some
places the subterraneous fires are in the highest state of activity, in
some they are inert, and in others they appear to be extinct. Yet there
are few countries that are not subject to earthquakes of greater or less
intensity; the tremors are propagated like a sonorous undulation to such
distances that it is impossible to say in what point they originate. In
some recent instances their power must have been tremendous. In South
America, so lately as 1822, an area of 100,000 square miles, which is
equal in extent to the half of France, was raised several feet above its
present level—a most able account of which is given in the ‘Transactions
of the Geological Society,’ by an esteemed friend of the author’s, the
late Mrs. Graham, who was present during the whole time of that
formidable earthquake, which recurred at short intervals for more than
two months, and who possessed talents to appreciate, and had
opportunities of observing, its effects under the most favourable
circumstances at Valparaiso, and for miles along the coast where it was
most intense. A considerable elevation of the land has again taken place
along the coast of Chile, in consequence of the violent earthquake which
happened on the 20th of February, 1835. In 1819 a ridge of land
stretching for 50 miles across the delta of the Indus, 16 feet broad,
was raised 10 feet above the plain. The reader is referred to Sir
Charles Lyell’s excellent ‘Principles of Geology,’ already mentioned,
for most interesting details of the phenomena and extensive effects of
volcanoes and earthquakes, too numerous to find a place here. It may
however be mentioned that innumerable earthquakes are from time to time
shaking the solid crust of the globe, and carrying destruction to
distant regions, progressively though slowly accomplishing the great
work of change. A most disastrous instance took place on the 15th of
December, 1857, in the Neapolitan provinces of La Basilicata and
Principato Citeriore, where the destruction was extensive and terrible;
the number of victims, according to the official accounts, being
returned at upwards of ten thousand. These terrible engines of ruin,
fitful and uncertain as they may seem, must, like all durable phenomena,
have a law which may in time be discovered by long-continued and
accurate observations.

The shell of volcanic fire that girds the globe at a small depth below
our feet has been attributed to different causes. By some it is supposed
to originate in an ocean of incandescent matter, still existing in the
central abyss of the earth. Some conceive it to be superficial, and due
to chemical action, in strata at no very great depth when compared with
the size of the globe. The more so as matter on a most extensive scale
is passing from old into new combinations, which, if rapidly effected,
are capable of producing the most intense heat. According to others,
electricity, which is so universally diffused in all its forms
throughout the earth, if not the immediate cause of the volcanic
phenomena, at least determines the chemical affinities that produce
them. It is clear that a subject so involved in mystery must give rise
to much speculation, in which every hypothesis is attended with
difficulties that observation alone can remove.

But the views of Mr. Babbage and Sir John Herschel on the general cause
of volcanic action, and the changes in the equilibrium of the internal
heat of the globe, accord more with the laws of mechanics and radiant
heat than any that have been proposed. The theory of these distinguished
philosophers, formed independently of each other, is equally consistent
with observed phenomena, whether the earth be a solid crust encompassing
a nucleus of liquid lava, or that there is merely a vast reservoir or
stratum of melted matter at a moderate depth below the superficial
crust. The author is indebted to the kindness of Sir Charles Lyell for
the perusal of a most interesting letter from Sir John Herschel, in
which he states his views on the subject.

Supposing that the globe is merely a solid crust, resting upon fluid or
semi-fluid matter, whether extending to the centre or not, the transfer
of pressure from one part of its surface to another by the degradation
of existing continents, and the formation of new ones, would be
sufficient to subvert the equilibrium of heat in the interior, and
occasion volcanic eruptions. For, since the internal heat of the earth
is transmitted outwards by radiation, an accession of new matter on any
part of the surface, like an addition of clothing, by keeping it in,
would raise the temperature of the strata below, and in the course of
ages would even reduce those at a great depth to a state of fusion. Some
of the substances might be converted into gases; and should the
accumulation of new matter take place at the bottom of the sea, as is
generally the case, this lava would be mixed with water in a state of
ignition in consequence of the enormous pressure of the ocean, and of
the newly superimposed matter which would prevent it from expanding into
steam. Now Sir Charles Lyell has shown, with his usual talent, that the
quantity of matter carried down by rivers from the surface of the
continents is comparatively trifling, and that the great transfer to the
bottom of the ocean is produced at the coast-line by the action of the
sea; hence, says Sir John Herschel, “the greatest accumulation of local
pressure is in the central area of the deep sea, while the greatest
local relief takes place along the abraded coast-lines. Here then should
occur the chief volcanic vents.” As the crust of the earth is much
weaker on the coasts than elsewhere, it is more easily ruptured, and, as
Mr. Babbage observes, immense rents might be produced there by its
contraction in cooling down after being deprived of a portion of its
original thickness. The pressure on the bottom of the ocean would force
a column of lava mixed with ignited water and gas to rise through an
opening thus formed, and, says Sir John Herschel, “when the column
attains such a height that the ignited water can become steam, the joint
specific gravity of the column is suddenly diminished, and up comes a
jet of mixed steam and lava, till so much has escaped that the matter
deposited at the bottom of the ocean takes a fresh bearing, when the
evacuation ceases and the crack becomes sealed up.”

This theory perfectly accords with the phenomena of nature, since there
are very few active volcanoes at a distance from the sea, and the
exceptions that do occur are generally near lakes, or they are connected
with volcanoes on the maritime coasts. Many break out even in the bottom
of the ocean, probably owing to some of the supports of the superficial
crust giving way, so that the steam and lava are forced up through the
fissures.

Finally, Mr. Babbage observes that, “in consequence of changes
continually going on, by the destruction of forests, the filling up of
seas, the wearing down of elevated lands, the heat radiated from the
earth’s surface varies considerably at different periods. In consequence
of this variation, and also in consequence of the covering up of the
bottom of the sea by the detritus of the land, the surfaces of equal
temperature within the earth are continually changing their form, and
exposing thick beds near the exterior to alterations of temperature. The
expansion and contraction of these strata may form rents and veins,
produce earthquakes, determine volcanic eruptions, elevate continents,
and, possibly, raise mountain chains.”

The numerous vents for the internal heat formed by volcanoes, hot
springs, and the emission of steam, so frequent in volcanic regions, no
doubt maintain the tranquillity of the interior fluid mass, which seems
to be perfectly inert unless when put in motion by unequal pressure.

But, to whatever cause the increasing heat of the earth and the
subterranean fires may ultimately be referred, it is certain that,
except in some local instances, they have no sensible effect on the
temperature of its surface. It may therefore be concluded that the heat
of the earth, above the zone of uniform temperature, is entirely owing
to the sun.

The power of the solar rays depends much upon the manner in which they
fall, as we readily perceive from the different climates on our globe.
Although the sun is about three millions of miles nearer to the earth in
winter than in summer, his rays strike the atmosphere in the northern
hemisphere so obliquely that it absorbs a much greater quantity of heat
than when they are more direct (N. 217). Indeed it is so great that,
when the sun has an altitude of 30°, one half of his heat is absorbed by
the atmosphere, and it increases very rapidly as he sinks towards the
horizon. However, that heat is not lost: it is most beneficial to the
earth, being really the heat which supplies the greatest part of that
which is radiated into space during the absence of the sun. Professor
Dove has shown, by taking at all seasons the mean of the temperatures of
points on the earth’s surface diametrically opposite to each other, that
the average temperature of the whole earth’s surface in June, when we
are farthest from the sun, considerably exceeds that in December, when
we are nearest to him, owing to the excess of water in the southern
hemisphere, and that of land in the northern, which gives a general
insular climate to the former, and a continental climate to the latter.

The observations of the north polar navigators, and those of Sir John
Herschel at the Cape of Good Hope, show that the direct heating
influence of the solar rays is greatest at the equator, and that it
diminishes gradually as the latitude increases. At the equator the
maximum is 48-3/4°, while in Europe it has never exceeded 29-1/2°.

M. Pouillet has estimated with singular ingenuity, from a series of
observations made by himself, that the whole quantity of heat which the
earth receives annually from the sun is such as would be sufficient to
melt a stratum of ice covering the whole globe 46 feet deep. Part of
this heat is radiated back into space; but by far the greater part
descends into the earth during the summer, towards the zone of uniform
temperature, whence it returns to the surface in the course of the
winter, and tempers the cold of the ground and the atmosphere in its
passage to the ethereal regions, where it is lost, or rather where it
combines with the radiation from the other bodies of the universe in
maintaining the temperature of space. The sun’s power being greatest
between the tropics, the heat sinks deeper there than elsewhere, and the
depth gradually diminishes towards the poles; but the heat is also
transmitted laterally from the warmer to the colder strata north and
south of the equator, and aids in tempering the severity of the polar
regions.

The mean heat of the earth, above the stratum of constant temperature,
is determined from that of springs; and, if the spring be on elevated
ground, the temperature is reduced by computation to what it would be at
the level of the sea, assuming that the heat of the soil varies
according to the same law as the heat of the atmosphere, which is about
1° of Fahrenheit’s thermometer for every 333·7 feet. From a comparison
of the temperature of numerous springs with that of the air, Sir David
Brewster concludes that there is a particular line passing nearly
through Berlin, at which the temperature of springs and that of the
atmosphere coincide; that in approaching the arctic circle the
temperature of springs is always higher than that of the air, while,
proceeding towards the equator, it is lower.

Since the warmth of the superficial strata of the earth decreases from
the equator to the poles, there are many places in both hemispheres
where the ground has the same mean temperature. If lines were drawn
through all those points in the upper strata of the globe which have the
same mean annual temperature, they would be nearly parallel to the
equator between the tropics, and would become more and more irregular
and sinuous towards the poles. These are called isogeothermal lines. A
variety of local circumstances disturb their parallelism, even between
the tropics.

The temperature of the ground at the equator is lower on the coasts and
islands than in the interior of continents; the warmest part is in the
interior of Africa; but it is obviously affected by the nature of the
soil, especially if it be volcanic.

Much has been done to ascertain the manner in which heat is distributed
over the surface of our planet, and the variations of climate, which, in
a general view, mean every change of the atmosphere, such as of
temperature, humidity, variations of barometric pressure, purity of air,
the serenity of the heavens, the effects of winds, and electric tension.
Temperature depends upon the property which all bodies possess, more or
less, of perpetually absorbing and emitting or radiating heat. When the
interchange is equal, the temperature of a body remains the same; but,
when the radiation exceeds the absorption, it becomes colder, and _vice
versâ_. In order to determine the distribution of heat over the surface
of the earth, it is necessary to find a standard by which the
temperature in different latitudes may be compared. For that purpose it
is requisite to ascertain, by experiment, the mean temperature of the
day, of the month, and of the year, at as many places as possible
throughout the earth. The annual average temperature may be found by
adding the mean temperatures of all the months in the year, and dividing
the sum by twelve. The average of ten or fifteen years will give it
approximately; for, although the temperature in any place maybe subject
to very great variations, yet it never deviates more than a few degrees
from its mean state, which consequently offers a good standard of
comparison. As a standard, however, much greater accuracy is required.

If climate depended solely upon the heat of the sun, all places having
the same latitude would have the same mean annual temperature. The
motion of the sun in the ecliptic, indeed, occasions perpetual
variations in the length of the day, and in the direction of the rays
with regard to the earth; yet, as the cause is periodic, the mean annual
temperature from the sun’s motion alone must be constant in each
parallel of latitude; for it is evident that the accumulation of heat in
the long days of summer, which is but little diminished by radiation
during the short nights, is balanced by the small quantity of heat
received during the short days in winter, and its radiation in the long,
frosty, and clear nights. In fact, if the globe were everywhere on a
level with the surface of the sea, and of uniform substance, so as to
absorb and radiate heat equally, the mean heat of the sun would be
regularly distributed over its surface in zones of equal annual
temperature parallel to the equator, from which it would decrease to
each pole as the square of the cosine of the latitude; and its quantity
would only depend upon the altitude of the sun and atmospheric currents.
The distribution of heat, however, in the same parallel, is very
irregular in all latitudes except between the tropics, where the
isothermal lines, or the lines passing through places of equal mean
annual temperature, are more nearly parallel to the equator. The causes
of disturbance are very numerous; but such as have the greatest
influence, according to M. de Humboldt, to whom we are indebted for the
greater part of what is known on the subject, are the elevation of the
continents, the distribution of land and water over the surface of the
globe exposing different absorbing and radiating powers; the variations
in the surface of the land, as forests, sandy deserts, verdant plains,
rocks, &c.; mountain-chains covered with masses of snow, which diminish
the temperature; the reverberation of the sun’s rays in the valleys,
which increases it; and the interchange of currents, both of air and
water, which mitigates the rigour of climates; the warm currents from
the equator softening the severity of the polar frosts, and the cold
currents from the poles tempering the intense heat of the equatorial
regions. To these may be added cultivation, though its influence extends
over but a small portion of the globe, only a fourth part of the land
being inhabited.

Temperature decreases with the height above the level of the sea, as
well as with the latitude. The air in the higher regions of the
atmosphere is much cooler than that below, because the warm air expands
as it rises, by which its capacity for heat is increased, a great
proportion becomes latent or absorbed, and less of it sensible. A
portion of air at the surface of the earth whose temperature is 70° of
Fahrenheit, if carried to the height of two miles and a half, would
expand so much that its temperature would be reduced 50°; and in the
ethereal regions the temperature is 239° below the zero point of
Fahrenheit.

The height at which snow lies perpetually decreases from the equator to
the poles, and is higher in summer than in winter; but it varies from
many circumstances. Snow rarely falls when the cold is intense and the
atmosphere dry. Extensive forests produce moisture by their evaporation;
and high table-lands, on the contrary, dry and warm the air, because the
air at great elevations is too rare to absorb much of the sun’s heat. In
the Cordilleras of the Andes, plains of only twenty-five square leagues
from their extent raise the temperature as much as 3° or 4° above what
is found at the same altitude on the rapid declivity of a mountain,
consequently the line of perpetual snow varies according as one or other
of these causes prevails. Aspect in general has also a great influence;
yet the line of perpetual snow is much higher on the northern than on
the southern side of the Himalaya, partly because the air is nearly
deprived of its moisture by precipitation before it arrives at the
northern side of the mountains. On the whole, it appears that the mean
height between the tropics at which the snow lies perpetually is about
15,207 feet above the level of the sea; whereas snow does not cover the
ground continually at the level of the ocean till near the north pole.
In the southern hemisphere, however, the cold is greater than in the
northern. In Sandwich Land, between the 54th and 58th degrees of
latitude, perpetual snow and ice extend to the sea-level; and in the
island of S. Georgia, in the 53rd degree of south latitude, which
corresponds with the latitude of the central counties of England,
perpetual snow descends even to the level of the ocean. It has been
shown that this excess of cold in the southern hemisphere cannot be
attributed to the winter being longer than ours by 7-3/4 days. It is
probably owing to the open sea surrounding the south pole, which permits
the icebergs to descend to a lower latitude by 10° than they do in the
northern hemisphere, on account of the numerous obstructions opposed to
them by the islands and continents about the north pole. Icebergs from
the Arctic seas seldom float farther to the south than the Azores;
whereas those that come from the south pole descend to as low a latitude
as that of the Cape of Good Hope.

The influence of mountain-chains does not wholly depend upon the line of
perpetual congelation. They attract and condense the vapours floating in
the air, and send them down in torrents of rain. They radiate heat into
the atmosphere at a lower elevation, and increase the temperature of the
valleys by the reflection of the sun’s rays, and by the shelter they
afford against prevailing winds. But, on the contrary, one of the most
general and powerful causes of cold arising from the vicinity of
mountains is the freezing currents of wind which rush from their lofty
peaks along the rapid declivities, chilling the surrounding valleys:
such is the cutting north wind called the bise in Switzerland.

Next to elevation, the difference in the radiating and absorbing powers
of the sea and land has the greatest influence in disturbing the regular
distribution of heat. The extent of the dry land is not above the fourth
part of that of the ocean; so that the general temperature of the
atmosphere, regarded as the result of the partial temperatures of the
whole surface of the globe, is most powerfully modified by the sea.
Besides, the ocean acts more uniformly on the atmosphere than the
diversified surface of the solid mass does, both by the equality of its
curvature and its homogeneity. In opaque substances the accumulation of
heat is confined to the stratum nearest the surface. The seas become
less heated at their surface than the land, because the solar rays,
before being extinguished, penetrate the transparent liquid to a greater
depth and in greater numbers than in the opaque masses. On the other
hand, water has a considerable radiating power, which, together with
evaporation, would reduce the surface of the ocean to a very low
temperature, if the cold particles did not sink to the bottom on account
of their superior density. The seas preserve a considerable portion of
the heat they receive in summer, and from their saltness do not freeze
so soon as fresh water. So that, in consequence of all these
circumstances, the ocean is not subject to such variations of heat as
the land, and, by imparting its temperature to the winds and by its
currents, it diminishes the rigour of climate on the coasts and in the
islands, which are never subject to such extremes of heat and cold as
are experienced in the interior of continents, though they are liable to
fogs and rain from the evaporation of the adjacent seas. On each side of
the equator to the 48th degree of latitude, the surface of the ocean is
in general warmer than the air above it. The mean of the difference of
the temperature at noon and midnight is about 1°·37, the greatest
deviation never exceeding from 0°·36 to 2°·16, which is much cooler than
the air over the land.

On land the temperature depends upon the nature of the soil and its
products, its habitual moisture or dryness. From the eastern extremity
of the Sahara desert quite across Africa, the soil is almost entirely
barren sand; and the Sahara desert itself extends over an area of
194,000 square leagues, equal to twice the area of the Mediterranean
Sea, and raises the temperature of the air by radiation from 90° to
100°, which must have a most extensive influence. On the contrary,
vegetation cools the air by evaporation and the apparent radiation of
cold from the leaves of plants, because they absorb more caloric than
they give out. The graminiferous plains of South America cover an extent
ten times greater than France, occupying no less than about 50,000
square leagues, which is more than the whole chain of the Andes, and all
the scattered mountain-groups of Brazil. These, together with the plains
of North America and the steppes of Europe and Asia, must have an
extensive cooling effect on the atmosphere if it be considered that in
calm and serene nights they cause the thermometer to descend 12° or 14°,
and that in the meadows and heaths in England the absorption of heat by
the grass is sufficient to cause the temperature to sink to the point of
congelation during the night for ten months in the year. Forests cool
the air also by shading the ground from the rays of the sun, and by
evaporation from the boughs. Hales found that the leaves of a single
plant of helianthus three feet high exposed nearly forty feet of
surface; and, if it be considered that the woody regions of the river
Amazons, and the higher part of the Orinoco, occupy an area of 260,000
square leagues, some idea may be formed of the torrents of vapour which
rise from the leaves of the forests all over the globe. However, the
frigorific effects of their evaporation are counteracted in some measure
by the perfect calm which reigns in the tropical wildernesses. The
innumerable rivers, lakes, pools, and marshes interspersed through the
continents absorb caloric, and cool the air by evaporation; but, on
account of the chilled and dense particles sinking to the bottom, deep
water diminishes the cold of winter, so long as ice is not formed.

In consequence of the difference in the radiating and absorbing powers
of the sea and land, their configuration greatly modifies the
distribution of heat over the surface of the globe. Under the equator
only one-sixth part of the circumference is land; and the superficial
extent of land in the northern and southern hemispheres is in the
proportion of three to one. The effect of this unequal division is
greater in the temperate than in the torrid zones, for the area of land
in the northern temperate zone is to that in the southern as thirteen to
one, whereas the proportion of land between the equator and each tropic
is as five to four. It is a curious fact, noticed by Mr. Gardner, that
only one twenty-seventh part of the land of the globe has land
diametrically opposite to it. This disproportionate arrangement of the
solid part of the globe has a powerful influence on the temperature of
the southern hemisphere. But, besides these greater modifications, the
peninsulas, promontories, and capes, running out into the ocean,
together with bays and internal seas, all affect temperature. To these
may be added the position of continental masses with regard to the
cardinal points. All these diversities of land and water influence
temperature by the agency of the winds. On this account the temperature
is lower on the eastern coasts both of the New and Old World than on the
western; for, considering Europe as an island, the general temperature
is mild in proportion as the aspect is open to the Atlantic Ocean, the
superficial temperature of which, as far north as the 45th and 50th
degrees of latitude, does not fall below 48° or 51° of Fahrenheit, even
in the middle of winter. On the contrary, the cold of Russia arises from
its exposure to the northern and eastern winds. But the European part of
that empire has a less rigorous climate than the Asiatic, because it
does not extend to so high a latitude.

The interposition of the atmosphere modifies all the effects of the
sun’s heat. The earth communicates its temperature so slowly, that M.
Arago has occasionally found as much as from 14° to 18° of difference
between the heat of the soil and that of the air two or three inches
above it.

The circumstances which have been enumerated, and many more, concur in
disturbing the regular distribution of heat over the globe, and occasion
numberless local irregularities. Nevertheless the mean annual
temperature becomes gradually lower from the equator to the poles. But
the diminution of mean heat is most rapid between the 40th and 45th
degrees of latitude both in Europe and America, which accords perfectly
with theory; whence it appears that the variation in the square of the
cosine of the latitude (N. 127), which expresses the law of the change
of temperature, is a maximum towards the 45th degree of latitude. The
mean annual temperature under the equator in America is about 81-1/2° of
Fahrenheit: in Africa it is said to be nearly 83°. The difference
probably arises from the winds of Siberia and Canada, whose chilly
influence is sensibly felt in Asia and America, even within 18° of the
equator.

The isothermal lines are nearly parallel to the equator, till about the
22nd degree of latitude on each side of it, where they begin to lose
their parallelism, and continue to do so more and more as the latitude
augments. With regard to the northern hemisphere, the isothermal line of
59° of Fahrenheit passes between Rome and Florence in latitude 43°; and
near Raleigh in North Carolina, latitude 36°: that of 50° of equal
annual temperature runs through the Netherlands, latitude 51°; and near
Boston in the United States, latitude 42-1/2°: that of 41° passes near
Stockholm, latitude 59-1/2°; and St. George’s Bay, Newfoundland,
latitude 48°: and lastly, the line of 32°, the freezing point of water,
passes between Ulea in Lapland, latitude 66°, and Table Bay, on the
coast of Labrador, latitude 54°.

Thus it appears that the isothermal lines, which are nearly parallel to
the equator for about 22°, afterwards deviate more and more. From
observations made during the numerous voyages in the Arctic Seas, it is
found that the isothermal lines of Europe and America entirely separate
in the high latitudes, and surround two poles of maximum cold: one, in
79° N. lat. and 120° E. long., has a mean temperature of 2° Fahrenheit;
and the other, whose temperature was determined by Sir David Brewster to
be 3-1/2° Fahrenheit, from the observations of Sir Edward Parry is near
Melville Island. The pole of the earth’s rotation, whose mean
temperature is probably not below 15° Fahrenheit, is nearly midway
between the two; and the line which joins these points of maximum cold
is almost coincident with that diameter of the polar basin which bisects
it, and passes through its two great outlets into the Pacific and
Atlantic Oceans, a most remarkable feature, and strongly indicative of
the absence of land, and of the prevalence of a materially milder
climate in the polar Ocean, probably not under 15° Fahrenheit.[12] It is
believed that two corresponding poles of maximum cold exist in the
southern hemisphere, though observations are wanting to trace the course
of the southern isothermal lines with the same accuracy as the northern.

The isothermal lines, or such as pass through places where the mean
annual temperature of the air is the same, do not always coincide with
the isogeothermal lines, which are those passing through places where
the mean temperature of the ground is the same. Sir David Brewster, in
discussing this subject, finds that the isogeothermal lines are always
parallel to the isothermal lines; consequently the same general formula
will serve to determine both, since the difference is a constant
quantity obtained by observation, and depending upon the distance of the
place from the neutral isothermal line. These results are confirmed by
the observations of M. Kupffer of Kasan during his excursions to the
north, which show that the European and the American portions of the
isogeothermal line of 32° of Fahrenheit actually separate, and go round
the two poles of maximum cold. This traveller remarked, also, that the
temperature both of the air and of the soil decreases most rapidly
towards the 45th degree of latitude.

It is evident that places may have the same mean annual temperature, and
yet differ materially in climate. In one, the winters may be mild and
the summers cool; whereas another may experience the extremes of heat
and cold. Lines passing through places having the same mean summer or
winter temperature are neither parallel to the isothermal, the
geothermal lines, nor to one another, and they differ still more from
the parallels of latitude. In Europe, the latitude of two places which
have the same annual heat never differs more than 8° or 9°; whereas the
difference in the latitude of those having the same mean winter
temperature is sometimes as much as 18° or 19°. At Kasan, in the
interior of Russia, in latitude 55°·48, nearly the same with that of
Edinburgh, the mean annual temperature is about 37°·6; at Edinburgh it
is 47°·84. At Kasan the mean summer temperature is 64°·84, and that of
winter 2°·12; whereas at Edinburgh the mean summer temperature is
58°·28, and that of winter 38°·66. Whence it appears that the difference
of winter temperature is much greater than that of summer. At Quebec the
summers are as warm as those in Paris, and grapes sometimes ripen in the
open air: whereas the winters are as severe as in Petersburgh; the snow
lies five feet deep for several months, wheel carriages cannot be used,
the ice is too hard for skating, travelling is performed in sledges, and
frequently on the ice of the river St. Lawrence. The cold at Melville
Island on the 15th of January, 1820, according to Sir Edward Parry, was
55° below the zero of Fahrenheit’s thermometer; and when Dr. Kane was on
the northern coast of Greenland it was 70° below that point; yet the
summer heat during the day in these high latitudes is insupportable.

Observations tend to prove that all the climates of the earth are
stable, and that their vicissitudes are only periods or oscillations of
more or less extent, which vanish in the mean annual temperature of a
sufficient number of years. This constancy of the mean annual
temperature of the different places on the surface of the globe shows
that the same quantity of heat which is annually received by the earth
is annually radiated into space; and that would be the case even if the
quantity of heat emitted by the sun should vary with his spots, for, if
more were received, more would be radiated. Nevertheless, a variety of
causes may disturb the climate of a place; cultivation may make it
warmer; but it is at the expense of some other place, which becomes
colder in the same proportion. There may be a succession of cold summers
and mild winters, but in some other country the contrary takes place to
effect the compensation; wind, rain, snow, fog, and the other meteoric
phenomena, are the ministers employed to accomplish the changes. The
distribution of heat may vary with a variety of circumstances; but the
absolute quantity lost and gained by the whole earth in the course of a
year, if not invariably the same, is at least periodical.




                             SECTION XXVI.

Influence of Temperature on Vegetation—Vegetation varies with the
  Latitude and Height above the Sea—Geographical Distribution of Land
  Plants—Distribution of Marine Plants—Corallines, Shell-fish, Reptiles,
  Insects, Birds, and Quadrupeds—Varieties of Mankind, yet identity of
  Species.


THE gradual decrease of temperature in the air and in the earth, from
the equator to the poles, is clearly indicated by its influence on
vegetation. In the valleys of the torrid zone, where the mean annual
temperature is very high, and where there is abundance of light and
moisture, nature adorns the soil with all the luxuriance of perpetual
summer. The palm, the bombax ceiba, and a variety of magnificent trees,
tower to the height of 150 or 200 feet above the banana, the bamboo, the
arborescent fern, and numberless other tropical productions, so
interlaced by creeping and parasitical plants, as often to present an
impenetrable barrier. But the richness of vegetation gradually
diminishes with the temperature; the splendour of the tropical forest is
succeeded by the regions of the vine and olive; these again yield to the
verdant meadows of more temperate climes; then follow the birch and the
pine, which probably owe their existence in very high latitudes more to
the warmth of the soil than to that of the air. But even these enduring
plants become dwarfish shrubs, till a verdant carpet of mosses and
lichens, enamelled with flowers, exhibits the last sign of vegetable
life during the short but fervid summers at the polar regions. Such is
the effect of cold and diminished light on the vegetable kingdom, that
the number of species growing under the equator and in the northern
latitudes of 45° and 68° are in the proportion of the numbers 12, 4, and
1. Notwithstanding the remarkable difference between a tropical and
polar flora, light and moisture seem to be almost the only requisites
for vegetation, since neither heat, cold, nor even comparative darkness,
absolutely destroy the fertility of nature. In salt plains and sandy
deserts alone hopeless barrenness prevails. Plants grow on the borders
of hot springs: they form the oases wherever moisture exists among the
burning sands of Africa; they are found in caverns almost void of light,
though generally blanched and feeble. The ocean teems with vegetation.
The snow itself not only produces a red lichen, discovered by Saussure
in the frozen declivities of the Alps, found in abundance by the author
crossing the Col de Bonhomme from Savoy to Piedmont, and by the polar
navigators in the Arctic regions, but it affords shelter to the
productions of these inhospitable climes against the piercing winds that
sweep over fields of everlasting ice. Those undaunted mariners narrate
that under this cold defence plants spring up, dissolve the snow a few
inches round, and the part above, being again quickly frozen into a
transparent sheet of ice, admits the sun’s rays, which warm and cherish
the plants in this natural hothouse, till the returning summer renders
such protection unnecessary.

The chemical action of light is, however, absolutely requisite for the
growth of plants which derive their principal nourishment from the
atmosphere. They consume the carbonic acid gas, nitrogen, aqueous
vapour, and ammonia it contains; but it is the chemical agency of light
that enables them to absorb, decompose, and consolidate these substances
into wood, leaves, flowers, and fruit. The atmosphere would soon be
deprived of these elements of vegetable life were they not perpetually
supplied by the animal creation; while, in return, plants decompose the
moisture they imbibe, and, having assimilated the carbonic acid gas,
they exhale oxygen for the maintenance of the animated creation, and
thus preserve a just equilibrium. Hence it is the combined and powerful
influences of the whole solar beams that give such brilliancy to the
tropical forests, while, with their decreasing energy in the higher
latitudes, vegetation becomes less vigorous. On that account it is vain
to expect that the fruit and flowers raised in our hothouses can ever
have the flavour, perfume, or colouring equal to that which they acquire
from the vivid light of their native skies.

By far the greater number of the known species of plants are indigenous
in equinoctial America; Europe contains about half the number; Asia,
with its islands, somewhat less than Europe; Australia, with the islands
in the Pacific, still less; and in Africa there are fewer known
vegetable productions than in any part of the globe of equal extent, for
that rich and luxuriant region discovered by Dr. Livingstone has yet to
be explored botanically. Very few social plants, such as grasses and
heaths that cover large tracts of land, are to be found between the
tropics, except on the sea-coasts and elevated plains. Some exceptions
to this, however, are to be met with in the jungles of the Deccan, &c.
In the equatorial regions, where the heat is always great, the
distribution of plants depends upon the mean annual temperature; whereas
in temperate zones the distribution is regulated in some degree by the
summer heat. Some plants require a gentle heat of long continuance,
others flourish most where the extremes of heat and cold are greater.
The range of wheat is very great; it may be cultivated as far north as
the 60th degree of latitude; but in the torrid zone it will seldom form
an ear below an elevation of 4500 feet above the level of the sea from
exuberance of vegetation; nor will it ripen generally above the height
of 12,000 feet; in Tibet it ripens at a still greater elevation. Colonel
Sykes states that in the Deccan wheat thrives as low as 1800 feet above
the sea. The best wines are produced between the 30th and 45th degrees
of north latitude. With regard to the vegetable kingdom, elevation is
equivalent to latitude as far as temperature is concerned. In ascending
the mountains of the torrid zone, the richness of the tropical
vegetation diminishes with the height; a succession of plants similar
to, though not identical with, those found in latitudes of corresponding
mean temperature takes place; the lofty forests by degrees lose their
splendour; stunted shrubs succeed; till at last the progress of the
lichen is checked by perpetual snow. On the volcano of Teneriffe there
are five successive zones, each producing distinct families of plants.
The first is the region of vines, the next that of laurels; these are
followed by the region of pines, of Ericas or heaths, of grass; the
whole covering the declivity of the peak through an extent of 11,200
feet of perpendicular height.

Near the equator oaks flourish at the height of 9200 feet above the sea;
and, on the lofty range of the Himalaya, the primula, the convallaria,
and the veronica flower, but not the primrose, the lily of the valley,
or the veronica, which adorn our meadows; for, although the herbarium
collected by Moorcroft, on his route from Neetee to Daba and Gartope in
Chinese Tartary, at elevations as high or even higher than Mont Blanc,
abound in Alpine and European genera, the species are universally
different, with the single exception of the Rhodiola rosea, which is
identical with the species that blooms in Scotland. It is not in this
instance alone that similarity of climate obtains without identity of
productions; throughout the whole globe a certain analogy both of
structure and appearance is frequently discovered between plants under
corresponding circumstances which are yet specifically different. It is
even said that a difference of 25° of latitude occasions a total change,
not only of vegetable productions, but of organised beings. Certain it
is that each separate region both of land and water, from the frozen
shores of the polar circles to the burning regions of the torrid zone,
possesses a flora peculiarly its own. The whole globe has been divided
by physical geographers into various botanical districts, differing
almost entirely in their specific vegetable productions, the limits of
which are most decided when they are separated by a wide expanse of
ocean, mountain chains, sandy deserts, salt plains, or internal seas. A
considerable number of plants are common to the northern regions of
Asia, Europe, and America, where the continents almost unite; but, in
approaching the south, the floras of these three great divisions of the
globe differ more and more even in the same parallels of latitude, which
shows that temperature alone is not the cause of the almost complete
diversity of species that everywhere prevails. The floras of China,
Siberia, Tartary, of the European district including central Europe and
the coast of the Mediterranean, and the Oriental region comprising the
countries round the Black and Caspian Seas, all differ in specific
character. Only twenty-four species were found by MM. Humboldt and
Bonpland in Equinoctial America identical with those of the Old World;
and Dr. Robert Brown not only found that a peculiar vegetation exists in
Australia between the 33rd and 35th parallels of south latitude, but
that at the eastern and western extremities of these parallels not one
species is common to both, and that certain genera also are almost
entirely confined to these spots. The number of species common to
Australia and Europe are only 166 out of 4100, and probably some of
these have been conveyed thither by the colonists; but the greater part
of that continent is still unexplored. However, this proportion exceeds
what has hitherto been observed in southern Africa, and, from what has
been already stated, the proportion of European species in Equinoctial
America is still less.

Islands partake of the vegetation of the nearest continents; but, when
very remote from land, their floras are altogether peculiar. The
Aleutian Islands, extending between Asia and America, partake of the
vegetation of the northern parts of both continents, and may have served
as a chain of communication. In Madeira and Teneriffe, the plants of
Portugal, Spain, the Azores, and of the northern coast of Africa, are
found; and the Canaries contain a great number of plants belonging to
the African coast. But each of these islands possesses a flora that
exists nowhere else; and St. Helena, standing alone in the midst of the
Atlantic Ocean, produces only two or three species of plants recognised
as belonging to any other part of the world.

It appears from the investigations of M. de Humboldt that between the
tropics the plants, such as grasses and palms, which have only one
seed-lobe, are to the tribe which have two seed-lobes, like most of the
European species, in the proportion of one to four; in the temperate
zones they are as one to six; and in the Arctic regions, where mosses
and lichens, which form the lowest order of the vegetable creation,
abound, the proportion is as one to two. Annuals with one and two
seed-lobes, in the temperate zones, amount to one-sixth of the whole,
omitting the cryptogamia (N. 218); in the torrid zone they scarcely form
one-twentieth, and in Lapland one-thirtieth part. In approaching the
equator the ligneous exceed the number of herbaceous plants; in America
there are 120 different species of forest trees, whereas in the same
latitudes in Europe only 34 are to be found.

Similar laws regulate the distribution of marine plants. Groups of algæ,
or marine plants, affect particular temperatures or zones of latitude
and different depths, though some few genera prevail throughout the
ocean. The polar Atlantic basin to the 40th degree of north latitude
presents a well-defined vegetation. The West India seas, including the
Gulf of Mexico, the eastern coast of South America, the Indian Ocean and
its gulfs, the shores of New Holland, and the neighbouring islands, have
each their distinct species. The Mediterranean possesses a vegetation
peculiar to itself, extending to the Black Sea; and the species of
marine plants on the coast of Syria and in the port of Alexandria differ
almost entirely from those of Suez and the Red Sea. It is observed that
shallow seas have a different set of plants from such as are deeper and
colder; and, unlike terrestrial vegetation, the algæ are more numerous
in the mean latitudes than either towards the equator or the poles. They
vary also with the depth: completely different kinds affect different
depths, their seeds being of such specific gravity as to remain and
germinate where the parent plant grew. The quantity of algæ in that
accumulation known as the sargassa or grassy sea is so great, that the
early navigators, Columbus and Lerius, compared it to extensively
inundated meadows: it impeded their ships, and alarmed their sailors. It
is in the North Atlantic, a little to the west of the meridian of Fayal,
one of the Azores, between the 25th and 36th parallels of latitude. A
smaller bank lies between the 22nd and 26th degrees of north latitude,
about 80 leagues west of the meridian of the Bahama Islands. These
masses chiefly consist of one or two species of sargassa, the most
extensive genus of the order Fucoideæ.

Some of the seaweeds grow to enormous lengths, and all are highly
coloured, though many of them must grow in deep water. Light, however,
may not be the only principle on which the colour of vegetables depends,
since Baron Humboldt met with green plants growing in complete darkness
in one of the mines at Freyberg.

In the dark and tranquil caves of the ocean, on the shores alternately
covered and deserted by the restless waves, on the lofty mountain and
extended plain, in the chilly regions of the north, and in the genial
warmth of the south, specific diversity is a general law of the
vegetable kingdom, which cannot be accounted for by diversity of
climate; and yet the similarity, though not identity, of species is
such, under the same isothermal lines, that if the number of species
belonging to one of the great families of plants be known in any part of
the globe, the whole number of the flowering or more perfect plants, and
also the number of species composing the other vegetable families, may
be estimated with considerable accuracy.

Various opinions have been formed on the original or primitive
distribution of plants over the face of the globe; but, since botanical
geography has become a science, the phenomena observed have led to the
conclusion that vegetable creation must have taken place in a number of
distinctly different centres, as the islands and continents rose above
the ocean, each of which was the original seat of a certain number of
peculiar species which at first grew there and nowhere else. Heaths are
exclusively confined to the Old World; and no indigenous rose-tree has
ever been seen in the New, the whole southern hemisphere being destitute
of that beautiful and fragrant plant. But this is still more confirmed
by multitudes of particular plants, having an entirely local and
insulated existence, growing spontaneously in some particular spot, and
in no other place: for example, the cedar of Lebanon, which grows
indigenously on that mountain, and in no other part of the world. On the
other hand, as there can be no doubt that many races of plants have been
extinguished, Sir John Herschel thinks it possible that these solitary
instances may be the last surviving remnants of the same group
universally disseminated, but in course of extinction, or that perhaps
two processes may be going on at the same time:—“Some groups may be
spreading from their foci, others retreating to their last holds.”

The same laws obtain in the distribution of the animal creation. Even
the microscopic existences, which seem to be the most widely spread,
have their specific localities; and the zoophyte (N. 219), occupying the
next lowest place in animated nature, is widely scattered through the
seas of the torrid zone, each species being confined to the district and
depth best suited to its wants. Mollusks, or the animals of shells,
decrease in size and beauty with their distance from the equator; and
not only each sea and every basin of the ocean, but each depth, is
inhabited by its peculiar tribe of fish. Indeed, MM. Peron and Le Sueur
assert that, among the many thousands of marine animals which they had
examined, there is not a single animal of the southern regions which is
not distinguishable by essential characters from the analogous species
in the northern seas.

Reptiles are not exempt from the general law. The saurian (N. 220)
tribes of the four quarters of the globe differ in species; and,
although warm countries abound in venomous snakes, they are specifically
different in different localities, and decrease both in numbers and in
the virulence of their poison with decrease of temperature. The
dispersion of insects necessarily follows that of the vegetables which
supply their food; and in general it is observed that each kind of plant
is peopled by its peculiar inhabitants. Each species of bird has its
peculiar haunt, notwithstanding the locomotive powers of the winged
tribes. The emu is confined to Australia, the condor to the Andes and
their declivities, and the bearded vulture or lemmergeyer to the Alps.
Some birds, like the common sparrow, have a wide range; but those met
with in every country are few in number. Quadrupeds are distributed in
the same manner wherever man has not interfered. Such as are indigenous
in one country are not the same with their congeners in another; and,
with the exception of some kind of bats, no mammiferous animal is
indigenous in the Polynesian Archipelago, nor in any of the islands on
the borders of the central part of the Pacific.

In reviewing the infinite variety of organised beings that people the
surface of the globe, nothing is more remarkable than the distinctions
which characterise the different tribes of mankind, from the ebony skin
of the torrid zone to the fair and ruddy complexion of the
Scandinavian—a difference which existed in the earliest recorded times,
since the African is represented in the sacred writings to have been as
black as he is at the present day, and the most ancient Egyptian
paintings confirm that truth; yet it appears, from a comparison of the
principal circumstances relating to the animal economy or physical
character of the various tribes of mankind, that the different races are
identical in species. Many attempts have been made to trace the various
tribes back to a common origin, by collating the numerous languages
which are or have been spoken. Some classes of these have few or no
words in common, yet exhibit a remarkable analogy in the laws of their
grammatical construction. The languages spoken by the native American
nations afford examples of these; indeed, the refinement in the
grammatical construction of the tongues of the American savages leads to
the belief that they must originally have been spoken by a much more
civilised class of mankind. Some tongues have little or no resemblance
in structure, though they correspond extensively in their vocabularies,
as the Syrian dialects. In all these cases it may be inferred that the
nations speaking the languages in question descended from the same
stock; but the probability of a common origin is much greater in the
Indo-European nations, whose languages, such as the Sanscrit, Greek,
Latin, German, &c., have an affinity both in structure and
correspondence of vocables. In many tongues not the smallest resemblance
can be traced; length of time, however, may have obliterated original
identity; but so many ages have passed before the subject became a
study, and so many languages have worn out of use, that it may be
doubted whether any satisfactory result will ever be arrived at with
regard to the original speech of mankind.




                             SECTION XXVII.

Terrestrial Heat—Radiation—Transmission—Melloni’s experiments—Heat
  in Solar Spectrum—Polarization of Heat—Nature of
  Heat—Absorptions—Dew—Rain—Combustion—Expansion—Compensation
  Pendulum—Transmission through Crystals—Propagation—Dynamic Theory
  of Heat—Mechanical equivalent of Heat—Latent Heat is the Force of
  Expansion—Steam—Work performed by Heat—Conservation of
  Force—Mechanical Power in the Tides—Dynamical Power of
  Light—Analogy between Light, Heat, and Sound.


THAT heat producing rays exist independently of those of light is a
matter of constant experience in the abundant emission of them from
boiling water. They dart in divergent straight lines from flame and from
each point in the surfaces of hot bodies, in the same manner as
diverging rays of light proceed from every point of those that are
luminous. According to the experiments of Sir John Leslie, radiation
proceeds not only from the surface of substances, but also from the
particles at a minute depth below it. He found that the emission is most
abundant in a direction perpendicular to the radiating surface, and that
it is more rapid from a rough than from a polished surface: radiation,
however, can only take place in air and in vacuo; it is altogether
imperceptible when the hot body is enclosed in a solid or liquid. Heated
substances, when exposed to the open air, continue to radiate heat till
they become nearly of the temperature of the surrounding medium. The
radiation is very rapid at first, but diminishes according to a known
law with the temperature of the heated body. It appears, also, that the
radiating power of a surface is inversely as its reflecting power; and
bodies that are most impermeable to heat radiate least. Substances,
however, have an elective power, only reflecting heat of a certain
refrangibility. Mr. Grove gives paper, snow, and lime as instances,
which, although all white, radiate heat of different refrangibilities,
while metals, whatever their colour may be, radiate all kinds alike.

Rays of heat, whether they proceed from the sun, from flame, or other
terrestrial sources, luminous or non-luminous, are instantaneously
transmitted through solid and liquid substances, there being no
appreciable difference in the time they take to pass through layers of
any nature or thickness whatever. They pass also with the same facility
whether the media be agitated or at rest; and in these respects the
analogy between light and heat is perfect. Radiant heat passes through
the gases with the same facility as light; but a remarkable difference
obtains in the transmission of light and heat through most solid and
liquid substances, the same body being often perfectly permeable to the
luminous, and altogether impermeable to the calorific rays. For example,
thin and perfectly transparent plates of alum and citric acid sensibly
transmit all the rays of light from an argand lamp, but stop eight or
nine tenths of the concomitant heat; whilst a large piece of brown
rock-crystal gives a free passage to the radiant heat, but intercepts
almost all the light. Alum united to green glass is also capable of
transmitting the brightest light, but it gives not the slightest
indication of heat; while rock-salt covered thickly over with soot, so
as to be perfectly opaque to light, transmits a considerable quantity of
heat. M. Melloni has established the general law in uncrystallized
substances such as glass and liquids, that the property of
instantaneously transmitting heat is in proportion to their refractive
powers. The law, however, is entirely at fault in bodies of a
crystalline texture. Carbonate of lead, for instance, which is
colourless, and possesses a very high refractive power with regard to
light, transmits less radiant heat than Iceland spar or rock-crystal,
which are very inferior to it in the order of refrangibility; whilst
rock-salt, which has the same transparency and refractive power with
alum and citric acid, transmits six or eight times as much heat. This
remarkable difference in the transmissive power of substances having the
same appearance is attributed by M. Melloni to their crystalline form,
and not to the chemical composition of their molecules, as the following
experiments prove. A block of common salt cut into plates entirely
excludes calorific radiation; yet, when dissolved in water, it increases
the transmissive power of that liquid: moreover, the transmissive power
of water is increased in nearly the same degree, whether salt or alum be
dissolved in it; yet these two substances transmit very different
quantities of heat in their solid state. Notwithstanding the influence
of crystallization on the transmissive power of bodies, no relation has
been traced between that power and the crystalline form.

The transmission of radiant heat is analogous to that of light through
coloured media. When common white light passes through a red liquid,
almost all the more refrangible rays, and a few of the red, are
intercepted by the first layer of the fluid; fewer are intercepted by
the second, still less by the third, and so on: till at last the losses
become very small and invariable, and those rays alone are transmitted
which give the red colour to the liquid. In a similar manner, when
plates of the same thickness of any substance, such as glass, are
exposed to an argand lamp, a considerable portion of the radiant heat is
arrested by the first plate, a less portion by the second, still less by
the third, and so on, the quantity of lost heat decreasing till at last
the loss becomes a constant quantity. The transmission of radiant heat
through a solid mass follows the same law. The losses are very
considerable on first entering it, but they rapidly diminish in
proportion as the heat penetrates deeper, and become constant at a
certain depth. Indeed, the only difference between the transmission of
radiant heat through a solid mass, or through the same mass when cut
into plates of equal thickness, arises from the small quantity of heat
that is reflected at the surface of the plates. It is evident,
therefore, that the heat gradually lost is not intercepted at the
surface, but absorbed in the interior of the substance, and that heat
which has passed through one stratum of air experiences a less
absorption in each of the succeeding strata, and may therefore be
propagated to a greater distance before it is extinguished. The
experiments of M. de Laroche show that glass, however thin, totally
intercepts the obscure rays of heat when they flow from a body whose
temperature is lower than that of boiling water; that, as the
temperature increases, the calorific rays are transmitted more and more
abundantly; and, when the body becomes highly luminous, that they
penetrate the glass with perfect ease. The extreme brilliancy of the sun
is probably the reason why his heat, when brought to a focus by a lens,
is more intense than any that has been produced artificially. It is
owing to the same cause that glass screens, which entirely exclude the
heat of a common fire, are permeable by the solar heat.

The results obtained by M. de Laroche have been confirmed by the
experiments of M. Melloni on heat radiated from sources of different
temperatures, whence it appears that the calorific rays pass less
abundantly not only through glass, but through rock-crystal, Iceland
spar, and other diaphanous bodies, both solid and liquid, according as
the temperature of their origin is diminished, and that they are
altogether intercepted when the temperature is about that of boiling
water.

In fact, he has proved that the heat emanating from the sun or from a
bright flame consists of rays which differ from each other as much as
the coloured rays do which constitute white light. This explains the
reason of the loss of heat as it penetrates deeper and deeper into a
solid mass, or in passing through a series of plates; for, of the
different kinds of rays which dart from a vivid flame, all are
successively extinguished by the absorbing nature of the substance
through which they pass, till those homogeneous rays alone remain which
have the greatest facility in passing through that particular substance;
exactly as in a red liquid the violet, blue, green, orange, and yellow
rays are extinguished, and the red are transmitted.

M. Melloni employed four sources of heat, two of which were luminous and
two obscure; namely, an oil-lamp without a glass, incandescent platina,
copper heated to 696°, and a copper vessel filled with water at the
temperature of 178-1/2° of Fahrenheit. Rock-salt transmitted heat in the
proportion of 92 rays out of 100 from each of these sources; but all
other substances pervious to radiant heat, whether solid or liquid,
transmitted more heat from sources of high temperature than from such as
are low. For instance, limpid and colourless fluate of lime transmitted
in the proportion of 78 rays out of 100 from the lamp, 69 from the
platina, 42 from the copper, and 33 from the hot water; while
transparent rock-crystal transmitted 38 rays in 100 from the lamp, 28
from the platina, 6 from the copper, and 9 from the hot water. Pure ice
transmitted only in the proportion of 6 rays in the 100 from the lamp,
and entirely excluded those from the other three sources. Out of 39
different substances, 34 were pervious to the calorific rays from hot
water, 14 excluded those from the hot copper, and 4 did not transmit
those from the platinum.

Thus it appears that heat proceeding from these four sources is of
different kinds: this difference in the nature of the calorific rays is
also proved by another experiment, which will be more easily understood
from the analogy of light. Red light, emanating from red glass, will
pass in abundance through another piece of red glass, but it will be
absorbed by green glass; green rays will more readily pass through a
green medium than through one of any other colour. This holds with
regard to all colours; so in heat. Rays of heat of the same intensity,
which have passed through different substances, are transmitted in
different quantities by the same piece of alum, and are sometimes
stopped altogether; showing that rays which emanate from different
substances possess different qualities. It appears that a bright flame
furnishes rays of heat of all kinds, in the same manner as it gives
light of all colours; and, as coloured media transmit some coloured rays
and absorb the rest, so bodies transmit some rays of heat and exclude
the others. Rock-salt alone resembles colourless transparent media in
transmitting all kinds of heat, even that of the hand, just as they
transmit white light, consisting of rays of all colours. Radiant heat is
unequally refracted by a prism of rock-salt like light, and the rays of
heat thus dispersed are found to possess properties analogous to the
rays of the coloured spectrum.

The property of transmitting the calorific rays diminishes to a certain
degree with the thickness of the body they have to traverse, but not so
much as might be expected. A piece of very transparent alum transmitted
three or four times less radiant heat from the flame of a lamp than a
piece of nearly opaque quartz about a hundred times as thick. However,
the influence of thickness upon the phenomena of transmission increases
with the decrease of temperature in the origin of the rays, and becomes
very great when that temperature is low. This is a circumstance
intimately connected with the law established by M. de Laroche; for M.
Melloni observed that the difference between the quantities of heat
transmitted by the same plate of glass, exposed successively to several
sources of heat, diminished with the thinness of the plate, and vanished
altogether at a certain limit; and that a film of mica transmitted the
same quantity of heat, whether it was exposed to incandescent platinum
or to a mass of iron heated to 360°.

Coloured glasses transmit rays of light of certain degrees of
refrangibility, and absorb those of other degrees. For example, red
glass absorbs the more refrangible rays, and transmits the red, which
are the least refrangible. On the contrary, violet glass absorbs the
least refrangible, and transmits the violet, which are the most
refrangible. Now M. Melloni has found, that, although the colouring
matter of glass diminishes its power of transmitting heat, yet red,
orange, yellow, blue, violet, and white glass transmit calorific rays of
all degrees of refrangibility; whereas green glass possesses the
peculiar property of transmitting the least refrangible calorific rays,
and stopping those that are most refrangible. It has therefore the same
elective action for heat that coloured glass has for light, and its
action on heat is analogous to that of red glass on light. Alum and
sulphate of lime are exactly opposed to green glass in their action on
heat, by transmitting the most refrangible rays with the greatest
facility.

The heat which has already passed through green or opaque black glass
will not pass through alum, whilst that which has been transmitted
through glasses of other colours traverses it readily.

By reversing the experiment, and exposing different substances to heat
that had already passed through alum, M. Melloni found that the heat
emerging from alum is almost totally intercepted by opaque substances,
and is abundantly transmitted by all such as are transparent and
colourless, and that it suffers no appreciable loss when the thickness
of the plate is varied within certain limits. The properties of the heat
therefore which issues from alum nearly approach to those of light and
solar heat.

Radiant heat in traversing various media is not only rendered more or
less capable of being transmitted a second time, but, according to the
experiments of Professor Powell, it becomes more or less susceptible of
being absorbed in different quantities by black or white surfaces.

M. Melloni has proved that solar heat contains rays which are affected
by different substances in the same way as if the heat proceeded from a
terrestrial source; whence he concludes that the difference observed
between the transmission of terrestrial and solar heat arises from the
circumstance of solar heat containing all kinds of heat, whilst in other
sources some of the kinds are wanting.

Radiant heat, from sources of any temperature whatever, is subject to
the same laws of reflection and refraction as rays of light. The index
of refraction from a prism of rock-salt, determined experimentally, is
nearly the same for light and heat.

Liquids, the various kinds of glass, and probably all substances,
whether solid or liquid, that do not crystallize regularly, are more
pervious to the calorific rays according as they possess a greater
refractive power. For example, the chloride of sulphur, which has a high
refractive power, transmits more of the calorific rays than the oils,
which have a less refractive power: oils transmit more radiant heat than
the acids; the acids more than aqueous solutions; and the latter more
than pure water, which of all the series has the least refractive power,
and is the least pervious to heat. M. Melloni observed also that each
ray of the solar spectrum follows the same law of action with that of
terrestrial rays having their origin in sources of different
temperatures; so that the very refrangible rays may be compared to the
heat emanating from a focus of high temperature, and the least
refrangible to the heat which comes from a source of low temperature.
Thus, if the calorific rays emerging from a prism be made to pass
through a layer of water contained between two plates of glass, it will
be found that these rays suffer a loss in passing through the liquid as
much greater as their refrangibility is less. The rays of heat that are
mixed with the blue or violet light pass in great abundance, while those
in the obscure part which follows the red light are almost totally
intercepted. The first, therefore, act like the heat of a lamp, and the
last like that of boiling water.

These circumstances explain the phenomena observed by several
philosophers with regard to the point of greatest heat in the solar
spectrum, which varies with the substance of the prism. Sir William
Herschel, who employed a prism of flint glass, found that point to be a
little beyond the red extremity of the spectrum; but, according to M.
Seebeck, it is found to be upon the yellow, upon the orange, on the red,
or at the dark limit of the red, according as the prism consists of
water, sulphuric acid, crown or flint glass. If it be recollected that,
in the spectrum from crown glass, the maximum heat is in the red part,
and that the solar rays, in traversing a mass of water, suffer losses
inversely as their refrangibility, it will be easy to understand the
reason of the phenomenon in question. The solar heat which comes to the
anterior face of the prism of water consists of rays of all degrees of
refrangibility. Now, the rays possessing the same index of refraction
with the red light suffer a greater loss in passing through the prism
than the rays possessing the refrangibility of the orange light, and the
latter lose less in their passage than the heat of the yellow. Thus the
losses, being inversely proportional to the degree of refrangibility of
each ray, cause the point of maximum heat to tend from the red towards
the violet, and therefore it rests upon the yellow part. The prism of
sulphuric acid, acting similarly, but with less energy than that of
water, throws the point of greatest heat on the orange; for the same
reason, the crown and flint glass prisms transfer that point
respectively to the red and to its limit. M. Melloni, observing that the
maximum point of heat is transferred farther and farther towards the red
end of the spectrum, according as the substance of the prism is more and
more permeable to heat, inferred that a prism of rock-salt, which
possesses a greater power of transmitting the calorific rays than any
known body, ought to throw the point of greatest heat to a considerable
distance beyond the visible part of the spectrum,—an anticipation which
experiment fully confirmed, by placing it as much beyond the dark limits
of the red rays as the red part is distant from the blueish green band
of the spectrum.

In all these experiments M. Melloni employed a thermomultiplier,—an
instrument that measures the intensity of the transmitted heat with an
accuracy far beyond what any thermometer ever attained. It is a very
elegant application of M. Seebeck’s discovery of thermo-electricity; but
the description of this instrument is reserved for a future occasion,
because the principle on which it is constructed has not yet been
explained.

In the beginning of the present century, not long after M. Malus had
discovered the polarization of light, he and M. Berard proved that the
heat which accompanies the sun’s light is capable of being polarized;
but their attempts totally failed with heat derived from terrestrial,
and especially from non-luminous sources. M. Berard, indeed, imagined
that he had succeeded; but, when his experiments were repeated by Mr.
Lloyd and Professor Powell, no satisfactory result could be obtained. M.
Melloni resumed the subject, and endeavoured to effect the polarization
of heat by tourmaline, as in the case of light. It was already shown
that two slices of tourmaline, cut parallel to the axis of the crystal,
transmit a great portion of the incident light when looked through with
their axes parallel, and almost entirely exclude it when they are
perpendicular to one another. Should radiant heat be capable of
polarization, the quantity transmitted by the slices of tourmaline in
their former position ought greatly to exceed that which passes through
them in the latter, yet M. Melloni found that the quantity of heat was
the same in both cases: whence he inferred that heat from a terrestrial
source is incapable of being polarized. Professor Forbes of Edinburgh,
who prosecuted this subject with great acuteness and success, came to
the same conclusion in the first instance; but it occurred to him, that,
as the pieces of tourmaline became heated by being very near the lamp,
the secondary radiation from them rendered the very small difference in
the heat that was transmitted in the two positions of the pieces of
tourmaline imperceptible. Nevertheless he succeeded in proving, by
numerous observations, that heat from various sources is polarized by
the tourmaline; but that the effect with non-luminous heat is very
minute and difficult to perceive, on account of the secondary radiation.
Though light is almost entirely excluded in one position of the pieces
of tourmaline, and transmitted in the other, a vast quantity of radiant
heat passes through them in all positions. Eighty-four per cent. of the
heat from an argand lamp passed through them in the case where light was
altogether stopped. It is only the difference in the quantity of
transmitted heat that gives evidence of its polarization. The second
slice of tourmaline, when perpendicular to the first, stops all the
light, but transmits a great proportion of heat; alum, on the contrary,
stops almost all the heat, and transmits the light; whence it may be
concluded that heat, though intimately partaking the nature of light,
and accompanying it under certain circumstances, as in reflection and
refraction, is capable of almost complete separation from it under
others. The separation has since been perfectly effected by M. Melloni,
by passing a beam of light through a combination of water and green
glass, coloured by the oxide of copper. Even when the transmitted light
was concentrated by lenses, so as to render it almost as brilliant as
the direct light of the sun, it showed no sensible heat.

Professor Forbes next employed two bundles of laminæ of mica, placed at
the polarizing angle, and so cut that the plane of incidence of the heat
corresponded with one of the optic axes of this mineral. The heat
transmitted through this apparatus was polarized from a source whose
temperature was even as low as 200°; heat was also polarized by
reflection; but the experiments, though perfectly successful, are more
difficult to conduct.

It appears, from the various experiments of M. Melloni and Professor
Forbes, that all the calorific rays emanating from the sun and
terrestrial sources are equally capable of being polarized by reflection
and by refraction, whether double or single, and that they are also
capable of circular polarization by all the methods employed in the
circular polarization of light. Plates of quartz cut at right angles to
the axis of the prism possess the property of turning the calorific rays
in one direction, while other plates of the same substance from a
differently modified prism cause the rays to rotate in the contrary
direction; and two plates combined, when of different affection, and of
equal thickness, counteract each other’s effects as in the case of
light. Tourmaline separates the heat into two parts, one of which it
absorbs, while it transmits the other; in short, the transmission of
radiant heat is precisely similar to that of light.

Since heat is polarized in the same manner as light, it may be expected
that polarized heat transmitted through doubly refracting substances
should be separated into two pencils, polarized in planes at right
angles to each other; and that when received on an analyzing plate they
should interfere and produce invisible phenomena, perfectly analogous to
those described in Section XXII. with regard to light (N. 221).

It was shown, in the same section, that if light polarized by reflection
from a pane of glass be viewed through a plate of tourmaline, with its
longitudinal section vertical, an obscure cloud, with its centre wholly
dark, is seen on the glass. When, however, a plate of mica uniformly
about the thirteenth of an inch in thickness is interposed between the
tourmaline and the glass, the dark spot vanishes, and a succession of
very splendid colours are seen; and, as the mica is turned round in a
plane perpendicular to the polarized ray, the light is stopped when the
plane containing the optic axis of the mica is parallel or perpendicular
to the plane of polarization. Now, instead of light, if heat from a
non-luminous source be polarized in the manner described, it ought to be
transmitted and stopped by the interposed mica under the same
circumstances under which polarized light would be transmitted or
stopped. Professor Forbes found that this is really the case, whether he
employed heat from luminous or non-luminous sources: and he had
evidence, also, of circular and elliptical polarization of heat. It
therefore follows, that if heat were visible, under similar
circumstances we should see figures perfectly similar to those given in
Note 213, and those following; and, as these figures are formed by the
interference of undulations of light, it may be inferred that heat, like
light, is propagated by undulations of the ethereal medium, which
interfere under certain conditions, and produce figures analogous to
those of light. It appears also, from Mr. Forbes’s experiments, that the
undulations of heat are longer than the undulations of light; and it has
already been mentioned that Professor Draper considers them to be
normal, like those of sound.

That light and heat are both vibrations of the ethereal medium is not
the less true on account of the rays of heat being unseen, for the
condition of visibility or invisibility may only depend upon the
construction of our eyes, and not upon the nature of the motion which
produces these sensations in us. The sense of seeing may be confined
within certain limits. The chemical rays beyond the violet end of the
spectrum may be too rapid, or not sufficiently excursive, in their
vibrations, to be visible to the human eye; and the calorific rays
beyond the other end of the spectrum may not be sufficiently rapid, or
too extensive, in their undulations, to affect our optic nerves, though
both may be visible to certain animals or insects. We are altogether
ignorant of the perceptions which direct the carrier-pigeon to his home,
or of those in the antennæ of insects which warn them of the approach of
danger; nor can we understand the telescopic vision which directs the
vulture to his prey before he himself is visible even as a speck in the
heavens. So, likewise, beings may exist on earth, in the air, or in the
waters, which hear sounds our ears are incapable of hearing, and which
see rays of light and heat of which we are unconscious. Our perceptions
and faculties are limited to a very small portion of that immense chain
of existence which extends from the Creator to evanescence.

The identity of action under similar circumstances is one of the
strongest arguments in favour of the common nature of the chemical,
visible, and calorific rays. They are all capable of reflection from
polished surfaces, of refraction through diaphanous substances, of
polarization by reflection and by doubly refracting crystals; their
velocity is prodigious; they may be concentrated and dispersed by convex
and concave mirrors; they pass with equal facility through rock-salt and
are capable of radiation; and they are subject to the same law of
interference with those of light: hence there can be no doubt that the
whole assemblage of rays visible and invisible which constitute a solar
beam are propagated by the undulations of the ethereal medium, and
consequently as motions they come under the same laws of analysis.

When radiant heat falls upon a surface, part of it is reflected and part
of it is absorbed; consequently, the best reflectors possess the least
absorbing powers. The temperature of very transparent fluids is not
raised by the passage of the sun’s rays, because they do not absorb any
of them; and, as his heat is very intense, transparent solids arrest a
very small portion of it. The absorption of the sun’s rays is the cause
both of the colour and temperature of solid bodies. A black substance
absorbs all the rays of light, and reflects none; and since it absorbs,
at the same time, all the calorific rays, it becomes sooner warm, and
rises to a higher temperature, than bodies of any other colour. Blue
bodies come next to black in their power of absorption. And, since
substances of a blue tint absorb all the other colours of the spectrum,
they absorb by far the greatest part of the calorific rays, and reflect
the blue where they are least abundant. Next in order come the green,
yellow, red, and, last of all, white bodies, which reflect nearly all
the rays both of light and heat. However, there are certain limpid and
colourless media, which in some cases intercept calorific radiations and
become heated, while in other cases they transmit them and undergo no
change of temperature.

All substances may be considered to radiate heat, whatever their
temperature may be, though with different intensities, according to
their nature, the state of their surfaces, and the temperature of the
medium into which they are brought. But every surface absorbs as well as
radiates heat; and the power of absorption is always equal to that of
radiation; for, under the same circumstances, matter which becomes soon
warm also cools rapidly. There is a constant tendency to an equal
diffusion of heat, since every body in nature is giving and receiving it
at the same instant; each will be of uniform temperature when the
quantities of heat given and received during the same time are
equal—that is, when a perfect compensation takes place between each and
all the rest. Our sensations only measure comparative degrees of heat:
when a body, such as ice, appears to be cold, it imparts fewer calorific
rays than it receives; and when a substance seems to be warm—for
example, a fire—it gives more heat than it takes. The phenomena of dew
and hoar-frost are owing to this inequality of exchange; the heat
radiated during the night by substances on the surface of the earth,
into a clear expanse of sky, is lost to us, and no return is made from
the blue vault, so that their temperature sinks below that of the air,
whence they abstract a part of that heat which holds the atmospheric
humidity in solution, and a deposition of dew takes place. If the
radiation be great, the dew is frozen and becomes hoar-frost, which is
the ice of dew. Cloudy weather is unfavourable to the formation of dew,
by preventing the free radiation of heat; and actual contact is
requisite for its deposition, since it is never suspended in the air
like fog. Plants derive a great part of their nourishment from this
source; and, as each possesses a power of radiation peculiar to itself,
they are capable of procuring a sufficient supply for their wants. The
action of the chemical rays imparts to all substances more or less the
power of condensing vapour on those parts on which they fall, and must
therefore have a considerable influence on the deposition of dew. There
may be a low degree of humidity in the air which may yet contain a great
quantity of aqueous vapour, for vapour while it exists as gas is dry.
The temperature at which the atmosphere can contain no more vapour
without precipitation is called the dew point, and is measured by the
hygrometer. In foretelling the changes of weather it is scarcely
inferior to the barometer.

Steam is formed throughout the whole mass of a boiling liquid, whereas
evaporation takes place only at the free surface of liquids, and that
under the ordinary temperature and pressure of the atmosphere. There is
a constant evaporation from the land and water all over the earth. The
rapidity of the formation does not depend altogether on the dryness of
the air; according to Dr. Dalton’s experiments, it depends also on the
difference between the tension of the vapour which is forming, and that
which is already in the atmosphere. In calm weather vapour accumulates
in the stratum of air immediately above the evaporating surface, and
retards the formation of more; whereas a strong wind accelerates the
process by carrying off the vapour as soon as it rises, and making way
for a succeeding portion of dry air.

Rain is formed by the mixing of two masses of air of different
temperatures; the colder part, by abstracting from the other the heat
which holds it in solution, occasions the particles to approach each
other and form drops of water, which, becoming too heavy to be sustained
by the atmosphere, sink to the earth by gravitation in the form of rain.
The contact of two strata of air of different temperatures, moving
rapidly in opposite directions, occasions an abundant precipitation of
rain. When the masses of air differ very much in temperature, and meet
suddenly, hail is formed. This happens frequently in hot plains near a
ridge of mountains, as in the south of France, from the sudden descent
of an intensely cold current of wind into a mass of air nearly saturated
with vapour. Such also is the cause of the severe hail-storms which
occasionally take place on extensive plains within the tropics.

An accumulation of heat invariably produces light: with the exception of
the gases, all bodies which can endure the requisite degree of heat
without decomposition begin to emit light at the same temperature; but,
when the quantity of heat is so great as to render the affinity of their
component particles less than their affinity for the oxygen of the
atmosphere, a chemical combination takes place with the oxygen, light
and heat are evolved, and fire is produced. Combustion—so essential for
our comfort, and even existence—takes place very easily from the small
affinity between the component parts of atmospheric air, the oxygen
being nearly in a free state; but, as the cohesive force of the
particles of different substances is very variable, different degrees of
heat are requisite to produce their combustion. The tendency of heat to
a state of equal diffusion or equilibrium, either by radiation or
contact, makes it necessary that the chemical combination which
occasions combustion should take place instantaneously; for, if the heat
were developed progressively, it would be dissipated by degrees, and
would never accumulate sufficiently to produce a temperature high enough
for the evolution of flame.

It is a general law that all bodies expand by heat and contract by cold.
The expansive force of heat has a constant tendency to overcome the
attraction of cohesion, and to separate the constituent particles of
solids and fluids; by this separation the attraction of aggregation is
more and more weakened, till at last it is entirely overcome, or even
changed into repulsion. By the continual addition of heat, solids may be
made to pass into liquids, and from liquids to the aëriform state, the
dilatation increasing with the temperature; and every substance expands
according to a law of its own. Gases expand more than liquids, and
liquids more than solids. The expansion of air is more than eight times
that of water, and the increase in the bulk of water is at least
forty-five times greater than that of iron. Metals dilate uniformly from
the freezing to the boiling points of the thermometer; the uniform
expansion of the gases extends between still wider limits; but, as
liquidity is a state of transition from the solid to the aëriform
condition, the equable dilatation of liquids has not so extensive a
range. This change of bulk, corresponding to the variation of heat, is
one of the most important of its effects, since it furnishes the means
of measuring relative temperature by the thermometer and pyrometer. The
rate of expansion of solids varies at their transition to liquidity, and
that of liquidity is no longer equable near their change to an aëriform
state. There are exceptions, however, to the general laws of expansion;
some liquids have a maximum density corresponding to a certain
temperature, and dilate whether that temperature be increased or
diminished. For example—water expands whether it be heated above or
cooled below 40°. The solidification of some liquids, and especially
their crystallization, is always accompanied by an increase of bulk.
Water dilates rapidly when converted into ice, and with a force
sufficient to split the hardest substances. The formation of ice is
therefore a powerful agent in the disintegration and decomposition of
rocks, operating as one of the most efficient causes of local changes in
the structure of the crust of the earth; of which we have experience in
the tremendous _éboulemens_ of mountains in Switzerland. But Professor
W. Thomson has proved experimentally that it requires a lower
temperature to freeze water under pressure than when free.

The dilatation of substances by heat, and their contraction by cold,
occasion such irregularities in the rate of clocks and watches as would
render them unfit for astronomical or nautical purposes, were it not for
a very beautiful application of the laws of unequal expansion. The
oscillations of a pendulum are the same as if its whole mass were united
in one dense particle, in a certain point of its length, called the
centre of oscillation. If the distance of this point from the point by
which the pendulum is suspended were invariable, the rate of the clock
would be invariable also. The difficulty is to neutralize the effects of
temperature, which is perpetually increasing or diminishing its length.
Among many contrivances, Graham’s compensation pendulum is the most
simple. He employed a glass tube containing mercury. When the tube
expands from the effects of heat, the mercury expands much more; so that
its surface rises a little more than the end of the pendulum is
depressed, and the centre of oscillation remains stationary. Harrison
invented a pendulum which consists of seven bars of steel and of brass,
joined in the shape of a gridiron, in such a manner that, if by change
of temperature the bars of brass raise the weight at the end of the
pendulum, the bars of steel depress it as much. In general, only five
bars are used; three being of steel, and two a mixture of silver and
zinc. The effects of temperature are neutralized in chronometers upon
the same principle; and to such perfection are they brought, that the
loss or gain of one second in twenty-four hours for two days running
would render one unfit for use. Accuracy in surveying depends upon the
compensation rods employed in measuring bases. Thus, the laws of the
unequal expansion of matter judiciously applied have an immediate
influence upon our estimation of time; of the motions of bodies in the
heavens, and of their fall upon the earth; on our determination of the
figure of the globe, and on our system of weights and measures; on our
commerce abroad, and the mensuration of our lands at home.

The expansion of the crystalline substances takes place under very
different circumstances from the dilatation of such as are not
crystallized. The latter become both longer and thicker by an accession
of heat, whereas M. Mitscherlich has found that the former expand
differently in different directions; and, in a particular instance,
extension in one direction is accompanied by contraction in another: for
example, Iceland spar is dilated in the direction of its axis of double
refraction (N. 205), but at right angles to that axis it is contracted,
which brings the crystal nearer to the form of the cube and diminishes
its double refractive power. When heat is applied to crystals of
sulphate of lime, the two optical axes (N. 207) gradually approach, and
at last coincide; when the heat is increased, the axes open again, but
in a direction at right angles to their former position. By experiment
M. Senarmont has concluded, that in media constituted like crystals of
the rhomboidal (N. 169) system the conducting power varies in such a
manner, that, supposing a centre of heat to exist within them, and the
medium to be indefinitely extended in all directions, the isothermal
surfaces are concentric ellipsoids of revolution round the axes of
symmetry, or at least surfaces differing but little from them. The
internal structure of crystallized matter must be very peculiar thus to
modify the expansive power of heat.

Heat applied to the surface of a fluid is propagated downwards very
slowly, the warmer, and consequently lighter strata, always remaining at
the top. This is the reason why the water at the bottom of lakes fed
from Alpine chains is so cold; for the heat of the sun is transfused but
a little way below the surface. When the heat is applied below a liquid,
the particles continually rise as they become specifically lighter, and
diffuse the heat through the mass, their place being perpetually
supplied by those that are more dense. The power of conducting heat
varies materially in different liquids. Mercury conducts twice as fast
as an equal bulk of water, and therefore it appears to be very cold. A
hot body diffuses its heat in the air by a double process: the air in
contact with it becoming lighter ascends and scatters its heat by
transmission, while at the same time another portion is discharged in
straight lines by the radiating power of the surface. Hence a substance
cools more rapidly in air than in vacuo, because in the latter case the
process is carried on by radiation alone. It is probable that the earth
having been originally of very high temperature has become cooler by
radiation alone, the ethereal medium being too rare to carry off much
heat by contact.

Heat is propagated with more or less rapidity through all bodies; air is
the worst conductor, and consequently mitigates the severity of cold
climates by preserving the heat imparted to the earth by the sun. On the
contrary, dense bodies, especially metals, possess the power of
conduction in the greatest degree, but the transmission requires time.
If a bar of iron twenty inches long be heated at one extremity, the heat
takes four minutes in passing to the other. The particle of the metal
that is first heated communicates the heat to the second, and the second
to the third: so that the temperature of the intermediate molecule at
any instant is increased by the excess of the temperature of the first
above its own, and diminished by the excess of its own temperature above
that of the third. That however will not be the temperature indicated by
the thermometer, because as soon as the particle is more heated than the
surrounding atmosphere it loses its heat by radiation, in proportion to
the excess of its actual temperature above that of the air. The velocity
of the discharge is directly proportional to the temperature, and
inversely as the length of the bar. As there are perpetual variations in
the temperature of all terrestrial substances, and of the atmosphere,
from the rotation of the earth, and its revolution round the sun, from
combustion, friction, fermentation, electricity, and an infinity of
other causes, the tendency to restore the equability of temperature by
the transmission of heat must maintain all the particles of matter in a
state of perpetual oscillation, which will be more or less rapid
according to the conducting powers of the substances. From the motion of
the heavenly bodies about their axes, and also round the sun, exposing
them to perpetual changes of temperature, it may be inferred that
similar causes will produce like effects in them too. The revolutions of
the double stars show that they are not at rest; and although we are
totally ignorant of the changes that may be going on in the nebulæ and
millions of other remote bodies, it is hardly possible that they should
be in absolute repose; so that, as far as our knowledge extends, motion
is a law of the universe and the immediate cause of heat, as in the
sunbeam so also in all terrestrial phenomena.

This is by no means hypothetical, but founded upon fact and experiment.
Heat is produced by motion and is equivalent to it, for we measure heat
by motion in the thermometer. The heat evolved by percussion is
proportional to the force of the blow; by repeated blows iron becomes
red hot; and the quantity of heat produced by friction, whether the
matter be solid or fluid, is always in proportion to the force employed:
in cold weather we rub our hands to make them warm, and the harder we
rub the warmer they become. The warmth of the sea after a storm is in
proportion to the force of the wind; and in Sir Humphry Davy’s
experiment of melting ice by friction in the receiver of an air-pump
kept at the freezing point, the heat which melted the ice was exactly
proportional to the force of friction. This experiment proves the
immateriality of heat, since the capacity of ice for heat is less than
that of water. Thus mechanical action and heat are equivalent to one
another. Mr. Joule of Manchester[13] has proved that the quantity of
heat requisite to raise the temperature of a pound of water one degree
of Fahrenheit’s thermometer, is equivalent to the mechanical force
developed by the fall of a body weighing 772·69 pounds through the
perpendicular height of one foot. This quantity is the mechanical
equivalent of heat. Thus heat is motion, and it is measured by force. In
fact, for every unit of force expended in friction or percussion, a
definite quantity of heat is generated; and conversely, when work is
performed by the consumption of heat, for each unit of force gained, a
unit of heat disappears. For since heat is a dynamical force of
mechanical effect, there must be an equivalent between mechanical work
and heat as between cause and effect. (N. 222.)

Besides the temperature indicated by the thermometer, bodies absorb
heat, and their capacity for heat is so various that very different
quantities of heat are required to raise different substances to the
same sensible temperature. It is evident, therefore, that much of the
heat is absorbed and becomes insensible to the thermometer. That portion
of heat requisite to raise a body to a given temperature is its specific
heat, but the latent or absorbed heat is an expansive force or energy,
which, acting upon the ether surrounding the ultimate particles of
bodies, changes them from solid to liquid, and from liquid to vapour or
gas. According to the law of absorption, the transfer of heat from a
warm body to one that is cold is a mere transfer of force, in which the
force of compression is exactly proportional to the force of expansion.
Ice remains at the temperature of 32° Fahrenheit till it has absorbed
140° of heat, and then it melts, but without raising the temperature of
the water above 32°. On the contrary, when a liquid is converted into a
solid, a quantity of heat leaves it without any diminution of
temperature. Thus water at 32° must part with 140° of heat before it
freezes. The slowness with which water freezes or ice thaws, is a
consequence of the time required for the ethereal atmospheres round the
particles of the water to contract or expand with a force equivalent to
140° of heat. A considerable degree of cold is felt during a thaw,
because the ice in its transition from a solid to a liquid state absorbs
sensible heat from the atmosphere and surrounding objects. The heat
absorbed and evolved by the rarefaction and condensation of air is
exactly proportional to the force evolved and absorbed in these
operations. In fact, the changes of temperature produced by these
rarefactions and condensations of air show that the heat of elastic
fluids is the mechanical force possessed by them; and since the
temperature of a gas determines its elastic force, it follows that the
elastic force or pressure must be the effect of the motion of the
constituent particles in any gas. Sir Humphry Davy, who first
demonstrated the immateriality of heat, assumed the hypothesis that the
motion we call heat is a rotation or vibration among the particles of
the fluid, which, according to Mr. Joule, agrees perfectly with the
observed phenomena, but he prefers the more simple view of Mr. Herapath,
that the elastic force or pressure is due to the impact of the particles
against any surface presented to them. Absorbed or latent heat may be
regarded as a quiescent energy ready to be restored to the form of
sensible heat when called forth: its vibrations as heat are extinguished
for the time by being transferred to the internal expansive force, and
are restored by compression. The absorbed heat of air and all elastic
fluids may be forced out by sudden compression like squeezing water out
of a sponge. The quantity of heat brought into action in this way is
well illustrated by the experiment of igniting tinder by the sudden
compression of air by a piston thrust into a cylinder closed at one end.
The development of heat on a stupendous scale is exhibited in lightning:
it is proportional to the square of the quantity of electricity
discharged, and is due to its excessive velocity and the violent
compression of the air in its transit through the atmosphere. Prodigious
quantities of heat are constantly absorbed or disengaged by the changes
to which substances are liable in passing from the solid to the liquid
and from the liquid to the gaseous form and the contrary, causing
endless vicissitudes of temperature over the globe, and endless
expansions and contractions, which are correlative terms for heat and
cold, while radiation of heat is merely a transfer of motion from the
particles on the surface of bodies to the adjacent particles of the
atmosphere.

By the continual application of heat, that is of the expansive force,
liquids are converted into steam or vapour, which is invisible and
highly elastic. Under the mean pressure of the atmosphere, that is when
the barometer stands at 30 inches, water in a boiler absorbs heat
continually till it attains the temperature of the boiling point, which
is 212° Fahrenheit. After that it ceases to show any increase of
sensible heat; but when it has absorbed an additional 1000° of heat or
expansive energy, that energy converts it into steam, and a condensing
force equivalent to 1000° of heat reduces it again to water. Water boils
at different temperatures under different degrees of pressure. It boils
at a lower temperature on the top of a mountain than on the plain below,
because the weight of the atmosphere is less at the higher station.
There is no limit to the temperature to which water might be raised: it
might even be made red hot, could a vessel be found strong enough to
resist the pressure, for the intensity of the expansive force prevented
from having effect by the extreme pressure of the boiler would be
converted into sensible heat which might eventually render the water red
hot. Thus, since the force of steam is in proportion to the temperature
at which the water boils, or to the pressure, it is under control, and,
perhaps with the exception of electricity, it is the greatest power that
has been made subservient to the wants of man.

It is found that the absolute quantity of heat consumed in the process
of converting water into steam is the same at whatever temperature water
may boil, but that the absolute heat of the steam is greater exactly in
proportion as its sensible heat is less. Thus, steam raised at 212°
Fahrenheit under the mean pressure of the atmosphere, and steam raised
at 180° under half the pressure, contain the same quantity of heat, with
this difference, that the one has more absorbed heat and less sensible
heat than the other. It is evident that, as the same quantity of heat is
requisite for converting a given weight of water into steam, at whatever
temperature or under whatever pressure the water may be boiled,
therefore, in the steam engine, equal weights of steam at a high
pressure and a low pressure are produced by the same quantity of fuel;
and whatever the pressure of the steam may be, the consumption of fuel
is proportional to the quantity of water converted into vapour. Steam of
whatever tension expands on being set free, but the expansion of high
pressure steam at the expense of its sensible heat is so great, that the
hand may be plunged into it without injury the instant it issues from
the orifice of a boiler. The steam becomes hotter by friction in issuing
through the orifice which maintains it in its dry form, for there is no
doubt that high-pressure steam is dry.

The elasticity or tension of steam, like that of common air, varies
inversely as its volume—that is, when the space it occupies is doubled,
its elastic force is reduced to one half. The expansion of steam is
indefinite; the smallest quantity of water expanded into vapour will
occupy many millions of cubic feet; a wonderful illustration of the
minuteness of the ultimate particles of matter.

The force of steam, tremendous as the lightning itself when
uncontrolled, is merely the result of chemical affinity: it is the
chemical attraction between the particles of carbon, of coal or wood,
and the oxygen of the atmosphere. Mr. Joule has ascertained that a pound
of the best coal when burnt gives sufficient heat to raise the
temperature of 8086 pounds of water one degree of the Centigrade
thermometer, whence it has been computed by M. Helmholtz that the
chemical force arising from the combustion of that pound of coal is
capable of lifting a body of one hundred pounds weight to the height of
twenty miles. That is the _work_ performed by the heat arising from the
combustion of a pound of coal. In all cases where work is produced by
heat, a quantity of heat proportional to the work done is expended; and
conversely, by the expenditure of a like quantity of work, the same
amount of heat may be produced. The equivalence of heat and work is a
law of nature. The mechanical force exerted by the steam engine for
example is exactly proportional to the consumption of heat, nor more nor
less; if we could produce a greater quantity than its equivalent we
should have perpetual motion, which is impossible. Mechanical engines
generate no force. We cannot create force; we can only avail ourselves
of the inexhaustible stores of nature, the lightning, fire, water, wind,
chemical action, &c. The quantity of mechanical power in nature is ever
the same; it is never increased, it is never diminished, throughout the
whole circuit of natural powers. The conservation of force is as
permanent and unchangeable as matter. It may be dormant for a time, but
it ever exists. We are unconscious of the enormous dynamic power that is
either active or latent throughout the globe, because we do not attend
to it. By the ebb and flow of the tide alone a power is exerted by which
25,000 cubic miles of water is moved over a quarter of the globe every
twelve hours; and Professor W. Thomson has computed, by means of
Pouillet’s data of solar radiation and Mr. Joule’s mechanical equivalent
of heat, that the mechanical value of the whole energy active and
potential of the disturbances kept up in the ethereal medium by the
vibrations of the solar light within a cubic mile of our atmosphere is
equal to 12,050 times the unit of mechanical force, that is to say,
12,050 times the force that would raise a pound of matter to the height
of one foot, whence some idea may be formed of the vast amount of force
exerted by the sun’s light within the limits of the whole terrestrial
atmosphere. (N. 223.)

The dynamic energy of the undulations of the solar light gives the
leaves of plants the power of decomposing carbonic acid, and of
separating the particles of carbon and hydrogen from the oxygen for
which they have so strong an affinity. In this operation the undulations
of the sunbeam are extinguished as light and heat, and Professor W.
Thomson has proved that the quantity of these undulations thus
extinguished is precisely equal to the potential or quiescent energy
thus created, and that precisely that very quantity of light and heat is
restored when the plants are burned, whatever state they may be in; and
that thus, as Mr. George Stephenson[14] has truly and beautifully
observed, our coal fires and gas lamps restore to our use the light and
heat of the sun of the early geological epochs which have rested as
dormant powers under the seas and mountains for unnumbered ages. The sun
is therefore the source of the mechanical energy of all the heat and
motion of inanimate things, of all the motions of the heat and light of
fires and artificial flames, and of the heat of all living creatures.
For animal heat, and weights raised or resistance overcome, are
mechanical effects of the chemical combination of food with oxygen; and
food is either directly or indirectly vegetable, consequently dependent
upon the sun.

Professor Helmholtz of Bonn has put in a strong point of view the
enormous store of force possessed by our system by comparing it with its
equivalent of heat. The force with which the earth moves in its orbit is
such, that if brought to rest by a sudden shock, a quantity of heat
would be generated by the blow equal to that produced by the combustion
of fourteen such earths of solid coal; and supposing the capacity of the
earth for heat as low as that of water, the globe would be heated to
11,200° Cent. It would be quite fused and for the most part reduced to
vapour. If it should fall to the sun, which it would certainly do, the
quantity of heat developed by the shock would be four hundred times as
great.

The application of heat to the various branches of the mechanical and
chemical arts has within the present century effected a greater change
in the condition of man than had been accomplished in any equal period
of his existence. Armed by the expansion and condensation of fluids with
a power equal to that of the lightning itself, conquering time and
space, he flies over plains, and travels on paths cut by human industry
even through mountains with a velocity and smoothness more like
planetary than terrestrial motion; he crosses the deep in opposition to
wind and tide; by releasing the strain on the cable, he rides at anchor
fearless of the storm; he makes the lightning his messenger; and like a
magician he raises from the gloomy abyss of the mine the sunbeam of
former ages to dispel the midnight darkness.

The principal phenomena of heat may be illustrated by a comparison with
those of sound. Their excitation is not only similar but identical, as
in friction and percussion; they are both communicated by contact and
radiation; and Dr. Young observes that the effect of radiant heat in
raising the temperature of a body upon which it falls, resembles the
sympathetic agitation of a string when the sound of another string which
is in unison with it is transmitted through the air. Light, heat, sound,
and the waves of fluids are all subject to the same laws; their
undulatory theories are perfectly similar: hence the interference of two
hot rays must produce cold, that is, they must extinguish one another:
darkness results from the interference of two undulations of light,
silence ensues from the interference of two undulations of sound, and
still water or no tide is the consequence of the interference of two
tides. The propagation of sound, however, requires a much denser medium
than that of light and heat; its intensity diminishes as the rarity of
the air increases: so that, at a very small height above the surface of
the earth, the noise of the tempest ceases, and the thunder is heard no
more in those boundless regions where the heavenly bodies accomplish
their periods in eternal and sublime silence.

A consciousness of the fallacy of our senses is one of the most
important consequences of the study of nature. This study teaches us
that no object is seen by us in its true place, owing to aberration;
that the colours of substances are solely the effects of the action of
matter upon light; and that light itself as well as heat and sound are
not real beings, but mere motions communicated to our perceptions by the
nerves. The human frame may therefore be regarded as an elastic system,
the different parts of which are capable of receiving the tremors of
elastic media, and of vibrating in unison with any number of
superimposed undulations, all of which have their perfect and
independent effect. Here our knowledge ends: the mysterious influence of
matter on mind will in all probability be for ever hid from man.




                            SECTION XXVIII.

Common or Static Electricity, or Electricity of Tension—A Dual
  Power—Methods of exciting it—Attraction and
  Repulsion—Conduction—Electrics and
  Non-electrics—Induction—Dielectrics—Tension—Law of the Electric
  Force—Distribution—Laws of Distribution—Heat of Electricity—Electrical
  Light and its Spectrum—Velocity—Atmospheric Electricity—Its
  cause—Electric Clouds—Violent effects of Lightning—Back
  Stroke—Electric Glow—Phosphorescence.


ELECTRICITY is a dual power which gives no visible sign of its existence
when in equilibrio, but when elicited forces are developed capable of
producing the most sudden, violent, and destructive effects in some
cases, while in others their action, though generally less energetic, is
of indefinite and uninterrupted continuance. These modifications of the
electric forces, incidentally depending upon the manner in which they
are excited, present phenomena of great diversity, but yet so connected
as to justify the conclusion that they originate in a common principle.
The hypothesis of electricity being a fluid is untenable in the present
advanced state of the science; we only know that it is a force whose
action is twofold; that bodies in one electric state attract, and in
another repel each other; in the former the electricity is said to be
positive, in the latter negative; and thus regarding it as a force, its
modes of action come under the laws of mechanics and mathematical
analysis.

Electricity may be called into activity by the friction of heterogeneous
substances, as in the common electrifying machine, by mechanical power,
heat, chemical action, and the influence of magnetism. We are totally
ignorant why it is roused from its neutral state by these means, or of
the manner of its existence in bodies; but when excited it seems to
produce a molecular polarity or chemical change in the ultimate
particles of matter.

The science is divided into various branches, of which static or common
electricity comes first under consideration, including that of the
atmosphere. Substances in a neutral state neither attract nor repel.
There is a numerous class called electrics in which the electric
equilibrium is destroyed by friction; then the positive and negative
electricities are called into action or separated; the positive is
impelled in one direction, and the negative in another. Electricities of
the same kind repel, whereas those of different kinds attract each
other. The attractive power is exactly equal to the repulsive power at
equal distances, and when not opposed they coalesce with great rapidity
and violence, producing the electric flash, explosion, and shock; then
the equilibrium is restored. One kind of electricity cannot be evolved
without the evolution of an equal quantity of the opposite kind. Thus
when a glass rod is rubbed with a piece of silk, as much positive
electricity is elicited in the glass as there is negative in the silk.
The kind of electricity depends more upon the mechanical condition than
on the nature of the surface; for when two plates of glass, one polished
and the other rough, are rubbed against each other, the polished surface
acquires positive and the rough negative electricity. The manner in
which friction is performed also alters the kind of electricity. Equal
lengths of black and white ribbon applied longitudinally to one another,
and drawn between the finger and thumb so as to rub their surfaces
together, become electric. When separated the white ribbon is found to
have acquired positive electricity, and the black negative; but if the
whole length of the black ribbon be drawn across the breadth of the
white, the black will be positively and the white negatively electric
when separated. The friction of the rubber on the glass plate of the
electrifying machine produces abundance of static electricity. The
friction of the steam on the valve of an insulated locomotive
steam-engine produces seven times the quantity of electricity that an
electrifying machine would do with a plate three feet in diameter,
worked at the rate of 70 revolutions in a minute. Pressure is a source
of electricity which M. Becquerel has found to be common to all bodies;
but it is necessary to separate them to prevent the reunion of the
electricities. When two substances of any kind whatever are insulated
and pressed together they assume different electric states, but they
only show contrary electricities when one of them is a good conductor.
When both are good conductors they must be separated with extreme
rapidity to prevent a return to equilibrium. When the separation is very
sudden the tension of the two electricities may be great enough to
produce light. M. Becquerel attributes the light produced by the
collision of icebergs to this cause. Iceland spar is made electric by
the smallest pressure between the finger and the thumb, and retains it
for a long time. All these circumstances are modified by the temperature
of the substances, the state of their surfaces and that of the
atmosphere. Several crystalline bodies become electric when heated,
especially tourmaline, one end of which acquires positive, and the other
negative electricity, while the intermediate part is neutral. If the
tourmaline be broken through the middle, each fragment is found to
possess positive electricity at one end and negative at the other.
Electricity is evolved by substances passing from a liquid to a solid
state, and by chemical action during the production and condensation of
vapour, which is a great source of atmospheric electricity. In short, it
may be generally stated, that when any cause whatever tends to destroy
molecular attraction there is a development of electricity; if, however,
the substances be not immediately separated, there will be an
instantaneous restoration of equilibrium.

Electricity may be transferred from one body to another in the same
manner as heat is communicated, and like it too the body loses by the
transmission.

Although no substance is altogether impervious to electricity, nor is
there any that does not offer some resistance to its passage, yet it
moves with more facility through a certain class of substances called
conductors, such as metals, water, the human body, &c., than through
atmospheric air, glass, silk, &c., which are therefore called
non-conductors. The conducting power is affected both by temperature and
moisture. The terrestrial globe is a conductor on account of its
moisture, though dry earth is not. Though metals are the best conductors
of electricity, it affects their molecular structure, for the heat which
accompanies its passage acts as a transverse expansive force, which
increases their breadth by diminishing their length, as may be seen by
passing electricity through a platinum wire sufficiently thick to resist
fusion. Through air the force is disruptive on account of its
non-conducting quality, and it seems to act chemically on the oxygen,
producing the substance known as ozone during its passage through the
atmosphere. If a conductor be good and of sufficient size the
electricity passes imperceptibly but it is shivered to pieces in an
instant if it be a bad conductor or too small to carry off the charge.
In that case the physical change is generally a separation of the
particles, or expansion from the heat, as in trees, where it turns the
moisture into steam, but all these effects are in proportion to the
obstacles opposed to the freedom of its course.

Bodies surrounded by non-conductors are said to be insulated, because
when charged the electricity cannot escape. When that is not the case,
the electricity is conveyed to the earth: consequently it is impossible
to accumulate electricity in a conducting substance that is not
insulated. There are a great many substances called non-electrics in
which electricity is not sensibly developed by friction unless they be
insulated, because it is carried off by their conducting power as soon
as elicited. Metals, for example, which are said to be non-electrics can
be excited, but being conductors they cannot retain this state if in
communication with the earth. It is probable that no bodies exist which
are either perfect non-electrics or perfect non-conductors. But it is
evident that electrics must be non-conductors to a certain degree,
otherwise they could not retain their electric state.

A body charged with electricity, although perfectly insulated, so that
all escape of electricity is prevented, tends to produce an electric
state of the opposite kind in all bodies in its vicinity. Positive
electricity tends to produce negative electricity in a body near to it,
and _vice versâ_, the effect being greater as the distance diminishes.
This power which electricity possesses of causing an opposite electrical
state in its vicinity is called induction. A Leyden jar, for example, or
glass jar coated half way up both outside and in with tin foil, when
charged with positive electricity, immediately induces negative
electricity on the tin foil outside. Notwithstanding their strong mutual
attraction they are prevented from coalescing by the glass, which is a
non-conductor; but if the tin inside and out be connected by a
conducting wire they instantly unite. When a body in either electric
state is presented to a neutral one, its tendency in consequence of the
law of induction is to disturb the condition of the neutral body by
inducing electricity contrary to its own in the adjacent side, and
therefore an electrical state similar to its own in the remote part.
Hence the neutrality of the second body is destroyed by the action of
the first, and the adjacent parts of the two, having now opposite
electricities, will attract each other. The attraction between
electrified and unelectrified substances is a consequence of the altered
state of their molecules. Induction depends upon the facility with which
the equilibrium of the neutral body can be overcome, a facility which is
proportional to its conducting power. Consequently the attraction
exerted by an electrified substance upon another substance previously
neutral will be much more energetic if the latter be a conductor than if
it be a non-conductor.

It is clear that one body cannot act upon another at a distance without
some means of communication. Dr. Faraday has proved that the intervening
non-conducting substance or dielectric has a great influence upon
induction. Thus the inductive force is greater when sulphur is
interposed between the two bodies than when shellac is the dielectric,
and greater when shellac is the dielectric than glass, &c. Professor
Matteucci has proved by the following experiment that the intervening
substance is itself polarized by induction. A number of plates of mica
in contact were placed between two plates of metal, one of which was
electrified, so that the whole was charged like a Leyden jar. On
separating the plates with insulating handles, each plate of mica was
electrified; one side of it was positive and the other negative, showing
decidedly a polarization by induction throughout the whole intervening
non-conducting substance; and thus, although the interposed substance or
dielectric is incapable of conducting the electrical force from one body
to the other, it becomes by induction capable of transmitting it. In the
atmosphere induction is transmitted by that of the intervening strata of
air. It is true that induction takes place through the most perfect
vacuum we can make, but there always remains some highly elastic air;
and even if air could be altogether excluded, the ethereal medium
cannot, and it must be capable of induction, since, however attenuated,
it must consist of material atoms, otherwise it would be a nonentity.

The law of electrical attraction and repulsion has been determined by
suspending a needle of gum-lac horizontally by a silk fibre, the needle
carrying at one end a piece of electrified gold leaf. A globe in the
same or opposite electrical state when presented to the gold leaf will
repel or attract it, and will therefore cause the needle to vibrate more
or less rapidly according to the distance of the globe. A comparison of
the number of oscillations performed in a given time at different
distances will determine the law of the variation of the electrical
intensity, in the same manner that the force of gravitation is measured
by the oscillations of the pendulum. Coulomb invented an instrument
which balances the forces in question by the force of the torsion of a
thread, which consequently measures the intensity; and Sir William Snow
Harris has constructed an instrument with which he has measured the
intensity of the electrical force in terms of the weight requisite to
balance it. By these methods it has been found that the intensity of
electrical attraction and repulsion varies inversely as the square of
the distance. However, the law of repulsive force is liable to great
disturbances from inductive action, which Sir William Snow Harris has
found to exist not only between a charged and neutral body, but also
between bodies similarly charged; and that, in the latter case, the
inductive process may be indefinitely modified by the various
circumstances of the quantity and intensity of the electricity and the
distance between the charged bodies.

The quantity of electricity bodies are capable of receiving does not
follow the proportion of their bulk, but depends principally upon the
form and extent of their surface. It appears from the experiments of Sir
W. S. Harris that a given quantity of electricity, divided between two
perfectly equal and similar bodies, exerts upon external bodies only one
fourth of the attractive force apparent when disposed upon one of them;
and if it be distributed among three equal and similar bodies, the force
is one ninth of that apparent when it is disposed on one of them. Hence,
if the quantity of electricity be the same, the force varies inversely
as the square of the surface on which it is disposed; and if the surface
be the same, the force varies directly as the square of the quantity of
electricity. These laws however do not hold when the form of the surface
is changed. A given quantity of electricity disposed on a given surface
has the greatest intensity when the surface has a circular form, and the
least intensity when the surface is expanded into an indefinite straight
line. The decrease of intensity seems to arise from some peculiar
arrangement of the electricity depending on the extension of the
surface. It is quite independent of the extent of the edge, the area
being the same; for Sir W. S. Harris found that the electrical intensity
of a charged sphere is the same with that of a plane circular area of
the same superficial extent, and that of a charged cylinder the same as
if it were cut open and expanded into a plane surface.

The same able electrician has shown that the attractive force between an
electrified and a neutral uninsulated body is the same whatever be the
forms of their unopposed parts. Thus two hemispheres attract each other
with precisely the same force as if they were spheres; and as the force
is as the number of attracting points in operation directly, and as the
squares of the respective distances inversely, it follows that the
attraction between a mere ring and a circular area is no greater than
that between two similar rings, and the force between a sphere and an
opposed spherical segment of the same curvature is no greater than that
of two similar segments, each equal to the given segment.

Electricity may be accumulated to a great extent in insulated bodies,
and so long as it is quiescent it occasions no sensible change in their
properties. When restrained by the non-conducting power of the
atmosphere, its tension or the pressure it exerts is proportional to the
coercive force of the air. If the pressure be less than the coercive
force, the electricity is retained; but the instant it exceeds that
force in any one point it escapes, and that more readily when the air is
attenuated or saturated with moisture, for the resistance of the air is
proportional to the square of its density, but the inductive action of
electricity on distant bodies is independent of atmospheric pressure.
The power of retaining electricity depends also on the shape of the
charged body. It is most easily retained by a sphere, next to that by a
spheroid, but it readily escapes from a point, and a pointed object
receives it with most facility.

The heat produced by the electric shock is proportional to the square of
the quantity of electricity discharged, and is so intense that it fuses
metals and volatilizes substances, but its intensity is not felt to its
full extent on account of the shortness of its duration. It is only
accompanied by light when the electricity is obstructed in its passage
through substance.

Electrical light when analysed by a prism differs very much from solar
light. Fraunhofer found that, instead of the fixed dark lines, the
spectrum of an electric spark is crossed by numerous bright lines; and
Professor Wheatstone has observed that the number and position of the
lines differ with the metal from which the spark is taken, and believes
the spark itself results from the ignition and volatilization of the
matter of the conductor.

According to the experiments of Sir Humphry Davy, the density of the air
has an influence on the colour. He passed the electric spark through a
vacuum over mercury, which from green became successively sea-green,
blue, and purple, on admitting different quantities of air. When the
vacuum was made over a fusible alloy of tin and bismuth, the spark was
yellowish and extremely pale. Sir Humphry thence concluded that
electrical light principally depends upon some properties belonging to
the ponderable matter through which it passes, and that space is capable
of exhibiting luminous appearances, though it does not contain an
appreciable quantity of matter. He thought that the superficial
particles of bodies which form vapour, when detached by the repulsive
power of heat, might be equally separated by the electric forces, and
produce luminous appearances in vacuo by the destruction of their
opposite electric states.

The velocity of electricity is so great that the most rapid motion which
can be produced by art appears to be actual rest when compared with it.
A wheel revolving with celerity sufficient to render its spokes
invisible, when illuminated by a flash of lightning, is seen for an
instant with all its spokes distinct, as if it were in a state of
absolute repose; because, however rapid the rotation may be, the light
has come and already ceased before the wheel has had time to turn
through a sensible space. This beautiful experiment is due to Professor
Wheatstone, as well as the following variation of it, which is not less
striking: If a circular piece of pasteboard be divided into three
sectors, one of which is painted blue, another yellow, and a third red,
it will appear to be white when revolving quickly, because of the
rapidity with which the impressions of the colours succeed each other on
the retina. But, the instant it is illuminated by an electric spark, it
seems to stand still, and each colour is as distinct as if it were at
rest. This transcendent speed of electricity has been ingeniously
measured, as follows, by Professor Wheatstone, who has ascertained that
it much surpasses the velocity of light.

In the horizontal diameter of a small disc, fixed on the wall of a
darkened room, are disposed six small brass balls, well insulated from
each other. An insulated copper wire, half a mile long, is disjointed in
its middle, and also near its two extremities; the six ends thus
obtained are connected with the six-balls on the disc. When an electric
discharge is sent through the wire by connecting its two extremities,
one with the positive, and the other with the negative coating of a
Leyden jar, three sparks are seen on the disc, apparently at the same
instant. At the distance of about ten feet a small revolving mirror is
placed so as to reflect these three sparks during its revolution. From
the extreme velocity of the electricity, it is clear that, if the three
sparks be simultaneous, they will be reflected, and will vanish before
the mirror has sensibly changed its position, however rapid its rotation
may be, and they will be seen in a straight line. But if the three
sparks be not simultaneously transmitted to the disc—if one, for
example, be later than the other two—the mirror will have time to
revolve through an indefinitely small arc in the interval between the
reflection of the two sparks and that of the single one. However, the
only indication of this small motion of the mirror will be, that the
single spark will not be reflected in the same straight line with the
other two, but a little above or below it, for the reflection of all
three will still be apparently simultaneous, the time intervening being
much too short to be appreciated.

Since the number of revolutions which the revolving mirror makes in a
second is known, and the angular deviation of the reflection of the
single spark from the reflection of the other two can be measured, the
time elapsed between their consecutive reflections can be ascertained.
And, as the length of that part of the wire through which the
electricity has passed is given, its velocity may be found.

The number of pulses in a second, requisite to produce a musical note of
any pitch, are known; hence the number of revolutions accomplished by
the mirror in a given time may be determined from the musical note
produced by a tooth or peg, in its axis of rotation, striking against a
card, or from the notes of a siren attached to the axis. It was thus
that Professor Wheatstone found the mirror which he employed in his
experiments made 800 revolutions in a second; and, as the angular
velocity of the reflected image in a revolving mirror is double that of
the mirror itself, an angular deviation of one degree in the appearance
of the two sparks would indicate an interval of the 576,000th of a
second; the deviation of half a degree would, therefore, indicate more
than the millionth of a second. The use of sound as a measure of
velocity is a happy illustration of the connexion of the physical
sciences.

The earth possesses a powerful electrical tension, and the atmosphere
when clear is almost always positively electric. Its electricity is
stronger in winter than in summer, during the day than in the night. The
intensity increases for two or three hours from the time of sunrise,
comes to a maximum between seven and eight, then decreases towards the
middle of the day, arrives at its minimum between one and two, and again
augments as the sun declines till about the time of sunset, after which
it diminishes and continues feeble during the night. The mere
condensation of vapour is a source of atmospheric electricity; but
although it is also produced by the vapour that rises from the surface
of the earth, it is not under all circumstances. M. Pouillet found that
electricity is only developed when accompanied by chemical action: for
example, when the water whence the vapour proceeds contains lime, chalk,
or any solid alkali, negative electricity is produced; and when it holds
in solution either gas, acid, or some of the salts, the vapour is
positively electric. Besides, the contact of earth with salt and fresh
water generates positive electricity, and the contact of fresh and salt
currents of water negative, so that the ocean must afford a great supply
to the atmosphere; hence thunderstorms are most frequent near the
coasts: but as electricity of one kind or another is developed whenever
the molecules of matter are deranged from their natural state of
equilibrium, there must be many partial variations in the electric state
of the air. When the invisible vapour rises charged with electricity
into the cold regions of the atmosphere, it is condensed into cloud, in
which the tension is increased because the electricity is confined to a
smaller space; and if the condensation be sufficient to produce drops of
rain, they carry the electricity to the ground, so that in general a
shower is a conductor between the clouds and the earth. When two clouds
charged with opposite kinds, but of equal tension, approach within a
certain distance, the intensity increases on the sides of the clouds
that are nearest to one another; and when the tension is great enough to
overcome the coercive pressure of the atmosphere, a discharge takes
place which causes a flash of lightning, the stroke being given either
by the cloud or the rain. The actual quantity of electricity in any part
of a cloud is extremely small. The intensity of the flash arises from
the great extent of surface over which it is spread, so that clouds may
be compared to enormous Leyden jars thinly coated with electricity,
which only acquires its intensity by its instantaneous condensation. The
rapid and irregular motions of thunder clouds are probably more owing to
strong electrical attractions and repulsions among themselves than to
currents of air, though both are no doubt concerned in these hostile
movements. The atmosphere becomes intensely electric on the approach of
rain, hail, snow, sleet, and wind; but it varies afterwards, and the
transitions are very rapid on the approach of a thunderstorm.

Since air is a non-conductor, it does not convey the electricity from
the clouds to the earth, but it acquires from them an opposite kind, and
when the tension is very great the force of the electricity becomes
irresistible, and an interchange takes place between the clouds and the
earth; but so rapid is the motion of lightning, that it is difficult to
ascertain whether it goes from the clouds to the earth or shoots upwards
from the earth to the clouds, though there can be no doubt that it does
both. In a storm that occurred at Manchester in June 1835, the lightning
was observed to issue from various points of a road, attended by
explosions as if pistols had been fired out of the ground, and a man
seems to have been killed by one of these explosions taking place under
his foot. M. Gay Lussac ascertained that a flash of lightning sometimes
darts more than three miles in a straight line. A person may be killed
by lightning, although the explosion takes place at a distance of twenty
miles, by what is called the back stroke. Suppose that the two
extremities of a highly charged cloud hang down towards the earth, they
will repel the electricity from the earth’s surface if it be of the same
kind with their own, and will attract the other kind; and if a discharge
should suddenly take place at one end of the cloud, the equilibrium will
be instantly restored by a flash at that point of the earth which is
under the other. Though the back stroke is often sufficiently powerful
to destroy life, it is never so terrible in its effects as the direct
stroke, which is often of inconceivable intensity. Instances have
occurred when large masses of iron and stone, and even many feet of a
stone wall, have been carried to a considerable distance by a stroke of
lightning. Rocks and the tops of mountains often bear the marks of
fusion from its intense heat; and occasionally vitreous tubes descending
many feet into banks of sand mark its path. Dr. Fiedler exhibited
several of these fulgorites in London of considerable length, which had
been dug out of the sandy plains of Silesia and Eastern Prussia. One
found at Paderborn was forty feet long. Their ramifications generally
terminate in pools or springs of water below the sand, which are
supposed to determine the course of the lightning. No doubt the soil and
substrata must influence its direction, since it is found by experience
that places which have been once struck by lightning are often struck
again. An insulated conductor on the approach of a storm gives out such
quantities of sparks that it is dangerous to approach it, as was fatally
experienced by Professor Richman at Petersburg, who was struck dead by a
globe of fire from the extremity of a conductor, while making
experiments on atmospheric electricity. Copper conductors afford the
best protection, especially if they expose a broad surface, since
electricity is conveyed along the surface of bodies. There is no
instance of an electric cloud of high tension being dispelled by a
conductor, yet those invented by Sir William Snow Harris, and
universally employed in the navy, afford a complete protection in the
most imminent danger. The Shannon, a 50-gun frigate, commanded by the
brave and lamented Sir William Peel, was enveloped in a thunder-storm
when about 90 miles to the north-west of Java. It began at fifty minutes
past four in the afternoon; the ship was driven before the storm, in a
high sea, amid streams of vivid lightning, deafening thunder, hail, and
rain. At five o’clock an immense ball of fire covered the maintopgallant
mast, ran up the royal pole, and exploded in the air with a terrific
concussion, covering all the surrounding space with sparks of electric
light, which were driven rapidly to leeward by the wind. Fifteen minutes
later an immense mass of lightning struck the mainmast, attended by a
violent gust of wind; and another heavy discharge fell on it a quarter
of an hour afterwards. From that time till six o’clock the ship was
continually encompassed by sharp forked lightning, accompanied by
incessant peals of thunder. Though actually enveloped in electricity,
and struck three times, neither the hull nor the rigging sustained the
slightest injury.

When the air is rarefied by heat, its coercive power is diminished, so
that the electricity escapes from the clouds in those lambent diffuse
flashes without thunder so frequent in warm summer evenings; and when
the atmosphere is highly charged with electricity, it not unfrequently
happens that electric light, in the form of a star, is seen on the
topmasts and yard-arms of ships. In 1831 the French officers at Algiers
were surprised to see brushes of light on the heads of their comrades,
and at the points of their fingers when they held up their hands. This
phenomenon was well known to the ancients, who reckoned it a lucky omen.

Many substances, in decaying, emit light, which is attributed to
electricity, such as fish and rotten wood. Oyster-shells, and a variety
of minerals, become phosphorescent at certain temperatures when exposed
to electric shocks or friction: indeed, most of the causes which disturb
molecular equilibrium give rise to phosphoric phenomena. The minerals
possessing this property are generally coloured or imperfectly
transparent; and, though the colour of this light varies in different
substances, it has no fixed relation to the colour of the mineral. An
intense heat entirely destroys this property, and the phosphorescent
light developed by heat has no connexion with light produced by
friction; for Sir David Brewster observed that bodies deprived of the
faculty of emitting the one are still capable of giving out the other.
Among the bodies which generally become phosphorescent when exposed to
heat, there are some specimens which do not possess this property;
wherefore phosphorescence cannot be regarded as an essential character
of the minerals possessing it. Sulphuret of calcium, known as Canton’s
phosphorus, and the sulphuret of barium, or Bologna stone, possess the
phosphorescent property in an eminent degree.

Multitudes of fish are endowed with the power of emitting light at
pleasure, no doubt to enable them to pursue their prey at depths where
the sunbeams cannot penetrate. Flashes of light are frequently seen to
dart along a shoal of herrings or pilchards; and the Medusa tribes are
noted for their phosphorescent brilliancy, many of which are extremely
small, and so numerous as to make the wake of a vessel look like a
stream of silver. Nevertheless, the luminous appearance which is
frequently observed in the sea during the summer months cannot always be
attributed to marine animalculæ, as the following narrative will show:—

Captain Bonnycastle, coming up the Gulf of St. Lawrence on the 7th of
September, 1826, was roused by the mate of the vessel in great alarm
from an unusual appearance. It was a starlight night, when suddenly the
sky became overcast in the direction of the high land, and an
instantaneous and intensely vivid light, resembling the aurora, shot out
of the hitherto gloomy and dark sea on the lee bow, which was so
brilliant that it lighted everything distinctly even to the mast-head.
The light spread over the whole sea between the two shores, and the
waves, which before had been tranquil, now began to be agitated. Captain
Bonnycastle describes the scene as that of a blazing sheet of awful and
most brilliant light. A long and vivid line of light, superior in
brightness to the parts of the sea not immediately near the vessel,
showed the base of the high, frowning, and dark land abreast; the sky
became lowering and more intensely obscure. Long tortuous lines of light
showed immense numbers of very large fish darting about as if in
consternation. The sprit-sail yard and mizen-boom were lighted by the
glare, as if gaslights had been burning directly below them; and until
just before daybreak, at four o’clock, the most minute objects were
distinctly visible. Day broke very slowly, and the sun rose of a fiery
and threatening aspect. Rain followed. Captain Bonnycastle caused a
bucket of this fiery water to be drawn up; it was one mass of light when
stirred by the hand, and not in sparks as usual, but in actual
coruscations. A portion of the water preserved its luminosity for seven
nights. On the third night, the scintillations of the sea reappeared;
the sun went down very singularly, exhibiting in its descent a double
sun; and, when only a few degrees high, its spherical figure changed
into that of a long cylinder, which reached the horizon. In the night
the sea became nearly as luminous as before, but on the fifth night the
appearance entirely ceased. Captain Bonnycastle did not think it
proceeded from animalculæ, but imagined it might be some compound of
phosphorus, suddenly evolved and disposed over the surface of the sea.
It had probably been that peculiar form of electricity known as the glow
discharge, of which the author once saw a very remarkable instance.

M. E. Becquerel assures us that almost all substances are phosphorescent
after being exposed to the sun if instantly withdrawn into darkness, and
that it depends upon the arrangement of the particles and not upon
chemical action. The salts of uranium give the same kind of
phosphorescent light as that produced by the violet rays of the solar
spectrum. A solution of the bisulphate of quinine emits a yellow
phosphorescent light, whereas the fluorescent light of that liquid is
blue. The colours of these two kinds of light are generally
complementary to one another.

Phosphorescence is probably more or less concerned in some, at least, of
a series of very curious experiments made by M. Niepcé de Saint-Victor,
on what he calls the saturation of substances with light. It has long
been known that, if a person in an intensely dark room should expose his
arm to the sun through a hole in a window-shutter, it will shine on
being drawn into the darkness. Now, M. de Saint-Victor found that if an
engraving be exposed for a certain time to the sun, and instantly
brought into darkness, it will make a photographic impression on a
collodion or argentine surface, and that anything written or drawn with
tartaric acid, or a solution of the salts of uranium, in large
characters, is reproduced even at a small distance from a sensitive
surface. It may be presumed that the light communicates its vibrations
to the surfaces exposed to it with sufficient force to enable them to
disturb the unstable equilibrium of such sensitive substances as
collodion or the argentine salts. M. de Saint-Victor has shown that
tartaric acid, which is readily impressed by sunlight, is neither
fluorescent nor phosphorescent, whence he concludes that his experiments
are independent of both of these modes of action. Uranium appears to
have very peculiar properties: its salts are strongly luminous when
exposed to the sun; they are very fluorescent; and the crystallized
azitote of uranium becomes phosphorescent by percussion.




                             SECTION XXIX.

Voltaic Electricity—The Voltaic Battery—Intensity—Quantity—Static
  Electricity, and Electricity in Motion—Luminous Effects—Mr.
  Grove on the Electric Arc and Light—Decomposition of Water—Formation
  of Crystals by Voltaic Electricity—Photo-galvanic
  Engraving—Conduction—Heat of Voltaic Electricity—Electric Fish.


VOLTAIC or Dynamic electricity is elicited by the force of chemical
action. It is connected with some of the most brilliant periods of
British science, from the splendid discoveries to which it led Sir
Humphry Davy and Dr. Faraday.

In 1790, while Galvani, Professor of Anatomy in Bologna, was making
experiments on electricity, he was surprised to see convulsive motions
in the limbs of a dead frog accidentally lying near the machine during
an electrical discharge. Though a similar action had been noticed long
before his time, he was so much struck with this singular phenomenon,
that he examined all the circumstances carefully, and at length found
that convulsions take place when the nerve and muscle of a frog are
connected by a metallic conductor. This excited the attention of all
Europe; and it was not long before Volta, Professor at Pavia, showed
that the mere contact of different bodies is sufficient to disturb
electrical equilibrium, and that a current of electricity flows in one
direction through a circuit of three conducting substances. From this he
was led, by acute reasoning and experiment, to the construction of the
Voltaic pile, which, in its early form, consisted of alternate discs of
zinc and copper, separated by pieces of wet cloth, the extremities being
connected by wires. This simple apparatus, perhaps the most wonderful
instrument that has been invented by the ingenuity of man, by divesting
electricity of its sudden and uncontrollable violence, and giving in a
continued stream a greater quantity at a diminished intensity, has
exhibited that force under a new and manageable form, possessing powers
the most astonishing and unexpected. The expression current has no
relation to a fluid, which is now considered to be as inconsistent with
the phenomena of dynamic as with static electricity. It was shown by
Grotthus that the transmission of Voltaic electricity through liquids
consists of a series of chemical affinities acting in definite
directions; and Mr. Grove, from an examination of its action on the
various kinds of matter, has come to the same conclusion. Indeed it is
now the generally received opinion that a current of electricity is
merely a continuous transmission of chemical affinity from particle to
particle of the substance through which it is passing, and consequently
that it is a continuous transmission of force. As the Voltaic battery
has become one of the most important engines of physical research, some
account of its present condition may not be out of place.

The disturbance of electric equilibrium, and a development of
electricity, invariably accompany the chemical action of a fluid on
metallic substances, and the electricity is most plentiful when that
action occasions oxidation. Metals vary in the quantity of electricity
afforded by their combination with oxygen. But the greatest abundance is
developed by the oxidation of zinc by weak sulphuric acid. And, in
conformity with the law that one kind of electricity cannot be evolved
without an equal quantity of the other being brought into activity, it
is found that the acid is positively, and the zinc negatively electric.
It has not yet been ascertained why equilibrium is not restored by the
contact of these two substances, which are both conductors, and in
opposite electrical states. However, the electrical and chemical changes
are so connected, that, unless equilibrium be restored, the action of
the acid will go on languidly, or stop as soon as a certain quantity of
electricity is accumulated in it. Equilibrium, nevertheless, will be
restored, and the action of the acid will be continuous, if a plate of
copper be placed in contact with the zinc, both being immersed in the
fluid; for the copper, not being acted upon by the acid, will serve as a
conductor to convey the positive electricity from the acid to the zinc,
and will at every instant restore the equilibrium, and then the
oxidation of the zinc will go on rapidly. Thus three substances are
concerned in forming a Voltaic circuit, but it is indispensable that one
of them should be a fluid. The electricity so obtained will be very
feeble in overcoming resistances offered by imperfect conductors
interposed in the circuit, or by very long wires, but it may be
augmented by increasing the number of plates. In the common Voltaic
battery, the electricity which the fluid has acquired from the first
plate of zinc exposed to its action is taken up by the copper plate
belonging to the second pair, and transferred to the second zinc plate,
with which it is connected. The second plate of zinc, possessing equal
powers, and acting in conformity with the first, having thus acquired a
larger portion of electricity than its natural share, communicates a
larger quantity to the fluid in the second cell. This increased quantity
is again transferred to the next pair of plates; and thus every
succeeding alternation is productive of a further increase in the
quantity of the electricity developed. This action, however, would stop
unless a vent were given to the accumulated electricity, by establishing
a communication between the positive and negative poles of the battery
by means of wires attached to the extreme plate at each end. When the
wires are brought into contact, the Voltaic circuit is completed, the
electricities meet and neutralize each other, producing the shock and
other electrical phenomena; and then the electric current continues to
flow uninterruptedly in the circuit, as long as the chemical action
lasts. The stream of positive electricity flows from the zinc to the
copper. The construction and power of the Voltaic battery have been much
improved of late years, but the most valuable improvement is the
constant battery of Professor Daniell. In all batteries of the ordinary
construction, the power, however energetic at first, rapidly diminishes,
and ultimately becomes very feeble. Professor Daniell found that this
diminution of power is occasioned by the adhesion of the evolved
hydrogen to the surface of the copper, and by the precipitation of the
sulphate formed by the action of the acid on the zinc. He prevents the
latter by interposing between the copper and the zinc, in the cell
containing the liquid, a membrane which, without impeding the electric
current, prevents the transfer of the salt; and the former, by placing
between the copper and the membrane solution of sulphate of copper,
which being reduced by the hydrogen prevents the adhesion of this gas to
the metallic surface. Each element of the battery consists of a hollow
cylinder of copper, in the axis of which is placed a cylindrical rod of
zinc; between the zinc and the copper a membranous bag is placed, which
divides the cell into two portions, the inner of which is filled with
dilute acid, and the one nearer the copper is supplied with crystals of
the sulphate of that metal. The battery consists of several of these
elementary cells connected together by metallic wires, the zinc rod of
one with the copper cylinder of that next to it. The zinc rods are
amalgamated, so that local action, which, in ordinary cases, is so
destructive of the zinc, does not take place, and no chemical action is
manifested unless the circuit be completed. The rods are easily
detached, and others substituted for them when worn out. This battery,
which possesses considerable power, and is constant in its effects for a
very long time, is greatly superior to all former arrangements, either
as an instrument of research, or for exhibiting the ordinary phenomena
of Voltaic electricity.

A battery charged with water alone, instead of acid, is constant in its
action, but the quantity of electricity it develops is comparatively
very small. Mr. Cross, of Broomfield in Somersetshire, kept a battery of
this kind in full force during twelve months. M. Becquerel had invented
an instrument for comparing the intensities of the different kinds of
electricity by means of weights; but, as it is impossible to make the
comparison with Voltaic electricity produced by the ordinary batteries,
on account of the perpetual variation to which the intensity of the
current is liable, he has constructed a battery which affords a
continued stream of electricity of uniform power, but it is also of very
feeble force. The current is produced by the chemical combination of an
acid with an alkali.

Metallic contact is not necessary for the production of Voltaic
electricity, which is entirely due to chemical action. The intensity of
the Voltaic electricity is in proportion to the intensity of the
affinities concerned in its production, and the quantity produced is in
proportion to the quantity of matter which has been chemically active
during its evolution. Dr. Faraday considers this definite production to
be one of the strongest proofs that electricity is of chemical origin.

Galvanic or Voltaic electricity is manifested by two continuous forces
or currents passing in opposite directions through the circuit: the zinc
is the positive end or pole of the battery, and the copper the negative.

Voltaic electricity is distinguished by two marked characters. Its
intensity increases with the number of plates, its quantity with the
extent of their surfaces. The most intense concentration of force is
displayed by a numerous series of large plates: light and heat are
copiously evolved, and chemical decomposition is accomplished with
extraordinary energy; whereas the electricity from one pair of plates,
whatever their size may be, is so feeble that it gives no sign either of
attraction or repulsion. Common or static electricity is of greater
intensity and has a greater power of overcoming resistance than Voltaic
electricity, but it acts upon a smaller quantity of matter. However, by
diminishing the size of the plates, and increasing their number, the
intensity of a battery may be increased till it becomes equal to that of
the electrical machine.

The action of Voltaic electricity differs in some respects materially
from that of the ordinary kind. When a quantity of common electricity is
accumulated, the restoration of equilibrium is attended by an
instantaneous violent explosion, accompanied by the development of
light, heat, and sound. The concentrated power of the electricity forces
its way through every obstacle, disrupting and destroying the cohesion
of the particles of the bodies through which it passes, and occasionally
increasing its destructive effects by the conversion of fluids into
steam from the intensity of the momentary heat, as when trees are torn
to pieces by a stroke of lightning. Even the vivid light which marks the
path of the electricity is probably owing in part to the sudden
compression of the air and the rapidity of its passage. But the instant
equilibrium is restored by this energetic action the whole is at an end.
On the contrary, when an accumulation takes place in a Voltaic battery,
equilibrium is restored the moment the circuit is completed. But so far
is the electric stream from being exhausted, that it continues to flow
silently and invisibly in an uninterrupted current supplied by a
perpetual reproduction. And, although its action on bodies is neither so
sudden nor so intense as that of common electricity, yet it acquires
such power from constant accumulation and continued action, that it
ultimately surpasses the energy of the other. The two kinds of
electricity differ in no circumstance more than in the development of
heat. Instead of a momentary evolution, the circulation of the Voltaic
electricity is accompanied by a continued development of heat, lasting
as long as the circuit is complete, without producing either light or
sound. Its intensity from a very powerful battery is greater than that
of any heat that can be obtained by artificial means, so that it fuses
substances which resist the action of the most powerful furnaces. The
temperature of every part of a Voltaic battery itself is raised during
its activity. With the greater number of metals Mr. Grove found that the
positive terminal or pole is hotter than the negative.

According to Mr. Joule, the quantity of heat generated in a unit of time
is proportional to the strength of the current, and when a galvanic
current is employed in chemical analysis, the heat in the entire circuit
generated in a unit of time is equal to the work expended in producing
it, minus that employed in the analysis. In fact, a current of
electricity cannot pass through a homogeneous conductor without
generating heat in overcoming resistance, an effect proved by Mr. Joule
to be proportional to the square of the force of the current, and the
same in whatever direction the current may be flowing. Any other thermal
action that can take place must depend upon the heterogeneousness of the
circuit, and must be reversible with the current. For example, if a
semicircle of bismuth be joined to a semicircle of antimony, an electric
current in passing through it produces cold where it passes from the
bismuth to the antimony by absorption, and heat where it passes from the
antimony to the bismuth.

The transit of the electricity from pole to pole is accompanied by
light, and in consequence of the continuous current sparks occur every
time the contact of the wires is either broken or renewed; but
considerable intensity is requisite to enable the electricity to force
its way through atmospheric air or gas. Both its length and colour are
affected by the density of the medium through which it passes. If the
medium be gradually rarefied the discharge increases from a spark to a
luminous glow, differing in colour in different gases, but white in air.
When very much attenuated a discharge may be made to pass across 6 or 7
feet of space, while in air of the ordinary density it will not pass
through an inch. In rarefied gas it resembles the Aurora by its
continuous flashes. When the battery is powerful the luminous effects
are very brilliant.

The most splendid artificial light known is produced by fixing pencils
of charcoal at the extremities of the wires, and bringing them into
contact. This light is the more remarkable as it is independent of
combustion, since the charcoal suffers no apparent change, and,
likewise, because it is equally vivid in such gases as do not contain
oxygen. It depends upon the molecular arrangement of the charcoal; for
Mr. Grove observes that “carbon in a transparent crystalline state, as
diamond, is as perfect a non-conductor as we know, while in an opaque
amorphous state, as graphite or charcoal, it is one of the best
conductors: thus in one state it transmits light and stops electricity,
in the other it transmits electricity and stops light. It is a
circumstance worthy of remark, that the arrangement of molecules which
renders a solid body capable of transmitting light is most unfavourable
to the transmission of electricity, transparent solids being very
imperfect conductors of electricity; so all gases readily transmit
light, but are amongst the worst conductors of electricity, if indeed
they can be said to conduct it at all. The fact that the molecular
structure or arrangement of a body influences, indeed I may say
determines, its conducting power, is by no means explained by the theory
of a fluid; but if electricity be only a transmission of force or
motion, the influence of the molecular state is just what would be
expected.”

Professor Wheatstone, by fixing metallic points at the extremities of
the wires or poles, has found that the appearance of the spectrum of the
voltaic arc or vivid flame that is seen between the terminals of a
battery, depends, as in static electricity, upon the metal from whence
it is taken. The spectrum of that from mercury consists of seven
definite rays, separated from each other by dark intervals; these
visible rays are two orange lines close together, a bright green line,
two blueish-green lines near each other, a very bright purple line, and,
lastly, a blue line. It is the same when it passes through carbonic acid
gas, oxygen gas, air, or vacuum. The light from zinc, cadmium, tin,
bismuth, and lead, in a melted state, gives similar results; but the
number, position, and colour of the lines vary so much in each case, and
the appearances are so different, that the metals may easily be
distinguished from one another by this mode of investigation. The
electric spark is considered by M. Angström to be the overlapping of two
spectra, one of which belongs to the metal, and the other to the gas
through which the spark passes, and that the bright lines vary with the
gas as well as with the metal. In an oxygen spectrum the greatest number
of bright lines occur in the blue and violet, in nitrogen in the green
and yellow, and in hydrogen in the red. These effects must necessarily
be connected with the chemical and thermal properties of the gases.

Mr. Grove considers that the colour of the voltaic arc, or flame, which
appears between the poles of a very powerful battery, depends upon the
substance of the metal from whence it proceeds and on the medium through
which it passes. The spark from zinc is blue, from silver it is green,
from iron it is red and scintillating—precisely the colours afforded by
these metals in their ordinary combustion. But the colour varies also
with the medium through which the light passes, for when the medium is
changed a change takes place in the colour, showing an affection of the
intervening matter. A portion of the metal terminals or poles is
actually transmitted with every electrical or Voltaic discharge, whence
Mr. Grove concludes that the electrical discharge arises, at least in
part, from an actual repulsion and severance of the electrified matter
itself, which flies off at the points of least resistance. He observes
that “the phenomena attending the electric spark or Voltaic arc tends to
modify considerably our previous idea of the nature of the electric
force as a producer of ignition and combustion. The Voltaic arc is
perhaps, strictly speaking, neither ignition nor combustion. It is not
simply ignition; because the matter of the terminals is not merely
brought to a state of incandescence, but is physically separated, and
partially transferred from one terminal to another, much of it being
dissipated in a vaporous state. It is not combustion; for the phenomena
will take place independently of atmospheric air, oxygen gas, or any of
the bodies usually called supporters of combustion; combustion being in
fact chemical union attended with heat and light. In the Voltaic arc we
may have no chemical union, for if the experiment be performed in an
exhausted receiver, or in nitrogen, the substance forming the terminals
is condensed and precipitated upon the interior of the vessel, in,
chemically speaking, an unaltered state. Thus, to take a very striking
example, if the Voltaic discharge be taken between zinc terminals in an
exhausted receiver, a fine black powder of zinc is deposited on the
sides of the receiver; this can be collected, and takes fire readily in
air by being touched with a match, or ignited wire, instantly burning
into white oxide of zinc. To an ordinary observer the zinc would appear
to be burned twice—first in the receiver, where the phenomenon presents
all the appearance of combustion, and, secondly, in the real combustion
in air. With iron the experiment is equally instructive. Iron is
volatilized by the Voltaic arc in nitrogen, or in an exhausted receiver;
and when a scarcely perceptible film has lined the receiver, if it be
washed with an acid, it then gives, with ferrocyanide of potassium, the
Prussian-blue precipitate. In this case we readily distil iron, a metal
by ordinary means _fusible_ only at a very high temperature.”

Another strong evidence that the Voltaic discharge consists of the
material itself of which the terminals are composed, is the peculiar
rotation which is observed in the light when iron is employed, the
magnetic character of this metal causing its particles to rotate by the
influence of the Voltaic current. In short, Mr. Grove concludes that,
although it would be hasty to assert that the electrical disruptive
discharge can in no case take place without the terminals being
affected, yet he had met with no instance of such a result, provided the
discharge had been sufficiently prolonged, and the terminals in such a
state as could be expected to render manifest slight changes![15]

Some years ago Mr. Grove discovered that the electrical discharge
possesses certain phases or fits of an alternate character, forming
rings of alternate oxidation and deoxidation on metallic surfaces. A
highly polished silver plate in an air-pump was connected with the pole
of a powerful inductive battery, while a fine metallic wire, or even a
common sewing needle, was fixed at the other pole, and so arranged as to
be perpendicular to the silver plate, and very near, but not touching
it. By means of this apparatus the electrical discharge could be sent
through any kind of rarefied media. In some of the experiments a series
of concentric coloured rings of oxide alternating with rings of polished
or unoxidated silver were formed on the plate under the point of the
needle or wire. When the plate was previously coated with a film of
oxide, the oxide was removed in concentric spaces by the discharge, and
increased on the alternate ones, showing an alternate positive and
negative electricity, or electricity of an opposite character in the
same discharge.

When the silver plate was polished the centre of the rings formed on it
was yellow-green surrounded by blue-green; then a ring of polished
silver, followed by a crimson ring with a slight orange tint on the
inner side and deep purple on the outer; lastly the indication of a
polished one. When the air-pump was filled with attenuated olefiant gas
the rings were precisely the same with those seen in thin plates; hence
the effect is the same as that produced by the interference of light. In
these experiments the luminous appearance extended from three quarters
of an inch to an inch round the point of the needle or wire.

When the silver plate was connected with the negative pole of the
battery a polished point appeared upon it opposite the needle,
surrounded by a dusky ill-defined areola of a brown colour tinged with
purple when viewed in one direction, and greenish-white when seen in
another.

In the present year Mr. Gassiot, Vice-President of the Royal Society,
has shown that the stratified character of the electric discharge is
remarkably developed in the Torricellian vacuum. Among the various
experiments made by that gentleman two may be selected as strongly
illustrative of this new and singular property of electrical light.

In a closed glass tube about an inch internal diameter and 38 inches
long, in which a vacuum had been made, two platinum wires were
hermetically sealed, 32 inches apart, and connected with the poles of an
inductive battery. The luminous appearance at the two poles was very
different when electricity passed through the wires. A glow surrounded
the negative pole, and in close approximation to the glow a well-defined
dark space appeared, while from the positive pole or wire the light
proceeded in a stream; but unless the charge be great or the tube short,
the stream will not extend to the black band, which is totally different
from the intervening space. When discharges of electricity were sent
through this vacuum tube a series of bands or stratifications were
formed which were concave towards the positive pole; and as in the
changes in making and breaking the circuit the electricity emanates from
the different terminals or wires, their concavities were in opposite
directions.

When instead of platinum wires narrow tinfoil coatings were placed round
the exterior of the glass tube and connected with the wires of the
battery, brilliant stratifications filled the interior of the tube
between the foil coatings, but no dark band appeared. At present Mr.
Gassiot is inclined to believe that the dark band is due to
interference; but that the stratifications arise from pulsations or
impulses of a force acting in a highly attenuated but resisting medium,
for even with the best air-pumps it is impossible to make a perfect
void; he is still occupied with experiments on this new subject, and no
doubt will obtain very remarkable results, of which none can be more
extraordinary than his discovery of the powerful influence of the magnet
on this electric light. The stratifications are formed in rapid
succession in the tube with platinum wires and are turned different
ways, but they can be separated at any part of the tube by the pole of a
magnet round which the whole stratifications have a tendency to revolve.
In the second experiment, where the tinfoil was used, the discharge was
divided in two by the pole of a magnet, and the two parts had a tendency
to rotate round the magnet in opposite directions.

Voltaic electricity is a powerful agent in chemical analysis. When
transmitted through conducting fluids, it separates them into their
constituent parts, which it conveys in an invisible state through a
considerable space or quantity of liquid to the poles, where they come
into evidence. Numerous instances might be given, but the decomposition
of water is perhaps the most simple and elegant. Suppose a glass tube
filled with water, and corked at both ends; if one of the wires of an
active Voltaic battery be made to pass through one cork, and the other
through the other cork, into the water, so that the extremities of the
two wires shall be opposite and about a quarter of an inch asunder,
chemical action will immediately take place, and gas will continue to
rise from the extremities of both wires till the water has vanished. If
an electric spark be then sent through the tube, the water will
reappear. By arranging the experiment so as to have the gas given out by
each wire separately, it is found that water consists of two volumes of
hydrogen and one of oxygen. The hydrogen is given out at the positive
wire of the battery, and the oxygen at the negative. The oxides are also
decomposed; the oxygen appears at the positive pole, and the metal at
the negative. The decomposition of the alkalies and earths by Sir
Humphry Davy formed a remarkable era in the history of science. Soda,
potash, lime, magnesia, and other substances heretofore considered to be
simple bodies incapable of decomposition, were resolved by electric
agency into their constituent parts, and proved to be metallic oxides,
by that illustrious philosopher. All chemical changes produced by
electricity are accomplished on the same principle; and it appears that,
in general, combustible substances, metals, and alkalies go to the
negative wire, while acids and oxygen are evolved at the positive. The
transfer of these substances to the poles is not the least wonderful
effect of the Voltaic battery. Though the poles be at a considerable
distance from one another, nay, even in separate vessels, if a
communication be only established by a quantity of wet thread, as the
decomposition proceeds the component parts pass through the thread in an
invisible state, and arrange themselves at their respective poles.
According to Dr. Faraday, electro-chemical decomposition is simply a
case of the preponderance of one set of chemical affinities more
powerful in their nature over another set which are less powerful. And
in electro-chemical action of any kind produced by a continuous current,
the amount of action in a given time is nearly, if not rigorously,
proportional to the strength of the current. The great efficacy of
Voltaic electricity in chemical decomposition arises not from its
tension, but from the quantity set in motion and the continuance of its
action. Its agency appears to be most exerted on fluids and substances
which by conveying the electricity partially and imperfectly impede its
progress. But it is now proved to be as efficacious in the composition
as in the decomposition or analysis of bodies.

It had been observed that, when metallic solutions are subjected to
galvanic action, a deposition of metal, sometimes in the form of minute
crystals, takes place on the negative wire. By extending this principle,
and employing a very feeble Voltaic action, M. Becquerel has succeeded
in forming crystals of a great proportion of the mineral substances,
precisely similar to those produced by nature. The electric state of
metallic veins makes it possible that many natural crystals may have
taken their form from the action of electricity bringing their ultimate
particles, when in solution, within the narrow sphere of molecular
attraction. Both light and motion favour crystallization. Crystals which
form in different liquids are generally more abundant on the side of the
jar exposed to the light; and it is well known that still water, cooled
below 32°, starts into crystals of ice the instant it is agitated. A
feeble action is alone necessary, provided it be continued for a
sufficient time. Crystals formed rapidly are generally imperfect and
soft, and M. Becquerel found that even years of constant Voltaic action
were necessary for the crystallization of some of the hard substances.
If this law be general, how many ages may be required for the formation
of a diamond!

The deposition of metal from a metallic solution by galvanic electricity
has been most successfully applied to the arts of plating and gilding,
as well as to the more delicate process of copying medals and copper
plates. Indeed, not medals only, but any object of art or nature, may be
coated with precipitated metal, provided it be first covered with the
thinnest film of plumbago, which renders a non-conductor sufficiently
conducting to receive the metal. Photo-galvanic engraving depends upon
this. Gelatine mixed with bichromate of potash, nitrate of silver, and
iodide of potassium, is spread over a plate of glass, and when dry a
positive print is laid upon it with its face downwards, which, when
exposed to the sun, leaves its impression. When soaked in water the
gelatine swells around all those parts where the light had fallen, thus
forming an intaglio, a cast of which is taken in gutta-percha, which is
then coated with copper by the electro process, whence a copper plate in
relief is obtained.

Static electricity, on account of its high tension, passes through water
and other liquids as soon as it is formed, whatever the length of its
course may be. Voltaic electricity, on the contrary, is weakened by the
distance it has to traverse. Pure water is a very bad conductor; but ice
absolutely stops a current of Voltaic electricity altogether, whatever
be the power of the battery, although static or common electricity has
sufficient power to overcome its resistance. Dr. Faraday has discovered
that this property is not peculiar to ice; that, with a few exceptions,
bodies which do not conduct electricity when solid acquire that
property, and are immediately decomposed, when they become fluid, and,
in general, that decomposition takes place as soon as the solution
acquires the capacity of conduction, which has led him to suspect that
the power of conduction may be only a consequence of decomposition.

Heat increases the conducting power of some substances for Voltaic
electricity, and of the gases for both kinds. Dr. Faraday has given a
new proof of the connexion between heat and electricity, by showing
that, in general, when a solid, which is not a metal, becomes fluid, it
almost entirely loses its power of conducting heat, while it acquires a
capacity for conducting electricity in a high degree. M. Becquerel
regards the production of heat and that of electricity to be
concomitant; their dependence being such, that when one is increased the
other diminishes, and _vice versâ_, so that one may altogether disappear
with the increase of the other. For instance, when electricity
circulates in a metallic wire, the greater the heat produced, the less
the quantity of electricity which passes, and the contrary, so that the
affair proceeds as if electricity were converted into heat, and heat
into electricity. Again, in a closed galvanic circuit the sum of the
heat produced in the chemical action of the acidulated water upon the
zinc and in the conducting wire is constant, so that the quantity of
heat disengaged in the reaction is greater in proportion as less
electricity passes through the wire. These, and other circumstances,
prove such an intimate connexion between the production of heat and
electricity, that in the change of condition of substances the
electrical effects might disappear or be annulled by the calorific
effects.

The galvanic current affects all the senses: nothing can be more
disagreeable than the shock, which may even be fatal if the battery be
very powerful. A bright flash of light is perceived with the eyes shut,
when one of the wires touches the face, and the other the hand. By
touching the ear with one wire, and holding the other, strange noises
are heard; and an acid taste is perceived when the positive wire is
applied to the tip of the tongue, and the negative wire touches some
other part of it. By reversing the poles the taste becomes alkaline. It
renders the pale light of the glow-worm more intense. Dead animals are
roused by it, as if they started again into life, and it may ultimately
prove to be the cause of muscular action in the living.

Several fish possess the faculty of producing electrical effects. The
most remarkable are the gymnotus electricus, found in South America; and
the torpedo, a genus of ray, frequent in the Mediterranean. The
electrical action of the torpedo depends upon an apparatus apparently
analogous to the Voltaic pile, which the animal has the power of
charging at will, consisting of membranous columns filled throughout
with laminæ, separated from one another by a fluid. The absolute
quantity of electricity brought into circulation by the torpedo is so
great, that it effects the decomposition of water, has power sufficient
to make magnets, gives very severe shocks and the electric spark. It is
identical in kind with that of the galvanic battery, the electricity of
the under surface of the fish being the same with the negative pole, and
that in the upper surface the same with the positive pole. Its manner of
action is, however, somewhat different; for, although the evolution of
the electricity is continued for a sensible time, it is interrupted,
being communicated by a succession of discharges.




                              SECTION XXX.

Discovery of Electro-magnetism—Deflection of the Magnetic Needle by a
  Current of Electricity—Direction of the Force—Rotatory Motion by
  Electricity—Rotation of a Wire and a Magnet—Rotation of a Magnet about
  its Axis—Of Mercury and Water—Electro-Magnetic Cylinder or
  Helix—Suspension of a Needle in a Helix—Electro-Magnetic
  Induction—Temporary Magnets—The Galvanometer.


THE disturbing effects of the aurora and lightning on the mariner’s
compass had been long known. In the year 1819 M. Oersted, Professor of
Natural Philosophy at Copenhagen, discovered that a current of Voltaic
electricity exerts a powerful influence on a magnetized needle. This
observation has given rise to the theory of electro-magnetism—one of the
most interesting sciences of modern times, whether it be considered as
leading us a step farther in generalization, by identifying two agencies
hitherto referred to different causes, or as developing a new force,
unparalleled in the system of the world, which, overcoming the
retardation from friction, and the obstacle of a resisting medium,
maintains a perpetual motion as long as the action of a Voltaic battery
is continued.

When the two poles of a Voltaic battery are connected by a metallic
wire, so as to complete a circuit, the electricity flows without
ceasing. If a straight portion of that wire be placed parallel to, and
horizontally above, a magnetized needle at rest in the magnetic
meridian, but freely poised like the mariner’s compass, the action of
the electric current flowing through the wire will instantly cause the
needle to change its position. Its extremity will deviate from the north
towards the east or west, according to the direction in which the
current is flowing; and, on reversing the direction of the current, the
motion of the needle will be reversed also. The numerous experiments
that have been made on magnetism and electricity, as well as those on
the various relative motions of a magnetic needle under the influence of
galvanic electricity, arising from all possible positions of the
conducting wire, and every direction of the Voltaic current, together
with all the other phenomena of electro-magnetism, are explained by Dr.
Roget in some excellent articles on these subjects in the Library of
Useful Knowledge.

All experiments tend to prove that the force emanating from the electric
current, which produces such effects on the magnetic needle, acts at
right angles to the current. The action of an electrical current upon
either pole of a magnet has no tendency to cause the pole to approach or
recede, but to rotate about it. If the stream of electricity be supposed
to pass through the centre of a circle whose plane is perpendicular to
the current, the direction of the force exerted by the electricity will
always be in the tangent to the circle, or at right angles to its radius
(N. 223). Consequently, the tangential force of the electricity has a
tendency to make the pole of a magnet move in a circle round the wire of
the battery.

Rotatory motion was suggested by Dr. Wollaston. Dr. Faraday was the
first who actually succeeded in making the pole of a magnet rotate about
a vertical conducting wire. In order to limit the action of the
electricity to one pole, about two-thirds of a small magnet were
immersed in mercury, the lower end being fastened by a thread to the
bottom of the vessel containing the mercury. When the magnet was thus
floating almost vertically with its north pole above the surface, a
current of positive electricity was made to descend perpendicularly
through a wire touching the mercury, and immediately the magnet began to
rotate from left to right about the wire. The force being uniform, the
rotation was accelerated till the tangential force was balanced by the
resistance of the mercury, when it became constant. Under the same
circumstances the south pole of the magnet rotates from right to left.
It is evident, from this experiment, that the wire may also be made to
perform a rotation round the magnet, since the action of the current of
electricity on the pole of the magnet must necessarily be accompanied by
a corresponding reaction of the pole of the magnet on the electricity in
the wire. This experiment has been accomplished by a vast number of
contrivances, and even a small battery, consisting of two plates, has
performed the rotation. Dr. Faraday produced both motions at the same
time in a vessel containing mercury; the wire and the magnet revolved in
one direction about a common centre of motion, each following the other.

The next step was to make a magnet, and also a cylinder, revolve about
their own axes, which they do with great rapidity. Mercury has been made
to rotate by means of Voltaic electricity, and Professor Ritchie
exhibited in the Royal Institution the singular spectacle of the
rotation of water by the same means, while the vessel containing it
remained stationary. The water was in a hollow double cylinder of glass,
and, on being made the conductor of electricity, was observed to revolve
in a regular vortex, changing its direction as the poles of the battery
were alternately reversed. Professor Ritchie found that all the
different conductors hitherto tried by him, such as water, charcoal,
&c., give the same electro-magnetic results when transmitting the same
quantity of electricity, and that they deflect the magnetic needle in an
equal degree when their respective axes of conduction are at the same
distance from it. But one of the most extraordinary effects of this
force is exhibited by coiling a copper wire, so as to form a helix or
corkscrew, and connecting the extremities of the wire with the poles of
a galvanic battery. If a magnetized steel bar or needle be placed within
the screw, so as to rest upon the lower part, the instant a current of
electricity is sent through the wire of the helix, the steel bar starts
up by the influence of this invisible power, and remains suspended in
the air in opposition to the force of gravitation (N. 224). The effect
of the electro-magnetic power exerted by each turn of the wire is to
urge the north pole of the magnet in one direction, and the south pole
in the other. The force thus exerted is multiplied in degree and
increased in extent by each repetition of the turns of the wire, and in
consequence of these opposing forces the bar remains suspended. This
helix has all the properties of a magnet while the electrical current is
flowing through it, and may be substituted for one in almost every
experiment. It acts as if it had a north pole at one extremity and a
south pole at the other, and is attracted and repelled by the poles of a
magnet exactly as if it were one itself. All these results depend upon
the course of the electricity; that is, on the direction of the turns of
the screw, according as it is from right to left, or from left to right,
being contrary in the two cases.

The action of Voltaic electricity on a magnet is not only precisely the
same with the action of two magnets on one another, but its influence in
producing temporary magnetism in iron and steel is also the same with
magnetic induction. The term induction, when applied to electric
currents, expresses the power which these currents possess of inducing a
particular state upon matter in their immediate neighbourhood, otherwise
neutral or indifferent. For example, the connecting wire of a galvanic
battery holds iron filings suspended like a magnet as long as the
current continues to flow through it: the iron becomes magnetic by the
induction of the current. The most powerful temporary magnets are
obtained by bending a thick cylinder of soft iron into the form of a
horseshoe, and surrounding it with a coil of thick copper wire covered
with silk to prevent communication between its coils. When this wire
forms part of a galvanic circuit the iron becomes so highly magnetic by
the induction of the current flowing through the wire that a temporary
magnet of this kind made by Professor Henry of the Albany Academy in the
United States sustained a weight of nearly a ton. Another by Mr. Gage
has been applied with considerable success as a moving power: its spark
is a bright flash, and the snap as loud as a pistol. But the most
powerful known is that employed by Mr. Joule in his experiments, which
sustains a weight of 2080 lbs. The iron loses its magnetism the instant
the electricity ceases to flow, and acquires it again as instantaneously
when the circuit is renewed.

The action of an electric current causes a deviation of the compass from
the plane of the magnetic meridian. In proportion as the needle recedes
from the meridian, the intensity of the force of terrestrial magnetism
increases, while at the same time the electro-magnetic force diminishes;
the number of degrees at which the needle stops, showing where the
equilibrium between these two forces takes place, will indicate the
intensity of the galvanic current. The galvanometer, constructed upon
this principle, is employed to measure the intensity of galvanic
currents collected and conveyed to it by wires. This instrument is
rendered much more sensible by neutralizing the effects of the earth’s
magnetism on the needle, which is accomplished by placing a second
magnetised needle so as to counteract the action of the earth on the
first—a precaution requisite in all delicate magnetical experiments.

It has been ascertained by means of this instrument that the action of
an electrical current upon a magnet is inversely as the square of the
distance, and the energy with which an electro magnet acts is directly
as the power of the galvanic battery and the number of coils round the
core, and inversely as the resistance of the wire.




                             SECTION XXXI.

Electro-Dynamics—Reciprocal Action of Electric Currents—Identity of
  Electro-Dynamic Cylinders and Magnets—Differences between the Action
  of Voltaic Electricity and Electricity of Tension—Effects of a Voltaic
  Current—Ampère’s Theory—Dr. Faraday’s Experiment of Electrifying and
  Magnetising a Ray of Light.


THE science of electro-magnetism, which must render the name of M.
Oersted ever memorable, relates to the reciprocal action of electrical
and magnetic currents: M. Ampère, by discovering the mutual action of
electrical currents on one another, has added a new branch to the
subject, to which he has given the name of electro-dynamics.

When electric currents are passing through two conducting wires, so
suspended or supported as to be capable of moving both towards and from
one another, they show mutual attraction or repulsion, according as the
currents are flowing in the same or in contrary directions; the
phenomena varying with the relative inclinations and positions of the
streams of electricity. The mutual action of such currents, whether they
flow in the same or in contrary directions, whether they be parallel,
perpendicular, diverging, converging, circular, or heliacal, all produce
different kinds of motion in a conducting wire, both rectilineal and
circular, and also the rotation of a wire helix, such as that described,
now called an electro-dynamic cylinder on account of some improvements
in its construction (N. 225). And, as the hypothesis of a force varying
inversely as the square of the distance accords perfectly with all the
observed phenomena, these motions come under the same laws of dynamics
and analysis as any other branch of physics.

Electro-dynamic cylinders act on each other precisely as if they were
magnets during the time the electricity is flowing through them. All the
experiments that can be performed with the cylinder might be
accomplished with a magnet. That end of the cylinder in which the
current of positive electricity is moving in a direction similar to the
motion of the hands of a watch, acts as the south pole of a magnet, and
the other end, in which the current is flowing in a contrary direction,
exhibits northern polarity.

The phenomena mark a very decided difference between the action of
electricity in motion or at rest, that is, between Voltaic and static
electricity; the laws they follow are in many respects of an entirely
different nature, though the electricities themselves are identical.
Since Voltaic electricity flows perpetually, it cannot be accumulated,
and consequently has no tension, or tendency to escape from the wires
which conduct it. Nor do these wires either attract or repel light
bodies in their vicinity, whereas static or ordinary electricity can be
accumulated in insulated bodies to a great degree, and in that state of
rest the tendency to escape is proportional to the quantity accumulated
and the resistance it meets with. In ordinary electricity, the law of
action is, that dissimilar electricities attract and similar
electricities repel one another. In Voltaic electricity, on the
contrary, similar currents, or such as are moving in the same direction,
attract one another, while a mutual repulsion is exerted between
dissimilar currents, or such as flow in opposite directions. Common
electricity escapes when the pressure of the atmosphere is removed, but
the electro-dynamical effects are the same whether the conductors be in
air or in vacuo.

The effects produced by a current of electricity depend upon the
celerity of its motion through a conducting wire. Yet we are ignorant
whether the motion be uniform or varied, but the method of transmission
has a marked influence on the results; for, when it flows without
intermission, it occasions a deviation in the magnetic needle, but it
has no effect whatever when its motion is discontinuous or interrupted,
like the current produced by the common electrical machine when a
communication is made between the positive and negative conductors.

M. Ampère has established a theory of electro-magnetism suggested by the
analogy between electro-dynamic cylinders and magnets, founded upon the
reciprocal attraction of electro-currents, to which he reduces all the
phenomena of magnetism and electro-magnetism, by assuming that the
magnetic properties which bodies possess derive these properties from
currents of electricity, circulating about every part in one uniform
direction. Although every particle of a magnet possesses like properties
with the whole, yet the general effect is the same as if the magnetic
properties were confined to the surface. Consequently, Ampère concludes
that the internal electro-currents must compensate one another, and that
the magnetism of a body must therefore arise from a superficial current
of electricity constantly circulating in a direction perpendicular to
the axis of the magnet; so that the reciprocal action of magnets and all
the phenomena of electro-magnetism are reduced to the action and
reaction of superficial currents of electricity, acting at right angles
to their direction.

Notwithstanding the experiments made by Ampère to elucidate the subject,
there is still an uncertainty in the theory of the induction of
magnetism by an electric current in a body near it. It does not appear
whether electric currents which did not previously exist are actually
produced by induction, or if its effect be only to give one uniform
direction to the infinite number of electric currents previously
existing in the particles of the body, and thus rendering them capable
of exhibiting magnetic phenomena, in the same manner as polarization
reduces the undulations of light to one plane, which had previously been
performed in every plane. Possibly both may be combined in producing the
effect; for the action of the electric current may not only give a
common direction to those already existing, but may also increase their
intensity. However that may be, by assuming that the attractions and
repulsions of the elementary portions of electric currents vary
inversely as the square of the distance, the actions being at right
angles to the direction of the current, it is found that the attraction
and repulsion of a current of indefinite length on the elementary
portion of a parallel current at any distance from it are in the simple
ratio of the shortest distance between them: consequently, the
reciprocal action of electric currents is reduced to the composition and
resolution of forces, so that the phenomena of electro-magnetism are
brought under the laws of mechanics by the theory of Ampère. It appears
that Dr. Faraday’s very remarkable experiment of electrifying and
magnetising a ray of polarized light may possibly afford a demonstration
of the reality of Ampère’s explanation of the ultimate nature of
magnetism.

In this experiment a copper wire 501 feet long was arranged in four
concentric spirals, the extremities of which were connected with the
poles of a powerful galvanic battery, and a polished prism of heavy
glass, or silicated borate of lead, was placed in the axis of the spiral
as a core, through the length or axis of which a ray of polarized light
was sent. This ray, viewed through a piece of tourmaline or a Nichol’s
eye-piece, vanished and reappeared as usual at each quarter revolution
of the eye-piece; but when a current of electricity was sent through the
spiral at the time the ray had vanished, it instantly reappeared, and
remained as long as the electric current continued to flow; but the
instant the electricity ceased the light vanished, and as often as the
electric current flowed through the spiral, or was interrupted, so often
did the polarized ray appear and vanish.

The character of the force thus impressed on the heavy glass is that of
rotation, for the stopping and renewing of the electric current had the
same effect as the revolving motion of the eye-piece in making the light
alternately appear and vanish. Accordingly, Dr. Faraday found that, when
the electricity flowed through the spiral in one direction, the rotation
of the plane of polarization was right-handed; and when it flowed in the
other direction, the rotation of the plane of polarization was
left-handed, the rotation increasing with the length of the prism and
the intensity of the electricity. The same phenomena were produced by a
very powerful magnet when a ray of polarized light was sent through the
heavy glass parallel to the line of magnetic force.

Heavy glass or silico-borate of lead has the property more than any
other substance of making light rotate under electric and magnetic
influence; but many substances have the property more or less, as flint
and crown glass, rock salt, all the fixed and essential oils, water, and
many other liquids, but none of the gases possess it. In those
substances that have the power of circular polarization naturally, the
magnetic and electric influences increase or diminish the rotation
according to its direction.

Polarized heat is made to revolve in the same manner, when the medium
through which it passes is subject to magnetic influence.

Mr. Grove observes that if light and heat be merely modes of force,
which there is every reason to believe that they are, it may be fairly
stated that in these experiments magnetism affects these forces
directly; for light and heat being, in that view, motions of ordinary
matter, magnetism in affecting these movements affects the forces which
occasion them. If, however, this effect of magnetism be a molecular
change of the matter transmitting the light and heat, then it follows
that the light and heat are indirectly affected by the electricity or
magnetism. Dr. Faraday says that the magnetic forces do not act on the
ray of light directly, without the intervention of matter, but through
the mediation of the substance in which they and the ray have a
simultaneous existence; the substances and the forces giving to and
receiving from each other the power of acting on the light. Dr. Thomson
has shown, by a mathematical investigation of the subject, that Dr.
Faraday’s discovery seems to prove the truth of Ampère’s explanation of
the ultimate nature of magnetism. However, in Ampère’s theory, the
current of electricity flowing round the iron makes it a permanent
magnet, but it does not make the heavy glass or the other bodies, which
have the same property, either temporary magnets when the light is
rotating within them, or permanent magnets when the inductive action of
the current of electricity ceases. Hence the molecular condition of the
substances, when the light is rotating in them, must be specifically
distinct from that of magnetised iron: it must therefore be a new
magnetic condition, and the force which the matter in this state
possesses must be a new magnetic force.

After describing his admirable experiment, Dr. Faraday observes that “it
has established for the first time a true, direct relation and
dependence between light and the magnetic and electric forces; and thus
a great addition is made to the facts and considerations which tend to
prove that all natural forces are tied together, and have one common
origin. It is no doubt difficult, in the present state of our knowledge,
to express our expectations in exact terms; and though I have said that
another of the powers of nature is in these experiments directly related
to the rest, I ought perhaps rather to say that another form of the
great power is distinctly and directly related to the other forms; or
that the great power manifested by particular phenomena in particular
forms is here further identified and recognised by the direct relation
of its form of light to its forms of electricity and magnetism. The
relation existing between _polarized_ light and magnetism and
electricity is even more interesting than if it had been shown to exist
with common light only. It cannot but extend to common light; and, as it
belongs to light made in a certain respect more precise in its character
and properties by polarization, it collates and connects it with these
powers in that duality of character which they possess, and yields an
opening, which before was wanting to us, for the appliances of these to
the investigation of the nature of this and other radiant agencies.”
Thus Dr. Faraday’s experiment not only shows the increasing connexion
between the sciences, but the tendency of all the forces of nature to
merge in one great and universal power.

In the action of a magnet upon the stratifications of an electrical
discharge Mr. Gassiot has discovered a new instance of the connexion
between magnetism and light.




                             SECTION XXXII.

Magneto-Electricity—Volta-Electric Induction—Magneto-Electric
  Induction—Identity in the Action of Electricity and
  Magnetism—Description of a Magneto-Electric Apparatus and its
  Effects—Identity of Magnetism and Electricity—The Submarine Telegraph.


FROM the law of action and reaction being equal and contrary, it might
be expected that, as electricity powerfully affects magnets, so,
conversely, magnetism ought to produce electrical phenomena. By proving
this very important fact from the following series of interesting and
ingenious experiments, Dr. Faraday has added another branch to the
science which he has named magneto-electricity. A great quantity of
copper wire was coiled in the form of a helix round one half of a ring
of soft iron, and connected with a galvanic battery; while a similar
helix connected with a galvanometer was wound round the other half of
the ring, but not touching the first helix. As soon as contact was made
with the battery, the needle of the galvanometer was deflected. But the
action was transitory; for, when the contact was continued, the needle
returned to its usual position, and was not affected by the continual
flow of the electricity through the wire connected with the battery. As
soon, however, as the contact was broken, the needle of the galvanometer
was again deflected, but in the contrary direction. Similar effects were
produced by an apparatus consisting of two helices of copper wire coiled
round a block of wood, instead of iron, from which Dr. Faraday infers
that the electric current passing from the battery through one wire
induces a similar current through the other wire, but only at the
instant of contact, and that a momentary current is induced in a
contrary direction when the passage of the electricity is suddenly
interrupted. These brief currents or waves of electricity were found to
be capable of magnetizing needles, of passing through a small extent of
fluid, and, when charcoal points were interposed in the current of the
induced helix, a minute spark was perceived as often as the contacts
were made or broken, but neither chemical action nor any other electric
effects were obtained. A deviation of the needle of the galvanometer
took place when common magnets were employed instead of the Voltaic
current; so that the magnetic and electric forces are identical in their
effects in this experiment. Again, when a helix formed of 220 feet of
copper wire, into which a cylinder of soft iron was introduced, was
placed between the north and south poles of two bar magnets, and
connected with the galvanometer by means of wires from each extremity,
as often as the magnets were brought into contact with the iron cylinder
it became magnetic by induction, and produced a deflection in the needle
of the galvanometer. On continuing the contact the needle resumed its
natural position, and, when the contact was broken, deflection took
place in the opposite direction; when the magnetic contacts were
reversed, the deflection was reversed also. With strong magnets, so
powerful was the action, that the needle of the galvanometer whirled
round several times successively; and similar effects were produced by
the mere approximation or removal of the helix to the poles of the
magnets. Thus it was proved that magnets produce the very same effects
on the galvanometer that electricity does. Though at that time no
chemical decomposition was effected by these momentary currents which
emanate from the magnets, they agitated the limbs of a frog; and Dr.
Faraday justly observes, that “an agent which is conducted along
metallic wires in the manner described, which, whilst so passing,
possesses the peculiar magnetic actions and force of a current of
electricity, which can agitate and convulse the limbs of a frog, and
which finally can produce a spark by its discharge through charcoal, can
only be electricity.” Soon after he completely established the identity
of the two powers by producing the spark, heating metallic wires, and
accomplishing chemical decomposition. Hence it appears that electrical
currents are evolved by magnets, which produce the same phenomena with
the electrical currents from the Voltaic battery: they, however, differ
materially in this respect—that time is required for the exercise of the
magnetico-electric induction, whereas Volta-electric induction is
instantaneous.

Thus the effect of induction or the influence of the spiral wire in
increasing the electric and magnetic power is very great indeed, and to
that we are indebted for the electric telegraph, for Voltaic electricity
alone is too feeble to overcome the resistance of a long wire.

Electric currents, whatever their tension may be, produce the phenomena
of induction; these again induce other currents in bodies capable of
induction, and so on indefinitely; the first and second flow in the same
direction, the others alternately opposite and direct. They all give the
shock and can decompose water, but with Volta-electric currents the
elevation of temperature as well as their physiological and magnetic
effects are produced by instantaneous actions, which only depend upon
the quantity and tension of the current, and by no means on its
duration, for induced currents only exist for a moment when the circuit
of the battery is broken. The most energetic physiological effects are
produced by a small quantity of electricity moving with great velocity.
The apparatus first employed by Dr. Faraday is in effect a battery,
where the agent is the magnetic instead of the Voltaic force, or, in
other words, electricity, and is thus constructed:—

A very powerful horseshoe magnet, formed of twelve steel plates in close
approximation, is placed in a horizontal position. An armature,
consisting of a bar of the purest soft iron, has each of its ends bent
at right angles, so that the faces of those ends may be brought directly
opposite and close to the poles of the magnet when required. Ten copper
wires—covered with silk, in order to insulate them—are wound round one
half of the bar of soft iron, as a compound helix: ten other wires, also
insulated, are wound round the other half of the bar. The extremities of
the first set of wires are in metallic connexion with a circular disc,
which dips into a cup of mercury, while the ends of the other ten wires
in the opposite direction are soldered to a projecting screw-piece,
which carries a slip of copper with two opposite points. The steel
magnet is stationary; but when the armature, together with its
appendages, is made to rotate vertically, the edge of the disc always
remains immersed in the mercury, while the points of the copper slip
alternately dip in it and rise above it. By the ordinary laws of
induction, the armature becomes a temporary magnet while its bent ends
are opposite the poles of the steel magnet, and ceases to be magnetic
when they are at right angles to them. It imparts its temporary
magnetism to the helices which concentrate it; and, while one set
conveys a current to the disc, the other set conducts the opposite
current to the copper slip. As the edge of the revolving disc is always
immersed in the mercury, one set of wires is constantly maintained in
contact with it, and the circuit is only completed when a point of the
copper slip dips in the mercury also; but the circuit is broken the
moment that point rises above it. Thus, by the rotation of the armature,
the circuit is alternately broken and renewed; and as it is only at
these moments that electric action is manifested, a brilliant spark
takes place every time the copper point leaves the surface of the
mercury. Platinum wire is ignited, shocks smart enough to be
disagreeable are given, and water is decomposed with astonishing
rapidity, by the same means; which proves, beyond a doubt, the identity
of the magnetic and electric agencies, and places Dr. Faraday, whose
experiments established the principle, in the first rank of experimental
philosophers.

A magneto-electric machine has been recently constructed by Mr. Henley,
of enormous power. It consists of two permanent magnets, from which the
induction is obtained; each of these is formed of thirty horseshoe steel
magnets, two feet and a half long, and from four to five inches broad,
and each is surrounded by a coil of wire six miles long, coated with
silk to insulate the coils. A shock from these wires would be
instantaneous death. This apparatus will ultimately be employed to send
a stream of electricity through long submarine and subterraneous wires;
but a Volta-electric machine has hitherto been used, in which the
electricity is generated by a galvanic battery instead of magnets.

Induction, or the effect of the spiral wires in augmenting the power of
Voltaic electricity, is admirably illustrated in the Atlantic telegraph.

Wires that are to convey electricity under ground, or through water,
must be defended from injury and insulated to prevent the lateral escape
of the electricity. For that purpose the cable that is laid at the
bottom of the Atlantic, from near Valentia in Ireland to Trinity Bay in
Newfoundland, is formed of seven fine copper wires which convey the
electricity, bound together by a coating of gutta percha, over which
there are layers of cloth dipped in pitch, and then the whole is covered
by steel wires twisted together in strands and twined round in long
close spirals, forming a cord or cable not more than an inch and a
quarter in diameter, and 2100 miles long. The use of the gutta percha is
to insulate the wires; the other coatings are merely for protection.

The Voltaic battery which generates the electricity consists of 40
cells, the plates of which are alternately of zinc and platinized
silver, each about nine inches square, the exciting fluid being dilute
sulphuric acid. Although the force developed by this battery is so great
that a piece of iron three inches long and three eighths of an inch in
diameter placed in contact with the poles may be consumed in a few
minutes, it is absolutely incapable of sending a current of electricity
through wires 2500 miles long, on account of their resistance, without
the aid of Dr. Faraday’s inductive action. It is only the primary agent
for inducing a current of sufficient strength.

To accomplish that, many thousand yards of fine copper wire coated with
silk are wound round a hollow soft iron cylinder; the whole is then
coated by gutta percha, and the end of the wire is joined to the wires
in the cable so as to form a continuous line from Valentia to
Newfoundland. A second copper wire, shorter but thicker than the
preceding, and also insulated by a coating of silk, is wound round the
cylinder above the gutta percha: when the ends of this thick wire are
brought into contact with the poles of the battery, currents of
electricity flow through it, between pole and pole, and in their passage
temporarily convert the hollow iron cylinder into a powerful
electro-magnet, which by its reaction induces a current of electricity
in the fine wire of sufficient power to cross the Atlantic. The
efficiency of the electric telegraph depends upon the power we possess
of breaking and renewing the current at pleasure, since by that means
distinct and successive signals are made from station to station. In the
Atlantic cable positive and negative electricity are transmitted
alternately; the electricity is sent to America from alternate poles,
and the current returns again through the water, which completes the
circuit.

The passage of electricity through a cable or telegraphic wire in air is
sensibly instantaneous; that through a cable, whether extended in water
or under ground, requires time on account of lateral induction through
the gutta percha; for the electricity, in passing through the wires,
induces the opposite electricity on the surface of the water or moist
earth in contact with the cable, and in that respect it is precisely
like a Leyden jar, the gutta percha representing the glass. As the power
of induction is proportional to the tension of the electricity, and as
the tension is continually diminished by the resistance of the wires,
the induction is continually diminished and requires a longer time.
Electricity took two seconds to pass through a cable 768 miles long,
laid under ground from London to Manchester, and back again twice; while
in air it was all but instantaneous, because the inductive capacity of
air is very much less than that of water or moist earth. In the
experiment with the cable under ground it took two-thirds of a second to
overcome the resistance of the wires, and then the velocity of the
electricity was 1000 miles in a second, and it was the same whatever the
intensity of the electricity.

It has already been mentioned that the efficiency of the electric
telegraph depends upon the breaking and renewing the current of
electricity by means of which a succession of waves of electricity are
sent through the conducting wires. Now it has been ascertained that
three electric waves may travel simultaneously through the wires of the
Atlantic telegraph with sufficient intervals between them to record the
indications they are intended to convey; that is, three signals can be
intelligibly and practically transmitted in two seconds.

The original design, structure, and difficulty of depositing the cable
are only equalled by the talent and perseverance with which it has been
done. The 5th of August, 1858, will be memorable for the accomplishment
of the boldest enterprise that ever was undertaken by man, and which is
only the beginning of a vast submarine communication that will
ultimately encircle the globe. It has been granted to British genius
thus to annihilate time and space, in order to connect all mankind into
one great family for their moral and religious advancement; and,
whatever may be the fate of the British Islands in the course of ages,
to their energetic race the glory will remain of having been the chief
instruments in the hands of Providence for the civilization of the
world—a civilization which will extend with the development of their
numerous colonies into great independent Christian states, like those of
the Union in North America. The thunderbolt snatched from heaven by
Franklin now passes through the depths of the Atlantic as a messenger of
peace between the kindred nations.[16]

In telegraphs on land the intensity of the battery or magnets is
increased by induction on the same principle. It is by intensity that
the electric current is enabled to pass through the wires, and that is
augmented by increasing the number of coils round the cylinder: however,
it is only advantageous when the distance between the stations is great,
for then the resistance in the additional coils bears a small proportion
to the resistance offered by very long wires, but a very great
proportion to that opposed in very short ones. The nice adjustment for
each case has been determined by the experiments of eminent
electricians, and all the arrangements have been brought to great
perfection in this wonderful triumph of science, which is due to Volta,
who called into existence the fiery stream, and to Faraday, who has
given it the energy of the lightning.

When the length of the wire in the helices of an electro-magnet is very
great, it offers increasing resistance to the passage of the
electricity, so that the cessation of magnetism is not instantaneous
when the contact with the Voltaic battery is broken. To remedy that
defect an instrument has been invented which instantaneously deprives
the apparatus of the remaining electricity. A great length of fine wire
gives the severest shocks, while a shorter and thicker wire gives the
longest sparks and ignites the greatest quantity of platinum wire.

Ruhmkorff’s electro-inductive apparatus has either been improved, or new
machines constructed, by Messrs. Grove, Gassiot, and Joule, of intense
energy. Indeed, so great is the energy of electro-induction, that hopes
were entertained of its superseding steam as a motive power. For the
current of electricity from an electro-magnet can be made to flow in
opposite directions, so as to produce alternate attractions and
repulsions, and consequently a continued motion, which might be applied
as a motive force to machinery. However, Mr. Joule has proved that the
power developed by one pound of coal in combustion is to that produced
by one pound of zinc consumed in Mr. Grove’s powerful electro-magnetic
apparatus as nine to one, so that, even if zinc were as cheap as coal,
and a Voltaic battery as easily kept in order as an engine-furnace,
electricity will not supersede steam as a motive power.

A current of electricity traversing a conductor gives out a quantity of
heat determined by fixed laws, the amount of which is invariable as long
as the machine to which it is applied remains at rest; but the instant
the machine is set in motion a reaction takes place in the intensity of
the current, causing a diminution in the quantity of heat, because the
heat that disappears is converted into the mechanical force exerted by
the engine.

Mr. Joule’s experiments prove that, whenever a current of electricity is
generated by a magneto-electric machine, the quantity of heat evolved by
that current has a constant relation to the power required to work the
machine; and on the other hand, whenever an engine is worked by a
Voltaic battery, that the power developed is at the expense of the
calorific force of the battery for a given consumption of zinc, the
mechanical effect produced having a fixed relation to the heat lost in
the Voltaic current. The obvious conclusion Mr. Joule draws from these
experiments is, that heat and mechanical power are convertible into one
another, and it becomes evident, therefore, that heat is either the vis
viva or living force of ponderable particles, or a state of attraction
and repulsion capable of generating vis viva (N. 222).




                            SECTION XXXIII.

Electricity produced by Rotation—Direction of the Currents—Electricity
  from the Rotation of a Magnet—M. Arago’s Experiment explained—Rotation
  of a Plate of Iron between the Poles of a Magnet—Relation of
  Substances to Magnets of three Kinds—Thermo-Electricity.


M. ARAGO discovered a source of magnetism in rotatory motion. If a
circular plate of copper be made to revolve immediately above or below a
magnetic needle or magnet, suspended in such a manner that it may rotate
in a plane parallel to that of the copper plate, the magnet tends to
follow the circumvolution of the plate; or, if the magnet revolves, the
plate tends to follow its motion; so powerful is the effect, that
magnets and plates of many pounds weight have been carried round. This
is quite independent of the motion of the air, since it is the same when
a pane of glass is interposed between the magnet and the copper. When
the magnet and the plate are at rest, not the smallest effect,
attractive, repulsive, or of any kind, can be perceived between them. In
describing this phenomenon, M. Arago states that it takes place not only
with metals, but with all substances, solids, liquids, and even gases,
although the intensity depends upon the kind of substance in motion.
Experiments made by Dr. Faraday explain this singular action. He found
that, if a piece of metal or a metallic wire forming a circuit of any
form be moved from right to left across the lines of force proceeding
from the pole of a bar magnet, these lines of force induce a current of
electricity flowing in one direction; and when the motion of the metal
or wire is reversed, the direction of the current is reversed also: the
rotation of the magnet about its axis has no effect on these results,
and no current is induced when the metal or wire is at rest. A plate of
copper, twelve inches in diameter and one fifth of an inch thick, was
placed between the poles of a powerful horseshoe magnet, consequently
crossing the magnetic lines of force at right angles, and connected at
certain points with a galvanometer by copper wires. When the plate was
at rest no effect was produced; but as soon as the plate was made to
revolve rapidly the galvanometer needle was deflected sometimes as much
as 90°, and by a uniform rotation the deflection was constantly
maintained at 45°. When the motion of the copper plate was reversed, the
needle was deflected in the contrary direction, and thus a permanent
current of electricity was evolved by an ordinary magnet. The intensity
of the electricity collected by the wires, and conveyed by them to the
galvanometer, varied with the position of the plate relatively to the
poles of the magnet.

The motion of the electricity in the copper plate may be conceived by
considering that, merely by moving a single wire, like the spoke of a
wheel, before a magnetic pole, a current of electricity tends to flow
through it from one end to the other. Hence, if a wheel be constructed
of a great many such spokes, and revolved near the pole of a magnet in
the manner of the copper disc, each radius or spoke will tend to have a
current produced in it as it passes the pole. Now, as the circular plate
is nothing more than an infinite number of radii or spokes in contact,
the currents will flow in the direction of the radii if a channel be
open for their return; and, in a continuous plate, that channel is
afforded by the lateral portions on each side of the particular radius
close to the magnetic pole. This hypothesis is confirmed by observation;
for the currents of positive electricity set from the centre to the
circumference, and the negative from the circumference to the centre,
and _vice versâ_, according to the position of the magnetic poles and
the direction of rotation; so that a collecting wire at the centre of
the copper plate conveys positive electricity to the galvanometer in one
case, and negative in another; that collected by a conducting wire in
contact with the circumference of the plate is always the opposite of
the electricity conveyed from the centre. It is evident that, when the
plate and magnet are both at rest, no effect takes place, since the
electric currents which cause the deflection of the galvanometer are
only induced by motion across the magnetic lines of force. When the
plate is placed edgewise so as to be parallel to these lines of force,
no revolution of it with the most powerful magnet produces the slightest
signs of a current at the galvanometer. The same phenomena may be
produced by electro-magnets. The effects are similar when the magnet
rotates and the plate remains at rest. When the magnet revolves
uniformly about its own axis, electricity of the same kind is collected
at its poles, and the opposite electricity at its equator.

The phenomena which take place in M. Arago’s experiments may be
explained on this principle. When both the copper plate and the magnet
are revolving, the action of the induced electric current tends
continually to diminish their relative motion, and to bring the moving
bodies into a state of relative rest; so that, if one be made to revolve
by an extraneous force, the other will tend to revolve about it in the
same direction, and with the same velocity.

When a plate of iron, or of any substance capable of being made either a
temporary or permanent magnet, revolves between the poles of a magnet,
it is found that dissimilar poles on opposite sides of the plate
neutralize each other’s effects, so that no electricity is evolved;
while similar poles on each side of the revolving plate increase the
quantity of electricity, and a single pole end-on is sufficient. But
when copper, and substances not sensible to ordinary magnetic
impressions, revolve, similar poles on opposite sides of the plate
neutralize each other; dissimilar poles on each side exalt the action;
and a single pole at the edge of the revolving plate, or end-on, does
nothing. This forms a test for distinguishing the ordinary magnetic
force from that produced by rotation. If unlike poles, that is, a north
and south pole, produce more effect than one pole, the force will be due
to electric currents; if similar poles produce more effect than one,
then the power is not electric. These investigations show that there are
really very few bodies magnetic in the manner of iron. Dr. Faraday
therefore arranges substances in three classes, with regard to their
relation to magnets:—those affected by the magnet when at rest, like
iron, steel, and nickel, which possess ordinary magnetic properties;
those affected when in motion, in which electric currents are evolved by
the inductive force of the magnet, such as copper; and, lastly, those
which are perfectly indifferent to the magnet, whether at rest or in
motion.

It has already been observed that three bodies are requisite to form a
galvanic circuit, one of which must be fluid. But, in 1822, Professor
Seebeck, of Berlin, discovered that electric currents may be produced by
the partial application of heat to a circuit formed of two solid
conductors. For example, when a semicircle of bismuth, joined to a
semicircle of antimony, so as to form a ring, is heated at one of the
junctions by a lamp, a current of electricity flows through the circuit
from the antimony to the bismuth; and such thermo-electric currents
produce all the electro-magnetic effects. A compass needle, placed
either within or without the circuit, and at a small distance from it,
is deflected from its natural position, in a direction corresponding to
the way in which the electricity is flowing. If such a ring be suspended
so as to move easily in any direction, it will obey the action of a
magnet brought near it, and may even be made to revolve. According to
the researches of M. Seebeck, the same substance, unequally heated,
exhibits electrical currents; and M. Nobili observed, that in all
metals, except zinc, iron, and antimony, the electricity flows from the
hot part towards that which is cold. That philosopher attributes
terrestrial magnetism to a difference in the action of heat on the
various substances of which the crust of the earth is composed; and, in
confirmation of his views, he has produced electrical currents by the
contact of two pieces of moist clay, of which one was hotter than the
other.

M. Becquerel constructed a thermo-electric battery of one kind of metal,
by which he has determined the relation between the heat employed and
the intensity of the resulting electricity. He found that, in most
metals, the intensity of the current increases with the heat to a
certain limit, but that this law extends much farther in metals that are
difficult to fuse, and which do not rust. The experiments of Professor
Cumming show that the mutual action of a magnet and a thermo-electric
current is subject to the same laws as those of magnets and galvanic
currents; consequently all the phenomena of repulsion, attraction, and
rotation may be exhibited by a thermo-electric current. M. Botto, of
Turin, has decomposed water and some solutions by thermo-electricity;
and the Cav. Antinori of Florence succeeded in obtaining a brilliant
spark with the aid of an electro-dynamic coil.

The principle of thermo-electricity has been employed by MM. Nobili and
Melloni for measuring extremely minute quantities of heat in their
experiments on the instantaneous transmission of radiant heat. The
thermo-multiplier, which they constructed for that purpose, consists of
a series of alternate bars, or rather fine wires of bismuth and
antimony, placed side by side, and the extremities alternately soldered
together. When heat is applied to one end of this apparatus, the other
remaining at its natural temperature, currents of electricity flow
through each pair of bars, which are conveyed by wires to a delicate
galvanometer, the needle of which points out the intensity of the
electricity conveyed, and consequently that of the heat employed. This
instrument is so delicate that the comparative warmth of different
insects has been ascertained by means of it.

The conservation of force is strictly maintained throughout the whole
science and different forms of electricity. In static electricity the
positive and negative forces exactly balance one another; they are
always simultaneous, and related often by curved lines of force; there
is no defect or surplus, and the existence of one kind without the other
is utterly impossible—it is absolutely a dual force. The very same may
be said of electric currents, whether produced by the Voltaic battery or
in any other way—the current in one part of the circuit is absolutely
the same in amount and dual character as the other; and in the insulated
Voltaic battery, where the sustaining power is internal, not the
slightest development of the forces of either of these can occur till
the circuit is completed or induction allowed at the extremities; for if
when there is no circuit the induction be prevented, not merely no
current, but no quantity of electricity at the poles ready to produce a
current, can be evolved in the slightest degree.[17]




                             SECTION XXXIV.

Magnetism a Dual Power—Antithetic Character of Paramagnetism and
  Diamagnetism—The Earth Paramagnetic—Properties of Paramagnetic
  Bodies—Polarity—Induction—Lines of Magnetic Force—Currents of
  Electricity induced by them—Proved to be Closed Curves—Analogy and
  Identity of Electricity and Magnetism—Terrestrial Magnetism—Mean
  Values of the Three Magnetic Elements—Their Variations in Double
  Progression proved to consist of Two Superposed Variations—Discovery
  of the Periodicity of the Magnetic Storms—The Decennial Period of the
  Magnetic Elements the same with that of the Solar Spots—Magnetism of
  the Atmosphere—Diamagnetism—Action of Electro-Magnetism on
  Paramagnetic, Diamagnetic Bodies, and on Copper, very different—Proof
  of Diamagnetic Polarity and Induction—Magnecrystallic Action—Effects
  of Compression, Heat, and Cleavage on Magnetic Bodies—Mutual
  Dependence of Light, Heat, Electricity, &c. &c.—The Conservation of
  Force and the Permanency of Matter Primary Laws of Nature—Definition
  of Gravity not according to that Law—Gravity only the Residual Force
  of a Universal Power—Magnetism of the Ethereal Medium.


MAGNETISM may be regarded as a new science in consequence of the
profound researches and admirable discoveries of Dr. Faraday. Since the
magnetism of matter is only known by the action of a magnet or of
electricity upon it, by using an extremely energetic magnet or
electro-magnet he has proved that all known substances, whether solid,
liquid, or aëriform, are more or less magnetic, but that the magnetism
is very different in different substances. For example, if a bar of iron
be freely suspended between the poles of a very powerful magnet or
electro-magnet, it will be attracted by both poles, and will set or rest
in the direction of a straight line joining them; but if a similar bar
of bismuth be freely suspended in the same manner, it will rest in a
direction at right angles to that which the iron bar assumed. Thus the
direction in which the iron sets is axial or in the line of force, while
that which the bismuth assumes is equatorial or perpendicular to the
line of force. Substances that are magnetic after the manner of iron are
said to be paramagnetic, those that are magnetic after the manner of
bismuth are diamagnetic. As far as we know, all matter comes under one
or other of these laws. Many bodies are paramagnetic besides iron, as
the loadstone, which consists of the peroxide and protoxide of iron
mixed with small portions of silica and alumina; also some of the gems
and metals, as cobalt, nickel, &c. A substance is often paramagnetic if
it contains only the 130,000th part of its weight of iron; but by far
the greater number are diamagnetic, as all animal and vegetable matter,
acids, oils, sugar, starch, bread, &c., and all the gases except oxygen,
which is highly paramagnetic; and its force increases with its density:
but notwithstanding the predominance of diamagnetic matter at the
surface, the terrestrial globe is paramagnetic—in fact it is a powerful
magnet.

Besides the substances which are paramagnetic naturally, that property
may be imparted by a variety of methods, as by friction with magnets or
even juxtaposition with them; and a bar of hard steel held at the angle
of the dip will become a magnet on receiving a few strokes with a hammer
on its upper end.

Polarity is one of the most distinguishing characters of magnetism: it
is the property which a magnet possesses when freely suspended of
resting spontaneously in the magnetic meridian, or nearly north and
south, and always returning to that position when disturbed in
consequence of the mean magnetic attraction of the earth; yet the magnet
has no tendency to move to the north or south even when floating on
water, because the same pole that attracts one end repels the other.
Both poles of a magnet attract iron, which in return attracts either
pole of the magnet with an equal and contrary force. The action of a
magnet on unmagnetised iron is confined to attraction, whereas the
reciprocal agency of magnets is characterised by a repulsive as well as
by an attractive force; for a north pole repels a north pole, and a
south pole repels a south pole; but a north and south pole mutually
attract one another—which proves that paramagnetism is a dual power in
which the conservation of force is perfectly maintained, for the force
of attraction is exactly equal to the force of repulsion. One kind of
polarity cannot exist without the other: they are absolutely
simultaneous, dependent, and of equal intensity.

Induction is the power which a magnet possesses of exciting temporary or
permanent paramagnetism in such bodies in its vicinity as are capable of
receiving it. By this property the mere approach of a magnet renders
iron and steel paramagnetic, the more powerfully the less the distance,
but the induced force is always exactly equal to the force which
produces it. When the north end of a magnet is brought near to, and in
the line with, an unmagnetised iron bar, the bar acquires all the
properties of a perfect magnet; the end next the north pole of the
magnet becomes a south pole, while the remote end becomes a north pole.
Exactly the reverse takes place when the south end is presented to the
bar, so that each pole of a magnet induces the opposite polarity in the
adjacent end of the bar, and the same polarity in the remote extremity;
consequently the nearest extremity of the bar is attracted, and the
farther repelled; but as the action is greater on the adjacent than on
the distant part, the resulting force is that of attraction. By
induction the iron bar not only acquires polarity, but the power of
inducing paramagnetism in a third body; and although all these
properties vanish from the iron as soon as the magnet is removed, a
lasting increase of intensity is generally imparted to the magnet itself
by the reaction of the temporary paramagnetism of the iron. Iron
acquires the inductive force more rapidly than steel, yet it loses it as
quickly on the removal of the magnet, whereas the steel is impressed
with a lasting polarity.

A certain time is requisite for induction, and it may be accelerated by
anything that excites a vibratory motion in the particles of the steel;
such as the smart stroke of a hammer, or heat succeeded by sudden cold.
A steel bar may be converted into a magnet by the transmission of an
electric discharge through it; and as its efficacy is the same in
whatever direction the electricity passes, the effect arises from its
mechanical operation exciting a vibration among the particles of the
steel. It has been observed that the particles of iron easily resume
their neutral state after induction, while those of steel resist the
restoration of equilibrium, or a return to the neutral state: it is
therefore evident that any cause which removes or diminishes the
resistance of the particles will tend to destroy the paramagnetism of
the steel; consequently the same mechanical means which develop the
power will also destroy it. On that account a steel bar may lose its
paramagnetism by any mechanical concussion, such as by falling on a hard
substance, a blow with a hammer, and heating to redness, which makes the
steel soft. The circumstances which determine whether it shall gain or
lose are its position with respect to the magnetic equator, and the
higher or lower intensity of its previous magnetic state.

A comparison of the number of vibrations accomplished by the same
magnetised needle during the same time at different distances from a
magnet gives the law of paramagnetic intensity, which follows the
inverse ratio of the square of the distance—a law that is not affected
by the intervention of any substance whatever between the magnet and the
needle, provided the substance be not itself susceptible of magnetism.
Induction and the reciprocal action of magnets are therefore subject to
the laws of mechanics; but the composition and resolution of the forces
are complicated in consequence of four forces being constantly in
activity, two in each magnet. Mr. Were Fox discovered that the law of
the paramagnetic force changes from the inverse square of the distance
to the simple inverse ratio when the distance between two magnets is as
small as from the fourth to the eighth of an inch, or even as much as
half an inch when the magnets are large; and in the case of repulsion,
that the change takes place at a still greater distance, especially when
the two magnets differ materially in intensity.

Without assuming any hypothesis of what magnetism is, or how that force
is originated or sustained, Dr. Faraday regards a magnet as a source of
power surrounded by curved lines of force which are not only
representants of the magnetic power in quality and direction, but also
in quantity—an hypothesis which accords perfectly with experiment, and
with the action both of electricity and magnetism. The nature and form
of these lines may be seen by placing a bar magnet upon a table,
spreading a sheet of stiff paper over it so as to be perfectly level and
free from creases, and then sifting very clean iron filings through a
fine sieve equably over it. The filings will instantly assume the form
of the curved lines represented by fig. 1, plate 7, in consequence of
the action of the magnet. These lines are the true representatives of
the magnetic forces, and being related to a polar power, they have
opposite qualities in opposite directions. When a magnet is broken
across the middle, each part is at once converted into a perfect magnet;
the part that originally had a south pole acquires a north pole at the
fractured end; the part that had originally a north pole gets a south
pole; and as far as mechanical division can be carried, it is found that
each fragment is a perfect magnet. Fig. 2, plate 7, shows the lines of
force in a fractured magnet when the ends are not yet separated; fig. 3
shows them when they are.

Currents of electricity are produced in conducting bodies moved across
these lines of magnetic force. If a copper wire at a little distance
above the north pole of a bar magnet be moved from left to right, at any
angle across the lines of magnetic force, they will induce a current of
electricity in the wire flowing from right to left; if the wire be moved
with the same velocity in the contrary direction, the induced current
will be of equal intensity, but it will flow from left to right. Similar
results are obtained from the south pole, and the phenomena are the same
when the magnet is moved and the wire is at rest; in both cases the
intensity is greater the swifter the motion. It appears that the
quantity of electricity induced is directly as the amount of the
magnetic curves intersected, and when a wire is moving uniformly in a
field of equal magnetic force, the current of electricity generated is
proportional to the time, and also to the velocity of motion; for when a
metallic disc is made to revolve through the lines of force, the current
induced is strongest near the edge where the velocity is greatest; and
in different substances moving across the lines of force the intensity
of the induced current is directly as the conducting power of the
substance. Thus bodies moved near a magnet have an electrical current
developed in them, and conversely bodies affected by an electric current
are definitely moved by a magnet near them.

By the preceding experiments it appears that magnetic polarity is
manifested in two ways; in the magnetised needle, by attraction and
repulsion, and in a wire moving across lines of magnetic force it is
shown by the opposite directions in which the induced current flows
according as the body is moved from the right to the left, or left to
right. Hence polarity consists in the opposite and antithetical actions
manifested at the opposite ends or opposite sides of a limited or
unlimited line of force. Antithesis is the true and most general
character of magnetism, whatever may be its mode of action.

It was by the induction of electric currents in copper wires moving
across the lines of magnetic force that Dr. Faraday proved that the
lines of force issuing from a magnet are closed curves which return
again and pass through the interior of the magnet. He placed two bar
magnets of the same length, size, and intensity with their similar poles
together, so that they might act as one magnet. A copper wire was then
passed between their axes, which after extending through half their
length was bent up equatorially and turned back along the outside, so
that the whole wire formed a loop, the two ends being connected with a
galvanometer. When the whole wire was made to revolve, no effect was
produced, although it crossed the lines of magnetic force; but when it
was cut in two, so as to separate the external from the internal part,
electrical currents of equal intensity, but in contrary directions, were
induced in each portion of the wire as they were made separately to
cross the lines of force, for the apparatus was so constructed that that
could be done. The exterior wire crossed the lines of force which issued
from the magnets at right angles to their axes, while the equatorial
part of the interior wire traversed the returning lines of force. It is
evident that these forces neutralized each other when the whole wire
revolved: consequently the internal and external lines of force must
have been of equal intensity and opposite in direction, so as to balance
one another. By this and a very great number of other experiments Dr.
Faraday has proved that the magnetic lines of force are continuous
closed curves alike in shape, size, and power. They extend indefinitely
beyond the magnet, and undergo no change by distance.

Thus the magnetic force pervades the interior of the mass; if
electricity does the same, a compensation must either take place, or it
also must move in lines of force, sensible only at the surface.
Electricity has a perpetual tendency to escape, and does escape, when
not prevented by the coercive power of the air, and other non-conducting
substances. Such a tendency does not exist in magnetism, which never
leaves the substance containing it under any circumstances whatever.
There must be some coercive force, analogous to friction, which arrests
the magnetic forces, so as first to oppose their separation, and then to
prevent their reunion. In soft iron the coercive force is either wanting
or extremely feeble, since iron is easily rendered paramagnetic by
induction, and as easily loses that quality; whereas in steel the
coercive force is extremely energetic, because it prevents the steel
from acquiring the paramagnetic properties rapidly, and entirely hinders
it from losing them when acquired. The feebleness of the coercive force
in iron, and its energy in steel, with regard to the paramagnetic force,
is perfectly analogous to the facility of transmission afforded to
electricity by non-electrics, and the resistance it experiences in
electrics. At every step the analogy between electricity and magnetism
becomes more striking. The agency of attraction and repulsion is common
to both; the positive and negative electricities are similar to the
northern and southern polarities, and are governed by the same
laws—namely, that between like powers there is repulsion, and between
unlike powers there is attraction. Each of these four forces is capable
of acting most energetically when alone; but as the electric equilibrium
is restored by the union of the two electric states, and magnetic
neutrality by the combination of the two polarities, they respectively
neutralise each other when joined. All these forces vary inversely as
the square of the distance, and consequently come under the same
mechanical laws.

A like analogy extends to magnetic and electric induction. Iron and
steel are in a state of equilibrium when neutral; but this equilibrium
is immediately disturbed on the approach of the pole of a magnet, which
by induction transfers one kind of polarity to one end of an iron or
steel bar, and the opposite kind to the other—effects exactly similar to
electrical induction. There is even a correspondence between the
fracture of a magnet and that of an electric conductor; for if an oblong
conductor be electrified by induction, its two extremities will have
opposite electricities; and if in that state it be divided across the
middle, the two portions, when removed to a distance from one another,
will each retain the electricity that has been induced upon it. The
analogy, however, does not extend to transference. A body may transfer a
redundant quantity of positive electricity to another, or deprive
another of its electricity—the one gaining at the expense of the other;
but a body cannot possess only one kind of polarity. With that
exception, there is such perfect correspondence between the theories of
magnetic attractions and repulsions, and electric forces in conducting
bodies, that they not only are the same in principle, but are determined
by the same formulæ. Experiment concurs with theory in proving the
identity of these two influences. Hence, if the electrical phenomena be
due to a modification of the ethereal medium, the magnetic phenomena
must be owing to an analogous cause.

Curved lines of magnetic force issue from every point of the earth’s
surface where there is sensible dip, and bending round enter the earth
again at the magnetic equator. They induce electric currents in
conducting-wires, moving across them exactly the same as in artificial
magnets; and when a hollow helix, or coil of copper wire, whose
extremities are connected with a galvanometer, is placed in the magnetic
dip, and suddenly moved across the lines of force, the needle of the
galvanometer will vibrate through an arc of 80° or 90°, in consequence
of the electric current induced by these lines of magnetic force in the
wire, and the action is greater when a core of soft iron is placed in
the helix, which becomes a temporary magnet by induction. Again, if a
copper plate be connected with a galvanometer by two copper wires, one
from the centre, and another from the circumference, in order to collect
and convey the electricity, it is found that, when the plate is made to
revolve in a plane passing through the line of the dip, the galvanometer
is not affected. But as soon as the plate is inclined to that plane,
electricity begins to be developed by its motion across the lines of
magnetic force; it becomes more powerful as the inclination increases,
and arrives at a maximum when the plate revolves at right angles to the
line of dip. When the revolution is in the same direction with that of
the hands of a watch, the current of electricity flows from its centre
to the circumference; and when the rotation is in a contrary direction,
the current sets the opposite way. Thus a copper plate, revolving at
right angles to the line of the dip, becomes a new electrical machine,
differing from the common plate-glass machine by the copper being the
most perfect conductor, whereas glass is the most perfect non-conductor;
besides insulation, which is essential to the glass machine, is fatal to
the copper one. The quantity of electricity evolved by the metal does
not appear to be inferior to that devolved by the glass, though very
different in intensity. Even a ship crossing the lines of force must
have electric currents running through her. Dr. Faraday observes that
such is the facility with which electricity is generated by the magnetic
lines of force, that scarcely any piece of metal can be moved without a
development of it; consequently, among the arrangements of steam-engines
and metallic machinery, curious electro-magnetic combinations probably
exist which have never yet been noticed. Thus magnetic lines of force
certainly issue from the surface of the globe.

No doubt the earth is a magnet on a vast scale, but it differs from all
others in having four poles of maximum magnetic force of different
intensities, the two in the northern hemisphere having a secular motion
in a contrary direction from the two in the southern. They are not even
symmetrically placed; hence the magnetic intensity varies so much in the
different points on the earth’s surface, that the dynamic equator, or
line passing through all the points of least intensity, is a very
irregular curve surrounding the globe, but by no means coinciding with
the terrestrial equator. In consequence of the mean action of these four
forces, the north end of a magnetised needle, arranged so as to revolve
in a vertical plane, dips or inclines beneath the horizon in the
northern hemisphere, and the south end in the southern. The two
hemispheres are separated by a line encircling the earth, called the
magnetic equator, or line of no dip, in which the dipping or inclination
needle is horizontal. On each side of this line the inclination
increases till at last the needle becomes perpendicular to the horizon
in two points, or rather small spaces, in each hemisphere, known as the
magnetic poles, which are quite different from the poles of the earth’s
rotation. The mean action of the four poles of magnetic intensity causes
the mariner’s compass, or a magnetic needle suspended so as to revolve
in a horizontal plane, to remain at rest when pointing to the two
magnetic poles. It is then in the magnetic meridian of the place of
observation, which is thus determined by the mean action of all the four
magnetic forces.

These mean values of the three magnetic elements, namely, the
declination, inclination or dip, and magnetic intensity, are well known
to be subject to secular, annual, and diurnal variations. The secular
only become sensible after some years, but the annual and diurnal
variations have a double progression—that is to say, two maximum and two
minimum values in their respective periods of a year and twenty-four
hours; for example, the declination needle makes two deviations to the
west and two to the east in the course of twenty-four hours, and that
with great regularity. Now General Sabine discovered that the double
progression arises from two combined or superposed variations having
different hours of maxima and minima, and that they are due to two
distinctly different causes—the one being the difference in the sun’s
position relatively to the place of observation at the different seasons
of the year, and hours of the day and night; the other being a mean
annual and diurnal variation proved by General Sabine to exist in those
great magnetic storms or casual disturbances which affect the magnetic
elements simultaneously over enormously extensive tracts of the globe.

Moreover the General discovered that, besides these annual and diurnal
variations, the magnetic storms have a variation which accomplishes its
vicissitudes in ten or more nearly eleven years, the increase from year
to year being gradual, till its maximum becomes twice as great as its
minimum value. In consequence of this inequality in the storms or casual
disturbances, each of the magnetic elements has a variation of similar
period and similar maxima and minima. Now the number and magnitude of
the spots on the sun had been observed by M. Schwabe, of Dessau, to
increase to a maximum, and decrease again to a minimum, regularly in the
very same period of between ten and eleven years; and General Sabine
found that this variation in the solar spots, and that in the magnetic
elements, not only have the same periods of maxima and minima, but that
they correspond in all their minutest vicissitudes. Thus a very
remarkable and unexpected connexion exists between terrestrial and solar
magnetism. The dual and antagonist principle is perfectly maintained in
the earth’s magnetism, all the phenomena and their variations being in
opposite directions in the two hemispheres. (N. 226.)

No doubt the magnetic lines of force in the earth are closed curves, as
in artificial magnets; but in their circuitous courses they may extend
to any distance in space, or rather in the ethereal medium, even to
thousands or tens of thousands of miles; for the ethereal medium is
permeable to lines of magnetic force, or rather transmits them,
otherwise the solar spots could not affect the variations of terrestrial
magnetism; besides, they pass through the Torricellian vacuum, which is
nearly a void with respect to air, but not to the ethereal medium.

The atmosphere which surrounds the earth to the height of about fifty
miles with sensible density, consists of three and a half parts by
weight of nitrogen gas and one part of oxygen, uniformly mixed. The
nitrogen is neutral whether dense or rare, hot or cold, while the oxygen
is highly paramagnetic; but it loses a great part of its force when
rarefied by heat; consequently the magnetic force of the atmosphere must
increase from the equator to the poles of maximum cold; it must vary
summer and winter, night and day. Its effect upon terrestrial magnetism
is unknown; but it can hardly be without some influence. M. E. Becquerel
observes—“If we reflect that the earth is encompassed by a mass of air
equivalent in weight to a layer of mercury of 30 inches, we may inquire
whether such a mass of magnetic gas, continually agitated, and submitted
to the regular and irregular variations of pressure and temperature,
does not intervene in some of the phenomena dependent upon terrestrial
magnetism. If we calculate, in fact, what is the magnetic force of this
fluid mass, we find that it is equivalent to an immense plate of iron,
of a thickness little more than 1/250 of an inch, which covers the whole
surface of the globe.” Both the conducting power of the air and its
density are increased by cold; and as the sum of the magnetic forces
which issue from the earth on one side of the line of no dip is equal to
their sum on the other side, the intensity and concentration in our
winter are coincident with a diffusion and feebleness in the opposite
hemisphere, so that the line of no dip will move annually from north to
south and back again. The same holds with regard to day and night. Thus
the law of the conservation of force is rigorously maintained; and it is
equally so in the effect of the atmosphere on the magnetic lines of
force, which refracts them as they pass through it, in one direction in
summer, and in the opposite direction in winter—in one direction in the
enlightened hemisphere, in the other in that which is dark. The whole of
the magnetic lines about the earth are held by their mutual tension in
one connected, sensitive system, which feels in every part, even to the
antipodes, a change in any particular place.

It may be mentioned as a well-known fact, that apparent anomalies have
been found in the diurnal variation of the declination in the high
magnetic latitudes of the northern hemisphere when compared with their
great regularity in other parts of the same hemisphere, and that the
magnetic storms are of much greater magnitude there than in lower
latitudes. Moreover, although Captain Maguire’s observations at Cape
Barrow, in the North Polar Ocean, show that the annual and diurnal
variations of the casual disturbances or magnetic storms, as well as
those of the decennial period, are maintained, yet it appears that at
certain hours of the day the disturbance in the declination may be
easterly at Point Barrow, and westerly at the Magnetic Observatory at
Toronto, in Upper Canada, and _vice versâ_: in fact, the magnetic storms
are simultaneous at these two stations, but in opposite directions—a
circumstance not yet accounted for, and may possibly be due to the
increased magnetism of the air in these cold regions. The heat of the
sun has no effect upon terrestrial magnetism unless possibly by its
indirect action on the oxygen of the atmosphere; but hitherto it has
been imperceptible. It is hardly possible that the aurora can be
independent of the magnetic character of the air, since it occurs in the
high latitudes, where the atmospheric magnetism is most powerful.
Captain Maguire remarked that it frequently appeared at Point Barrow
when the magnetic storms were at a maximum.

We are totally ignorant of the cause of terrestrial magnetism, though
the powerful influence of the solar spots renders it highly probable
that it will ultimately be found to originate in the sun himself. Mr.
Barlow’s theory of electric currents revolving round the globe is borne
out by Mr. Fox’s observations in the Cornish mines, which show that
electro-magnetism is extremely active in metallic veins; that not only
the nature of the metalliferous deposits must have been determined by
their relative electrical conditions, but that the direction of the
metallic veins must have been influenced by the direction of the
magnetic meridians, and in fact almost all the metallic deposits in the
world tend from east to west, or from north-east to south-west. However,
these currents of electricity may be regarded as magnetic lines of
force, and are more likely to be the effect than the cause of
terrestrial magnetism. They are found to have a powerful inductive
effect on the Atlantic telegraph, disturbing the needles and
galvanometers at each end of the line to a considerable degree, and on
the night of the 6th of September, 1858, a magnetic storm passed over
the cable, which violently agitated the reflecting galvanometer in
connection with the telegraphic wires.

We are equally ignorant of the cause of the secular magnetic variations,
but we have no reason to believe that the earth is alone magnetic; on
the contrary, the planets are probably magnets, and we know that the sun
and moon are magnetic; hence, as the magnetic, like the gravitating
force, is transmitted through the ethereal medium, the induction of the
sun, moon, and planets, in all their secular and periodic changes, may
cause perpetual variations in terrestrial magnetism, and it may not be
beyond the delicacy of modern observation to ascertain whether a planet,
when nearest to the earth, has any sensible magnetism.

Diamagnetism is also a dual power, but in complete antithesis to
paramagnetism under the same circumstances. Dr. Faraday first discovered
this property in heavy glass, or silico-borate of lead, a piece of which
was repelled by the pole of a powerful electro-magnet, and an elongated
prism of the same heavy glass, when freely suspended between the poles,
set equatorially. He then found that so great a number of substances
followed the same law, that it established the very remarkable fact of a
hitherto unknown force having acted upon the substances submitted to its
influence, a discovery which he subsequently confirmed by many
experiments, all of which proved the antithesis between the two modes of
magnetic action. He also discovered that magnetic bodies differ
exceedingly in their magnetic power: of paramagnetic bodies iron is the
most powerful; then follow nickel, cobalt, and a long gradation down to
osmium and a vacuum. The body that seems to have the lowest diamagnetic
power is arsenic, and the series ascends to heavy glass, antimony,
phosphorus, and bismuth; so iron and bismuth are the most powerful in
their respective classes, and both have a small conducting power for
electricity. It may be presumed that many remarkable instances of
diamagnetism are to be met with in nature; among others, Dr. Faraday has
suggested the idea that Saturn’s ring, from its position, may be
diamagnetic with regard to the planet.

With very powerful magnets or electro-magnets, which are absolutely
necessary for all these experiments, it is found that no _simple_
substance is neutral, but that such may be compounded by mixing in due
proportion a diamagnetic and paramagnetic liquid, as water and
protosulphate of iron.

Professor Tyndall proved diamagnetic polarity by placing two bismuth
bars within two vertical coils or spirals of insulated copper wire,
through which electric currents were transmitted from a galvanic
battery, and caused to act upon a steel magnet freely suspended without
the spirals. Now, when the excited magnetism is merely by induction, the
electric current, being momentary, only causes a shock or momentary
deviation in the magnet, which returns to its original position when the
current ceases. When, on the contrary, the magnetism is permanent, the
suspended magnet does not return to its original position when the
current ceases. In Professor Tyndall’s experiment the deviation was
permanent, and it was equally so when a bismuth bar was freely suspended
and the cores within the spirals were steel magnets. Had the effect been
from currents induced in the mass of the bar of bismuth, division of the
bar would have stopped them, but the result was the same with powdered
bismuth as with the solid mass. Moreover, since the strength of induced
currents depends upon the conducting power of the substance, and as the
conducting power of copper is forty times as great as that of bismuth,
had the polarity been induced and not real, the effect ought to have
been forty times greater when copper instead of bismuth cores were put
in the spirals, whereas it was scarcely sensible. Besides these proofs,
Dr. Tyndall made experiments with eleven different diamagnetic
substances, of which water was one, with similar results. He then
determined the polarity of twelve paramagnetic bodies by the same
method, whence it appeared that the same action which produced a north
pole in the paramagnetic bodies produced a south pole in those that were
diamagnetic, and _vice versâ_, whence he concludes that diamagnetic
polarity is one of the most firmly established truths of science. It
follows from this that, when a man is standing, his head is a north pole
and his feet a south, and the top of an iron railing on which he may be
leaning is a south pole and the lower end a north. Diamagnetic bodies
thus possess a polarity, the same in kind but opposite in direction to
that possessed by paramagnetic ones.[18] They are both dual powers, and
the two diamagnetic forces like the two paramagnetic being coexistent,
simultaneous, and mutually dependent, there can be no doubt that the
diamagnetic forces also are represented, or rather consist of curved and
closed lines of force passing through the interior of the substance. Dr.
Tyndall has proved that the attraction of iron, and the repulsion of
bismuth, are as the square of the electro-magnetic current producing
them, and that diamagnetic substances are capable of induction.

The molecular structure of substances freely suspended between the poles
of a magnet has a decided effect upon the position they assume.

It has already been mentioned that the optic axis is a symmetrical line
in a doubly refracting crystal in which there is no double refraction,
and that in some crystals there are two such symmetrical lines. Now,
Professor Plücker of Bonn discovered, when such crystals are submitted
to powerful magnetic influence, that the single optic axis in the one,
and the resultant or mean line between the double optic axes in the
other, set diametrically or at right angles to the line of magnetic
force; and so powerful did the Professor find the action of magnetism on
crystalline form, that the mineral cyanite, when suspended, arranges
itself so definitely with regard to terrestrial magnetism, that it might
be used as a compass needle.

Dr. Faraday afterwards observed that amorphous substances, cut in the
form of a sphere, have no tendency to set or be attracted or repelled in
one direction in preference to any other; but if the sphere be formed of
a crystallized substance, it is a general fact that, whether it be
paramagnetic or diamagnetic, it is more powerfully attracted or repelled
in one direction than in any other—a property named by Dr. Faraday
magnecrystallic action. For example, a sphere of calcareous spar, which
is a diamagnetic crystal, is most strongly repelled in the direction of
its principal optic axis, and least strongly in the direction of its
least axis. In a sphere of carbonate of iron, which has exactly the same
crystalline form and is highly paramagnetic, the line which in carbonate
of lime sets equatorially, in this case sets axially, and more strongly
in that direction than in any other. The law according to which the
attraction of the carbonate of iron increases from the least to its
greatest or principal optic axis, is precisely the same as that
according to which the repulsion of the calcareous spar increases from
the least to the principal optic axis. These relations are not altered
by the immersion of the spheres in liquids of either magnetism. Dr.
Faraday observed that a line at right angles to the planes of principal
cleavage in crystals takes the axial position, and on that account he
called it the magnecrystallic axis. Its position was proved by MM.
Tyndall and Knoblauch to depend upon the general fact, that the mass is
most strongly repelled in the direction of the planes of principal
cleavage, and that the elective position of crystals depends more upon
the direction of these planes with respect to the electric force, than
upon the optic axis. The planes of principal cleavage set themselves
equatorially in diamagnetic, and axially in paramagnetic substances: it
was thence inferred that the phenomena offered by crystals in the
magnetic field is a particular case of the general law, that the
superior action of magnets upon matter in a particular direction is due
to the particles of the body being closer together in that direction
than in any other: in short, the line of maximum density; the force
exerted being attractive or repulsive according as the particles are
paramagnetic or diamagnetic.

It appears, however, that the set of crystals with regard to the line of
magnetic force does not depend solely upon their density in particular
directions. Professor Matteucci, of Pisa, has proved that the
diamagnetic force is inversely as the conducting power of substances for
electricity, that the conducting power is a maximum in the planes of
principal cleavage, and that a needle of crystallized bismuth, in which
the planes of cleavage are parallel to its length, places itself
equatorially with more force when these planes are vertical, or at right
angles to the force, than when they are horizontal or parallel to it.
Experiments had hitherto been made only with diamagnetic or slightly
paramagnetic bodies, which induced M. le Roux to try the effect of
magnetism on pulverized iron compressed by the hydraulic press, which
reduced the grains of iron to lamellæ equivalent to planes of cleavage.
Cubes of this substance, suspended by a thread over a horseshoe magnet,
oscillated for a longer time when the lamellæ were perpendicular than
when they were horizontal; that is, the force was stronger when the
lamellæ were equatorial than when they were axial, exactly the same
result as in Professor Matteucci’s experiment with the needle of
bismuth. Thus the vertical position of the cleavages, which increases
the diamagnetism of the bismuth, increases also the paramagnetism of the
iron. M. le Roux observes that these results are independent of the
influence of the currents of electricity induced in the oscillating
body, for the fundamental character of the phenomena of Arago’s
discovery of rotation by induction is, that the oscillations diminish
rapidly in extent without any sensible diminution in their duration,
while in his experiments the time of the oscillations varied. He
concludes that the arrangement of the molecules must be intimately
connected with paramagnetism or diamagnetism itself, since the effect of
that arrangement is equally sensible in bismuth and iron, although the
diamagnetism of the former is 25,000 times weaker than the paramagnetism
of the latter.

The diamagnetism of conducting substances and metals, such as gold,
silver, and copper, is augmented by division. Compression has also a
great effect on magnetic action. For example, a bar of soft iron sets
with its longest dimensions from pole to pole of a magnet, but a bar of
compressed carbonate of iron-dust, whose shortest dimensions coincide
with the line of pressure, sets equatorially. A bar of bismuth whose
plane of principal cleavage is parallel to its length sets equatorially,
but a bar of compressed bismuth dust, whose shortest dimensions coincide
with the line of pressure, or a bar of bismuth whose principal planes of
cleavage are transverse to its length, sets with its length axially. The
antithesis is perfect whether the bars are under the influence of a
magnet or electro-magnet. For since the diamagnetic force is inversely
as the conducting power of a body for electricity, and that the latter
is a maximum in the direction of the planes of principal cleavage,
therefore when these planes are parallel to the axis of the bismuth bar
it sets equatorially; but as the conducting power is augmented when the
bismuth dust is compressed in the direction of the force, the
diamagnetic power is diminished, and the bar sets axially. Again, since
the paramagnetic force augments with the conducting power, the action of
the magnet on the iron is antithetic to that on the bismuth.

The action of an electro-magnet on copper is strongly contrasted with
that which it exerts on iron or bismuth. For when a copper bar suspended
by a thread revolves before its pole, it is brought to a dead halt as
soon as the electric current acts upon it, and maintains its position
with considerable tenacity, for it does not return when pushed out of
it, but keeps its new place with stiffness; however, as soon as the
electric current ceases, there is a strong revulsion, the bar revolving
the contrary way. Even when swinging with considerable force it may be
caught and retained in any position at pleasure, but there is no
revulsion when it is arrested either in the axial or equatorial
position; at any angle between these two, but especially midway, the
electricity will make it move towards the axis, but it is arrested
before it comes to it. The action depends much on the form and
dimensions of the bar and the magnetic pole, which ought to be flat. The
phenomena are due to the high electro-conducting power of the copper,
and are met with in some of the other pure metals, though in a far
inferior degree.

Great magnetic power is requisite for all these experiments. Dr. Faraday
employed a magnet that could sustain a weight of 450 lbs. at each pole,
and the poles were either pointed or flat surfaces at pleasure, as the
kind of experiment required.

Heat strongly affects the magnetic properties of bodies. Dr. Faraday
found that, when the temperature of nickel is increased, its magnetic
force diminishes; when that of iron is increased its magnetic force
remains the same, while that of cobalt increases; which seems to
indicate that there is a temperature at which the magnetic force is a
maximum, above and below which it diminishes. Nickel loses its magnetism
at the temperature of boiling oil, iron at a red heat, and cobalt near
the temperature at which copper melts. Calcareous spar retains its
magnetic character at a very high temperature; but the same substance
when it contains iron, and also oxide of iron, loses it entirely at a
dull red heat. A crystal of the ferrocarbonate of lime was absolutely
reversed by change of temperature, for at a low heat the optic axis
pointed axially, and at a high temperature equatorially. With the
exception of these substances, magnecrystals, whether paramagnetic or
diamagnetic, are generally all affected alike by heat. The difference
between the forces in any two different directions, as for instance the
greatest and least principal axes, diminishes as the temperature is
raised, increases as the temperature is lowered, and is constant for a
given temperature. No _unmixed_ or _pure_ substance has as yet passed by
heat from the paramagnetic to the diamagnetic state. No _simple_
magnecrystal has shown any inversion of this kind, nor have any of the
chief axes of power changed their characters or relations to one
another.

It appears that, as the molecules of crystals and compressed bodies
affect magnetism, so magnetism acts upon the molecules of matter, for
torsion diminishes the magnetic force, and the elasticity of iron and
steel is altered by magnetism. M. Matteucci has found that the
mechanical compression of glass alters the rotatory power of a polarized
ray of light transmitted through it, and that a change takes place in
the temper of glass under the influence of powerful magnetism.

Even from the limited view of the powers of nature which precedes, it is
evident that the progress of science based upon experiment tends to show
that the various forces of light, heat, motion, chemical affinity,
electricity, and magnetism will ultimately be traced to one common
origin; that they are so directly related, and mutually dependent, that
they are convertible, motion producing heat, and heat motion; chemical
affinity producing electricity, and electricity chemical action, &c.,
each mediately or immediately producing the other. These forces are
transmitted through substances; they act upon matter, causing changes in
the molecular structure of bodies either momentary or permanent, and
reciprocally the changes indicate the action of these forces. Matter and
force are only known to us as manifestations of Almighty power: we are
assured that we can neither create nor destroy them—that their amount is
the same now as in the beginning. In chemical attraction the powers with
which a molecule of matter is endowed, and which give rise to various
qualities, never change; even when passing through a thousand
combinations, the molecule and its power are ever the same.

Machinery does not create force; it only enables us to turn the forces
of nature to the best advantage; it is by the force of wind or falling
water that our corn is ground, and the steam engine owes its power to
the force of heat and chemical action. As force cannot be created,
neither can it be annihilated. It may be dispersed in various
directions, and subdivided so as to become evanescent to our
perceptions; it may be balanced so as to be in abeyance, or become
potential as in static electricity; but the instant the impediment is
removed the force is manifested by motion; it may also be turned into
heat by friction, but it is never lost. Every motion we make, every
breath, every word we utter, is a force that produces pulsations which
are communicated to continually increasing particles of air, and
conveyed through countless channels so as to become indeed imperceptible
to our senses, yet they are demonstrated to exist as witnesses of the
words we have spoken or the actions we have performed, by analysis, that
all-powerful instrument of human reason.[19]

A body acquires heat in the exact proportion that the adjacent
substances become cold, and when heat is absorbed by a body it becomes
an expansive force at the expense of those around that contract, but it
is not lost. In chemical action at a distance the principle of the
conservation of force is maintained, for a chemical action may be
produced miles away from an electro-magnet, perfectly equivalent to the
dominant chemical action in the battery. The two electricities are
developed in equal proportions, which may be combined so as to produce
many changes in their respective relations, yet the sum of the force of
one kind can never be made in the smallest degree either to exceed or to
come short of the sum of the other. Experimental research proves that
the conservation of force is an unalterable law of nature—“a principle
in physics as large and sure as that of the indestructibility of matter
or the invariability of gravity. No hypothesis should be admitted, nor
any assertion of a fact credited, that denies this principle. No view
should be inconsistent or incompatible with it. Many of our hypotheses
in the present state of science may not comprehend it, and may be unable
to suggest its consequences, but none should oppose or contradict it.”

Having thus expressed his conviction of the truth of this great
principle, Dr. Faraday considers the case of gravity, and concludes that
“the definition of gravity as an attractive force between the particles
of matter varying inversely as the square of the distance, while it
stands as a full definition of the power, is inconsistent with the
principle of the conservation of force.” For while in this definition
the principle is maintained of the constancy of the force _at the same
distance_, it implies a creation of force to an enormous amount when the
distance is diminished, and an equal amount annihilated when the
distance is increased,—“an effect,” he says, “which is equal in its
infinity and its consequences with creation, and only within the power
of Him who creates.” He continues, “It will not be imagined for a moment
that I am opposed to what may be called the _law of gravitating action_,
that is, the law by which all the known effects of gravity are governed;
what I am considering is the _definition_ of the _force_ of gravitation.
That the result of _one_ exercise of a power may be inversely as the
square of the distance, I believe and admit; and I know that it is so in
the case of gravity, and has been verified to an extent that could
hardly have been within the conception of Newton himself when he gave
utterance to the law; but that the _totality_ of a force can be employed
according to that law I do not believe either in relation to
gravitation, or electricity, or magnetism, or any other supposed form of
power. That there should be a power of gravitation existing by itself,
having no relation to the other natural powers, and no respect to the
law of the conservation of force, is as little likely as that there
should be a principle of levity as well as gravity. Gravity may be only
the residual part of the other forces of nature, as Mossotti has tried
to show; but that it should fall out from the law of all other forces,
and should be outside the reach either of farther experiment or
philosophical conclusions, is not probable. So we must strive to learn
more of this outstanding power, and endeavour to avoid any definition of
it which is incompatible with the principles of force generally, for all
the phenomena of nature lead us to believe that the great and governing
law is one. Thus gravitation can only be considered as part of a more
general force whose law has yet to be discovered.”

The definition of the gravitating force immediately suggests the
question of how it is transmitted; the full force of that question was
felt by Newton himself when, in his third letter to Bentley, he wrote,
“That gravity should be innate, inherent, and essential to matter, so
that one body may act upon another at a distance, through a _vacuum_,
without the mediation of anything else by and through which their action
and force may be conveyed from one to another, is to me so great an
absurdity that I believe no man who has in philosophic matters a
competent faculty of thinking can ever fall into it. Gravity must be
caused by an agent, acting constantly according to certain laws; but
whether this agent be material or immaterial I have left to the
consideration of my readers.”

Since Newton’s time the continual decrease in the periodic times of the
comets belonging to our system, and the undulatory theory of light and
heat, have proved the existence of an extremely rare elastic medium
filling space even to the most distant regions of which we are
cognizant. But, rare as it may be, it has inertia enough to resist the
motion of comets, and therefore must be material, whether considered to
be ether or, according to Mr. Grove, the highly attenuated atmospheres
of the celestial bodies. Professor William Thomson of Glasgow has
computed that in the space traversed by the earth in its annual
revolution, a cube whose side is 1000 miles would contain not less than
a pound weight of the ethereal medium, and that the earth, in moving
through it, would not displace the ·250th part of that pound of matter.
Yet that is enormously more dense than the continuation of the earth’s
atmosphere would be in interplanetary space, if rarefied according to
Bayle’s law. But whatever be the density or nature of the ether, there
is every reason to believe that it is the medium which transmits the
gravitating force from one celestial object to another, or possibly it
may possess a higher attribute with regard to gravity than its mere
transmission.

Dr. Faraday, who discovered the magnetism of the atmosphere, is led to
believe that the ethereal medium too is magnetic by the following
experiment. Three solutions of the protosulphate of iron, _l_, _m_, _n_,
the first of which contained 4 grains of the salt dissolved in a cubic
inch of water, the second 8 grains, and the third 16 grains—these were
respectively enclosed in three glass globules, all of which were
attracted by the pole of a magnet. A quantity of the mean solution _m_
was then put into a vessel, and the globule containing the strongest
solution _n_ was immersed in it, which was attracted as before, but the
globule _l_, containing the weakest solution, was repelled when plunged
into the same liquid. Here there was a diamagnetic phenomenon, although
the glass globules and the liquid in which they were immersed contained
iron. The effect was evidently differential, for when the liquid was
less attracted than the globule, the globule approached the pole, and
when the liquid was more attracted than the globule, the latter appeared
to recede from the pole. In fact, the effect is the same as that of
gravity on a body immersed in water; if it be more forcibly attracted
than the water, it sinks; if less forcibly attracted, it rises, the
effect being the same as if it were repelled by the earth. Hence the
question, are all magnetic phenomena the result of a differential action
of this kind, and is the ethereal medium less strongly attracted than
soft iron, and more strongly attracted than bismuth, thus permitting the
approach of the iron, but causing the bismuth to recede from the pole of
a magnet? If such a medium exist, that is, if the ethereal medium be
magnetic, then diamagnetism is the same with paramagnetism, and the
polarity of the magnetic force in iron and bismuth is one and the same.

The ethereal medium may be presumed to transmit the gravitating force;
it transmits the magnetism of the solar spots, its undulations
constitute light, heat, and all the influences bound up in the solar
beam; and the most perfect vacuum we can make is capable of transmitting
mechanical energy in enormous quantities, some of which differ but
little from that of air or oxygen at an ordinary barometric pressure;
and why not thus admit, says Mr. Thomson, the magnetic property, of
which we know so little that we have no right to pronounce a negative?

Mr. Waterstone is also of opinion that it would be taking too narrow a
view if we limited the function of the luminiferous ether to the
conveying of physical pulses only. The atmosphere also conveys physical
pulses, but that is the least important of its functions in the economy
of nature. There is nothing that should hinder us attributing to the
media concerned in the radiation of light and heat the higher functions
of electrical polarity and gravitation. The special dynamic arrangements
by which this is effected may ever elude our research; but as there is
no limit to the vis viva (N. 222) which such media may conserve in their
minutest parts, so there is no physical impossibility in that vis viva
being suddenly transferred to the molecules of ordinary matter in the
proportion and sequence required to carry out the order and system of
nature.

The fundamental principle of action in such media must be in accordance
with _elastic impact_, for upon that the dynamic theory of heat and
conservation of force rests as a foundation. The statical and dynamical
characteristics of gravitation and transfusion of force conform to it,
so that all the forces that hold the molecules of bodies together must
also be in subjection to it.[20]




                             SECTION XXXV.

Ethereal Medium—Comets—Do not disturb the Solar System—Their Orbits and
  Disturbances—M. Faye’s Comet probably the same with Lexel’s—Periods of
  other three known—Acceleration in the mean Motions of Encke’s and
  Biela’s Comets—The Shock of a Comet—Disturbing Action of the Earth and
  Planets on Encke’s and Biela’s Comets—Velocity of Comets—The Comet of
  1264—The great Comet of 1343—Physical Constitution—Shine by borrowed
  Light—Estimation of their Number.


IN considering the constitution of the earth, and the fluids which
surround it, various subjects have presented themselves to our notice,
of which some, for aught we know, are confined to the planet we inhabit;
some are common to it and to the other bodies of our system. But an
all-pervading ether must fill the whole visible creation, since it
conveys, in the form of light, tremors which may have been excited in
the deepest recesses of the universe thousands of years before we were
called into being. The existence of such a medium, though at first
hypothetical, is proved by the undulatory theory of light, and rendered
certain by the motion of comets, and by its action upon the vapours of
which they are chiefly composed. It has often been imagined that the
tails of comets have infused new substances into our atmosphere.
Possibly the earth may attract some of that nebulous matter, since the
vapours raised by the sun’s heat, when the comets are in perihelio, and
which form their tails, are scattered through space in their passage to
their aphelion; but it has hitherto produced no effect, nor have the
seasons ever been influenced by these bodies. The light of the comet of
the year 1811, which was so brilliant, did not impart any heat even when
condensed on the bulb of a thermometer of a structure so delicate that
it would have made the hundredth part of a degree evident. In all
probability, the tails of comets may have passed over the earth without
its inhabitants being conscious of their presence; and there is reason
to believe that the tail of the great comet of 1843 did so. M. Valz
observed that the light of a brilliant comet was eclipsed as it passed
over a star of the 7th magnitude, whence M. Babinet computed that the
light of the comet must have been sixty times less than that of the
star, and that matter so attenuated could not penetrate the earth’s
atmosphere, but the constitution of these bodies is still a matter of
conjecture.

The passage of comets has never sensibly disturbed the stability of the
solar system; their nucleus, being in general only a mass of vapour, is
so rare, and their transit so rapid, even when they had a solid part,
that the time has not been long enough to admit of a sufficient
accumulation of impetus to produce a perceptible action. Indeed, M.
Dusejour has shown that, under the most favourable circumstances, a
comet cannot remain longer than two hours and a half at a less distance
from the earth than 10,500 leagues. The comet of 1770 passed within
about six times the distance of the moon from the earth, without even
affecting our tides. According to La Place, the action of the earth on
the comet of 1770 augmented the period of its revolution by more than
two days; and, if comets had any perceptible disturbing energy, the
reaction of the comet ought to have increased the length of our year.
Had the mass of that comet been equal to the mass of the earth, its
disturbing action would have increased the length of the sidereal year
by 2^h 53^m; but, as Delambre’s computations from the Greenwich
observations of the sun show that the length of the year has not been
increased by the fraction of a second, its mass could not have been
equal to the 1/5000th part of that of the earth. This accounts for the
same comet having twice swept through the system of Jupiter’s satellites
without deranging the motion of these moons. M. Dusejour has computed
that a comet, equal in mass to the earth, passing at the distance of
12,150 leagues from our planet, would increase the length of the year to
367^d 16^h 5^m, and the obliquity of the ecliptic as much as 2°. So
the principal action of comets would be to alter the calendar, even if
they were dense enough to affect the earth.

Comets traverse all parts of the heavens; their paths have every
possible inclination to the plane of the ecliptic, and, unlike the
planets, the motion of more than half of those that have appeared has
been retrograde, that is, from east to west. They are only visible when
near their perihelia; then their velocity is such, that its square is
twice as great as that of a body moving in a circle at the same
distance: they consequently remain but a very short time within the
planetary orbits. And, as all the conic sections of the same focal
distance sensibly coincide, through a small arc, on each side of the
extremity of their axis, it is difficult to ascertain in which of these
curves the comets move, from observations made, as they necessarily must
be, near their perihelia (N. 227). Probably they all move in extremely
excentric ellipses; although, in most cases, the parabolic curve
coincides most nearly with their observed motions. Some few seem to
describe hyperbolas; such, being once visible to us, would vanish for
ever, to wander through boundless space, to the remote systems of the
universe. If a planet be supposed to revolve in a circular orbit, whose
radius is equal to the perihelion distance of a comet moving in a
parabola, the areas described by these two bodies in the same time will
be as unity to the square root of two, which forms such a connexion
between the motion of comets and planets, that, by Kepler’s law, the
ratio of the areas described during the same time by the comet and the
earth may be found; so that the place of a comet may be computed at any
time in its parabolic orbit, estimated from the instant of its passage
at the perihelion. It is a problem of very great difficulty to determine
all the other elements of parabolic motion—namely, the comet’s
perihelion distance, or shortest distance from the sun, estimated in
parts of the mean distance of the earth from the sun; the longitude of
the perihelion; the inclination of the orbit on the plane of the
ecliptic; and the longitude of the ascending node. Three observed
longitudes and latitudes of a comet are sufficient for computing the
approximate values of these quantities; but an accurate estimation of
them can only be obtained by successive corrections, from a number of
observations, distant from one another. When the motion of a comet is
retrograde, the place of the ascending node is exactly opposite to what
it is when the motion is direct. Hence the place of the ascending node,
together with the direction of the comet’s motion, show whether the
inclination of the orbit is on the north or south side of the plane of
the ecliptic. If the motion be direct, the inclination is on the north
side; if retrograde, it is on the south side.

The identity of the elements is the only proof of the return of a comet
to our system. Should the elements of a new comet be the same, or nearly
the same, with those of any one previously known, the probability of the
identity of the two bodies is very great, since the similarity extends
to no less than four elements, every one of which is capable of an
infinity of variations. But, even if the orbit be determined with all
the accuracy the case admits of, it may be difficult, or even
impossible, to recognize a comet on its return, because its orbit would
be very much changed if it passed near any of the large planets of this
or of any other system, in consequence of their disturbing energy, which
would be very great on bodies of so rare a nature.

By far the most curious and interesting instance of the disturbing
action of the great bodies of our system is found in the comet of 1770.
The elements of its orbit, determined by Messier, did not agree with
those of any comet that had hitherto been computed, yet Lexel
ascertained that it described an ellipse about the sun, whose major axis
was only equal to three times the length of the diameter of the
terrestrial orbit, and consequently that it must return to the sun at
intervals of five years and a half. This result was confirmed by
numerous observations, as the comet was visible through an arc of 170°;
yet this comet had never been observed before the year 1770, nor has it
ever again been seen till 1843, though very brilliant. The disturbing
action of the larger planets affords a solution of this anomaly, as
Lexel ascertained that in 1767 the comet must have passed Jupiter at a
distance less than the fifty-eighth part of its distance from the sun,
and that in 1779 it would be 500 times nearer Jupiter than the sun;
consequently the action of the sun on the comet would not be the
fiftieth part of what it would experience from Jupiter, so that Jupiter
became the primum mobile. Assuming the orbit to be such as Lexel had
determined in 1770, La Place found that the action of Jupiter, previous
to the year 1770, had so completely changed the form of it, that the
comet which had been invisible to us before 1770 was then brought into
view, and that the action of the same planet, producing a contrary
effect, has subsequently to that year removed it from our sight, since
it was computed to be revolving in an orbit whose perihelion was beyond
the orbit of Ceres. However, the action of Jupiter during the summer of
1840 must have been so great, from his proximity to that singular body,
that he seems to have brought it back to its former path as he had done
in 1767, for the elements of the orbit of a comet which was discovered
in November 1843, by M. Faye, agree so nearly with those of the orbit of
Lexel’s comet that the two bodies were supposed to be identical; by the
subsequent computation of M. le Verrier, it appears, however, that they
are not the same, that they were both brought to our system by Jupiter’s
attraction, and that they have been in it more than a century, and have
frequently come near the earth without having been seen. From the
smallness of the excentricity of Lexel’s comet, the orbit resembles
those of the planets, but this comet is liable to greater perturbations
than any other body in the system, because it comes very near the orbit
of Mars when in perihelion, and very near that of Jupiter when in
aphelion; besides, it passes within a comparatively small distance of
the orbits of the minor planets; and as it will continue to cross the
orbit of Jupiter at each revolution till the two bodies meet, its
periodic time, now about seven years, will again be changed, but in the
mean time it ought to have returned to its perihelion in the year 1851.
This comet might have been seen from the earth in 1776, had its light
not been eclipsed by that of the sun. There is still so much doubt with
regard to Lexel’s comet that during the present year, 1858, M. le
Verrier has constructed a table of all the orbits in which the comet may
have moved after leaving Jupiter in 1770, which will enable astronomers
to recognise the comet even should the elements of its orbit be much
altered. He thinks it possible that its path may have become hyperbolic,
but that it is more likely an augmentation of its periodic time may have
taken place. It is quite possible that comets frequenting our system may
be turned away, or others brought to the sun, by the attraction of
planets revolving beyond the orbit of Neptune, or by bodies still
farther removed from the solar influence.

Other comets, liable to less disturbance, return to the sun at stated
intervals. Halley computed the elements of the orbit of a comet that
appeared in the year 1682, which agreed so nearly with those of the
comets of 1607 and 1531, that he concluded it to be the same body
returning to the sun at intervals of about seventy-five years. He
consequently predicted its reappearance in the year 1758, or in the
beginning of 1759. Science was not sufficiently advanced in the time of
Halley to enable him to determine the perturbations this comet might
experience; but Clairaut computed that, in consequence of the attraction
of Jupiter and Saturn, its periodic time would be so much shorter than
during its revolution between 1607 and 1682, that it would pass its
perihelion on the 18th of April, 1759. The comet did arrive at that
point of its orbit on the 12th of March, which was thirty-seven days
before the time assigned. Clairaut subsequently reduced the error to
twenty-three days; and La Place has since shown that it would only have
been thirteen days if the mass of Saturn had been as well known as it is
now. It appears, from this, that the path of the comet was not quite
known at that period; and, although many observations were then made,
they were far from attaining the accuracy of those of the present day.
Besides, since the year 1759, the orbit of the comet has been altered by
the attraction of Jupiter in one direction, and that of Saturn, Uranus,
and Neptune in the other; yet, notwithstanding these sources of
uncertainty, and our ignorance of all the possible causes of derangement
from unknown bodies on the confines of our system, or in the regions
beyond it, the comet appeared exactly at the time, and not far from the
place assigned to it by astronomers; and its actual arrival at its
perihelion a little before noon on the 16th of November, 1835, only
differed from the computed time by a very few days, which was probably
owing to the attraction of Neptune.

The fulfilment of this astronomical prediction is truly wonderful, if it
be considered that the comet is seen only for a few weeks during its
passage through our system, and that it wanders from the sun for
seventy-five years to twice the distance of Uranus. This enormous orbit
is four times longer than it is broad; its length is about 3420 millions
of miles, or about thirty-six times the mean distance of the earth from
the sun. At its perihelion the comet comes within nearly fifty-seven
millions of miles of the sun, and at its aphelion it is sixty times more
distant. On account of this extensive range it must experience 3600
times more light and heat when nearest to the sun than in the most
remote point of its orbit. In the one position the sun will seem to be
four times larger than he appears to us, and at the other he will not be
apparently larger than a star (N. 228.)

On the first appearance of Halley’s comet, early in August 1835, it
seemed to be merely a globular mass of dim vapour, without a tail. A
concentration of light, a little on one side of the centre, increased as
the comet approached the sun and earth, and latterly looked so like the
disc of a small planet, that it might have been mistaken for a solid
nucleus. M. Struve, however, saw a central occultation of a star of the
ninth magnitude by the comet, at Dorpat, on the 29th of September. The
star remained constantly visible, without any considerable diminution of
light; and, instead of being eclipsed, the nucleus of the comet
disappeared at the moment of conjunction from the brilliancy of the
star. The tail increased as the comet approached its perihelion, and
shortly before it was lost in the sun’s rays it was between thirty and
forty degrees in length.

According to the observations of M. Valz, the nebulosity increased in
magnitude as it approached the sun; but no other comet on record has
exhibited such sudden and unaccountable changes of aspect. It was
invisible for two months when near its perihelion passage, and when it
reappeared on the 24th of January, 1836, its aspect was completely
changed; it had no tail, and to the naked eye was like a hazy star; but
with a powerful telescope it presented a small, round, planetary-looking
nucleus 2ʺ in diameter, surrounded by an extensive coma, and in the
centre it had a small, bright, solid part. The nucleus, clear and well
defined, like the disc of a planet, was observed on one occasion to
become obscure and enlarged in the course of a few hours. But by far the
most remarkable circumstance was the sudden appearance of certain
luminous brushes or sectors, diverging from the centre of the nucleus
through the nebulosity. M. Struve describes the nucleus of the comet, in
the beginning of October, as elliptical, and like a burning coal, out of
which there issued, in a direction nearly opposite to the tail, a
divergent flame, varying in intensity, form, and direction, appearing
occasionally even double, and suggesting the idea of luminous gas
bursting from the nucleus. On one occasion M. Arago saw three of these
divergent flames on the side opposite the tail, rising through the
nebulosity, which they greatly exceeded in brilliancy: after the comet
had passed its perihelion, it acquired another of these luminous fans,
which was observed by Sir John Herschel at the Cape of Good Hope.
Hevelius describes an appearance precisely similar, which he had
witnessed in this comet at its approach to the sun in the year 1682, and
something of the kind seems to have been noticed in the comet of 1744.
Possibly the second tail of the comet of 1724, which was directed
towards the sun, may have been of this nature.

The influence of the ethereal medium on the motions of Halley’s comet
will be known after another revolution, and future astronomers will
learn, by the accuracy of its returns, whether it has met with any
unknown cause of disturbance in its distant journey. Undiscovered
planets, beyond the visible boundary of our system, may change its path
and the period of its revolution, and thus may indirectly reveal to us
their existence, and even their physical nature and orbit. The secrets
of the yet more distant heavens may be disclosed to future generations
by comets which penetrate still farther into space, such as that of
1763, which, if any faith may be placed in the computation, goes nearly
forty-three times farther from the sun than Halley’s does, and shows
that the sun’s attraction is powerful enough, at the enormous distance
of 15,500 millions of miles, to recall the comet to its perihelion. The
periods of some comets are said to be of many thousand years, and even
the average time of the revolution of comets generally is about a
thousand years; which proves that the sun’s gravitating force extends
very far. La Place estimates that the solar attraction is felt
throughout a sphere whose radius is a hundred millions of times greater
than the distance of the earth from the sun.

Authentic records of Halley’s comet do not extend beyond the year 1456,
yet it may be traced, with some degree of probability, even to a period
preceding the Christian era. But as the evidence only rests upon
coincidences of its periodic time, which may vary as much as eighteen
months from the disturbing action of the planets, its identity with
comets of such remote times must be regarded as extremely doubtful.

This is the first comet whose periodicity has been established. It is
also the first whose elements have been determined from observations
made in Europe; for, although the comets which appeared in the years
240, 539, 565, and 837, are the most ancient of those whose orbits have
been traced, their elements were computed from Chinese observations.

Besides Halley’s and Lexel’s comets, ten or twelve others are now known
to form part of the solar system; that is to say, they return to the sun
at stated periods. Six of them have periods of less than eight years.
That generally called Encke’s comet, or the comet of the short period,
was first seen by MM. Messier and Mechain in 1786, again by Miss
Herschel in 1805, and its returns, in the years 1805 and 1819, were
observed by other astronomers, under the impression that all four were
different bodies. However, Professor Encke not only proved their
identity, but determined the circumstances of the comet’s motion. Its
reappearance in the years 1825, 1828, and 1832, accorded with the orbit
assigned by M. Encke, who thus established the length of its period to
be 1204 days, nearly. This comet is very small, of feeble light, and
invisible to the naked eye, except under very favourable circumstances,
and in particular positions. It has no tail, it revolves in an ellipse
of great excentricity inclined at an angle of 13° 22ʹ to the plane of
the ecliptic, and is subject to considerable perturbations from the
attraction of the planets, which occasion variations in its periodic
time. Among the many perturbations to which the planets are liable,
their mean motions, and therefore the major axes of their orbits,
experience no change; while, on the contrary, the mean motion of the
moon is accelerated from age to age—a circumstance at first attributed
to the resistance of an ethereal medium pervading space, but
subsequently proved to arise from the secular diminution of the
excentricity of the terrestrial orbit. Although the resistance of such a
medium has not hitherto been perceived in the motions of such dense
bodies as the planets and satellites, its effects on the revolutions of
the comets leave no doubt of its existence. From the numerous
observations that have been made on each return of the comet of the
short period, the elements have been computed with great accuracy on the
hypothesis of its moving in vacuo. Its perturbations occasioned by the
disturbing action of the planets have been determined; and, after
everything that could influence its motion had been duly considered, M.
Encke found that an acceleration of about two days in each revolution
has taken place in its mean motion, precisely similar to that which
would be occasioned by the resistance of an ethereal medium. And, as it
cannot be attributed to a cause like that which produces the
acceleration of the moon, it must be concluded that the celestial bodies
do not perform their revolutions in an absolute void, and that, although
the medium be too rare to have a sensible effect on the masses of the
planets and satellites, it nevertheless has a considerable influence on
so rare a body as a comet. Contradictory as it may seem that the motion
of a body should be accelerated by the resistance of an ethereal medium,
the truth becomes evident if it be considered that both planets and
comets are retained in their orbits by two forces which exactly balance
one another; namely, the centrifugal force producing the velocity in the
tangent, and the attraction of the gravitating force directed to the
centre of the sun. If one of these forces be diminished by any cause,
the other will be proportionally increased. Now, the necessary effect of
a resisting medium is to diminish the tangential velocity, so that the
balance is destroyed, gravity preponderates, the body descends towards
the sun till equilibrium is again restored between the two forces; and,
as it then describes a smaller orbit, it moves with increased velocity.
Thus, the resistance of an ethereal medium actually accelerates the
motion of a body; but, as the resisting force is confined to the plane
of the orbit, it has no influence whatever on the inclination of the
orbit, or on the place of the nodes. In computing its effect, M. Encke
assumed the increase to be inversely as the square of the distance, and
that its resistance acts as a tangential force proportional to the
squares of the comet’s actual velocity in each point of its orbit.
Another comet belonging to our system, which returns to its perihelion
after a period of 6-3/4 years, has been accelerated in its motion by a
whole day during one revolution, which puts the existence of ether
beyond a doubt, and confirms the undulatory theory of light. Since this
comet, which revolves nearly between the orbits of the earth and
Jupiter, is only accelerated one day at each revolution, while Encke’s,
revolving nearly between the orbits of Mercury and Pallas, is
accelerated two, the ethereal medium must increase in density towards
the sun. The comet in question was discovered by M. Biela at Josephstadt
on the 27th of February, 1826, and ten days afterwards it was seen by M.
Gambart at Marseilles, who computed its parabolic elements, and found
that they agreed with those of the comets which had appeared in the
years 1789 and 1795, whence he concluded them to be the same body moving
in an ellipse, and accomplishing its revolution in 2460 days. The
perturbations of this comet were computed by M. Damoiseau, who predicted
that it would cross the plane of the ecliptic on the 29th of October,
1832, a little before midnight, at a point nearly 18,484 miles within
the earth’s orbit; and as M. Olbers of Bremen, in 1805, had determined
the radius of the comet’s head to be about 21,136 miles, it was evident
that its nebulosity would envelop a portion of the earth’s orbit,—a
circumstance which caused some alarm in France, from the notion that, if
any disturbing cause had delayed the arrival of the comet for one month,
the earth must have passed through its head. M. Arago dispelled these
fears by his excellent treatise on comets, in the Annuaire of 1832,
where he proves that, as the earth would never be nearer the comet than
18,000,000 British leagues, there could be no danger of collision. The
earth is in more danger from these two small comets than from any other.
Encke’s crosses the terrestrial orbit sixty times in a century, and may
ultimately come into collision, but both are so extremely rare, that
little injury is to be apprehended.

The earth would fall to the sun in 64-1/2 days, if it were struck by a
comet with sufficient impetus to destroy its centrifugal force. What the
earth’s primitive velocity may have been it is impossible to say.
Therefore a comet may have given it a shock without changing the axis of
rotation, but only destroying part of its tangential velocity, so as to
diminish the size of the orbit—a thing by no means impossible, though
highly improbable. At all events, there is no proof of this having
occurred; and it is manifest that the axis of the earth’s rotation has
not been changed, because, as the ether offers no sensible resistance to
so dense a body as the earth, the libration would to this day be evident
in the variation it must have occasioned in the terrestrial latitudes.
Supposing the nucleus of a comet to have a diameter only equal to the
fourth part of that of the earth, and that its perihelion is nearer to
the sun than we are ourselves, its orbit being otherwise unknown, M.
Arago has computed that the probability of the earth receiving a shock
from it is only one in 281 millions, and that the chance of our coming
in contact with its nebulosity is about ten or twelve times greater.
Only comets with retrograde motions can come into direct collision with
the earth, and if the momentum were great the event might be fatal; but
in general the substance of comets is so rare, that it is likely they
would not do much harm if they were to impinge; and even then the
mischief would probably be local, and the equilibrium soon restored,
provided the nucleus were gaseous, or very small. It is, however, more
probable that the earth would only be deflected a little from its course
by the approach of a comet, without being touched by it. The comets that
have come nearest to the earth were that of the year 837, which remained
four days within less than 1,240,000 leagues from our orbit: that of
1770, which approached within about six times the distance of the moon.
The celebrated comet of 1680 also came very near to us; and the comet
whose period is 6-3/4 years was ten times nearer the earth in 1805 than
in 1832, when it caused so much alarm.

Encke’s and Biela’s comets are at present far removed from the influence
of Jupiter, but they will not always remain so, because, the aphelia and
nodes of the orbits of these two comets being the points which approach
nearest to the orbit of Jupiter at each meeting of the planet and
comets, the major axis of Encke’s comet will be increased and that of
Biela’s diminished, till in the course of time, when the proximity has
increased sufficiently, the orbits will be completely changed, as that
of Lexel’s was in 1770. Every twenty-third year, or after seven
revolutions of Encke’s comet, its greatest proximity to Jupiter takes
place, and at that time his attraction increases the period of its
revolution by nine days—a circumstance which took place in the end of
the years 1820 and 1843. But from the position of the bodies there is a
diminution of three days in the six following revolutions, which reduces
the increase to six days in seven revolutions. Thus, before the year
1819, the periodic time of Encke’s comet was 1204 days, and it was 1219
days in accomplishing the revolution that ended in 1845. By this
progressive increase the orbit of the comet will reach that of Jupiter
in seven or eight centuries, and then by the very near approach of the
two bodies it will be completely changed.

At present the Earth and Mercury have the most powerful influence on the
motions of Encke’s and Biela’s comets; and have had for so long a time
that, according to the computation of Mr. Airy, the present orbit of the
latter was formed by the attraction of the Earth, and that of Encke’s by
the action of Mercury. With regard to the latter comet, that event must
have taken place in February 1776. In 1786 Encke’s comet had both a tail
and a nucleus, now it has neither; a singular instance of the
possibility of their disappearance. It was in perihelio in 1855.

In 1846 Biela’s comet was divided into two distinct bodies, by what
strange accident is altogether a mystery. The nuclei of the two comets
were separated by about 150,000 miles, and they travelled together with
their tails parallel, and an arch of light over their heads. Till that
time Biela’s comet never had been seen with a tail. The new head was
dull at first, but increased in size and brightness till it surpassed
its companion in both; besides, it had a bright flashing diamond-like
point in its centre—gradually it resumed its dull appearance, and its
period was computed to be eight days longer than that of the original
head. They had separated to a greater distance from one another in 1853,
but were still travelling together, one having become smaller than the
other.

A comet discovered by M. Brorsen of Kiel, on the 26th of February, 1846,
came, on the 20th of April following, nearly as close to Jupiter as his
fourth satellite, when Jupiter’s attraction must have been ten times
greater than that of the sun; so there is every reason to believe that
the comet’s orbit will be as much altered as that of Lexel’s; and
another discovered by Padre de Vico at Rome, on the 22nd of August,
will, in all probability, be as much disturbed by the same cause. One of
the comets found by that astronomer has a period which varies, according
to different computations, from 55 to 99 years; it certainly has an
elliptical orbit. That discovered at Naples by Mr. Peters revolves about
the sun in 16 years; but Olbers’s comet of 1815 must go nearly the same
distance into space with Halley’s, since its period is 74 years. Two
discovered by M. Brorsen have periods, one of 500 and the other of 28
years; but of the latter there is some uncertainty.

The comet which appeared in 1596 and 1845 has a period of 249 years; and
should M. Argelander’s computation be accurate, the orbit which has
hitherto been assigned to the great comet of 1811 must be erroneous,
since he has ascertained its period to be 3066 years.

The great comet of 1264, which had a tail that extended over 100° of the
celestial vault, was observed and recorded by the Chinese, and was
ascertained to be the same that had appeared in 1556, and of whose
motions observations were taken at Vienna in the reign of the Emperor
Charles V., but it was then less brilliant. In consequence of the
discovery of the original observations of the comet of 1556, by
Fabricius at Vienna, and by Heller at Nuremburg, Mr. Hind was induced to
compute its orbit for that year; but after much labour, aided by all the
improved methods of calculation, he found Heller’s observations so
confused, and even erroneous, that he could not determine the curve
described by the comet at that time with any precision, and therefore
could only predict that the epoch of its return would be some time
between 1848 and 1861. Before comets reach the sun they are rarely
conspicuous; but if after passing their perihelion they come near the
earth, then they have tails, and become brilliant in consequence of the
sun’s action upon the matter of which they are formed. Now if the comet
in question should pass its perihelion between the months of March and
October, it possibly may be as remarkable as ever; but should it come
nearest to the sun in winter, such is the position of its orbit with
regard to the earth, that it may pass unnoticed—which is very unlikely,
as search is being made for it at almost all the observatories in Europe
and in the United States. Nearly the whole of its orbit lies below the
plane of the ecliptic, and far from the paths of the larger planets, but
it extends into space more than twice the distance of Neptune, or nearly
six thousand millions of miles from the sun.

Comets in or near their perihelion move with prodigious velocity. That
of 1680 appears to have gone half round the sun in ten hours and a half,
moving at the rate of 880,000 miles an hour. If its enormous centrifugal
force had ceased when passing its perihelion, it would have fallen to
the sun in about three minutes, as it was then less than 147,000 miles
from his surface. So near the sun, it would be exposed to a heat 27,500
times greater than that received by the earth; and as the sun’s heat is
supposed to be in proportion to the intensity of his light, it is
probable that a degree of heat so intense would be sufficient to convert
into vapour every terrestrial substance with which we are acquainted. At
the perihelion distance the sun’s diameter would be seen from the comet
under an angle of 73°, so that the sun, viewed from the comet, would
nearly cover the whole extent of the heavens from the horizon to the
zenith. As this comet is presumed to have a period of 575 years, the
major axis of its orbit must be so great, that at the aphelion the sun’s
diameter would only subtend an angle of about fourteen seconds, which is
not so great by half as the diameter of Mars appears to us when in
opposition. The sun would consequently impart no heat, so that the comet
would then be exposed to the temperature of the ethereal regions, which
is 239° below the zero point of Fahrenheit. A body of such tenuity as
the comet, moving with such velocity, must have met with great
resistance from the dense atmosphere of the sun, while passing so near
his surface at its perihelion. The centrifugal force must consequently
have been diminished, and the sun’s attraction proportionally augmented,
so that it must have come nearer to the sun in 1680 than in its
preceding revolution, and would subsequently describe a smaller orbit.
As this diminution of its orbit will be repeated at each revolution, the
comet will infallibly end by falling on the surface of the sun, unless
its course be changed by the disturbing influence of some large body in
the unknown expanse of creation. Our ignorance of the actual density of
the sun’s atmosphere, of the density of the comet, and of the period of
its revolution, renders it impossible to form any idea of the number of
centuries which must elapse before this event takes place.

The same cause may affect the motions of the planets, and ultimately be
the means of destroying the solar system. But, as Sir John Herschel
observes, they could hardly all revolve in the same direction round the
sun for so many ages without impressing a corresponding motion on the
ethereal medium, which may preserve them from the accumulated effects of
its resistance. Should this material medium revolve about the sun like a
vortex, it will accelerate the revolutions of such comets as have direct
motions, and retard those that have retrograde motions.

The comet which appeared unexpectedly in the beginning of the year 1843
was one of the most splendid that ever visited the solar system. It was
in the constellation of Antinous in the end of January, at a distance of
115 millions of miles from the earth, and it passed through its
perihelion on the 27th of February, when it was lost in the sun’s rays;
but it began to be visible about the 3rd of March, at which time it was
near the star Iota Cetæ, and its tail extended towards the Hare. Before
the passage at the perihelion it had no tail; but at that epoch the tail
suddenly darted out, and extended to a distance of 1826 millions of
miles in about an hour and a half—a most inexplicable speed of
development, which indicates some powerful repulsive force at the moment
of the greatest proximity to the sun, at which time the tails are
formed. The brightness of the comet and the length of its tail continued
to increase till the latter stretched far beyond the constellation of
the Hare towards a point above Sirius. Stars were distinctly seen
through it, and when near perihelion the comet was so bright that it was
seen in clear sunshine, in the United States, like a white cloud. The
motion was retrograde, and on leaving the solar system it retreated so
rapidly at once from the sun and earth that it was soon lost sight of
for want of light. On the 1st of April it was between the sun and the
earth, and only 40 millions of miles from the latter; and as its tail
was at least 60 millions of miles long, and 20 millions of miles broad,
we probably passed through it without being aware of it. There is some
discrepancy in the different computations of the elements of the orbit,
but in the greater number of cases the perihelion distance was found to
be less than the semidiameter of the sun, so that the comet must have
grazed his surface, if it did not actually impinge obliquely on him.

The perihelion distance of this comet differs little from that of the
great comet of 1668, which came so near the sun. The motion of both was
retrograde, and a certain resemblance in the two orbits makes it
probable that they are the same body performing a revolution in 175
years.

Though already so well acquainted with the motions of comets, we know
nothing of their physical constitution. A vast number, especially of
telescopic comets, are only like clouds or masses of vapour, often
without tails. The head commonly consists of a concentrated mass of
light, like a planet, surrounded by a very transparent atmosphere, and
the whole, viewed with a telescope, is so diaphanous, that the smallest
star may be seen even through the densest part of the nucleus; in
general their solid parts, when they have any, are so minute, that they
have no sensible diameter, like that of the comet of 1811, which
appeared to Sir William Herschel like a luminous point in the middle of
the nebulous matter. The nuclei, which seem to be formed of the denser
strata of that nebulous matter in successive coatings, are sometimes of
great magnitude. Those comets which came to the sun in the years 1799
and 1807 had nuclei whose diameters measured 180 and 275 leagues
respectively, and the second comet of 1811 had a nucleus 1350 leagues in
diameter.

It must, however, be stated that, as comets are generally at prodigious
distances from the earth, the solid parts of the nuclei appear like mere
points of light, so minute that it is impossible to measure them with
any kind of accuracy, so that the best astronomers often differ in the
estimation of their size by one-half of the whole diameter. The transit
of a comet across the sun would afford the best information with regard
to the nature of the nuclei. It was computed that such an event was to
take place in the year 1827; unfortunately the sun was hid by clouds
from the British astronomers, but it was examined at Viviers and at
Marseilles at the time the comet must have been projected on its disc,
but no spot or cloud was to be seen, so that it must have had no solid
part whatever. The nuclei of many comets which seemed solid and
brilliant to the naked eye have been resolved into mere vapour by
telescopes of high powers; in Halley’s comet there was no solid part at
all.

The nebulosity immediately round the nucleus is so diaphanous, that it
gives little light; but at a small distance the nebulous matter becomes
suddenly brilliant, so as to look like a bright ring round the body.
Sometimes there are two or three of these luminous concentric rings
separated by dark intervals, but they are generally incomplete on the
part next the tail.

These annular appearances are an optical effect, arising from a
succession of envelopes of the nebulous matter with intervals between
them, of which the first is sometimes in contact with the nucleus and
sometimes not. The thickness of these bright diaphanous coatings in the
comets of 1799 and 1807 was about 7000 and 10,000 leagues respectively;
and in the first comet of 1811 the luminous ring was 8000 leagues thick,
and the distance between its interior surface and the centre of the head
was 10,000 leagues. The latter comet was by much the most brilliant that
has been seen in modern times; it was first discovered in this country
by Mr. James Vietch of Inchbonny, and was observed in all its changes by
Sir William Herschel and M. Olbers. To the naked eye, the head had the
appearance of an ill-defined round mass of light, which was resolved
into several distinct parts when viewed with a telescope. A very
brilliant interior circular mass of nebulous matter was surrounded by a
black space having a parabolic form, very distinct from the dark blue of
the sky. This dark space was of a very appreciable breadth. Exterior to
the black interval there was a luminous parabolic contour of
considerable thickness, which was prolonged on each side in two
diverging branches, which formed the bifid tail of the comet. Sir
William Herschel found that the brilliant interior circular mass lost
the distinctness of its outline as he increased the magnifying power of
the telescope, and presented the appearance of a more and more diffuse
mass of greenish or blueish green light, whose intensity decreased
gradually, not from the centre, but from an eccentric brilliant speck,
supposed to be the truly solid part of the comet. The luminous envelope
was of a decided yellow, which contrasted strongly with the greenish
tint of the interior nebulous mass. Stars were nearly veiled by the
luminous envelope, whilst, on the contrary, Sir William Herschel saw
three extremely small stars shining clearly in the black space, which
was singularly transparent. As the envelopes were formed in succession
as the comet approached the sun, Sir William Herschel conceived them to
be vapours raised by his heat at the surface of the nucleus, and
suspended round it like a vault or dome by the elastic force of an
extensive and highly transparent atmosphere. In coming to the sun, the
coatings began to form when the comet was as distant as the orbit of
Jupiter, and in its return they very soon entirely vanished; but a new
one was formed after it had retreated as far as the orbit of Mars, which
lasted for a few days. Indeed, comets in general are subject to sudden
and violent convulsions in their interior, even when far from the sun,
which produce changes that are visible at enormous distances, and baffle
all attempts at explanation—probably arising from electricity, or even
causes with which we are unacquainted. The envelopes surrounding the
nucleus of the comet on the side next to the sun diverge on the opposite
side, where they are prolonged into the form of a hollow cone, which is
the tail. Two repulsive forces seem to be concerned in producing this
effect; one from the comet and another from the sun, the latter being
the most powerful. The envelopes are nearer the centre of the comet on
the side next to the sun, where these forces are opposed to one another;
but on the other side the forces conspire to form the tail, conveying
the nebulous particles to enormous distances.

The lateral edges of the tail reflect more light than the central part,
because the line of vision passes through a greater depth of nebulous
matter, which produces the effect of two streams somewhat like the
aurora. Stars shine with undiminished lustre through the central part of
the tail, because their rays traverse it perpendicularly to its
thickness; but, though distinctly seen through its edges, their light is
weakened by its oblique transmission. The tail of the great comet of
1811 was of wonderful tenuity; stars which would have been entirely
concealed by the slightest fog were seen through 64,000 leagues of
nebulous matter without the smallest refraction. Possibly some part of
the changes in the appearance of the tails arises from rotation. Several
comets have been observed to rotate about an axis passing through the
centre of the tail. That of 1825 performed its rotation in 20-1/2 hours,
and the rapid changes in the luminous sectors which issued from the
nucleus of Halley’s comet in all probability were owing to rotatory
motion.

The two streams of light which form the edges of the tail in most cases
unite at a greater or less distance from the nucleus, and are generally
situate in the plane of the orbit. The tails follow comets in their
descent towards the sun, but precede them in their return, with a small
degree of curvature; their apparent extent and form vary according to
the positions of the orbits with regard to the ecliptic. In some cases
the tail has been at right angles to the line joining the sun and comet.
The curvature is in part owing to the resistance of the ether, and
partly to the velocity of the comet being greater than that of the
particles at the extremity of its tail, which lag behind. The tails are
generally of enormous lengths; the comet of 1811 had one no less than a
hundred millions of miles in length, and those which appeared in the
years 1618, 1680, and 1769, had tails which extended respectively over
104, 90, and 97 degrees of space. Consequently, when the heads of these
comets were set, a portion of the extremity of their tails was still in
the zenith. Sometimes the tail is divided into several branches, like
the comet of 1744, which had six, separated by dark intervals, each of
them about 4° broad, and from 30° to 44° long. They were probably formed
by three hollow cones of the nebulous matter proceeding from the
different envelopes, and enclosing one another, with intervals between;
the lateral edges of these cones would give the appearance of six
streams of light. The tails do not attain their full magnitude till the
comet has left the sun. When comets first appear, they resemble round
films of vapour, with little or no tail. As they approach the sun, they
increase in brilliancy, and their tail in length, till they are lost in
his rays; and it is not till they emerge from the sun’s more vivid light
that they assume their full splendour. They then gradually decrease,
their tails diminish, and they disappear, nearly or altogether, before
they are beyond the sphere of telescopic vision. Many comets have no
tails, as, for example, Encke’s comet. Those which appeared in the years
1585, 1763, and 1682, were also without tails, though the latter is
recorded to have been as bright as Jupiter. The matter of the tail must
be extremely buoyant to precede a body moving with such velocity:
indeed, the rapidity of its ascent cannot be accounted for. It has been
attributed to that power in the sun which produces those vibrations of
ether which constitute light; but as this theory will not account for
the comet of 1824, which is said to have had two tails, one directed
towards the sun, and a very short one diametrically opposite to it, our
ignorance on this subject must be confessed. In this case the repelling
power of the comet seems to have been greater than that of the sun.
Whatever that unknown power may be, there are instances in which its
effects are enormous; for, immediately after the great comet of 1680 had
passed its perihelion, its tail was 100,000,000 miles in length, and was
projected from the comet’s head in the short space of two days. A body
of such extreme tenuity as a comet is most likely incapable of an
attraction powerful enough to recall matter sent to such an enormous
distance; it is therefore, in all probability, scattered in space or
absorbed by the zodiacal light or nebula that surrounds the sun, which
may account for the rapid decrease observed in the tails of comets every
time they return to their perihelia. Should the great comet of 1843
prove to be the same with that of 1668, its tail must have diminished
considerably.

It is remarkable that, although the tails of comets increase in length
as they approach their perihelia, there is reason to believe that the
real diameter of the head contracts on coming near the sun, and expands
rapidly on leaving him. Hevelius first observed this phenomenon, which
Encke’s comet has exhibited in a very extraordinary degree. On the 28th
of October, 1828, this comet was about three times as far from the sun
as it was on the 24th of December; yet at the first date its apparent
diameter was twenty-five times greater than at the second, the decrease
being progressive. M. Valz attributes the circumstance to a real
condensation of volume from the pressure of the ethereal medium, which
increases most rapidly in density towards the surface of the sun, and
forms an extensive atmosphere around him. It did not occur to M. Valz,
however, that the ethereal fluid would penetrate the nebulous matter
instead of compressing it. Sir John Herschel, on the contrary,
conjectures that it may be owing to the alternate conversion of
evaporable materials in the upper regions of the transparent atmosphere
of comets into the states of visible cloud and invisible gas by the
effects of heat and cold; or that some of the external nebulous
envelopes may come into view when the comet arrives at a darker part of
the sky, which were overpowered by the superior light of the sun while
in his vicinity. The first of these hypotheses he considers to be
perfectly confirmed by his observations on Halley’s comet, made at the
Cape of Good Hope, after its return from the sun. He thinks that, in all
probability, the whole comet, except the densest part of its head,
vanished, and was reduced to a transparent and invisible state during
its passage at its perihelion: for when it first came into view, after
leaving the sun, it had no tail, and its aspect was completely changed.
A parabolic envelope soon began to appear, and increased so much and so
rapidly that its augmentation was visible to the eye. This increase
continued till it became so large and so faint, that at last it vanished
entirely, leaving only the nucleus and a tail, which it had again
acquired, but which also vanished; so that at last the nucleus alone
remained. Not only the tails, but the nebulous part of comets,
diminishes every time they return to their perihelia; after frequent
returns they ought to lose it altogether, and present the appearance of
a fixed nucleus: this ought to happen sooner to comets of short periods.
M. de la Place supposes that the comet of 1682 must be approaching
rapidly to that state. Should the substances be altogether, or even to a
great degree, evaporated, the comet would disappear for ever. Possibly
comets may have vanished from our view sooner than they would otherwise
have done from this cause.

The comet discovered at Florence by Signore Donati, on the 2nd of June,
1858, was one of the most beautiful that has been seen from our planet
for many years, whether for the brightness of the _nucleus_, or the
length and graceful form of the _coma_; when first discovered it was
near the star λ in the constellation of the Lion, being then at a
distance of 288,000,000 miles from the earth; during the month of August
its nucleus assumed an almost planetary aspect from the concentration of
its light; on the 27th of September the head appeared almost as bright
as Mercury, but smaller; when near its perihelion passage, on September
30th, its diameter, as ascertained by Signore Donati, was 3ʺ; during the
early part of October it continued to increase in brilliancy, the tail
becoming more elongated, and describing a beautiful arc in the heavens,
occupying a space of nearly 40°, or a length of 40,000,000 miles in the
solar system. On the evening of the 5th of October it was seen from most
parts of Britain, within 20ʹ of Arcturus, the brightest star in the
northern heavens, across which the densest part nearly of the tail
passed, and through which notwithstanding the star shone with
undiminished brilliancy. On the 30th of October, when in perihelio, the
comet was only 55,000,000 miles from the sun; on the 10th it approached
nearest to the earth, from which it was then distant 51,000,000 miles;
and on the 15th of the same month near to Venus, being at that time less
than one-tenth the distance of the earth from the Sun; if the comet had
reached its perihelion a few days earlier, Venus might have passed
through its nucleus, the consequences of which to the planet it would be
very difficult to imagine. The motion of Donati’s comet is what
astronomer’s call _retrograde_, or from east to west. It ceased to be
visible in our northern latitudes in the last week in October, having
passed into the southern heavens, where it will traverse the
constellations of Sagittarius, Telescopium, and Indus, approaching the
large star of Toucan; after which it will disappear until it has nearly
completed its revolution round the sun. The observed orbit of this
remarkable comet coincides more nearly with an ellipse than a parabola;
the longer diameter of the ellipse being 184 times that of the earth’s
orbit, or the immense distance of 35,100,000,000 miles—a space which,
however great, is less than the thousandth of the distance of the
nearest fixed star. According to the calculations of M. Loewy, and
adopting an elliptic orbit, Donati’s comet will not return to the same
places in the heavens for 2495 years, being 500 less than the period of
revolution of the great comet of 1811.

Signore Donati observed that between the 25th and 30th September two
concentric, luminous, semicircular envelopes, with a dark space between
them, were formed in the head. From the extremities of these the cone of
the tail extended, and a non-luminous or dark space stretched for 20°
from the nucleus into the tail. On the 1st October the two envelopes
were combined into one. This comet, like Halley’s, has shown some
singular irregularities, supposed to arise from the action of the sun
when near its perihelion. At different periods of its apparition a
violent agitation was observed in its nucleus, with luminous jets,
spiral offshoots, &c., as in the great comets of 1680, 1744, 1811. A ray
of light was thrown out from one side of the nucleus towards the sun,
while a gas-like jet proceeded from the other side, which appeared to
form the origin of a second tail within the great tail, and which was
traced for half a degree by Mr. Hind on the 19th September. He observed
decided spiral convolutions in the tail, which show that this comet has
a rotatory motion about an axis passing through the tail.

If comets shine by borrowed light, they ought, in certain positions, to
exhibit phases like the moon; but no such appearance has been detected,
except in one instance, when they are said to have been observed by
Hevelius and La Hire, in the year 1682. In general, the light of comets
is dull—that of the comet of 1811 was only equal to the tenth part of
the light of the full moon—yet some have been brilliant enough to be
visible in full daylight, especially the comet of 1744, which was seen
without a telescope at one o’clock in the afternoon, while the sun was
shining. Hence it may be inferred that, although some comets may be
altogether diaphanous, others seem to possess a solid mass resembling a
planet. But whether they shine by their own or by reflected light has
never been satisfactorily made out till now. Even if the light of a
comet were polarized, it would not afford a decisive test, since a body
is capable of reflecting light, though it shines by its own. M. Arago,
however, has, with great ingenuity, discovered a method of ascertaining
this point, independent both of phases and polarization.

Since the rays of light diverge from a luminous point, they will be
scattered over a greater space as the distance increases, so that the
intensity of the light on a screen two feet from the object is four
times less than at the distance of one foot; three feet from the object
it is nine times less; and so on, decreasing in intensity as the square
of the distance increases. As a self-luminous surface consists of an
infinite number of luminous points, it is clear that, the greater the
extent of surface, the more intense will be the light; whence it may be
concluded that the illuminating power of such a surface is proportional
to its extent, and decreases inversely as the square of the distance.
Notwithstanding this, a self-luminous surface, plane or curved, viewed
through a hole in a plate of metal, is of the same brilliancy at all
possible distances as long as it subtends a sensible angle, because, as
the distance increases, a greater portion comes into view; and, as the
augmentation of surface is as the square of the diameter of the part
seen through the whole, it increases as the square of the distance.
Hence, though the number of rays from any one point of the surface which
pass through the hole decreases inversely as the square of the distance,
yet, as the extent of surface which comes into view increases also in
that ratio, the brightness of the object is the same to the eye as long
as it has a sensible diameter. For example—Uranus is about nineteen
times farther from the sun than we are, so that the sun, seen from that
planet, must appear like a star with a diameter of a hundred seconds,
and must have the same brilliancy to the inhabitants that he would have
to us if viewed through a small circular hole having a diameter of a
hundred seconds. For it is obvious that light comes from every point of
the sun’s surface to Uranus, whereas a very small portion of his disc is
visible through the hole; so that extent of surface exactly compensates
distance. Since, then, the visibility of a self-luminous object does not
depend upon the angle it subtends as long as it is of sensible
magnitude, if a comet shines by its own light, it should retain its
brilliancy as long as its diameter is of a sensible magnitude; and, even
after it has lost an apparent diameter, it ought to be visible, like the
fixed stars, and should only vanish in consequence of extreme
remoteness. That, however, is far from being the case—comets gradually
become dim as their distance increases, and vanish merely from loss of
light, while they still retain a sensible diameter, which is proved by
observations made the evening before they disappear. It may therefore be
concluded that comets shine by reflecting the sun’s light. The most
brilliant comets have hitherto ceased to be visible when about five
times as far from the sun as we are. Most of the comets that have been
visible from the earth have their perihelia within the orbit of Mars,
because they are invisible when as distant as the orbit of Saturn: on
that account there is not one on record whose perihelion is situate
beyond the orbit of Jupiter. Indeed, the comet of 1756, after its last
appearance, remained five whole years within the ellipse described by
Saturn without being once seen. More than a hundred and forty comets
have appeared within the earth’s orbit during the last century that have
not again been seen. If a thousand years be allowed as the average
period of each, it may be computed, by the theory of probabilities, that
the whole number which range within the earth’s orbit must be 1400; but,
Uranus being about nineteen times more distant, there may be no less
than 11,200,000 comets that come within the orbit of Uranus. M. Arago
makes a different estimate; he considers that, as thirty comets are
known to have their perihelion distance within the orbit of Mercury, if
it be assumed that comets are uniformly distributed in space, the number
having their perihelion within the orbit of Uranus must be to thirty as
the cube of the radius of the orbit of Uranus to the cube of the radius
of the orbit of Mercury, which makes the number of comets amount to
3,529,470. But that number may be doubled, if it be considered that, in
consequence of daylight, fogs, and great southern declination, one comet
out of two must be hid from us. According to M. Arago, more than seven
millions of comets come within the orbit of Uranus.

The different degrees of velocity with which the planets and comets were
originally propelled in space is the sole cause of the diversity in the
form of their orbits, which depends only upon the mutual relation
between the projectile force and the sun’s attraction.

When the two forces are exactly equal to one another, circular motion is
produced; when the ratio of the projectile to the central force is
exactly that of 1 to the square root of 2, the motion is parabolic; any
ratio between these two will cause a body to move in an ellipse, and any
ratio greater than that of 1 to the square root of 2 will produce
hyperbolic motion (N. 229).

The celestial bodies might move in any one of these four curves by the
law of gravitation: but, as one particular velocity is necessary to
produce either circular or parabolic motion, such motions can hardly be
supposed to exist in the solar system, where the bodies are liable to
such mutual disturbances as would infallibly change the ratio of the
forces, and cause them to move in ellipses in the first case, and
hyperbolas in the other. On the contrary, since every ratio between
equality and that of 1 to the square root of 2 will produce elliptical
motion, it is found in the solar system in all its varieties, from that
which is nearly circular to such as borders on the parabolic from
excessive ellipticity. On this depends the stability of the system; the
mutual disturbances only cause the orbits to become more or less
excentric without changing their nature.

For the same reason the bodies of the solar system might have moved in
an infinite variety of hyperbolas, since any ratio of the forces,
greater than that which causes parabolic motion, will make a body move
in one of these curves. Hyperbolic motion is however very rare; only two
comets appear to move in orbits of that nature, those of 1771 and 1824;
probably all such comets have already come to their perihelia, and
consequently will never return.

The ratio of the forces which fixed the nature of the celestial orbits
is thus easily explained; but the circumstances which determined these
ratios, which caused some bodies to move nearly in circles and others to
wander towards the limits of the solar attraction, and which made all
the heavenly bodies to rotate and revolve in the same direction, must
have had their origin in the primeval state of things; but as it pleases
the Supreme Intelligence to employ gravitation alone in the maintenance
of this fair system, it may be presumed to have presided at its
creation.




                             SECTION XXXVI.

The Fixed Stars—Their Number—The Milky Way—Double Stars—Binary
  Systems—Their Orbits and Periodic Times—Colours of the Stars—Stars
  that have vanished—Variable Stars—Variation in Sun’s Light—Parallax
  and Distances of the Fixed Stars—Masses of the Stars—Comparative Light
  of the Stars—Proper Motions of the Stars—Apparent Motions of the
  Stars—Motion and Velocity of the Sun and Solar System—The Nebulæ—Their
  Number—Catalogue of them—Consist of Two Classes—Diffuse
  Nebulæ—Definitely formed Nebulæ—Globular Clusters—Splendour of Milky
  Way—Distribution of the Nebulæ—The Magellanic Clouds—Nebulæ round η
  Argûs—Constitution of Nebulæ, and the Forces that maintain
  them—Meteorites and Shooting Stars.


GREAT as the number of comets appears to be, it is absolutely nothing in
comparison of the multitude of the fixed stars. About 2000 only are
visible to the naked eye; but when the heavens are viewed through a
telescope, their number seems to be limited only by the imperfection of
the instrument. The number registered amounts to 200,000; their places
are determined with great precision, and they are formed into a
catalogue, not only for the purpose of ascertaining geographical
positions by the occultations of the brightest among them, but also to
serve as points of reference for marking the places of comets and other
celestial phenomena. Sirius, α Centauri, and Arcturus are the brightest
stars in the heavens; the others are classed according to their apparent
lustre, from the first to the seventeenth magnitudes. Capella, α Lyræ,
Procyon, and twenty or twenty-one more, are of the first magnitude; α
Persei, γ Orionis, α Cygni, and in all fifty or sixty, are of the
second; and of the third there are about 200, such as η Bootis and η
Draconis, the numbers increasing as the magnitude diminishes. Those of
the eighth magnitude are scarcely visible to the naked eye, and it
requires a very good telescope to see stars of the seventeenth. This
sequence is perfectly arbitrary; but Sir John Herschel has ascertained
by actual measurement the comparative lustre of a great many—for
example, he found that the light of a star of the sixth magnitude is 100
times less than that of one of the first magnitude, and that Sirius
would make between three and four hundred of such little stars. Were the
photometric scale completed, it would be of the greatest importance with
regard to the variable stars.

The three or four brightest classes of stars are scattered pretty
equably over the sky, with the exception of a zone or belt following the
course of the great circle passing through ε Orionis and α Crucis, where
they are very numerous, especially in the southern hemisphere. The stars
of all magnitudes visible to the naked eye increase in numbers towards
the borders of the Milky Way, which derives its lustre and name from the
diffused light of myriads of stars; so numerous are they in some parts
of it that more than 50,000 passed through the field of Sir William
Herschel’s telescope in the course of an hour, in a zone only two
degrees broad; in many places they are numerous beyond estimation, and
most of them are extremely small on account of their enormous distances.

The Milky Way, which forms so conspicuous a part of the firmament, is a
vast and somewhat flattened stratum or congeries of stars, encircling
the heavens in a broad band, split through one part of its circumference
into two streams of stars, bearing a strong resemblance to fig. 5, plate
5. It is contorted and broken in some places, and occasionally
lengthened into branches stretching far into space. Its thickness is
small compared with its length and breadth; yet in some places it is
unfathomable even with the best telescopes; in others there is reason to
believe that it is possible to see through it, and even beyond it, in
its own plane. There is a gradual but rapid increase in the crowding of
the stars on each side of the flat stratum towards the centre.

The solar system is deeply though excentrically plunged into this mass
of stars, near that point where the circular stratum splits into two
streams. Sir John Herschel’s description of the stars of the southern
hemisphere shows that the Milky Way is a most magnificent object there.
“The general aspect of the southern circumpolar regions (including in
that expression 60° or 70° of south polar distance) is in a high degree
rich and magnificent, owing to the superior brilliancy and large
development of the Milky Way, which, from the constellation of Orion to
that of Antinous, is a blaze of light, strangely interrupted, however,
with vacant and entirely starless patches, especially in Scorpio, near α
Centauri and the Cross, while to the north it fades away pale and dim,
and is in comparison hardly traceable. I think it is impossible to view
this splendid zone, with the astonishingly rich and evenly distributed
fringe of stars of the 3rd and 4th magnitude, which forms a broad skirt
to its southern border like a vast curtain, without an impression
amounting almost to conviction, that the Milky Way is not a mere
stratum, but annular, or at least that our system is placed within one
of the poorer or almost vacant parts of its general mass, and that
eccentrically, so as to be much nearer to the region about the Cross
than to that diametrically opposite to it.”

Those dark vacuities called “Coal Sacks” by the ancient navigators,
which are so numerous between α Centauri and α Antaris, are among the
most extraordinary phenomena in the southern hemisphere; they are of
intense blackness, though by no means void of extremely small telescopic
stars; the darkness arises from the contrast these nearly vacant spaces
form with the excessive brilliancy of the surrounding part of the Milky
Way, and the sudden sharp transition from light to darkness. The largest
and most conspicuous of them is a pear-shaped vacuity close to the
Southern Cross. That portion of the Milky Way that is split
longitudinally through its centre lies between α Centauri and the
constellation of Cygnus: the two bands are joined here and there by
narrow bridges of condensed stars, stretching across the darker space
between them. In Scorpio and Sagittarius Sir John Herschel describes the
Milky Way as composed of definite clouds of light running into clusters
of extremely minute stars like sand, not strewed evenly as with a sieve,
but as if thrown down by handfuls, and by both hands at once, leaving
dark intervals. In this astonishing profusion the stars are of all
sizes, from the 14th to the 20th magnitude, and even down to nebulosity.
After an interval the same profusion is renewed, the stars being
inconceivably minute and numerous beyond description—they are in
millions and millions. Thus there is great irregularity in their
diffusion as well as magnitude—in some places intensely crowded, in
others the deep blackness of the sky, over which they are thinly
scattered, irresistibly led to believe that in these regions the power
of our telescopes fairly penetrates through the starry stratum, and
beyond it. Sometimes we look through a sheet of stars nearly of the same
size, of no great thickness compared with their distance from us, and
not unfrequently there is a double stratum, one of large stars spread
over another of very small ones.

The most southerly of the two streams of stars which form the Milky Way
in this part of the firmament maintains an unbroken course of extreme
brilliancy, containing some of the finest clusters of stars in the
heavens. One round γ Sagittarii is an intense aggregate of stars, in
some parts of which they are so crowded as to exceed enumeration; at a
very moderate estimate Sir John Herschel thinks this group cannot
contain fewer than a hundred thousand stars. Other two groups between
the constellations of the Shield and Ophiuchus stand out like
promontories of intense brilliancy in the dark space that separates the
starry streams of the Milky Way.

The distance of the fixed stars is too great to admit of their
exhibiting a sensible disc, but they must be spherical if gravitation
pervades all space, as there is every reason to believe it does. With a
powerful telescope the stars are like points of light: their
occultations by the moon are therefore instantaneous. Their twinkling
arises from sudden changes in the refractive power of the air, which
would not be sensible if they had discs like planets. Thus nothing can
be known of their distance from us or from one another by their apparent
diameters. Although from the appearance of the stars no inference can be
drawn as to their distance, yet among the multitudes in the heavens a
few are found near enough to exhibit distinct parallactic motions
arising from the revolution of the earth in its orbit, from whence their
distance from the sun has been computed: α Centauri, the brightest star
in the southern hemisphere, is a very remarkable instance. Professor
Henderson at the Cape of Good Hope determined its parallax to be 1ʺ by a
series of observations on its position at opposite periods of the year,
that is, from opposite points in the earth’s orbit. The result was
afterwards confirmed by Mr. Maclear, who found the amount to be 0ʺ·913.
The difference between the two is wonderfully small, considering the
many unavoidable sources of error in the determination of such minute
quantities (N. 230).

Since no star in the northern hemisphere has so great an amount of
parallax, an arc of 1ʺ is assumed as the parallactic unit. Now radius is
to the sine of 1ʺ as 206,265 is to 1; hence, α Centauri is 206,265 times
more distant from the sun than the sun is from the earth. Light flying
at the rate of 192,000 miles in a second must take 3 years and 83 days
to come to us from that star.

One or two tenths of a second becomes a very great error when the
maximum amount of parallax is only 1ʺ, and on that account, with the
exception of α Centauri, it has been found impracticable to determine
the annual changes in the apparent motions of single stars affected by
precession, nutation, aberration, and the variations of temperature of
the instruments used in observing. However, as two stars in
juxtaposition are equally affected by all of these; the difference in
their motions is independent of them. Of two stars apparently in close
approximation, one may be far behind the other in space. They may seem
near to one another when viewed from the earth in one part of its orbit,
but may separate widely when seen from the earth in another position,
just as two terrestrial objects appear to be one when viewed in the same
straight line, but separate as the observer changes his position. In
this case the stars would not have real, but only apparent motion. One
of them would seem to oscillate annually to and fro in a straight line
on each side of the other, a motion that could not be mistaken for that
of a binary system where one star describes an ellipse about the other;
or if the edge of the orbit be turned towards the earth, where the
oscillations require years for their accomplishment. The only
circumstances that can affect the stars unequally, and which must be
eliminated, are the proper motion of the stars in space, and specific
aberration, a very minute quantity arising from peculiarities in the
star’s light. This method of finding the distances of the fixed stars
was proposed by Galileo and attempted by Dr. Long without success. Sir
William Herschel afterwards applied it to some of the binary groups; and
although he did not find the thing he sought for, it led to the
discovery of the orbital motions of the double stars.

M. Struve was the first to apply this method, and that in a very
difficult case. He perceived that a very small star is close to α Lyræ,
and by a series of most accurate differential measurements from 1835 to
1838 he found that α Lyræ has a parallax of 0ʺ·261, which was afterwards
corroborated by the observations of M. Peters; hence α Lyræ is 789,600
times more distant from the sun than the earth is.

It was natural to suppose that in general the large stars are nearer to
the earth than the small ones; but there is now reason to believe that
some stars, though by no means brilliant, are nearer to us than others
which shine with greater splendour. This is inferred from the
comparative velocity of their proper motions; all the stars have a
general motion of translation, which tends ultimately to mix those of
the different constellations; but none that we know of moves so rapidly
as 61 Cygni, and on that account it was reckoned to be nearer to us than
any other, for an object seems to move more quickly the nearer it is.
Now M. Bessel saw that two minute and probably very remote stars are
very near 61 Cygni, their directions from that star being at right
angles to one another; so that, during the revolution of the earth, one
of these distances was a maximum and the other a minimum alternately
every three months. This alternation, although it indicated a parallax
or difference of parallaxes of only 0ʺ·348, was maintained with such
perfect regularity every three months, that it leaves not a doubt of its
accuracy, which was afterwards confirmed by the observations of M.
Peters at Polkova. It follows from that small parallax that 61 Cygni
must be 592,700 times farther from the earth than the sun is—a distance
that light would not pass over in less than nine years and three months.

Mr. Henderson found the parallax of Sirius, the brightest of all the
stars, to be only 0ʺ·230; it is consequently more distant than 61 Cygni,
though the latter is but of the 6th magnitude.

M. Argelander has calculated that the apparent magnitude of the stars
depends upon their distance. Supposing them all to be of the same size,
the smallest visible in Sir William Herschel’s 20 feet reflecting
telescope, namely those of the 17th magnitude, would be 228 times
farther off than those of the first magnitude; and M. Peters of Polkova
from the annual parallax of thirty-five, seven of which are now very
accurately determined, has ascertained the distance of the nearest of
them to be such, that light flying at the rate of 95 millions of miles
in a second would take 15 years and a half to come from them to the
earth, and that a star of the 17th magnitude might be extinguished for
3541 years before we should be aware of it. (N. 231.)

The great gulfs that separate the stars from the sun, and probably from
one another, no doubt maintain the stability of the stellar system, in
the same manner that in the solar system the distances of the planets
from the sun and the satellites from their primaries are so arranged as
to preserve their mutual disturbances within due limits. The stars
supposed to be nearest the sun are probably in a great zone which
crosses the Milky Way between η Argûs and α Crucis. It comprises the
bright stars of the constellations Orion, Canis Major, the Southern
Cross, Centaur, Lupus, and Scorpio. The axis of the zone is inclined at
an angle of 20° to the medial line, or circle, passing through the
centre of the Milky Way.

A very great number of stars undergo periodical changes of lustre,
varying in some cases from complete extinction to their original
brilliancy, strongly suggesting the idea that they are temporarily
obscured, and sometimes completely hid, by opaque bodies revolving round
them in regular periodic times, as the planets do about the sun.

The star Mira, or ω Ceti, which was first noticed to be periodical by
Fabricius, in 1596, appears about twelve times in eleven years, or in
periods of 331^d 8^h 4^m 16^s; it remains at its greatest brightness
about a fortnight, being then on some occasions equal to a large star of
the second magnitude; then it decreases during about three months, till
it becomes completely invisible to the naked eye, in which state it
remains about five months; after that it continues increasing during the
remainder of its period. Such is the general course of its changes; but
it does not always return to the same degree of brightness, nor increase
and diminish by the same gradations, neither are the successive
intervals of its maxima equal. From the observations and investigations
of M. Argelander, the mean period given is subject to fluctuation,
embracing 88 such periods, and having the effect of gradually
lengthening and shortening alternately those intervals to the extent of
25 days one way and the other. The irregularities in the degree of
brightness attained at the maximum are probably also periodical. For
four years previous to 1676 it did not appear at all; and on October 5,
1839, it exceeded α Ceti, and equalled β Aurigæ, in lustre. These
irregularities may be occasioned by periodical perturbations among
opaque bodies revolving about the star. Algol, or β Persei, is another
very remarkable instance of a variable star. It has the size of a star
of the second magnitude for two days and thirteen and a half hours, and
then suddenly begins to diminish in splendour, till, in about three
hours and a half, it is reduced to the size of a star of the fourth
magnitude; it then begins again to increase, and in three hours and a
half more regains its brightness, going through all these vicissitudes
in 2^d 20^h 48^m 54^s·7. Sir John Herschel and Mr. Goodricke, by
whom the variable nature of this star was discovered in 1782, considered
this to be a case strongly indicative of the revolution of an opaque
body, which, coming between us and Algol, cuts off a large portion of
the light. This star has been constantly observed, and the more recent
observations, compared with the ancient ones, indicated a diminution in
the periodic time. It is even proved that this decrease is not uniformly
progressive, but is actually proceeding with accelerated rapidity,
which, however, will probably not continue, but will by degrees relax,
and then be changed into increase, according to the laws of periodicity,
which, as well as their causes, remain to be discovered. The first
minimum of this star, in 1844, happened on January 3rd, at 4^h 14^m
Greenwich time. γ Hydræ also vanishes and reappears every 494 days. β
Lyræ was discovered to be variable, in 1784, by Mr. Goodricke, and its
period was ascertained by Argelander to be 12^d 21^h 53^m 10^s, in
which time a double maximum and minimum takes place, the two maxima
being nearly equal, but the two minima unequal; besides these
semi-periods, there is a slow aberration of period, which appears to be
periodical itself: from its discovery to 1840 the time was continually
lengthening, but more and more slowly, till, in 1840, it ceased to
increase, and has since been slowly on the decrease.

The stars δ Cephei and η Aquilæ, or Antinoi, were discovered to be
variable in 1784; their respective periods, being 5^d 8^h 47^m 39^s
and 7^d 4^h 13^m 53^s, have since been accurately determined.
Besides these, the variations of between 30 and 40 have been
approximately ascertained, and a great many more among the smaller stars
have been discovered to be variable by Mr. Hind, who has remarked that
many of those stars which continue visible at their minimum appear hazy
and indistinct, as though some cloudy or nebulous medium intervened.
Some of the variable stars are red, and others present successive
changes through blue, yellow, and red. When the brightness is increasing
the star has a blueish tinge, when it is past its maximum lustre it
assumes a yellow tint, and while on its decrease it becomes ruddy with
flashes of bright red light. These changes are very marked in a small
star near the star 77, at the extremity of the south wing of Virgo.

Sir John Herschel, after having described the glory of the starry
heavens, asks, “For what purpose are we to suppose such magnificent
bodies scattered through the abyss of space? Surely not to illuminate
_our_ nights, which an additional moon of the thousandth part the size
of our own would do much better, nor to sparkle as a pageant void of
meaning and reality, and bewilder us with vain conjectures. Useful, it
is true, they are to man as points of exact and permanent reference; but
he must have studied astronomy to little purpose who can suppose man to
be the only object of his Creator’s care, or who does not see in the
vast and wonderful apparatus around us provision for other races of
animated beings. The planets, we have seen, derive their light from the
sun, but that cannot be the case with the stars. These doubtless then
are themselves suns, and may perhaps, each in its sphere, be the
presiding centre round which other planets or bodies, of which we can
form no conception from any analogy offered by our own system, may be
circulating.”

Another circumstance shows how probable it is that dark bodies are
revolving among the stars. The proper motion of Sirius is very
irregular—sometimes it is rapid, and at other times slow; the cause is
ascribed by MM. Bessel and Peters to a dark companion which revolves
with Sirius about their common centre of gravity, and by its attraction
disturbs the equable motion of the star.

Sometimes stars have all at once appeared, shone with a bright light,
and vanished. Several instances of these temporary stars are on record.
A remarkable one occurred in the year 125, which is said to have induced
Hipparchus to form the first catalogue of stars. Another star appeared
suddenly near α Aquilæ in the year 389, which vanished after remaining
for three weeks as bright as Venus. On the 10th of October, 1604, a
brilliant star burst forth in the constellation of Serpentarius, which
continued visible for a year; and on the 11th of November, 1572, a star
all at once shone forth in Cassiopeia, which rapidly increased in
brightness till it surpassed that of Jupiter so much as to be visible at
midday. It began to decrease in December of the same year, and, in
March, 1574, it had entirely disappeared, having exhibited a variety of
tints. It is suspected, however, that this star is periodically variable
and identical with stars which appeared in the years 945 and 1264. A
more recent case occurred in the year 1670, when a new star was
discovered in the head of the Swan, which, after becoming invisible,
reappeared, and, having undergone many variations in light, vanished
after two years, and has never since been seen. On the 28th of April,
1848, Mr. Hind discovered a star of the 5th magnitude in the
constellation Ophiuchus, which was very conspicuous to the naked eye,
and where he was certain no star even so bright as the 9th magnitude had
ever existed, nor was there any record of such a star. From the time of
its discovery it continued to diminish till it became extinct. Its
colour was ruddy, and was thought to undergo remarkable changes,
probably an effect of its low position, as its polar distance was 102°
39ʹ 14ʺ.

Sir John Herschel discovered very singular variations in the star η of
the constellation Argo. It is surrounded by a wonderful nebula, and
between the years 1677 and 1826 it varied twice from the 4th to the 2nd
magnitude; but in the beginning of 1838 it suddenly increased in lustre,
so as to be nearly as bright as α Centauri. Thence it diminished, but
not below the first magnitude till April 1843, when it had again
increased, so as to surpass Canopus, and nearly equal Sirius in
splendour. With regard to this singular phenomenon, Sir John Herschel
observes, that “Temporary stars heretofore recorded have all become
totally extinct. Variable stars, as far as they have been carefully
attended to, have exhibited periodical and regular alternations (in some
degree at least) of splendour and comparative obscurity; but here we
have a star fitfully variable to an astonishing extent, and whose
fluctuations are spread over centuries, apparently in no settled period,
and in no regular progression. What origin can we ascribe to these
sudden flashes and relapses? What conclusions are we to draw as to the
comfort or habitability of a system depending for its supply of light
and heat on so variable a source? Its future career will be a subject of
high physical interest. To this account I will only add, that in the
beginning of 1838 the brightness of this star was so great as materially
to interfere with the observations of that part of the nebula
surrounding it.” Sir John has also discovered that α Orionis is
variable, a circumstance the more remarkable as it is one of the
conspicuous stars of our hemisphere, and yet its changes had never been
remarked. The inferences Sir John draws from the phenomena of variable
stars are too interesting not to be given in his own words. “A periodic
change existing to so great an extent in so large and brilliant a star
as α Orionis cannot fail to awaken attention to the subject, and to
revive the consideration of those speculations respecting the
possibility of a change in the lustre of our sun itself, which were
first put forth by my father. If there be really a community of nature
between the sun and the fixed stars, every proof that we obtain of the
extensive prevalence of such periodical changes in those remote bodies
adds to the probability of finding something of the kind nearer home. If
our sun were ever intrinsically much brighter than at present, the mean
temperature of the surface of our globe would of course be
proportionally greater. I speak now not of periodical, but secular
changes. But the argument is complicated with the consideration of the
possible imperfect transparency of space, which may be due to material
non-luminous particles, diffused irregularly in patches analogous to
nebulæ, but of great extent—to cosmical clouds, in short, of whose
existence we have, I think, some indication in the singular and
apparently capricious phenomena of temporary stars, and perhaps in the
recent extraordinary increase, and hardly less sudden diminution, of η
Argûs.” Mr. Hind has come to the same conclusion with Goodricke and Sir
John Herschel, that the changes in the variable stars are owing to
opaque bodies revolving round them; indeed there are strong reasons to
believe that there are solar systems analogous to our own in the remote
regions of space. Our sun requires nine times the period of Algol to
perform a revolution on its axis, while, on the other hand, the periodic
time of an opaque revolving body, sufficiently large to produce a
similar temporary obscuration of the sun seen from a fixed star, would
be less than fourteen hours.

It is possible that the decrease of light in some of the variable stars
may arise from large spots on their surface, like those occasionally
seen in the radiant fluid masses on the surface of the sun. One of these
spots which was measured by Sir John Herschel on the 20th of March,
1836, with its penumbra, occupied an area of 3780 millions of square
miles; and the black central part of a spot that appeared on the 25th of
May following would have allowed the globe of the earth to drop through
it, leaving a thousand miles clear of contact all around this tremendous
abyss.

All the variable stars on record of which the places are distinctly
indicated have occurred without exception in, or close upon, the borders
of the Milky Way, and that only within the following semicircle, the
preceding having offered no example of the kind.

Many stars have actually disappeared from the heavens. 42 Virginis seems
to be of the number, having been missed by Sir John Herschel on the 9th
of May, 1828, and not again found, though he frequently had occasion to
observe that part of the sky. Mr. Cooper, of the Markree Observatory,
has given a list of fifty stars that are missing since the publication
of his list of stars in 1847. Comparing the present state of the heavens
with more ancient catalogues, a much greater number have disappeared.

Thousands of stars that seem to be only brilliant points of light, when
carefully examined are found to be in reality systems of two or more
suns, many of which are known to revolve about one another. These binary
and multiple systems are very remote, requiring powerful telescopes to
show the stars separately. They are divided into eight classes,
according to the proximity of the two stars. The first class comprises
only such as are less than 1ʺ of space apart; those of the second class
are more apart than 1ʺ and less than 2ʺ, &c. &c. Sometimes the two stars
are of equal magnitude, but more frequently a conspicuous star is
accompanied by a smaller companion. In some cases the conspicuous star
itself is double, as in ζ Cancri, ξ Scorpio, 11 Monocerotis, and 12
Lyncis, which are triple stars. Each of the two stars of ε Lyræ is a
beautiful and close double star; so that which in a common telescope
appears merely to be a double star, is found to be quadruple with a very
excellent instrument. The multiple system of θ Orionis is one of the
most remarkable objects in our hemisphere. To the naked eye and with an
ordinary telescope it seems to be a single star, but it really consists
of four brilliant stars forming a trapezium, and accompanied by two
excessively minute and very close companions, to perceive _both_ of
which is the severest test of a telescope.

The first catalogue of double stars in which their places and relative
positions are given was accomplished by the talent and industry of Sir
William Herschel, who made so many great discoveries, and with whom the
idea of their combination in binary and multiple systems originated; and
that important fact he established by the discovery of a revolving
motion in 50 or 60, and by the determination of the revolution of one
star about the other of Castor or α Geminorum, the largest and finest
double star in the northern hemisphere. He even assigned the approximate
periodic times of this and of several other binary systems. More than
100 stars are now known to be stellar systems. The positions of many
hundreds were measured by Sir John Herschel and Sir James South; and the
catalogue of the double stars in the northern hemisphere, which have
been micrometrically measured, has been increased to more than 6000 by
MM. Bessel, Struve, and British astronomers.

Extensive catalogues of double stars in the southern hemisphere have
been published by the astronomers in our colonial establishments. To
these Sir John Herschel added 1081 during his residence at the Cape of
Good Hope: the angles of position and distances of the stars from one
another he measured, and found that many of them have very rapid orbital
motions. The elliptical elements of the orbits and periodic times of
fifteen have been determined by the most eminent astronomers with
wonderful accuracy, considering the enormous distances and the extreme
delicacy and difficulty of the subject. M. Savary has the merit of
having first determined the elements of the orbit of a double star from
observation. The difficulty of doing so is great, because the nearest
fixed star is 211,000 times farther from the sun than the earth is, and
the orbit itself is only visible with the best telescopes; consequently
a very small error in observation occasions an enormous error in the
determination of quantities at that distance.

In observing the relative position of the stars of a binary system, the
distance between them, and also the angle of position, that is, the
angle which the meridian, or a parallel to the equator, makes with the
line joining the two stars, are measured. The different values of the
angle of position show whether the revolving star moves from east to
west, or the contrary; whether the motion be uniform or variable, and at
what points it is greatest or least. The measures of the distances show
whether the two stars approach or recede from one another. From these
the form and nature of the orbit are determined. Were observations
perfectly accurate, four values of the angle of position, and of the
corresponding distances at given epochs, would be sufficient to assign
the form and position of the curve described by the revolving star;
this, however, scarcely ever happens. The accuracy of each result
depends upon taking the mean of a great number of the best observations,
and eliminating error by mutual comparison. The distances between the
stars are so minute that they cannot be measured with the same accuracy
as the angles of position; therefore, in order to determine the orbit of
a star independently of the distance, it is necessary to assume, as the
most probable hypothesis, that the stars are subject to the law of
gravitation, and consequently that one of the two stars revolves in an
ellipse about the other, supposed to be at rest, though not necessarily
in the focus. A curve is thus constructed graphically by means of the
angles of position and the corresponding times of observation. The
angular velocities of the stars are obtained by drawing tangents to this
curve at stated intervals, whence the apparent distances, or radii
vectores of the revolving star, become known for each angle of position,
because, by the laws of elliptical motion, they are equal to the square
roots of the apparent angular velocities. Now that the angles of
position estimated from a given line, and the corresponding distances of
the two stars, are known, another curve may be drawn, which will
represent on paper the actual orbit of the star projected on the visible
surface of the heavens; so that the elliptical elements of the true
orbit, and its position in space, may be determined by a combined system
of measurements and computation. But, as this orbit has been obtained on
the hypothesis that gravitation prevails in these distant regions, which
could not be known _à priori_, it must be compared with as many
observations as can be obtained, to ascertain how far the computed
ellipse agrees with the curve actually described by the star.

γ Virginis consists of two stars of nearly the same magnitude; they were
so far apart in the beginning and middle of last century, that they were
mentioned by Bradley, and marked in Mayer’s catalogue, as two distinct
stars. Since that time they have been continually approaching each
other, till in January, 1836, one star was seen to eclipse the other, by
Admiral Smyth at his Observatory at Bedford, and by Sir John Herschel at
the Cape of Good Hope. A series of observations since the beginning of
the present century has enabled Sir John to determine the form and
position of the elliptical orbit of the revolving star with
extraordinary truth by the preceding method. According to his
calculation, it came to its perihelion on the 18th of August of the year
1834. Its previous velocity was so great that the revolving star
described an angle of 68° in one year. By the laws of elliptical motion
its angular velocity must diminish till it arrives at its aphelion. The
accuracy with which the motions of the binary systems are measured, and
the skill employed in the deduction of the elliptical elements, are now
so great, that the periodic time of γ Virginis, determined by Sir John
Herschel and Admiral Smyth from their respective observatories, combined
with those of Sir William Herschel, only differ by two years, Sir John
having obtained a period of 182 years, Admiral Smyth that of 180. By the
aid of more numerous observations Mr. Fletcher has found that the true
period is 184·53 years, and that the revolving star passed its
perihelion in 1837. It is by such successive steps that astronomy is
brought to perfection (N. 232).

Some of the double stars have very long periods, such as ς Coronæ, where
the revolving star takes 737 years nearly to accomplish a circuit.
Others again have very short periods, as η Coronæ, ζ Cancri, and ξ Ursæ
Majoris, whose periodic times are 42·500, 58·91, and 58·26 years
respectively: therefore each of these has performed more than one entire
revolution since their motions were observed. ζ Herculis, whose periodic
time is only about 30-1/4 years, has accomplished two complete circuits,
the lesser star having been eclipsed by the greater each time. The first
of these two truly wonderful events, of one sun eclipsing another sun,
was seen by Sir William Herschel in 1782.

The orbits and periodic times of so many of these binary systems having
been determined proves beyond a doubt that sun revolves about sun in the
starry firmament by the same law of gravitation that makes the earth and
planets revolve about the sun (N. 232).

Since the parallax of 61 Cygni and that of α Centauri have been
determined, Sir John Herschel has made the following approximation to
the dimensions of their orbits and masses. The distance between the two
stars of 61 Cygni, that is the radius vector of the revolving star, has
hardly varied from 15ʺ·5 ever since the earliest observations; while in
that time the star has moved through 50°; it is evident therefore that
the orbit must be nearly circular. It is at right angles to the visual
ray, and the periodic time is 514 years. The parallax or radius of the
earth’s orbit as seen from the star is 0ʺ·348, while the radius of the
star’s orbit as seen from the earth is 15ʺ·5; hence the radius of the
star’s orbit is to that of the earth’s orbit as 15ʺ·5 to 0ʺ·348, or
nearly as 45 to 1. So the orbit described by the two stars of 61 Cygni
about one another greatly exceeds that which Neptune describes about the
sun. Since the mean distance of the stars and their periodic time are
given, the sum of the masses of the two stars is computed to be 0·3529,
that of the sun being 1. Thus our sun is not vastly greater nor vastly
less than the stars composing 61 Cygni, which is a small inconspicuous
star to the naked eye, not exceeding the 6th magnitude.

Of all the double stars α Centauri is the most beautiful: it is the
brightest star in the southern hemisphere, equal, if not superior, to
Arcturus in lustre. The distance between the two stars has been
decreasing at the rate of half a second annually since the year 1822,
while the angular motion has undergone very little change, which shows
that the plane of the orbit passes through the earth like the orbits of
44 Boötes, and π Serpentarii; that is to say, the edge of the orbit in
these three stellar systems is presented to the earth, so that the
revolving star seems to move in a straight line, and to oscillate on
each side of its primary. Were this libration owing to parallax, it
would be annual from the revolution of the earth about the sun; but as
years elapse before it amounts to a sensible quantity, it can only arise
from a real orbital motion seen obliquely. In this case five
observations are sufficient for the determination of the orbit, provided
they be exact; but the quantities to be measured are so minute, that it
is only by a very long series of observations that accuracy can be
attained. In 1834 Captain Jacob determined the periodic time of the
revolving star of α Centauri to be 77 years, and the distance between
the two to be 17ʺ·5; and since the decrease is half a second annually,
the distance or radius vector of the revolving star was 12ʺ·5 in the
year 1822; and as Mr. Henderson had determined the parallax or radius of
the earth’s orbit as seen from the star to be ·913, it follows that the
real semi-axis of the revolving star’s orbit is 13-1/2 times greater
than the semi-axis of the earth’s orbit as a minimum. The real
dimensions of the ellipse therefore cannot be so small as the orbit of
Saturn, and may possibly exceed that of Uranus. It is very probable that
an occultation of one of the suns by the other will take place in 1867,
or a very close appulse of the two stars.

Singular anomalies have appeared in the motions of 70 Ophiuchi, which
was discovered to be a binary system by Sir William Herschel in 1779,
and which has since nearly accomplished a revolution. Various orbits
have been computed: those which best represent the angles of position
fail with regard to the distances of the stars from one another, and
_vice versâ_. But it is a very remarkable fact that the errors are
periodical, being for considerable periods of time alternately in excess
and defect. Captain W. S. Jacob, who determined the periodic time of the
revolving star to be 93 years, attributes this anomaly to the disturbing
action of an opaque body revolving round the lesser star. Assuming that
to be the case, and computing, he found that the errors were
considerably diminished both in the angle of position and distance. It
is a subject of the highest interest, and well worthy of the attention
of such astronomers as have the means of making the necessary
observations. Among the triple systems, as ζ Cancri, two of the stars
revolve about one another in 58·9 years; but the motion of the third and
most distant is so slow, that it has only accomplished a tenth part of
its revolution about the other two since the system was discovered.

It appears from the calculations of Mr. Dunlop that ς Eridani
accomplishes a revolution in little more than 30 years. The motion of
Mercury is more rapid than that of any of the planets, being at the rate
of 107,000 miles an hour. The perihelion velocity of the comet of 1680
was 880,000 miles an hour; but, if the two stars of ς Eridani, or of ξ
Ursæ Majoris, be as remote from one another as the nearest fixed star is
from the sun, the velocity of the revolving star must exceed the power
of imagination to conceive. The elliptical motion of the double stars
shows that gravitation is not confined to the planetary motions, but
that systems of suns in the far distant regions of the universe are also
obedient to its laws. The stellar systems present a kind of sidereal
chronometer, by which the chronology of the heavens will be marked out
to future ages by epochs of their own, liable to no fluctuations from
such disturbances as take place in our system. Some stars are apparently
double, though altogether unconnected, one being far behind the other in
space, as α Lyræ, which apparently consists of two stars, one of the
first, the other of the eleventh magnitude. Aldebaran, α Aquilæ, and
Pollux are remarkable instances of these optically double stars. It has
been shown how favourable that circumstance is for ascertaining the
parallax of the nearest of the two. (N. 232.)

The double stars are of various hues: sometimes both stars are of the
same colour, as in α Centauri and 61 Cygni, where the larger stars are
of a bright orange and the smaller ones a deeper tint of the same, but
they most frequently exhibit the contrasted colours. The large star is
generally yellow, orange, or red; and the small star blue, purple, or
green. Sometimes a white star is combined with a blue or a purple, and
more rarely a red and white are united. In many cases these appearances
are due to the influence of contrast on our judgment of colours. For
example, in observing a double star, where the large one is a full ruby
red, or almost blood colour, and the small one a fine green, the latter
loses its colour when the former is hid by the cross wires of the
telescope. That is the case with γ Andromedæ, which is a triple star,
the small one, which appears green, being closely double. ι Cancri is an
instance of a large yellow star and a small one which appears blue by
contrast. Still there are a vast number where the colours are decidedly
different, and suggest the curious idea of two suns, a red and a green,
or a yellow and a blue, so that a planet circulating round one of them
may have the variety of a red day and a green day, a yellow day and a
blue day. Sir John Herschel observes, in one of his papers in the
Philosophical Transactions, as a very remarkable fact, that, although
red stars are common enough, no example of a solitary blue, green, or
purple star has yet been produced.

Sirius is the only star on record whose colour has changed. In the time
of Ptolemy it was red; now it is one of the whitest stars in the
heavens.

M. Struve has found that, out of 596 bright double stars, 375 pairs have
the same intensity of light and colour; 101 pairs have different
intensity, but the same colour; and 120 pairs have the colours of the
two stars decidedly different.

Certain rays, which exist in the sun’s light, are wanting in the spectra
of every coloured star, and probably never existed in the light of these
stars, as there is no reason to believe that they are absorbed by the
stars’ atmosphere, though they may be by the earth’s. There are no
defective rays in the white light of Sirius, Procyon, and others; but
Sir David Brewster found in the spectrum of the orange-coloured light of
ζ Herculis a defective band in the red space, and two or more in the
blue; consequently, the orange colour of the star is owing to a want of
blue rays; for flames in which certain rays are wanting take the colour
of the predominating rays. If the black rays in the solar spectrum were
owing to the absorption of the sun’s atmosphere, the light from the
margin of his disc, having to pass through a greater thickness of it,
would exhibit deeper lines than that which comes from his centre; but,
as no difference is perceptible, it may be inferred that the analogous
bands in the light of the coloured stars are not due to the absorption
of their atmospheres, but that they arise from the different kinds of
combustion by which these bodies are lighted up.

All the ordinary methods fail for finding the parallax when the
distances of the stars are very great. An angle even of one or two
seconds, viewed in the focus of our largest telescopes, does not equal
the thickness of a spider’s thread, which makes it impossible to measure
such minute quantities with any degree of accuracy. In some cases,
however, the binary systems of stars furnish a method of estimating an
angle of even the tenth of a second, which is thirty times more accurate
than by any other means. From them the actual distances of some of the
more remote stars will ultimately be known.

Suppose that one star revolves round another in an orbit which is so
obliquely seen from the earth as to look like an ellipse in a horizontal
position, then it is clear that one-half of the orbit will be nearer to
us than the other half. Now, in consequence of the time which light
takes to travel, we always see the satellite star in a place which it
has already left. Hence, when that star sets out from the point of its
orbit which is nearest to us, its light will take more and more time to
come to us in proportion as the star moves round to the most distant
point in its orbit. On that account the star will appear to us to take
more time in moving through that half of its orbit than it really does.
Exactly the contrary takes place on the other half; for the light will
take less and less time to arrive at the earth in proportion as the star
approaches nearer to us; and therefore it will seem to move through this
half of its orbit in less time than it really does. This circumstance
furnishes the means of finding the absolute breadth of the orbit in
miles, and from that the true distance of the star from the earth. For,
since the greatest and least distances of the satellite star from the
earth differ by the breadth of its orbit, the time which the star takes
to move from the nearest to the remotest point of its orbit is greater
than it ought to be by the whole time its light takes to cross the
orbit, and the period of moving through the other half is exactly as
much less. Hence the difference between the observed times of these two
semi-revolutions of the star is equal to twice the time that its light
employs to cross its orbit; and, as we know the velocity of light, the
diameter of the orbit may be found in miles, and from that its whole
dimensions; for the position of the orbit with regard to us is known by
observation, as well as the place, inclination, and apparent magnitude
of its major axis, or, which is the same thing, the angle under which it
is seen from the earth. Since, then, three things are known in this
great triangle, namely, the base or major axis of the orbit in miles,
the angle opposite to it at the earth, and the angle it makes with the
visual ray, the distance of the satellite star from the earth may be
found by the most simple of calculations. The merit of having first
proposed this very ingenious method of finding the distance of the stars
is due to M. Savary; but, unfortunately, it is not of general
application, as it depends upon the position of the orbit, and a long
time must elapse before observation can furnish data, since the shortest
period of any revolving star that we know of is 30 years. Still the
distances of a vast number of stars may ultimately be made out in this
way; and, as one important discovery almost always leads to another,
their masses may thus be weighed against that of the earth or sun.

The only data employed for finding the mass of the earth, as compared
with that of the sun, are, the angular motion of our globe round the sun
in a second of time, and the distance of the earth from the sun in miles
(N. 233). Now, by observations of the binary systems, we know the
angular velocity of the small star round the great one; and, when we
know the distance between the two stars in miles, it will be easy to
compute how many miles the small star would fall through by the
attraction of the great one in a second of time. A comparison of this
space with the space through which the earth would descend towards the
sun in a second will give the ratio of the mass of the great star to
that of the sun or earth. According to M. Bessel, the weight of the two
stars of 61 Cygni is equal to half the weight of the sun. Little as we
know of the absolute magnitude of the fixed stars, the quantity of light
emitted by many of them shows that they must be much larger than the
sun. Dr. Wollaston determined the approximate ratio which the light of a
wax candle bears to that of the sun, moon, and stars, by comparing their
respective images reflected from small glass globes filled with mercury,
whence a comparison was established between the quantities of light
emitted by the celestial bodies themselves. By this method he found that
the light of α Lyræ is five and a half times greater than that of the
sun. Sir John Herschel reflected the moon’s light _totally_ by a prism,
which, concentrated by a lens, was compared directly with that of α
Centauri. After making allowance for the quantity of the moon’s light
lost in passing through the lens and prism, he found that the mean
quantity of light sent to the earth by a full moon exceeds that sent by
α Centauri in the proportion of 27,408 to 1. Now, Dr. Wollaston found
the proportion of the sun’s light to that of the full moon to be that of
801,072 to 1. Hence, the light sent to us by the sun is to that sent by
α Centauri as about twenty-two thousand millions to one. But, as the
parallax of α Centauri is 1ʺ, it really is two and a half times brighter
than the sun. The light of Sirius is four times that of α Centauri, but
its parallax is only 0ʺ·230: hence it has an intrinsic splendour 63·02
times that of our luminary. It is therefore estimated to be a hundred
times as large; so that, were Sirius in the earth’s place, its surface
would extend 150 times as far as the orbit of the moon. The light of
Sirius, according to the observations of Sir John Herschel, is 324 times
greater than that of a star of the sixth magnitude; if we suppose the
two to be really of the same size, their distances from us must be in
the ratio of 57·3 to 1, because light diminishes as the square of the
distance of the luminous body increases.

So many of the stars have proper motions altogether independent of the
annual rotation of the earth in its orbit, that it may be doubted
whether there be such a thing as a fixed star. Groombridge is the most
rapid known: it has a proper motion of 7ʺ of arc annually; α Centauri
moves at the rate of 3ʺ·58 annually, and 61 Cygni describes a line in
space of 5ʺ·12 in the same time. These motions are probably in curves,
but at the distance of the earth they will appear to be rectilineal for
ages to come. The motion of little more than five seconds of space,
which 61 Cygni describes annually, seems to us to be extremely small;
but at the distance of that star an angle of one second corresponds to
twenty-four millions of millions of miles; consequently the annual
motion of 61 Cygni is 120 millions of millions of miles, and yet, as M.
Arago observes, we call it a fixed star. From the same cause it is
evident that the crowding of the stars in the Milky Way may be apparent
only, and that the stars may be at vast distances from one another, and
no doubt are.

Were the solar system and the whole of the stars visible to us carried
forward in space by a motion common to all, like ships drifting in a
current, it would be impossible for us, moving with the rest, to
ascertain its direction. Sir William Herschel perceived that a great
part of the motions of the stars is only apparent, arising from a real
motion of the sun in a contrary direction. Among many discrepancies he
found that the stars in the northern hemisphere have a general tendency
to move towards a point diametrically opposite to λ Herculis, which he
attributed to a motion of the solar system in a contrary direction. For
it was evident to him, that the stars, from the effects of perspective
alone, would seem to diverge in the direction to which the solar system
was going, and would converge towards the space it had left, and that
there would be a regularity in these apparent motions which would
hereafter be detected. Since Sir William Herschel’s time the proper
motions of the stars have been determined with much greater accuracy,
and many have been added to the list by comparing the ancient and modern
tables of their places; his views have been established by four of the
greatest astronomers of the age, MM. Lundahles, Argelander, Otto Struve,
and Peters, who have clearly proved the motion of the sun from that of
the stars in the northern hemisphere, and Mr. Galloway has come to the
same conclusion from the motions of the stars in the southern hemisphere
(N. 234). The result is, that the sun, accompanied by all his attendant
planets, is moving at the rate of 422,424 miles—or over a space nearly
equal to his own diameter—in the course of a day, and that the motion is
directed towards a point in a line joining the two stars μ and π
Herculis at a quarter of the apparent distance of these two stars,
reckoning from π Herculis. This investigation was founded upon no law
assumed or observed, such as the circulation of all the stars of our
firmament about a common centre, though philosophers have speculated as
to the probability of such a motion in the sun and stars in the plane of
the Milky Way. Should the sun and his stellar companions be moving in a
nearly circular orbit, the centre of motion would be in the plane
passing through the sun perpendicular to the direction of his motion.
The constellations through which that great circle would pass are
Pisces, Australis, Pegasus, Andromeda, Perseus, &c. M. Argelander is of
opinion that the sun’s orbit is nearly in the plane of the Milky Way,
and, therefore, that its centre must probably be in Perseus, while M.
Mädler places it in the Pleiades, which seems to be inadmissible; but
the data are too uncertain at present to admit of any absolute
conclusion as to the sun’s orbit and the general motion of the stellar
firmament: for though the stars in every region of the sky tend towards
a point in Hercules, it is not yet known whether their motions are
uniform or variable, whether the sun’s motion be gradually changing, and
whether the stars form different independent systems, each having its
own centre of attraction, or if all obey one powerful controlling force
which pervades the whole universe. Accurate observations of the places
of a select number of stars of all dimensions in the Milky Way continued
for a series of years would no doubt decide this point.

The proper motion of a star combined with the progressive velocity of
light alters the apparent periodic time of the revolving star of a
binary system. If the orbit of a double star be at right angles to the
visual ray, and both the sun and the star at rest, the periodic time of
the revolving star, say of 10,000 days, would always be the same. But if
the centre of gravity of the star were to recede in a direct line from
the sun with the velocity of one tenth of the radius of the earth’s
orbit in a day, then at the end of 10,000 days it would be more remote
from us by 1000 of such radii—a space light would take 57 days to
traverse: hence, although the periodic time of the star would really be
the same, the completion of its period would only be known to us 57 days
after it had taken place, so that the periodic time would appear to us
to be 10,057 days instead of 10,000. Were the star to approach to the
sun by the same quantity instead of receding, the apparent periodic time
would be diminished by 57 days.

As the sun is only a unit in the stellar system, so the Milky Way, and
all the stars that adorn the firmament of both hemispheres, constitute a
group which is but a unit among the infinite numbers of starry clusters
and nebulæ that are profusely scattered throughout the universe.

By the aid of a good telescope there may be seen on the clear vault of
heaven, between the stars of our own stellar system, and far in the
depths of space, an immense multitude of objects like comets or clouds
of white vapour of all forms and sizes. Some are mixed with stars,
others are entirely formed of them. Many appear as if they were stellar,
but required a telescope of higher power to resolve them, and vast
numbers appear to be matter rarefied in the highest possible degree,
giving no indication of a stellar nature; and these are in every state
of condensation, from a vague film hardly to be discerned to such as
have actually arrived at a solid nucleus of stars. The cloudy appearance
is merely the blending of the rays of innumerable stars which are
themselves invisible from their extreme distance, like parts of the
Milky Way. Sir William Herschel was at first of that opinion, and the
nebulæ that have been resolved by Lord Rosse’s telescope have led
astronomers to believe that such is the case. Yet the tails of comets,
the zodiacal light, and the extensive luminous atmospheres which
encompass many of the stars, show that, in all probability, a
self-luminous phosphorescent material substance in a highly diluted or
gaseous form exists in vast abundance.

The number of the nebulæ, like that of the stars, is only limited by the
imperfection of our instruments, for each improvement in the telescope
only enables us to penetrate a little farther into the infinity of
space—to see a few more of these shadowy existences in the far distance,
and to resolve a few more of those that are comparatively near. Sir
William Herschel examined the nature and determined the position of 2500
nebulæ in the northern hemisphere whose places were computed from his
observations, reduced to a common epoch, and arranged into a catalogue,
in order of right ascension, by his sister, Miss Caroline Herschel, who
added lustre to the name she bore by her eminence in astronomical
knowledge and discovery. Sir John Herschel revised his father’s
observations, and added 800 nebulæ to the catalogue before he went to
the Cape of Good Hope, in order to complete the survey of the heavens.
On his return he published a catalogue of 2049 nebulæ of the southern
hemisphere, of which 500 were previously unknown, with their position in
the heavens. In a work unparalleled for elegance of style, depth of
knowledge, and originality of views, he has given engravings from his
drawings of the most remarkable objects, so that whatever changes may
take place in their form, place, or condensation, will be known by
astronomers of future ages.

Though infinite in variety, the nebulæ are of two distinct classes; one
consists of patches of great dimensions, capriciously irregular,
assuming all the fantastic forms of clouds, now bright, now obscure;
sometimes like vapour flying before the wind; sometimes stretching long
arms into space. Many present an ill-defined surface, in which it is
difficult to say where the centre of the greatest brightness is. Large
portions are resolvable into stars; many have a granulated appearance,
as if they were resolvable; and others probably are not so merely from
the smallness and closeness of the stars, and possibly from their
remoteness, indicating the complex and irregular form the Milky Way
would present if seen from a distance. A wonderful nebula of this kind
is visible to the naked eye in the constellation of Orion; it is of vast
extent, sending branches even into the southern hemisphere; and,
although Lord Rosse’s telescope has resolved much that had hitherto
resisted others, there are parts that still maintain their nebulous
appearance from extreme remoteness, presenting a kind of mottled aspect,
like flocks or wisps of wool, or mackerel sky. There can be no doubt of
its being an unfathomable congeries of stars, which there is reason to
believe has changed its form in some parts within the last fifty years.
Vast multitudes of nebulæ of this kind are so faint as to be with
difficulty discerned at all till they have been for some time in the
field of the telescope, or are just about to quit it. Occasionally they
are so vague, that the eye is conscious of something being present,
without being able to define what it is; but the unchangeableness of its
position convinces the mind that it is a real object—“an image was
before mine eyes, but I could not discern the form thereof.”

No drawing can give an idea of the boundaries of such nebulæ as that of
Orion; even with Lord Rosse’s telescope the edges either fade into a
luminous mist, which becomes more rare till it is imperceptible, or end
in a tissue of faintish flocculi, or in filaments which become finer and
more scattered till they cease to be visible, showing that the real
boundaries have not been seen.

The other class of nebulæ, vastly inferior in size, of definite forms
and great variety of character, are scattered through the remote
heavens, or congregated in a great nebulous district far from the Milky
Way. Many cling to stars like wisps of clouds, others are exactly like
comets with comæ and tails; but the most definite forms are annular and
lenticular nebulæ, nebulous stars, planetary and elliptical nebulæ, and
starry clusters. However, there are two in the northern hemisphere
differing from all of these, which are described by Sir John Herschel as
amazing objects. One in Vulpecula is like an hourglass or dumb bell of
bright matter, surrounded by a thin hazy atmosphere so as to give the
whole an oval form, or the appearance of an oblate spheroid; with a
higher optical power its form is much the same, but the brighter part is
resolved into stars, and the hazy part, though still nebulous, assumes
that mottled appearance which shows that the whole is a stellar system
of the most peculiar structure: it is a phenomenon that bears no
resemblance to any known object. (Fig. 3, plate 8, and fig. 3, plate 9).
The other is indeed most wonderful, and its history shows the gradual
increase in the space-penetrating power of telescopes. To Messier it
appeared merely to be a double nebula with stars; with Sir William
Herschel’s telescope it presented the appearance of a bright round
nebula encompassed at a little distance by a halo or glory, and
accompanied by a companion; while in Sir John Herschel’s 20 feet
reflector it appeared to “consist of a bright round nucleus, surrounded
at a distance by a nebulous ring split through half its circumference,
and having the split portions separated at an angle of 45 degrees each
to the plane of the other.” (Fig. 1, plate 10.) This nebula appeared to
Sir John to “bear a strong similitude to the Milky Way, suggesting the
idea of a brother system bearing a real physical resemblance and strong
analogy of structure to our own.”

This object, which disclosed to Lord Rosse the astonishing phenomenon of
spiral nebulæ seen in his telescope, presents the appearance of the fig.
1 in plate 10, in which the partial division of the limb of the ring
into two branches is at once recognised in the bright convolutions of
the spiral. The outlying nebula is connected by a narrow curved band of
light with the ring; the whole is either resolved into stars, or
evidently might be with a still higher optical power. With regard to the
marvellous nebula in question Lord Rosse observes, that “with each
increase of optical power the structure has become more complicated, and
more unlike anything that could result from any form of a dynamical law
of which we find a counterpart in our system. The connection of the
companion with this great nebula, of which there is not the least doubt,
adds to the difficulty of forming any hypothesis. It is impossible that
such a system could exist without internal movement, to which may be
added a resisting medium; but it cannot be regarded as a case of mere
static equilibrium.” This is by no means the only instance of a spiral
nebula; Lord Rosse has discovered several others: some are easily
seen—others require the highest powers of his telescope. From the
numerous offsets that branch from the Milky Way and run far into space,
it may possibly partake also of the spiral form.

There are seven annular nebulæ in the northern hemisphere, since Lord
Rosse has discovered that five of the planetary nebulæ belong to this
class. One of the finest examples of an annular nebula is to be seen
midway between β and γ Lyræ (fig. 2, plate 9). According to Sir John
Herschel, it is elliptical in the ratio of 4 to 5, and is sharply
defined—the internal opening occupying about half the diameter. This
opening is not entirely dark, but filled with a faint hazy light like
fine gauze stretched over a hoop. Its diameter, if it is as far from us
as 61 Cygni, must be 1300 times greater than the diameter of the earth’s
orbit—dimensions that are most astounding. Lord Rosse’s telescope
resolves this object into stars of extreme minuteness, with filaments of
stars adhering to its edges and a pretty bright star in its interior.
These rings are like hollow shells whose borders seem brighter because
the nebulous substance, whatever it may be, is more condensed to
appearance than the central part. The other annular nebula in the
northern hemisphere described by Sir John Herschel is a small faint
object, and more easily resolvable into stars. One of the annular nebulæ
seen by Lord Rosse is surrounded by a faint external flat ring; another
has ansæ, as if an annular nebulous ring encompassed it and was
foreshortened. Two annular nebulæ have perforations as if the black sky
was seen through openings in the interior haze, for in no instance is
the central opening quite dark.

Some nebulæ are like very elliptical annular systems seen obliquely. If
they be elliptical flat rings, the dark centre may be a real opening;
but should the systems be a series of very long elliptical concentric
shells surrounding a hollow, the dark axis may be merely a line of
comparative darkness.

The connection of the elliptical nebulæ with double stars is mentioned
as very remarkable. In one elliptical nebula whose longer axis is 50ʺ
there are two individuals of a double star each of the 10th magnitude
symmetrically placed rather nearer the vertex of the ellipse than the
foci; in another the stars are unequal, but placed exactly at the
extremities of the major axis, as in plate 8: besides these there are
several other instances.

Double nebulæ are not unfrequent in both hemispheres, exhibiting all the
varieties of distance, position, and relative brightness, with their
counterparts the double stars. The rarity of single nebulæ as large,
faint, and as little condensed in the centre as these, makes it
extremely improbable that two such bodies should be accidentally so near
as to touch, and often in part to overlap each other, as these do. It is
much more likely that they constitute systems; and, if so, it will form
an interesting object of future inquiry to discover whether they possess
orbital motion.

Nebulous stars are beautiful objects, quite different from all the
preceding. They are round or oval, increasing in density towards the
centre. Sometimes the central matter is so vividly and sharply condensed
and defined that the nebula might be taken for a bright star surrounded
by a thin atmosphere. One is a star of the 8th magnitude exactly in the
centre of a round bright atmosphere 25ʺ in diameter; the star is quite
stellar, and not a nucleus: it has not the smallest appearance of being
resolvable. Another nebulous star is ι Orionis, which has a broad
atmosphere in which is a dark cavity not symmetrical with the star, and
a small double star with a similar opening on the edge of the
atmosphere. Lord Rosse observes that these openings appear to be of the
same nature with that within the bright stars in the trapezium of Orion,
the stars being at its edge; and he is convinced that the stars are not
only connected with the nebula, but that they are equidistant with it;
hence, if their parallax can be found, the distance of this nebula would
be determined. The zodiacal light or lenticular shaped luminous haze
surrounding the sun which may be seen extending beyond the orbits of
Mercury and Venus soon after sunset in the months of April and May, or
before dawn in November and December, seems to place our luminary in the
class of nebulous stars. The extensive and delicate atmosphere of these
nebulous stars assumes all degrees of ellipticity, from the circular to
the spindle-shaped ray, or almost the right line.

Planetary nebulæ have exactly the appearance of planets with round or
oval discs, sometimes sharply terminated, at other times hazy and
ill-defined. Their surface, which is blue or blueish white, is equable
or slightly mottled, and their light occasionally rivals that of the
planets in vividness. They are generally attended by minute stars, which
give the idea of accompanying satellites. These nebulæ are of enormous
dimensions. One near γ Aquarii has a sensible diameter of about twenty
seconds, and another presents a diameter of twelve. Sir John Herschel
has computed that, if these objects be as far from us as the stars,
their real magnitude, on the lowest estimation, must be such as would
fill the orbit of Uranus. He concludes that, if they be solid bodies of
a solar nature, their intrinsic splendour must be far inferior to that
of the sun, because a circular portion of the sun’s disc subtending an
angle of twenty seconds would give a light equal to that of a hundred
full moons; while, on the contrary, the objects in question are hardly,
if at all, visible to the naked eye. From the uniformity of the discs of
these planetary nebulæ, and their apparent want of condensation, he
presumes that they may be hollow shells emitting light from their
surface only. The southern hemisphere is very rich in them, where
twenty-eight or twenty-nine have been discovered, some in the midst of a
cluster of stars, with which they form a beautiful contrast. Three are
of a decided blue colour, one Prussian blue, or verditer green, the
other two of a bright sky blue, of great beauty and delicacy. One seems
to belong to the class of double nebulæ or double stellar nebulæ of the
utmost remoteness. Since Lord Rosse’s telescope has shown that five of
the planetary nebulæ are annular, some of those in the southern
hemisphere may ultimately be found to belong to the same class.

Probably nine tenths at least of the nebulous contents of the heavens
consist of spherical or elliptical forms presenting every variety of
elongation and central condensation. Of these a great number have been
resolved into stars, and a great many present that mottled appearance
which renders it certain that an increase of optical power would
decompose them. Those which resist do so on account of the smallness and
closeness of the stars of which they consist.

Elliptical nebulæ are very common; by much the finest may be seen near
the star υ in the girdle of Andromeda. It is visible to the naked eye,
and has frequently been taken for a comet. With a low optical power it
has the spindle-shaped form of fig. 6, plate 5, the brightness being at
first gradually and then rapidly condensed towards the centre, so that
it has been compared to a star shining through horn, but had never
appeared resolvable even with high optical powers till Mr. Bond examined
it at the observatory of Cambridge in the United States. He found that
its brightness extends over 2-1/2 degrees in length, and more than a
degree in breadth, including two small adjacent nebulæ, so that it is
oval. It is strongly and rapidly condensed into a nucleus on its
northern side; and although it was not all resolved, it was seen to be
strewed over with star dust, or extremely minute visible stars, which
leaves not a doubt of its being a starry system. The most remarkable
part of Mr. Bond’s discovery are two very narrow dark lines which extend
along one side of the oval parallel to its major axis. These black
streaks, difficult to distinguish, indicate a stratified structure, and
are not the only instance of that arrangement in nebulæ. Fig. 1, in
plate 9, is from Mr. Bond’s drawing of this nebula.

Multitudes of nebulæ appear to the unassisted eye, or are seen with
ordinary telescopes, like round comets without tails; but when viewed
with powerful instruments they convey the idea of a globular space,
insulated in the heavens and full of stars, constituting a family or
society apart from the rest, subject only to its own internal laws. To
attempt to count the stars in one of these globular clusters, Sir John
Herschel says, would be a vain task; they are not to be reckoned by
hundreds. On a rough computation, it appears that many clusters of this
description must contain ten or twenty thousand stars compacted and
wedged together in a round space, whose apparent area is not more than a
tenth part of that covered by the moon; so that its centre, where the
stars are seen projected on each other, is one blaze of light. If each
of these stars be a sun, and if they be separated by intervals equal to
that which separates our sun from the nearest fixed star, the distance
which renders the whole cluster barely visible to the naked eye must be
so great, that the existence of such a splendid assemblage can only be
known to us by light which must have left it at least a thousand years
ago. These magnificent globular or spheroidal aggregates of stars are so
arranged that the interior strata are more crowded and become more
nearly spherical as they approach the centre. A most splendid object of
this nature may be seen in the constellation Hercules (N. 235).

Of 131 of these magnificent objects in the southern hemisphere, two of
them are pre-eminently splendid. The globular cluster of α Centauri is
beyond comparison the finest of its kind: it is perfectly spherical, and
occupies a quarter of a square degree; the stars in it are literally
innumerable, crowding and densely aggregated towards the centre; and, as
its light is not more to the naked eye than that of a star of the 4th or
5th magnitude, their minuteness is extreme. It has a dark hole in its
centre, with a bridge of stars across,—a circumstance peculiar to this
cluster.

Lacaille’s globular cluster, or 47 Toucani, is completely insulated in a
very dark part of the sky not far from the lesser of the Magellanic
clouds. The stars, which are of the 14th magnitude, immensely numerous,
compressed and white, form three distinct stages round a centre, where
they suddenly change in hue, and form a blaze of rose-coloured light.
One cluster consists of large ruddy stars and small white ones; another
of greater beauty consists of shells or coats of stars of the 11th and
15th magnitude. There are thirty globular clusters of extreme beauty
collected within a circular space of not more than eighteen degrees
radius, which lies in the part of the sky occupied by the constellations
Corona Australis, the body and head of Sagittarius, the tail of Scorpio,
part of Telescopium and Ara. The Milky Way passes diametrically across
the circular area in question, which gives prodigious brilliancy to this
part of the sky. For besides these globular clusters, which all lie in
the starry part, and not in the dark spaces, there are the only two
annular nebulæ known to exist in the southern hemisphere. No part of the
heavens is fuller of objects beautiful and remarkable in themselves, and
rendered still more so by their mode of association, and by the peculiar
features assumed by the Milky Way, which are without a parallel for
richness and magnificence in any other part of the sky. Some of the
globular clusters are so remote that the stars are scarcely
discernible—mere star dust. There is a double globular cluster in the
southern hemisphere of very small dimensions, separated by a minute
interval,—a combination which suggests the idea of a globular cluster
revolving about a very oblate spheroidal one in the plane of the
equator, and in an orbit which is circular, and seen obliquely like the
central nebula itself, with a diameter somewhat more than four times the
latter,—a stupendous system doubtless, but of which the reality can
hardly be supposed improbable.

There appears to be some connexion between ellipticity of form and
difficulty of resolution, for spherical clusters are in general easily
resolved into their component stars, while there is scarcely an instance
of an elliptical cluster yielding except to a very high optical power.
Vast masses of the nebulæ have never been resolved. Lord Rosse’s great
telescope has resolved parts of the nebula of Orion, and various others
which had not yielded to instruments of less power; it enables the
astronomer to penetrate farther into space, and shows objects with
greater clearness, than any other. But, excellent as this instrument is,
thousands of nebulæ are not to be resolved even by it. Those who imagine
that any work of man can resolve all the nebulous matter in the heavens
must have a very limited idea of the extent and sublimity of creation.

Innumerable nebulæ in both hemispheres take the form of clusters of
stars, but are totally different from the globular clusters, inasmuch as
they are of irregular form and follow no uniform law of condensation.
The Pleiades is an instance in our own stellar system; for although only
7 or 8 stars are visible to the naked eye, telescopes show that more
than 200 belong to the group. In the constellation Cancer there is a
luminous spot called the Præsepe or Beehive, which a very low power
resolves into stars; and the constellation Coma Berenices is another
stellar group. Many are of exquisite beauty, as that round α Crucis,
which, though consisting of only a hundred and ten stars, is like a
piece of fancy jewellery, from the colours of the stars, which are
greenish white, green, blueish green, and red. Many of these clusters
contain thousands of stars, and are frequently in the poorer parts of
the sky, as if in the course of ages the stars had been attracted
towards a centre.

The existence of every degree of ellipticity in the nebulæ—from long
lenticular rays to the exact circular form—and of every shade of central
condensation, from the slightest increase of density to apparently a
solid nucleus—may be accounted for by supposing the general
constitutions of those nebulæ to be that of oblate spheroidal masses of
every degree of flatness from the sphere to the disc, and of every
variety in their density and ellipticity towards the centre. It would be
erroneous, however, to imagine that the forms of these systems are
maintained by forces identical with those already described, which
determine the form of a fluid mass in rotation; because, if the nebulæ
be only clusters of separate stars, as in the greater number of cases
there is every reason to believe them to be, no pressure can be
propagated through them. Consequently, since no general rotation of such
a system as one mass can be supposed, it may be conceived to be a
quiescent form, comprising within its limits an indefinite number of
stars, each of which may be moving in an orbit about the common centre
of the whole, in virtue of a law of internal gravitation resulting from
the compound gravitation of all its parts. Sir John Herschel has proved
that the existence of such a system is not inconsistent with the law of
gravitation under certain conditions.

The distribution of the nebulæ over the heavens is even more irregular
than that of the stars. In some places they are so crowded together as
scarcely to allow one to pass through the field of the telescope before
another appears, while in other parts hours elapse without a single
nebula occurring. They are in general only to be seen with the best
telescopes, and are most abundant in a zone whose general direction is
not far from the hour circles 0^h and 12^h, and which crosses the
Milky Way nearly at right angles. Where that nebulous zone passes over
the constellations Virgo, Coma Berenices, and the Great Bear, they are
to be found in multitudes.

The nebulous system is nearly divided into two parts by the Milky Way.
One-third of the whole visible nebulous contents of the heavens forms a
broad irregular mass, interspersed with vacant intervals, which fills
about an eighth of the surface of the northern hemisphere. It occupies
the constellations Leo, Leo Minor, the body, tail, and hind legs of Ursa
Major, the nose of Camelopard, the point of the tail of Draco, Canis
Venatica, Coma Berenices, the preceding leg of Boötes, and the head,
wings, and shoulder of Virgo, which is the richest part. There is a
lesser nebulous region in this hemisphere, but entirely separated from
the preceding, which occupies the chest and wing of Pegasus, the
constellations Pisces and Andromeda. If we could imagine the ring or
zone of the Milky Way to encircle or coincide with the horizon, the
great nebulous mass would form a canopy over head, descending down to a
considerable distance on all sides, chiefly towards the north pole; and
the richest part, which is in Virgo, would then be directly over head in
the north pole of the Milky Way, that is in 12^h 47^m right ascension,
and 64° north polar distance.

With the exception of the Magellanic clouds, there is a much greater
uniformity in the distribution of the nebulæ in the southern hemisphere
than in the northern. They are separated by spaces of vacuity of greater
or less dimensions. One of these barren regions extends for nearly
fifteen degrees all around the south pole, and close on its border; the
lesser of the Magellanic clouds occurs completely insulated; while the
greater Magellanic cloud is in connexion with something approaching to a
zone of connected nebulous patches which extends along the back of
Doradus, through a portion of Horologium and Eridanus, part of Fornix,
and over the paws of Cetus to the equator, where it unites with the
nebulous regions of Pisces.

The Magellanic clouds form two of the most striking features in the
southern hemisphere; both of these nebulæ are visible to the unassisted
eye, being nearly of the same intensity as the brighter portions of the
Milky Way; but the smaller is entirely effaced by moonlight, and the
larger nearly so. They are altogether unconnected with the Milky Way and
with one another. The Nubecula Major is far superior to the Nubecula
Minor in every respect, though they are similar in internal structure.
The former consists of large tracts and ill-defined patches of
irresolvable nebulæ, and nebulosity in every stage of resolution, up to
perfectly resolved stars like the Milky Way; and also of regular and
irregular nebulæ, properly so called; of globular clusters in every
stage of resolvability; and of clustering groups sufficiently insulated
and condensed to come under the designation of clusters of stars. Of
these the nebula known as Lacaille’s 30 Doradus is too remarkable to be
passed over. It is very large, situate within the Nubecula Major, and
consists of an assemblage of nearly circular loops uniting in a centre,
in or near which there is a circular black hole. In short, for the
number and variety of the objects, there is nothing like this cloud.
Within an area of only forty-two square degrees, Sir John Herschel has
determined the places, and registered 278 nebulæ and clusters of stars,
with fifty or sixty in outlying members immediately adjacent. Even the
most crowded parts of the stratum of Virgo, in the wing of that
constellation, or in Coma Berenices, offer nothing approaching to it. It
is evident, from the intermixture of stars and unresolved nebulosity,
which probably might be resolved with a higher optical power, that the
nubeculæ are to be regarded as systems _sui generis_, to which there is
nothing analogous in our hemisphere.

Next to the Magellanic clouds the great nebula round η Argûs is one of
the most wonderful objects of the southern sky. It is situate in that
part of the Milky Way which lies between the Centaur and the body of
Argus, in the midst of one of those rich and brilliant masses, a
succession of which is so curiously contrasted with the profoundly dark
adjacent spaces, and surrounded by one of the most beautiful parts of
the southern heavens. Sir John Herschel says: “It would be impossible,
by verbal description, to give any just idea of the capricious forms and
irregular gradations of light affected by the different branches and
appendages of this nebula. Nor is it easy for language to convey a full
impression of the beauty and sublimity of the spectacle it offers when
viewed in a sweep, ushered in as it is by so glorious and innumerable a
procession of stars, to which it forms a sort of climax, justifying
expressions which, though I find them written in my journal in the
excitement of the moment, would be thought extravagant if transferred to
these pages. In fact, it is impossible for any one, with the least spark
of astronomical enthusiasm about him, to pass soberly in review with a
powerful telescope, and on a fine night, that portion of the southern
sky which is comprised between the 6th and 13th degrees of right
ascension, and from 146° to 149° of north polar distance; such are the
variety and interest of the objects he will encounter, and such the
dazzling richness of the starry ground on which they are represented to
his gaze.” In that portion of the sky there are many fine double
stars—rich starry clusters; the elegant cluster of variously coloured
stars round κ Crucis; a large planetary nebula with a satellite star;
another of a bright blue colour, exquisitely beautiful and unique; and,
lastly, η Argûs itself, the most extraordinary instance of a variable
star in astronomical history.

It frequently occurred, during Sir John Herschel’s survey of the
southern heavens, that some parts of the sky were noted for deeper
blackness than others, and no stars could be seen; it frequently
happened that far from the Milky Way, or any large nebula or cluster of
stars, there were some indications of very remote branches of the Milky
Way, or of an independent sidereal system or systems, bearing a
resemblance to such branches. These were indicated by an exceedingly
delicate and uniform dotting or stippling of the sky by points of light
too small to admit of any one of them being steadily and fixedly viewed,
and too numerous to be counted even if possible to view them. The truth
of this existence was felt at the moment of observation; but the
conviction, though often renewed, was not permanent. The places where
these appearances occurred are given, in order that those who wish to
verify them may have it in their power.

Such is a brief account of a very few of the discoveries contained in
Sir John Herschel’s great work on the Nebulæ and other Phenomena of the
Southern Hemisphere,—a work which will rise in estimation with the lapse
of years. No doubt the form and internal structure of many of these
nebulæ will be changed by telescopes of higher power; but as the places
of the leading phenomena have been determined, the date of that great
work may be regarded as the epoch of nebular time whence the relative
changes that take place in the most distant regions of the universe will
be estimated for ages to come; and in the inimitable writings of the
highly gifted father and son the reader will find these subjects treated
of in a style worthy of it and of them. Of late years the excellence of
the instruments, and still more of the astronomers, in the foreign
observatories, have aided the progress of sidereal astronomy immensely.
Nor has it been cultivated with less success in our home and colonial
establishments: certainly one of the most remarkable features of the
times is the number of private observatories, built and furnished with
the best instruments by private gentlemen, whose zeal has been rewarded
by eminent success in all departments of the science. (N. 236.)

So numerous are the objects which meet our view in the heavens, that we
cannot imagine a point of space where some light would not strike the
eye;—innumerable stars, thousands of double and multiple systems,
clusters in one blaze with their tens of thousands of stars, and the
nebulæ amazing us by the strangeness of their forms and the
incomprehensibility of their nature, till at last, from the limit of our
senses, even these thin and airy phantoms vanish in the distance. If
such remote bodies shone by reflected light, we should be unconscious of
their existence. Each star must then be a sun, and may be presumed to
have its system of planets, satellites, and comets, like our own; and,
for aught we know, myriads of bodies may be wandering in space unseen by
us, of whose nature we can form no idea, and still less of the part they
perform in the economy of the universe. Even in our own system, or at
its farthest limits, minute bodies may be revolving like the telescopic
planets, which are so small that their masses have hitherto been
inappreciable, and there may be many still smaller. Nor is this an
unwarranted presumption; many such do come within the sphere of the
earth’s attraction, are ignited by the velocity with which they pass
through the atmosphere, but leave no residuum. These, which are known as
falling stars and meteors, are periodical; but that is by no means the
case with aërolites, which are also ignited by the sudden condensation
of the air on entering our atmosphere, and are precipitated in solid
masses with such violence on the earth’s surface that they are often
deeply buried in the ground.

The fall of meteoric stones is much more frequent than is generally
believed. Hardly a year passes without some instances occurring; and, if
it be considered that only a small part of the earth is inhabited, it
may be presumed that numbers fall in the ocean, or on the uninhabited
part of the land, unseen by man. They are sometimes of great magnitude;
the volume of several has exceeded that of the planet Ceres, which is
about 70 miles in diameter. One which passed within 25 miles of us was
estimated to weigh about 600,000 tons, and to move with a velocity of
about 20 miles in a second; a fragment of it alone reached the earth.
The obliquity of the descent of meteorites, the peculiar substances they
are composed of, and the explosion accompanying their fall, show that
they are foreign to our system; but whence derived is still a mystery.

Shooting stars and meteors burst from the clear azure sky, and, darting
along the heavens, are extinguished without leaving any residuum except
a vapour-like smoke, and generally without noise. Their parallax shows
them to be very high in the atmosphere, sometimes even beyond its
supposed limit, and the direction of their motion is for the most part
diametrically opposite to the motion of the earth in its orbit. The
astonishing multitudes of shooting stars and fire-balls that have
appeared at stated periods over different parts of the globe, warrant
the conclusion that there is either a nebula or that there are myriads
of bodies revolving in groups round the sun which only become visible
when inflamed by entering our atmosphere.

One of these nebulæ or groups seems to meet the earth in its annual
revolution on the 12th and 13th of November.

On the morning of the 12th of November, 1799, thousands of shooting
stars, mixed with large meteors, illuminated the heavens for many hours
over the whole continent of America, from Brazil to Labrador: it
extended to Greenland, and even Germany. Meteoric showers were seen off
the coast of Spain, and in the Ohio country, on the morning of the 13th
of November, 1831; and during many hours on the morning of the 13th
November, 1832, prodigious multitudes of shooting stars and meteors fell
at Mocha on the Red Sea, in the Atlantic, in Switzerland, and at many
places in England. But by much the most splendid meteoric shower on
record began at nine o’clock in the evening of the 12th of November,
1833, and lasted till sunrise next morning. It extended from Niagara and
the northern lakes of America to the south of Jamaica, and from 61° of
longitude in the Atlantic to 100° of longitude in central Mexico.
Shooting stars and meteors, of the apparent size of Jupiter, Venus, and
even the full moon, darted in myriads towards the horizon, as if every
star in the heavens had started from their spheres. They are described
as having been frequent as flakes of snow in a snow-storm, and to have
been seen with equal brilliancy over the greater part of the continent
of North America.

Those who witnessed this grand spectacle were surprised to see that
every one of the luminous bodies, without exception, moved in lines
which converged in one point in the heavens: none of them started from
that point; but their paths, when traced backwards, met in it like rays
in a focus, and the manner of their fall showed that they descended from
it in nearly parallel straight lines towards the earth.

By far the most extraordinary part of the whole phenomenon is, that this
radiant point was observed to remain stationary near the star γ Leonis
for more than two hours and a half, which proved the source of the
meteoric shower to be altogether independent of the earth’s rotation,
and its parallax showed it to be far above the atmosphere.

As a body could not be actually at rest in that position, the group or
nebula must either have been moving round the earth or the sun. Had it
been moving about the earth, the course of the meteors would have been
tangential to its surface; whereas they fell almost perpendicularly, so
that the earth in its annual revolution must have met with the group.
The bodies or the parts of the nebula that were nearest must have been
attracted towards the earth by its gravity, and, as they were estimated
to move at the rate of fourteen miles in a second, they must have taken
fire on entering our atmosphere, and been consumed in their passage
through it.

As all the circumstances of the phenomena were similar on the same day
and during the same hours in 1832, and as extraordinary flights of
shooting stars were seen at many places both in Europe and America on
the 13th of November, 1834, 1835, and 1836, tending also from a fixed
point in the constellation Leo, it has been conjectured, with much
apparent probability, that this nebula or group of bodies performs its
revolution round the sun in a period of about 182 days, in an elliptical
orbit, whose major axis is 119 millions of miles; and that its aphelion
distance, where it comes in contact with the earth’s atmosphere, is
about 95 millions of miles, or nearly the same with the mean distance of
the earth from the sun. This body must have met with disturbances after
1799, which prevented it from encountering the earth for 32 years, and
it may again deviate from its path from the same cause.

It is now well ascertained that great showers of shooting stars occur
also on the 12th of August, whose point of divergence is β
Camelopardali, so that the earth’s atmosphere comes into contact with a
zone of these small bodies twice in the year. By a systematic series of
observations, MM. Benzenberg and Brand have clearly made out that the
heights at which the falling stars appear and vanish vary from 16 miles
to 140, and their velocities from 18 to 36 miles in a second, velocities
so great as certainly to indicate a planetary revolution round the sun.
As shooting stars are seen almost every night when the sky is clear, Sir
John Lubbock has thought it probable that some of these bodies may have
come so near, that the attraction of the earth has overcome that of the
sun, and caused them to revolve as satellites round it. Should that be
the case, they might shine by the reflected light of the sun, and
suddenly cease to be visible on entering the earth’s shadow. The
splitting of the falling stars like a rocket, and the trains of light,
may be accounted for by supposing the stars to graze the surface of the
shadow before being eclipsed; and the disappearance would be more or
less rapid according to the breadth of the penumbra traversed. The
calculations of M. Petit, Director of the Observatory of Toulouse, not
only render probable the existence of small satellites, but tend to
establish the identity of a body revolving round the earth in three
hours and twenty minutes, at a distance of 5000 miles above its surface.
It is evident that in this case the same satellite would be seen very
often, and a very few would be sufficient to account for their nightly
appearance. It is possible, however, that some shooting stars may belong
to one class, and some to the other, since one group may be revolving
about the sun, and another round the earth. In the case of a satellite
shooting star, geometry furnishes the means of ascertaining its exact
distance from the spectator, or from the centre of the earth, if the
time and place of its disappearance be known with regard to the
neighbouring stars. Since the falling stars are consumed in the
atmosphere, their masses must be small, but it is possible that
occasionally one may be large enough to arrive at the surface of the
earth as an aërolite.




                            SECTION XXXVII.

Diffusion of Matter through Space—Gravitation—Its Velocity—Simplicity of
  its Laws—Gravitation independent of the Magnitude and Distances of the
  Bodies—Not impeded by the intervention of any Substance—Its Intensity
  invariable—General Laws—Recapitulation and Conclusion.


THE known quantity of matter bears a very small proportion to the
immensity of space. Large as the bodies are, the distances which
separate them are immeasurably greater; but, as design is manifest in
every part of creation, it is probable that, if the various systems in
the universe had been nearer to one another, their mutual disturbances
would have been inconsistent with the harmony and stability of the
whole. It is clear that space is not pervaded by atmospheric air of such
density as that we breathe, since its resistance would long ere this
have arrested the motion of the planets: it certainly is not a void, but
replete with a medium possibly in itself electric or magnetic, but at
all events capable of transmitting light, heat, magnetism, gravity, and
probably influences of which we can form no idea.

Whatever the laws may be that obtain in the more distant regions of
creation, we are assured that one alone regulates the motions, not only
of our own system, but also of the binary systems of the fixed stars;
and, as general laws form the ultimate object of philosophical research,
we cannot conclude these remarks without considering the nature of
gravitation—that extraordinary power whose effects we have been
endeavouring to trace through some of their mazes. It was at one time
imagined that the acceleration in the moon’s mean motion was occasioned
by the successive transmission of the gravitating force. It has been
proved that, in order to produce this effect, its velocity must be about
fifty millions of times greater than that of light, which flies at the
rate of 192,000 miles in a second. Its action, even at the distance of
the sun, may therefore be regarded as instantaneous; yet, remote as the
fixed stars are, the solar gravitation must have some influence on the
nearest of them, as, for example, α Centauri, which is only 20,602 times
the radius of the earth’s orbit from the sun, while La Place has
computed that the solar gravitation extends a hundred millions of times
farther than the semidiameter of the terrestrial orbit. Possibly the
star dust in the Milky Way may be beyond, or on the verge of, that
enormous limit; yet it is very unlikely that either the sun, or any of
the stars which form the great cluster to which we belong, should be
unconnected bodies.

The curves in which the celestial bodies move by the force of
gravitation are only lines of the second order. The attraction of
spheroids, according to any other law of force than that of gravitation,
would be much more complicated; and, as it is easy to prove that matter
might have been moved according to an infinite variety of laws, it may
be concluded that gravitation must have been selected by Divine Wisdom
out of an infinity of others, as being the most simple, and that which
gives the greatest stability to the celestial motions.

It is a singular result of the simplicity of the laws of nature, which
admit only of the observation and comparison of ratios, that the
gravitation and theory of the motions of the celestial bodies are
independent of their absolute magnitudes and distances. Consequently, if
all the bodies of the solar system, their mutual distances, and their
velocities, were to diminish proportionally, they would describe curves
in all respects similar to those in which they now move; and the system
might be successively reduced to the smallest sensible dimensions, and
still exhibit the same appearances.

The action of the gravitating force is not impeded by the intervention
even of the densest substances. If the attraction of the sun for the
centre of the earth, and of the hemisphere diametrically opposite to
him, were diminished by a difficulty in penetrating the interposed
matter, the tides would be more obviously affected. Its attraction is
the same also, whatever the substances of the celestial bodies may be;
for, if the action of the sun upon the earth differed by a millionth
part from his action upon the moon, the difference would occasion a
periodical variation in the moon’s parallax, whose maximum would be the
1/15 of a second, and also a variation in her longitude amounting to
several seconds—a supposition proved to be impossible by the agreement
of theory with observation. Thus all matter is pervious to gravitation,
and is equally attracted by it.

Gravitation is a feeble force, vastly inferior to electric action,
chemical affinity, and cohesion; yet, as far as human knowledge extends,
the intensity of gravitation has never varied within the limits of the
solar system; nor does even analogy lead us to expect that it should: on
the contrary, there is every reason to be assured that the great laws of
the universe are immutable, like their Author. Nor can we suppose the
structure of the globe alone to be exempt from the universal fiat of
general laws, though ages may pass before the changes it has undergone,
or that are now in progress, can be referred to existing causes with the
same certainty with which the motions of the planets, and all their
periodic and secular variations, are referable to the law of
gravitation. The traces of extreme antiquity perpetually occurring to
the geologist give that information, as to the origin of things, in vain
looked for in the other parts of the universe. They date the beginning
of time with regard to our system, since there is ground to believe that
the formation of the earth was contemporaneous with that of the rest of
the planets; but they show that creation is the work of Him with whom “a
thousand years are as one day, and one day as a thousand years.”

In the work now brought to a conclusion, it has been necessary to select
from the whole circle of the sciences a few of the most obvious of those
proximate links which connect them together, and to pass over
innumerable cases both of evident and occult alliance. Any one branch
traced through its ramifications would alone have occupied a volume; it
is hoped, nevertheless, that the view here given will suffice to show
the extent to which a consideration of the reciprocal influence of even
a few of these subjects may ultimately lead. It thus appears that the
theory of dynamics, founded upon terrestrial phenomena, is indispensable
for acquiring a knowledge of the revolutions of the celestial bodies and
their reciprocal influences. The motions of the satellites are affected
by the forms of their primaries, and the figures of the planets
themselves depend upon their rotations. The symmetry of their internal
structure proves the stability of these rotatory motions, and the
immutability of the length of the day, which furnishes an invariable
standard of time; and the actual size of the terrestrial spheroid
affords the means of ascertaining the dimensions of the solar system,
and provides an invariable foundation for a system of weights and
measures. The mutual attraction of the celestial bodies disturbs the
fluids at their surfaces, whence the theory of the tides and of the
oscillations of the atmosphere. The density and elasticity of the air,
varying with every alternation of temperature, lead to the consideration
of barometrical changes, the measurement of heights, and capillary
attraction; and the doctrine of sound, including the theory of music, is
to be referred to the small undulations of the aërial medium. A
knowledge of the action of matter upon light is requisite for tracing
the curved path of its rays through the atmosphere, by which the true
places of distant objects are determined, whether in the heavens or on
the earth. By this we learn the nature and properties of the sunbeam,
the mode of its propagation through the ethereal medium, or in the
interior of material bodies, and the origin of colour. By the eclipses
of Jupiter’s satellites the velocity of light is ascertained; and that
velocity, in the aberration of the fixed stars, furnishes a direct proof
of the real motion of the earth (N. 237). The effects of the invisible
rays of the spectrum are immediately connected with chemical action; and
heat, forming a part of the solar ray, so essential to animated and
inanimated existence, is too important an agent in the economy of
creation not to hold a principal place in the connexion of physical
sciences; whence follows its distribution in the interior and over the
surface of the globe, its power on the geological convulsions of our
planet, its influence on the atmosphere and on climate, and its effects
on vegetable and animal life, evinced in the localities of organized
beings on the earth, in the waters, and in the air. The correlation
between molecular and chemical action, light, heat, electricity, and
magnetism, is continually becoming more perfect, and there is every
reason to believe that these different modes of force, as well as
gravity itself, will ultimately be found to merge in one great and
universal power. Many more instances might be given in illustration of
the immediate connexion of the physical sciences, most of which are
united still more closely by the common bond of analysis, which is daily
extending its empire, and will ultimately embrace almost every subject
in nature in its formulæ.

These formulæ, emblematic of Omniscience, condense into a few symbols
the immutable laws of the universe. This mighty instrument of human
power itself originates in the primitive constitution of the human mind,
and rests upon a few fundamental axioms, which have eternally existed in
Him who implanted them in the breast of man when He created him after
His own image.




                                 NOTES.


NOTE 1, page 2. _Diameter._ A straight line passing through the centre,
and terminated both ways by the sides or surface of a figure, such as of
a circle or sphere. In fig. 1, q Q, N S, are diameters.


NOTE 2, p. 2. _Mathematical and mechanical sciences._ Mathematics teach
the laws of number and quantity; mechanics treat of the equilibrium and
motion of bodies.


NOTE 3, p. 2. _Analysis_ is a series of reasoning conducted by signs or
symbols of the quantities whose relations form the subject of inquiry.


NOTE 4, p. 3. _Oscillations_ are movements to and fro, like the swinging
of the pendulum of a clock, or waves in water. The tides are
oscillations of the sea.


NOTE 5, p. 3. _Gravitation._ _Gravity_ is the reciprocal attraction of
matter on matter; _gravitation_ is the difference between gravity and
the centrifugal force induced by the velocity of rotation or revolution.
Sensible gravity, or weight, is a particular instance of gravitation. It
is the force which causes substances to fall to the surface of the
earth, and which retains the celestial bodies in their orbits. Its
intensity increases as the squares of the distance decrease.


NOTE 6, p. 4. _Particles of matter_ are the indefinitely small or
ultimate atoms into which matter is believed to be divisible. Their form
is unknown; but, though too small to be visible, they must have
magnitude.


NOTE 7, p. 4. _A hollow sphere._ A hollow ball, like a bomb-shell. A
sphere is a ball or solid body, such, that all lines drawn from its
centre to its surface are equal. They are called radii, and every line
passing through the centre and terminated both ways by the surface is a
diameter, which is consequently equal to twice the radius. In fig. 3, Q
q or N S is a diameter, and C Q, C N are radii. A great circle of the
sphere has the same centre with the sphere as the circles Q E q d and Q
N q S. The circle A B is a lesser circle of the sphere.


NOTE 8, p. 4. _Concentric hollow spheres._ Shells, or hollow spheres,
having the same centre, like the coats of an onion.

[Illustration: _Fig. 1._]


NOTE 9, p. 4. _Spheroid._ A solid body, which sometimes has the shape of
an orange, as in fig. 1; it is then called an oblate spheroid, because
it is flattened at the poles N and S. Such is the form of the earth and
planets. When, on the contrary, it is drawn out at the poles like an
egg, as in fig. 2, it is called a prolate spheroid. It is evident that
in both these solids the radii C q, C a, C N, &c., are generally
unequal; whereas in the sphere they are all equal.

[Illustration: _Fig. 2._]


NOTE 10, p. 4. _Centre of gravity._ A point in every body, which if
supported, the body will remain at rest in whatever position it may be
placed. About that point all the parts exactly balance one another. The
celestial bodies attract each other as if each were condensed into a
single particle situate in the centre of gravity, or the particle
situate in the centre of gravity of each may be regarded as possessing
the resultant power of the innumerable oblique forces which constitute
the whole attraction of the body.


NOTE 11, pp. 4, 6. _Poles and equator._ Let fig. 1 or 3 represent the
earth, C its centre, N C S the axis of rotation, or the imaginary line
about which it performs its daily revolution. Then N and S are the north
and south poles, and the great circle q E Q, which divides the earth
into two equal parts, is the equator. The earth is flattened at the
poles, fig. 1, the equatorial diameter, q Q, exceeding the polar
diameter, N S, by about 26-1/2 miles. Lesser circles, A B G, which are
parallel to the equator, are circles or parallels of latitude, which is
estimated in degrees, minutes, and seconds, north and south of the
equator, every place in the same parallel having the same latitude.
Greenwich is in the parallel of 51° 28ʹ 40ʺ. Thus terrestrial latitude
is the angular distance between the direction of a plumb-line at any
place and the plane of the equator. Lines such as N Q S, N G E S, fig.
3, are called meridians; all the places in any one of these lines have
noon at the same instant. The meridian of Greenwich has been chosen by
the British as the origin of terrestrial longitude, which is estimated
in degrees, minutes, and seconds, east and west of that line. If N G E S
be the meridian of Greenwich, the position of any place, B, is
determined, when its latitude, Q C B, and its longitude, E C Q, are
known.

[Illustration: _Fig. 3._]


NOTE 12, p. 4. _Mean quantities_ are such as are intermediate between
others that are greater and less. The mean of any number of unequal
quantities is equal to their sum divided by their number. For instance,
the mean between two unequal quantities is equal to half their sum.


NOTE 13, p. 4. _A certain mean latitude._ The attraction of a sphere on
an external body is the same as if its mass were collected into one
heavy particle in its centre of gravity, and the intensity of its
attraction diminishes as the square of its distance from the external
body increases. But the attraction of a spheroid, fig. 1, on an external
body at m in the plane of its equator, E Q, is greater, and its
attraction on the same body when at mʹ in the axis N S less, than if it
were a sphere. Therefore, in both cases, the force deviates from the
exact law of gravity. This deviation arises from the protuberant matter
at the equator; and, as it diminishes towards the poles, so does the
attractive force of the spheroid. But there is one mean latitude, where
the attraction of a spheroid is the same as if it were a sphere. It is a
part of the spheroid intermediate between the equator and the pole. In
that latitude the square of the sine is equal to 1/3 of the equatorial
radius.


NOTE 14, p. 4. _Mean distance._ The mean distance of a planet from the
centre of the sun, or of a satellite from the centre of its planet, is
equal to half the sum of its greatest and least distances, and,
consequently, is equal to half the major axis of its orbit. For example,
let P Q A D, fig. 6, be the orbit or path of the moon or of a planet;
then P A is the major axis, C the centre, and C S is equal to C F. Now,
since the earth or the sun is supposed to be in the point S according as
P D A Q is regarded as the orbit of the moon or that of a planet, S A, S
P are the greatest and least distances. But half the sum of S A and S P
is equal to half of A P, the major axis of the orbit. When the body is
at Q or D, it is at its mean distance from S, for S Q, S D, are each
equal to C P, half the major axis by the nature of the curve.


NOTE 15, p. 4. _Mean radius of the earth._ The distance from the centre
to the surface of the earth, regarded as a sphere. It is intermediate
between the distances of the centre of the earth from the pole and from
the equator.


NOTE 16, p. 5. _Ratio._ The relation which one quantity bears to
another.


NOTE 17, p. 5. _Square of moon’s distance._ In order to avoid large
numbers, the mean radius of the earth is taken for unity: then the mean
distance of the moon is expressed by 60; and the square of that number
is 3600, or 60 times 60.

[Illustration: _Fig. 4_]


NOTE 18, p. 5. _Centrifugal force._ The force with which a revolving
body tends to fly from the centre of motion: a sling tends to fly from
the hand in consequence of the centrifugal force. A tangent is a
straight line touching a curved line in one point without cutting it, as
m T, fig. 4. The direction of the centrifugal force is in the tangent to
the curved line or path in which the body revolves, and its intensity
increases with the angular swing of the body, and with its distance from
the centre of motion. As the orbit of the moon does not differ much from
a circle, let it be represented by m d g h, fig. 4, the earth being in
C. The centrifugal force arising from the velocity of the moon in her
orbit balances the attraction of the earth. By their joint action, the
moon moves through the arc m n during the time that she would fly off in
the tangent m T by the action of the centrifugal force alone, or fall
through m p by the earth’s attraction alone. T n, the deflection from
the tangent, is parallel and equal to m p, the versed sine of the arc m
n, supposed to be moved over by the moon in a second, and therefore so
very small that it may be regarded as a straight line. T n, or m p, is
the space the moon would fall through in the first second of her descent
to the earth, were she not retained in her orbit by her centrifugal
force.


NOTE 19, p. 5. _Action and reaction._ When motion is communicated by
collision or pressure, the action of the body which strikes is returned
with equal force by the body which receives the blow. The pressure of a
hand on a table is resisted with an equal and contrary force. This
necessarily follows from the impenetrability of matter, a property by
which no two particles of matter can occupy the same identical portion
of space at the same time. When motion is communicated without apparent
contact, as in gravitation, attraction, and repulsion, the quantity of
motion gained by the one body is exactly equal to that lost by the
other, but in a contrary direction; a circumstance known by experience
only.


NOTE 20, p. 5. _Projected._ A body is projected when it is thrown: a
ball fired from a gun is projected; it is therefore called a projectile.
But the word has also another meaning. A line, surface, or solid body,
is said to be projected upon a plane, when parallel straight lines are
drawn from every point of it to the plane. The figure so traced upon a
plane is a projection. The projection of a terrestrial object is
therefore its daylight shadow, since the sun’s rays are sensibly
parallel.


NOTE 21, p. 5. _Space._ The boundless region which contains all
creation.

[Illustration: _Fig. 5._]

[Illustration: _Fig. 6._]


NOTE 22, pp. 5, 11. _Conic sections._ Lines formed by any plane cutting
a cone. A cone is a solid figure, like a sugar-loaf, fig. 5, of which A
is the apex, A D the axis, and the plane B E C F the base. The axis may
or may not be perpendicular to the base, and the base may be a circle,
or any other curved line. When the axis is perpendicular to the base,
the solid is a right cone. If a right cone with a circular base be cut
at right angles to the base by a plane passing through the apex, the
section will be a triangle. If the cone be cut through both sides by a
plane parallel to the base, the section will be a circle. If the cone be
cut slanting quite through both sides, the section will be an ellipse,
fig. 6. If the cone be cut parallel to one of the sloping sides as A B,
the section will be a parabola, fig. 7. And if the plane cut only one
side of the cone, and be not parallel to the other, the section will be
a hyperbola, fig. 8. Thus there are five conic sections.

[Illustration: _Fig. 7._]

[Illustration: _Fig. 8._]


NOTE 23, p. 5. _Inverse square of distance._ The attraction of one body
for another at the distance of two miles is four times less than at the
distance of one mile; at three miles, it is nine times less than at one;
at four miles, it is sixteen times less, and so on. That is, the
gravitating force decreases in intensity as the squares of the distance
increase.


NOTE 24, p. 5. _Ellipse._ One of the conic sections, fig. 6. An ellipse
may be drawn by fixing the ends of a string to two points, S and F, in a
sheet of paper, and then carrying the point of a pencil round in the
loop of the string kept stretched, the length of the string being
greater than the distance between the two points. The points S and F are
called the foci, C the centre, S C or C F the excentricity, A P the
major axis, Q D the minor axis, and P S the focal distance. It is
evident that, the less the excentricity C S, the nearer does the ellipse
approach to a circle; and from the construction it is clear that the
length of the string S m F is equal to the major axis P A. If T t be a
tangent to the ellipse at m, then the angle T m S is equal to the angle
t m F; and, as this is true for every point in the ellipse, it follows
that, in an elliptical reflecting surface, rays of light or sound coming
from one focus S will be reflected by the surface to the other focus F,
since the angle of incidence is equal to the angle of reflection by the
theories of light and sound.


NOTE 25, p. 5. _Periodic time._ The time in which a planet or comet
performs a revolution round the sun, or a satellite about its planet.


NOTE 26, p. 5. Kepler discovered three laws in the planetary motions by
which the principle of gravitation is established:—1st law, That the
radii vectores of the planets and comets describe areas proportional to
the time.—Let fig. 9 be the orbit of a planet; then, supposing the
spaces or areas P S p, p S a, a S b, &c., equal to one another, the
radius vector S P, which is the line joining the centres of the sun and
planet, passes over these equal spaces in equal times; that is, if the
line S P passes to S p in one day, it will come to S a in two days, to S
b in three days, and so on. 2nd law, That the orbits or paths of the
planets and comets are conic sections, having the sun in one of their
foci. The orbits of the planets and satellites are curves like fig. 6 or
9, called ellipses, having the sun in the focus S. Several comets are
known to move in ellipses; but the greater part seem to move in
parabolas, fig. 7, having the sun in S, though it is probable that they
really move in very long flat ellipses; others appear to move in
hyperbolas, like fig. 8. The third law is, that the squares of the
periodic times of the planets are proportional to the cubes of their
mean distances from the sun. The square of a number is that number
multiplied by itself, and the cube of a number is that number twice
multiplied by itself. For example, the squares of the numbers 2, 3, 4,
&c., are 4, 9, 16, &c., but their cubes are 8, 27, 64, &c. Then the
squares of the numbers representing the periodic times of two planets
are to one another as the cubes of the numbers representing their mean
distances from the sun. So that, three of these quantities being known,
the other may be found by the rule of three. The mean distances are
measured in miles or terrestrial radii, and the periodic times are
estimated in years, days, and parts of a day. Kepler’s laws extend to
the satellites.

[Illustration: _Fig. 9._]


NOTE 27, p. 5. _Mass._ The quantity of matter in a given bulk. It is
proportional to the density and volume or bulk conjointly.


NOTE 28, p. 5. _Gravitation proportional to mass._ But for the
resistance of the air, all bodies would fall to the ground in equal
times. In fact, a hundred equal particles of matter at equal distances
from the surface of the earth would fall to the ground in parallel
straight lines with equal rapidity, and no change whatever would take
place in the circumstances of their descent, if 99 of them were united
in one solid mass; for the solid mass and the single particle would
touch the ground at the same instant, were it not for the resistance of
the air.


NOTE 29, p. 5. _Primary_ signifies, in astronomy, the planet about which
a satellite revolves. The earth is primary to the moon.


NOTE 30, p. 6. _Rotation._ Motion round an axis, real or imaginary.


NOTE 31, p. 7. _Compression of a spheroid._ The flattening at the poles.
It is equal to the difference between the greatest and least diameters,
divided by the greatest, these quantities being expressed in some
standard measure, as miles.


NOTE 32, p. 7. SATELLITES. Small bodies revolving about some of the
planets. The moon is a satellite to the earth.


NOTE 33, p. 7. _Nutation._ A nodding motion in the earth’s axis while in
rotation, similar to that observed in the spinning of a top. It is
produced by the attraction of the sun and moon on the protuberant matter
at the terrestrial equator.


NOTE 34, p. 7. _Axis of rotation._ The line, real or imaginary, about
which a body revolves. The axis of the earth’s rotation is that
diameter, or imaginary line, passing through the centre and both poles.
Fig. 1 being the earth, N S is the axis of rotation.


NOTE 35, p. 7. _Nutation of lunar orbit._ The action of the bulging
matter at the earth’s equator on the moon occasions a variation in the
inclination of the lunar orbit to the plane of the ecliptic. Suppose the
plane N p n, fig. 13, to be the orbit of the moon, and N m n the plane
of the ecliptic, the earth’s action on the moon causes the angle p N m
to become less or greater than its mean state. The nutation in the lunar
orbit is the reaction of the nutation in the earth’s axis.


NOTE 36, p. 7. _Translated._ Carried forward in space.


NOTE 37, p. 7. _Force proportional to velocity._ Since a force is
measured by its effect, the motions of the bodies of the solar system
among themselves would be the same whether the system be at rest or not.
The real motion of a person walking the deck of a ship at sea is
compounded of his own motion and that of the ship, yet each takes place
independently of the other. We walk about as if the earth were at rest,
though it has the double motion of rotation on its axis and revolution
round the sun.


NOTE 38, p. 8. _Tangent._ A straight line which touches a curved line in
one point without cutting it. In fig. 4, m T is tangent to the curve in
the point m. In a circle the tangent is at right angles to the radius, C
m.


NOTE 39, p. 8. _Motion in an elliptical orbit._ A planet m, fig. 6,
moves round the sun at S in an ellipse P D A Q, in consequence of two
forces, one urging it in the direction of the tangent m T, and another
pulling it towards the sun in the direction m S. Its velocity, which is
greatest at P, decreases throughout the arc to P D A to A, where it is
least, and increases continually as it moves along the arc A Q P till it
comes to P again. The whole force producing the elliptical motion varies
inversely as the square of the distance. See note 23.


NOTE 40, p. 8. _Radii vectores._ Imaginary lines adjoining the centre of
the sun and the centre of a planet or comet, or the centres of a planet
and its satellite. In the circle, the radii are all equal; but in an
ellipse, fig. 6, the radius vector S A is greater, and S P less than all
the others. The radii vectores S Q, S D, are equal to C A or C P, half
the major axis P A, and consequently equal to the mean distance. A
planet is at its mean distance from the sun when in the points Q and D.


NOTE 41, p. 8. _Equal areas in equal times._ See Kepler’s 1st law, in
note 26, p. 5.


NOTE 42, p. 8. _Major axis._ The line P A, fig. 6 or 10.


NOTE 43, p. 8. _If the planet described a circle, &c._ The motion of a
planet about the sun, in a circle A B P, fig. 10, whose radius C A is
equal to the planet’s mean distance from him, would be equable, that is,
its velocity, or speed, would always be the same. Whereas, if it moved
in the ellipse A Q P, its speed would be continually varying, by note
39; but its motion is such, that the time elapsing between its departure
from P and its return to that point again would be the same whether it
moved in the circle or in the ellipse; for these curves coincide in the
points P and A.


NOTE 44, p. 8. _True motion._ The motion of a body in its real orbit P D
A Q, fig. 10.

[Illustration: _Fig. 10._]


NOTE 45, p. 9. _Mean motion._ Equable motion in a circle P E A B, fig.
10, at the mean distance C P or C m, in the time that the body would
accomplish a revolution in its elliptical orbit P D A Q.


NOTE 46, p. 9. _The equinox._ Fig. 11 represents the celestial sphere,
and C its centre, where the earth is supposed to be. q ♈ Q ♎ is the
equinoctial or great circle, traced in the starry heavens by an
imaginary extension of the plane of the terrestrial equator, and E ♈ e ♎
is the ecliptic, or apparent path of the sun round the earth. ♈ ♎, the
intersection of these two planes, is the line of the equinoxes; ♈ is the
vernal equinox, and ♎ the autumnal. When the sun is in these points, the
days and nights are equal. They are distant from one another by a
semicircle, or two right angles. The points E and e are the solstices,
where the sun is at his greatest distance from the equinoctial. The
equinoctial is everywhere ninety degrees distant from its poles N and S,
which are two points diametrically opposite to one another, where the
axis of the earth’s rotation, if prolonged, would meet the heavens. The
northern celestial pole N is within 1° 24ʹ of the pole star. As the
latitude of any place on the surface of the earth is equal to the height
of the pole above the horizon, it is easily determined by observation.
The ecliptic E ♈ e ♎ is also everywhere ninety degrees distant from its
poles P and p. The angle P C N, between the poles P and N of the
equinoctial and ecliptic, is equal to the angle e C Q, called the
obliquity of the ecliptic.

[Illustration: _Fig. 11._]


NOTE 47, p. 9. _Longitude._ The vernal equinox, ♈, fig. 11, is the zero
point in the heavens whence celestial longitudes, or the angular motions
of the celestial bodies, are estimated from west to east, the direction
in which they all revolve. The vernal equinox is generally called the
first point of Aries, though these two points have not coincided since
the early ages of astronomy, about 2233 years ago, on account of a
motion in the equinoctial points, to be explained hereafter. If S ♈,
fig. 10, be the line of the equinoxes, and ♈ the vernal equinox, the
true longitude of a planet p is the angle ♈ S p, and its mean longitude
is the angle ♈ C m, the sun being in S. Celestial longitude is the
angular distance of a heavenly body from the vernal equinox; whereas
terrestrial longitude is the angular distance of a place on the surface
of the earth from a meridian arbitrarily chosen, as that of Greenwich.


NOTE 48, pp. 9, 58. _Equation of the centre._ The difference between ♈ C
m and ♈ S p, fig. 10; that is, the difference between the true and mean
longitudes of a planet or satellite. The true and mean places only
coincide in the points P and A; in every other point of the orbit, the
true place is either before or behind the mean place. In moving from A
through the arc A Q P, the true place p is behind the mean place m; and
through the arc P D A the true place is before the mean place. At its
maximum, the equation of the centre measures C S, the excentricity of
the orbit, since it is the difference between the motion of a body in an
ellipse and in a circle whose diameter A P is the major axis of the
ellipse.


NOTE 49, p. 9. _Apsides._ The points P and A, fig. 10, at the
extremities of the major axis of an orbit. P is commonly called the
perihelion, a Greek term signifying _round the sun_; and the point A is
called the aphelion, a Greek term signifying _at a distance from the
sun_.


NOTE 50, p. 9. _Ninety degrees._ A circle is divided into 360 equal
parts, or degrees; each degree into 60 equal parts, called minutes; and
each minute into 60 equal parts, called seconds. It is usual to write
these quantities thus, 15° 16ʹ 10ʺ, which means fifteen degrees, sixteen
minutes, and ten seconds. It is clear that an arc m n, fig. 4, measures
the angle m C n; hence we may say, an arc of so many degrees, or an
angle of so many degrees; for, if there be ten degrees in the angle m C
n, there will be ten degrees in the arc m n. It is evident that there
are 90° in a right angle, m C d, or quadrant, since it is the fourth
part of 360°.


NOTE 51, p. 9. _Quadratures._ A celestial body is said to be in
quadrature when it is 90 degrees distant from the sun. For example, in
fig. 14, if d be the sun, S the earth, and p the moon, then the moon is
said to be in quadrature when she is in either of the points Q or D,
because the angles Q S d and D S d, which measure her apparent distance
from the sun, are right angles.


NOTE 52, p. 9. _Excentricity._ Deviation from circular form. In fig. 6,
C S is the excentricity of the orbit P Q A D. The less C S, the more
nearly does the orbit or ellipse approach the circular form; and, when C
S is zero, the ellipse becomes a circle.


NOTE 53, p. 9. _Inclination of an orbit._ Let S, fig. 12, be the centre
of the sun, P N A n the orbit of a planet moving from west to east in
the direction N p. Let E N m e n be the shadow or projection of the
orbit on the plane of the ecliptic, then N S n is the intersection of
these two planes, for the orbit rises above the plane of the ecliptic
towards N p, and sinks below it at N P. The angle p N m, which these two
planes make with one another, is the inclination of the orbit P N p A to
the plane of the ecliptic.


NOTE 54, p. 9. _Latitude of a planet._ The angle p S m, fig. 12, or the
height of the planet p above the ecliptic E N m. In this case the
latitude is north. Thus, celestial latitude is the angular distance of a
celestial body from the plane of the ecliptic, whereas terrestrial
latitude is the angular distance of a place on the surface of the earth
from the equator.

[Illustration: _Fig. 12._]


NOTE 55, p. 9. _Nodes._ The two points N and n, fig. 12, in which the
orbit N A n P of a planet or comet intersects the plane of the ecliptic
e N E n. The part N A n of the orbit lies above the plane of the
ecliptic, and the part n P N below it. The ascending node N is the point
through which the body passes in rising above the plane of the ecliptic,
and the descending node n is the point in which the body sinks below it.
The nodes of a satellite’s orbit are the points in which it intersects
the plane of the orbit of the planet.


NOTE 56, p. 10. _Distance from the sun._ S p in fig. 12. If ♈ be the
vernal equinox, then ♈ S p is the longitude of the planet p, m S p is
its latitude, and S p its distance from the sun. When these three
quantities are known, the place of the planet p is determined in space.


NOTE 57, pp. 10, 59. _Elements of an orbit._ Of these there are seven.
Let P N A n, fig. 12, be the elliptical orbit of a planet, C its centre,
S the sun in one of the foci, ♈ the point of Aries, and E N e n the
plane of the ecliptic. The elements are—the major axis A P; the
excentricity C S; the periodic time, that is, the time of a complete
revolution of the body in its orbit; and the fourth is the longitude of
the body at any given instant—for example, that at which it passes
through the perihelion P, the point of its orbit nearest to the sun.
That instant is assumed as the origin of time, whence all preceding and
succeeding periods are estimated. These four quantities are sufficient
to determine the form of the orbit, and the motion of the body in it.
Three other elements are requisite for determining the position of the
orbit in space. These are, the angle ♈ S P, the longitude of the
perihelion; the angle A N e, which is the inclination of the orbit to
the plane of the ecliptic; and, lastly, the angle ♈ S N, the longitude
of N the ascending node.


NOTE 58, p. 10. _Whose planes, &c._ The planes of the orbits, as P N A
n, fig. 12, in which the planets move, are inclined or make small angles
e N A with the plane of the ecliptic E N e n, and cut it in straight
lines, N S n passing through S, the centre of the sun.


NOTE 59, p. 11. _Momentum._ Force measured by the weight of a body and
its speed, or simple velocity, conjointly. The primitive momentum of the
planets is, therefore, the quantity of motion which was impressed upon
them when they were first thrown into space.


NOTE 60, p. 11. _Unstable equilibrium._ A body is said to be in
equilibrium when it is so balanced as to remain at rest. But there are
two kinds of equilibrium, _stable_ and _unstable_. If a body balanced in
stable equilibrium be slightly disturbed, it will endeavour to return to
rest by a number of movements to and fro, which will continually
decrease till they cease altogether, and then the body will be restored
to its original state of repose. But, if the equilibrium be unstable,
these movements to and fro, or oscillations, will become greater and
greater till the equilibrium is destroyed.


NOTE 61, p. 14. _Retrograde._ Going backwards, as from east to west,
contrary to the motion of the planets.


NOTE 62, p. 14. _Parallel directions._ Such as never meet, though
prolonged ever so far.

[Illustration: _Fig. 13._]

[Illustration: _Fig. 14._]


NOTE 63, pp. 14, 16. _The whole force, &c._ Let S, fig. 13, be the sun,
N m n the plane of the ecliptic, p the disturbed planet moving in its
orbit n p N, and d the disturbing planet. Now, d attracts the sun and
the planet p with different intensities in the directions d S, d p: the
difference only of these forces disturbs the motion of p; it is
therefore called the disturbing force. But this whole disturbing force
may be regarded as equivalent to three forces, acting in the directions
p S, p T, and p m. The force acting in the radius vector p S, joining
the centres of the sun and planet, is called the _radial force_. It
sometimes draws the disturbed planet p from the sun, and sometimes
brings it nearer to him. The force which acts in the direction of the
tangent p T is called the _tangential force_. It disturbs the motion of
p in longitude, that is, it accelerates its motion in some parts of its
orbit and retards it in others, so that the radius vector S p does not
move over equal areas in equal times. (See note 26.) For example, in the
position of the bodies in fig. 14, it is evident that, in consequence of
the attraction of d, the planet p will have its motion accelerated from
Q to C, retarded from C to D, again accelerated from D to O, and lastly
retarded from O to Q. The disturbing body is here supposed to be at
rest, and the orbit circular; but, as both bodies are perpetually moving
with different velocities in ellipses, the perturbations or changes in
the motions of p are very numerous. Lastly, that part of the disturbing
force which acts in the direction of a line p m, fig. 13, at right
angles to the plane of the orbit N p n, may be called the perpendicular
force. It sometimes causes the body to approach nearer, and sometimes to
recede farther from, the plane of the ecliptic N m n, than it would
otherwise do. The action of the disturbing forces is admirably explained
in a work on gravitation, by Mr. Airy, the Astronomer Royal.


NOTE 64, pp. 16, 74. _Perihelion._ Fig. 10, P, the point of an orbit
nearest the sun.


NOTE 65, p. 16. _Aphelion._ Fig. 10, A, the point of an orbit farthest
from the sun.


NOTE 66, pp. 16, 17. In fig. 15 the central force is greater than the
exact law of gravity; therefore the curvature P p a is greater than P p
A the real ellipse; hence the planet p comes to the point a, called the
aphelion, sooner than if it moved in the orbit P p A, which makes the
line P S A advance to a. In fig. 16, on the contrary, the curvature P p
a is less than in the true ellipse, so that the planet p must move
through more than the arc P p A, or 180°, before it comes to the
aphelion a, which causes the greater axis P S A to recede to a.

[Illustration: _Fig. 15._]

[Illustration: _Fig. 16._]


NOTE 67, pp. 16, 17. _Motion of apsides._ Let P S A, fig. 17, be the
position of the elliptical orbit of a planet, at any time; then, by the
action of the disturbing forces, it successively takes the position Pʹ S
Aʹ, Pʺ S Aʺ, &c., till by this direct motion it has accomplished a
revolution, and then it begins again; so that the motion is perpetual.

[Illustration: _Fig. 17._]


NOTE 68, p. 17. _Sidereal revolution._ The consecutive return of an
object to the same star.


NOTE 69, p. 17. _Tropical revolution._ The consecutive return of an
object to the same tropic or equinox.


NOTE 70, p. 17. _The orbit only bulges, &c._ In fig. 18 the effect of
the variation in the excentricity is shown where P p A is the elliptical
orbit at any given instant; after a time it will take the form P pʹ A,
in consequence of the decrease in the excentricity C S; then the forms P
pʺ A, P pʹʹʹ A, &c., consecutively from the same cause; and, as the
major axis P A always retains the same length, the orbit approaches more
and more nearly to the circular form. But, after this has gone on for
some thousands of years, the orbit contracts again, and becomes more and
more elliptical.

[Illustration: _Fig. 18._]


NOTE 71, pp. 18, 19. _The ecliptic_ is the apparent path of the sun in
the heavens. See note 46.


NOTE 72, p. 18. _This force tends to pull, &c._ The force in question,
acting in the direction p m, fig. 13, pulls the planet p towards the
plane N m n, or pushes it farther above it, giving the planet a tendency
to move in an orbit above or below its undisturbed orbit N p n, which
alters the angle p N m, and makes the node N and the line of nodes N n
change their positions.

[Illustration: _Fig. 19._]


NOTE 73, p. 18. _Motion of the nodes._ Let S, fig. 19, be the sun; S N n
the plane of the ecliptic; P the disturbing body; and p a planet moving
in its orbit p n, of which p n is so small a part that it is represented
as a straight line. The plane S n p of this orbit cuts the plane of the
ecliptic in the straight line S n. Suppose the disturbing force begins
to act on p, so as to draw the planet into the arc p pʹ; then, instead
of moving in the orbit p n, it will tend to move in the orbit p pʹ nʹ,
whose plane cuts the ecliptic in the straight line S nʹ. If the
disturbing force acts again upon the body when at pʹ, so as to draw it
into the arc pʹ pʺ, the planet will now tend to move in the orbit pʹ pʺ
nʺ, whose plane cuts the ecliptic in the straight line S nʺ. The action
of the disturbing force on the planet when at pʺ will bring the node to
nʹʹʹ, and so on. In this manner the node goes backwards through the
successive points n, nʹ, nʺ, nʹʹʹ, &c., and the line of nodes S n has a
perpetual retrograde motion about S, the centre of the sun. The
disturbing force has been represented as acting at intervals for the
sake of illustration: in nature it is continuous, so that the motion of
the node is continuous also; though it is sometimes rapid and sometimes
slow, now retrograde and now direct; but, on the whole, the motion is
slowly retrograde.


NOTE 74, p. 18. _When the disturbing planet_ is anywhere in the line S
N, fig. 19, or in its prolongation, it is in the same plane with the
disturbed planet; and, however much it may affect its motions in that
plane, it can have no tendency to draw it out of it. But when the
disturbing planet is in P, at right angles to the line S N, and not in
the plane of the orbit, it has a powerful effect on the motion of the
nodes: between these two positions there is great variety of action.


NOTE 75, p. 19. _The changes in the inclination_ are extremely minute
when compared with the motion of the node, as evidently appears from
fig. 19, where the angles n p nʹ, nʹ pʹ nʺ, &c., are much smaller than
the corresponding angles n S nʹ, S nʺ, &c.


NOTE 76, p. 20. _Sines and cosines._ Figure 4 is a circle; n p is the
sine, and C p is the cosine of an arc m n. Suppose the radius C m to
begin to revolve at m, in the direction m n a; then at the point m the
sine is zero, and the cosine is equal to the radius C m. As the line C m
revolves and takes the successive positions C n, C a, C b, &c., the
sines n p, a q, b r, &c., of the arcs m n, m a, m h, &c., increase,
while the corresponding cosines C p, C q, C r, &c., decrease; and when
the revolving radius takes the position C d, at right angles to the
diameter g m, the sine becomes equal to the radius C d, and the cosine
is zero. After passing the point d, the contrary happens; for the sines
e K, l V, &c., diminish, and the cosines C K, C V, &c., go on
increasing, till at g the sine is zero, and the cosine is equal to the
radius C g. The same alternation takes place through the remaining parts
g h, h m, of the circle, so that a sine or cosine never can exceed the
radius. As the rotation of the earth is invariable, each point of its
surface passes through a complete circle, or 360 degrees, in twenty-four
hours, at a rate of 15 degrees in an hour. Time, therefore, becomes a
measure of angular motion, and _vice versâ_, the arcs of a circle a
measure of time, since these two quantities vary simultaneously and
equably; and, as the sines and cosines of the arcs are expressed in
terms of the time, they vary with it. Therefore, however long the time
may be, and how often soever the radius may revolve round the circle,
the sines and cosines never can exceed the radius; and, as the radius is
assumed to be equal to unity, their values oscillate between unity and
zero.


NOTE 77, p. 20. The small excentricities and inclinations of the
planetary orbits, and the revolutions of all the bodies in the same
direction, were proved by Euler, La Grange, and La Place, to be
conditions necessary for the stability of the solar system.
Subsequently, however, the periodicity of the terms of the series
expressing the perturbations was supposed to be sufficient _alone_, but
M. Poisson has shown that to be a mistake; that these three conditions
are requisite for the necessary convergence of the series, and that
therefore the stability of the system depends on them _conjointly_ with
the periodicity of the sines and cosines of each term. The author is
aware that this note can only be intelligible to the analyst, but she is
desirous of correcting an error, and the more so as the conditions of
stability afford one of the most striking instances of design in the
original construction of our system, and of the foresight and supreme
wisdom of the Divine Architect.


NOTE 78, p. 22. _Resisting medium._ A fluid which resists the motions of
bodies, such as atmospheric air, or the highly elastic fluid called
ether, with which space is filled.


NOTE 79, p. 23. _Obliquity of the ecliptic._ The angle e ♈ q, fig. 11,
between the plane of the terrestrial equator q ♈ Q, and the plane of the
ecliptic E ♈ e. The obliquity is variable.


NOTE 80, p. 23. _Invariable plane._ In the earth the equator is the
invariable plane which nearly maintains a parallel position with regard
to itself while revolving about the sun, as in fig. 20, where E Q
represents it. The two hemispheres balance one another on each side of
this plane, and would still do so if all the particles of which they
consist were moveable among themselves, provided the earth were not
disturbed by the action of the sun and moon, which alters the
parallelism of the equator by the small variation called nutation, to be
explained hereafter.

[Illustration: _Fig. 20._]

[Illustration: _Fig. 21._]


NOTE 81, p. 24. _If each particle, &c._ Let P, Pʹ, Pʺ, &c., fig. 21, be
planets moving in their orbits about the centre of gravity of the
system. Let P S M, Pʹ S Mʹ, &c., be portions of these orbits moved over
by the radii vectores S P, S Pʹ, &c., in a given time, and let p S m, pʹ
S mʹ, &c., be their shadows or projections on the invariable plane.
Then, if the numbers which represent the masses of the planets P, Pʹ,
&c., be respectively multiplied by the numbers representing the areas or
spaces p S m, pʹ S mʹ, &c., the sum of the whole will be greater for the
invariable plane than it would be for any plane that could pass through
S, the centre of gravity of the system.


NOTE 82, p. 24. _The centre of gravity_ of the solar system lies within
the body of the sun, because his mass is much greater than the masses of
all the planets and satellites added together.


NOTE 83, pp. 25, 36. _Conjunction._ A planet is said to be in
conjunction when it has the same longitude with the sun, and in
opposition when its longitude differs from that of the sun by 180
degrees. Thus two bodies are said to be in conjunction when they are
seen exactly in the same part of the heavens, and in opposition when
diametrically opposite to one another. Mercury and Venus, which are
nearer to the sun than the earth, are called inferior planets; while all
the others, being farther from the sun than the earth, are said to be
superior planets. Suppose the earth to be at E, fig. 24; then a superior
planet will be in conjunction with the sun at C, and in opposition to
him when at O. Again, suppose the earth to be in O, then an inferior
planet will be in conjunction when at E, and in opposition when at F.


NOTE 84, p. 26. _The periodic inequalities_ are computed for a given
time; and consequently for a given form and position of the orbits of
the disturbed and disturbing bodies. Although the elements of the orbits
vary so slowly that no sensible effect is produced on inequalities of a
short period, yet, in the course of time, the secular variations of the
elements change the forms and relative positions of the orbits so much,
that Jupiter and Saturn, which would have come to the same relative
positions with regard to the sun and to one another after 850 years, do
not arrive at the same relative positions till after 918 years.


NOTE 85, p. 26. _Configuration._ The relative position of the planets
with regard to one another, to the sun, and to the plane of the
ecliptic.


NOTE 86, p. 27. In the same manner that the excentricity of an
elliptical orbit may be increased or diminished by the action of the
disturbing forces, so a circular orbit may acquire less or more
ellipticity from the same cause. It is thus that the forms of the orbits
of the first and second satellites of Jupiter oscillate between circles
and ellipses differing very little from circles.

[Illustration: _Fig. 22._]


NOTE 87, p. 28. _The plane of Jupiter’s equator_ is the imaginary plane
passing through his centre at right angles to his axis of rotation, and
corresponds to the plane q E Q e, in fig. 1. The satellites move very
nearly in the plane of Jupiter’s equator; for, if J be Jupiter, fig. 22,
P p his axis of rotation, e Q his equatorial diameter, which is 6000
miles longer than P p, and if J O and J E be the planes of his orbit and
equator seen edgewise, then the orbits of his four satellites seen
edgewise will have the positions J1, J2, J3, J4. These are extremely
near to one another, for the angle E J O is only 3° 5ʹ 30ʺ.


NOTE 88, p. 28. In consequence of the satellites moving so nearly in the
plane of Jupiter’s equator, when seen from the earth, they appear to be
always very nearly in a straight line, however much they may change
their positions with regard to one another and to their primary. For
example, on the evenings of the 3rd, 4th, 5th, and 6th of January, 1835,
the satellites had the configurations given in fig. 23, where O is
Jupiter, and 1, 2, 3, 4, are the first, second, third, and fourth
satellites. The satellite is supposed to be moving in a direction from
the figure towards the point. On the sixth evening the second satellite
was seen on the disc of the planet.

[Illustration: _Fig. 23._]


NOTE 89, p. 28. _Angular motion or velocity_ is the swiftness with which
a body revolves—a sling, for example; or the speed with which the
surface of the earth performs its daily rotation about its axis.


NOTE 90, p. 29. _Displacement of Jupiter’s orbit._ The action of the
planets occasions secular variations in the position of Jupiter’s orbit
J O, fig. 22, without affecting the plane of his equator J E. Again, the
sun and satellites themselves, by attracting the protuberant matter at
Jupiter’s equator, change the position of the plane J E without
affecting J O. Both of these cause perturbations in the motions of the
satellites.


NOTE 91, p. 29. _Precession_, with regard to Jupiter, is a retrograde
motion of the point where the lines J O, J E, intersect fig. 22.


NOTE 92, p. 30. _Synodic motion of a satellite._ Its motion during the
interval between two of its consecutive eclipses.

[Illustration: _Fig. 24._]


NOTE 93, p. 30. _Opposition._ A body is said to be in opposition when
its longitude differs from that of the sun by 180°. If S, fig. 24, be
the sun, and E the earth, then Jupiter is in opposition when at O, and
in conjunction when at C. In these positions the three bodies are in the
same straight line.


NOTE 94, p. 30. _Eclipses of the satellites._ Let S, fig. 25, be the
sun, J Jupiter, and a B b his shadow. Let the earth be moving in its
orbit, in the direction E A R T H, and the third satellite in the
direction a b m n. When the earth is at E, the satellite, in moving
through the arc a b, will vanish at a, and reappear at b, on the same
side of Jupiter. If the earth be in R, Jupiter will be in opposition;
and then the satellite, in moving through the arc a b, will vanish close
to the disc of the planet, and will reappear on the other side of it.
But, if the satellite be moving through the arc m n, it will appear to
pass over the disc, and eclipse the planet.

[Illustration: _Fig. 25._]


NOTE 95, pp. 30, 43. _Meridian._ A terrestrial meridian is a line
passing round the earth and through both poles. In every part of it noon
happens at the same instant. In figures 1 and 3, the lines N Q S and N G
S are meridians, C being the centre of the earth, and N S its axis of
rotation. The meridian passing through the Observatory at Greenwich is
assumed by the British as a fixed origin from whence terrestrial
longitudes are measured. And as each point on the surface of the earth
passes through 360°, or a complete circle, in twenty-four hours, at the
rate of 15° in an hour, time becomes a representative of angular motion.
Hence, if the eclipse of a satellite happens at any place at eight
o’clock in the evening, and the Nautical Almanac shows that the same
phenomenon will take place at Greenwich at nine, the place of
observation will be in the 15° of west longitude.


NOTE 96, p. 31. _Conjunction._ Let S be the sun, fig. 24, E the earth,
and J O Jʹ Cʹ the orbit of Jupiter. Then the eclipses which happen when
Jupiter is in O are seen 16^m 26^s sooner than those which take place
when the planet is in C. Jupiter is in conjunction when at C, and in
opposition when in O.

[Illustration: _Fig. 26._]


NOTE 97, p. 31. _In the diagonal, &c._ Were the line A S, fig. 26,
100,000 times longer than A B, Jupiter’s true place would be in the
direction A Sʹ, the diagonal of the figure A B Sʹ S, which is, of
course, out of proportion.


NOTE 98, p. 31. _Aberration of light._ The celestial bodies are so
distant that the rays of light coming from them may be reckoned
parallel. Therefore, let S A, Sʹ B, fig. 26, be two rays of light coming
from the sun, or a planet, to the earth moving in its orbit in the
direction A B. If a telescope be held in the direction A S, the ray S A,
instead of going down the tube, will impinge on its side, and be lost in
consequence of the telescope being carried with the earth in the
direction A B. But, if the tube be held in the position A E, so that A B
is to A S as the velocity of the earth to the velocity of light, the ray
will pass through Sʹ E A. The star appears to be in the direction A Sʹ,
when it really is in the direction A S; hence the angle S A Sʹ is the
angle of aberration.


NOTE 99, p. 32. _Density proportional to elasticity._ The more a fluid,
such as atmospheric air, is reduced in dimensions by pressure, the more
it resists the pressure.


NOTE 100, p. 32. _Oscillations of pendulum retarded._ If a clock be
carried from the pole to the equator, its rate will be gradually
diminished, that is, it will go slower and slower: because the
centrifugal force, which increases from the pole to the equator,
diminishes the force of gravity.


NOTE 101, p. 34. _Disturbing action._ The disturbing force acts here in
the very same manner as in note 63; only that the disturbing body d,
fig. 14, is the sun, S the earth, and p the moon.


NOTE 102, pp. 35, 36, 86. _Perigee._ A Greek word, signifying round the
earth. The perigee of the lunar orbit is the point P, fig. 6, where the
moon is nearest to the earth. It corresponds to the perihelion of a
planet. Sometimes the word is used to denote the point where the sun is
nearest to the earth.


NOTE 103, p. 35. _Evection._ The evection is produced by the action of
the radial force in the direction S p, fig. 14, which sometimes
increases and sometimes diminishes the earth’s attraction to the moon.
It produces a corresponding temporary change in the excentricity, which
varies with the position of the major axis of the lunar orbit in respect
of the line S d, joining the centres of the earth and sun.


NOTE 104, p. 35. _Variation._ The lunar perturbation called the
variation is the alternate acceleration and retardation of the moon in
longitude, from the action of the tangential force. She is accelerated
in going from quadratures in Q and D, fig. 14, to the points C and O,
called syzygies, and is retarded in going from the syzygies C and O to Q
and D again.


NOTE 105, p. 36. _Square of time._ If the times increase at the rate of
1, 2, 3, 4, &c., years or hundreds of years, the squares of the times
will be 1, 4, 9, 16, &c., years or hundreds of years.


NOTE 106, p. 37. In all investigations hitherto made with regard to the
acceleration, it was tacitly assumed that the areas described by the
radius vector of the moon were not permanently altered; that is to say,
that the tangential disturbing force produced no permanent effect. But
Mr. Adams has discovered that, in consequence of the constant decrease
in the excentricity of the earth’s orbit, there is a gradual change in
the central disturbing force which affects the aërial velocity, and
consequently it alters the amount of the acceleration by a very small
quantity, as well as the variation and other periodical inequalities of
the moon. On the latter, however, it has no permanent effect, because it
affects them in opposite directions in very moderate intervals of time,
whereas a very small error in the amount of the acceleration goes on
increasing as long as the excentricity of the earth’s orbit diminishes,
so that it would ultimately vitiate calculations of the moon’s place for
distant periods of time. This shows how complicated the moon’s motions
are, and what rigorous accuracy is required in their determination.

To give an idea of the labour requisite _merely_ to _perfect_ or
_correct_ the lunar tables, the moon’s place was determined by
observation at the Greenwich Observatory in 6000 different points of her
orbit, each of which was compared with the same points calculated from
Baron Plana’s formulæ, and to do that _sixteen computers_ were
constantly employed for _eight years_. Since the longitude is determined
by the motions of the moon, the lunar tables are of the greatest
importance.


NOTE 107, p. 37. _Mean anomaly._ The mean anomaly of a planet is its
angular distance from the perihelion, supposing it to move in a circle.
The true anomaly is its angular distance from the perihelion in its
elliptical orbit. For example, in fig. 10, the mean anomaly is P C m,
and the true anomaly is P S p.


NOTE 108, pp. 38, 68. _Many circumferences._ There are 360 degrees or
1,296,000 seconds in a circumference; and, as the acceleration of the
moon only increases at the rate of eleven seconds in a century, it must
be a prodigious number of ages before it accumulates to many
circumferences.


NOTE 109, p. 39. _Phases of the moon._ The periodical changes in the
enlightened part of her disc, from a crescent to a circle, depending
upon her position with regard to the sun and earth.


NOTE 110, p. 39. _Lunar eclipse._ Let S, fig. 27, be the sun, E the
earth, and m the moon. The space a A b is a section of the shadow, which
has the form of a cone or sugar-loaf, and the spaces A a c, A b d, are
the penumbra. The axis of the cone passes through A, and through E and
S, the centres of the sun and earth, and n m nʹ is the path of the moon
through the shadow.

[Illustration: _Fig. 27._]


NOTE 111, p. 39. _Apparent diameter._ The diameter of a celestial body
as seen from the earth.


NOTE 112, p. 40. _Penumbra._ The shadow or imperfect darkness which
precedes and follows an eclipse.


NOTE 113, p. 40. _Synodic revolution of the moon._ The time between two
consecutive new or full moons.


NOTE 114, p. 40. _Horizontal refraction._ The light, in coming from a
celestial object, is bent into a curve as soon as it enters our
atmosphere; and that bending is greatest when the object is in the
horizon.

[Illustration: _Fig. 28._]


NOTE 115, p. 40. _Solar eclipse._ Let S, fig. 28, be the sun, m the
moon, and E the earth. Then a E b is the moon’s shadow, which sometimes
eclipses a small portion of the earth’s surface at e, and sometimes
falls short of it. To a person at e, in the centre of the shadow, the
eclipse may be total or annular; to a person not in the centre of the
shadow a part of the sun will be eclipsed; and to one at the edge of the
shadow there will be no eclipse at all. The spaces P b E, Pʹ a E, are
the penumbra.


NOTE 116, p. 43. _From the extremities, &c._ If the length of the line a
b, fig. 29, be measured, in feet or fathoms, the angles S b a, S a b,
can be measured, and then the angle a S b is known, whence the length of
the line S C may be computed. a S b is the parallax of the object S; and
it is clear that, the greater the distance of S, the less the base a b
will appear, because the angle a Sʹ b is less than a S b.

[Illustration: _Fig. 29._]


NOTE 117, p. 44. _Every particle will describe a circle, &c._ If N S,
fig. 3, be the axis about which the body revolves, then particles at B,
Q, &c., will whirl in the circles B G A a, Q E q d, whose centres are in
the axis N S, and their planes parallel to one another. They are, in
fact, parallels of latitude, Q E q d being the equator.


NOTE 118, p. 44. _The force of gravity, &c._ Gravity at the equator acts
in the direction Q C, fig. 30. Whereas the direction of the centrifugal
force is exactly contrary, being in the direction C Q; hence the
difference of the two is the force called gravitation, which makes
bodies fall to the surface of the earth. At any point, m, not at the
equator, the direction of gravity is m b, perpendicular to the surface,
but the centrifugal force acts perpendicularly to N S, the axis of
rotation. Now the effect of the centrifugal force is the same as if it
were two forces, one of which acting in the direction b m, diminishes
the force of gravity, and another which, acting in the direction m t,
tangent to the surface at m, urges the particles towards Q, and tends to
swell out the earth at the equator.

[Illustration: _Fig. 30._]


NOTE 119, p. 45. _Homogeneous mass._ A quantity of matter, everywhere of
the same density.


NOTE 120, p. 45. _Ellipsoid of revolution._ A solid formed by the
revolution of an ellipse about its axis. If the ellipse revolve about
its minor axis Q D, fig. 6, the ellipsoid will be _oblate_, or flattened
at the poles like an orange. If the revolution be about the greater axis
A P, the ellipsoid will be prolate, like an egg.


NOTE 121, p. 45. _Concentric elliptical strata._ Strata, or layers,
having an elliptical form and the same centre.


NOTE 122, p. 46. _On the whole, &c._ The line N Q S q, fig. 1,
represents the ellipse in question, its major axis being Q q, its minor
axis N S.


NOTE 123, p. 46. _Increase in the length of the radii, &c._ The radii
gradually increase from the polar radius C N, fig. 30, which is least,
to the equatorial radius C Q, which is greatest. There is also an
increase in the lengths of the arcs corresponding to the same number of
degrees from the equator to the poles; for, the angle N C r being equal
to q C d, the elliptical arc N r is less than q d.


NOTE 124, p. 46. _Cosine of latitude._ The angles m C a, m C b, fig. 4,
being the latitudes of the points a, b, &c., the cosines are C q, C r,
&c.


NOTE 125, p. 47. _An arc of the meridian._ Let N Q S q, fig. 30, be the
meridian, and m n the arc to be measured. Then, if Zʹ m, Z n, be
verticals, or lines perpendicular to the surface of the earth, at the
extremities of the arc m n they will meet in p. Q a n, Q b m, are the
latitudes of the points m and n, and their difference is the angle m p
n. Since the latitudes are equal to the height of the pole of the
equinoctial above the horizon of the places m and n, the angle m p n may
be found by observation. When the distance m n is measured in feet or
fathoms, and divided by the number of degrees and parts of a degree
contained in the angle m p n, the length of an arc of one degree is
obtained.


NOTE 126, p. 47. _A series of triangles._ Let M Mʹ, fig. 31, be the
meridian of any place. A line A B is measured with rods, on level
ground, of any number of fathoms, C being some point seen from both ends
of it. As two of the angles of the triangle A B C can be measured, the
lengths of the sides A C, B C, can be computed; and if the angle m A B,
which the base A B makes with the meridian, be measured, the length of
the sides B m, A m, may be obtained by computation, so that A m, a small
part of the meridian, is determined. Again, if D be a point visible from
the extremities of the known line B C, two of the angles of the triangle
B C D may be measured, and the length of the sides C D, B D, computed.
Then, if the angle B m mʹ be measured, all the angles and the side B m
of the triangle B m mʹ are known, whence the length of the line m mʹ may
be computed, so that the portion A mʹ of the meridian is determined, and
in the same manner it may be prolonged indefinitely.

[Illustration: _Fig. 31._]


NOTE 127, pp. 47, 49. _The square of the sine of the latitude._ Q b m,
fig. 30, being the latitude of m, e m is the sine and b e the cosine.
Then the number expressing the length of e m, multiplied by itself, is
the square of the sine of the latitude; and the number expressing the
length of b e, multiplied by itself, is the square of the cosine of the
latitude.


NOTE 128, p. 48. The polar diameter of the earth determined by the
survey of Great Britain is 7900 miles; the equatorial is 7926, which
gives a compression of 1/299·33.


NOTE 129, p. 50. _A pendulum_ is that part of a clock which swings to
and fro.

[Illustration: _Fig. 32._]


NOTE 130, p. 52. _Parallax._ The angle a S b, fig. 29, under which we
view an object a b: it therefore diminishes as the distance increases.
The parallax of a celestial object is the angle which the radius of the
earth would be seen under, if viewed from that object. Let E, fig. 32,
be the centre of the earth, E H its radius, and m H O the horizon of an
observer at H. Then H m E is the parallax of a body m, the moon for
example. As m rises higher and higher in the heavens to the points mʹ,
mʺ, &c., the parallax H mʹ E, H mʺ E, &c., decreases. At Z, the zenith,
or point immediately above the head of the observer, it is zero; and at
m, where the body is in the horizon, the angle H m E is the greatest
possible, and is called the horizontal parallax. It is clear that with
regard to celestial bodies the whole effect of parallax is in the
vertical, or in the direction m mʹ Z; and as a person at H sees mʹ in
the direction H mʹ A, when it really is in the direction E mʹ B, it
makes celestial objects appear to be lower than they really are. The
distance of the moon from the earth has been determined from her
horizontal parallax. The angle E m H can be measured. E H m is a right
angle, and E H, the radius of the earth, is known in miles; whence the
distance of the moon E m is easily found. Annual parallax is the angle
under which the diameter of the earth’s orbit would be seen if viewed
from a star.


NOTE 131, p. 52. _The radii_ n B, n G, &c., fig. 3, are equal in any one
parallel of latitude, A a B G; therefore a change in the parallax
observed in that parallel can only arise from a change in the moon’s
distance from the earth; and when the moon is at her mean distance,
which is a constant quantity equal to half the major axis of her orbit,
a change in the parallax observed in different latitudes, G and E, must
arise from the difference in the lengths of the radii n G and C E.


NOTE 132, p. 52. _When Venus is in her nodes._ She must be in the line N
S n where her orbit P N A n cuts the plane of the ecliptic E N e n, fig.
12.


NOTE 133, p. 53. _The line described, &c._ Let E, fig. 33, be the earth,
S the centre of the sun, and V the planet Venus. The real transit of the
planet, seen from E the centre of the earth, would be in the direction A
B. A person at W would see it pass over the sun in the line v a, and a
person at O would see it move across him in the direction vʹ aʹ.

[Illustration: _Fig. 33._]


NOTE 134, p. 54. _Kepler’s law._ Suppose it were required to find the
distance of Jupiter from the sun. The periodic times of Jupiter and
Venus are given by observation, and the mean distance of Venus from the
centre of the sun is known in miles or terrestrial radii; therefore, by
the rule of three, the square root of the periodic time of Venus is to
the square root of the periodic time of Jupiter as the cube root of the
mean distance of Venus from the sun to the cube root of the mean
distance of Jupiter from the sun, which is thus obtained in miles or
terrestrial radii. The root of a number is that number which, once
multiplied by itself, gives its square; twice multiplied by itself,
gives its cube, &c. For example, twice 2 are 4, and twice 4 are 8; 2 is
therefore the square root of 4, and the cube root of 8. In the same
manner 3 times 3 are 9, and 3 times 9 are 27; 3 is therefore the square
root of 9, and the cube root of 27.


NOTE 135, p. 55. _Inversely, &c._ The quantities of matter in any two
primary planets are greater in proportion as the cubes of the numbers
representing the mean distances of their satellites are greater, and
also in proportion as the squares of their periodic times are less.


NOTE 136, p. 55. As hardly anything appears more impossible than that
man should have been able to weigh the sun as it were in scales and the
earth in a balance, the method of doing so may have some interest. The
attraction of the sun is to the attraction of the earth as the quantity
of matter in the sun to the quantity of matter in the earth; and, as the
force of this reciprocal attraction is measured by its effects, the
space the earth would fall through in a second by the sun’s attraction
is to the space which the sun would fall through by the earth’s
attraction as the mass of the sun to the mass of the earth. Hence, as
many times as the fall of the earth to the sun in a second exceeds the
fall of the sun to the earth in the same time, so many times does the
mass of the sun exceed the mass of the earth. Thus the weight of the sun
will be known if the length of these two spaces can be found in miles or
parts of a mile. Nothing can be easier. A heavy body falls through
16·0697 feet in a second at the surface of the earth by the earth’s
attraction; and, as the force of gravity is inversely as the square of
the distance, it is clear that 16·0697 feet are to the space a body
would fall through at the distance of the sun by the earth’s attraction,
as the square of the distance of the sun from the earth to the square of
the distance of the centre of the earth from its surface; that is, as
the square of 95,000,000 miles to the square of 4000 miles. And thus, by
a simple question in the rule of three, the space which the sun would
fall through in a second by the attraction of the earth may be found in
parts of a mile. The space the earth would fall through in a second, by
the attraction of the sun, must now be found in miles also. Suppose m n,
fig. 4, to be the arc which the earth describes round the sun in C, in a
second of time, by the joint action of the sun and the centrifugal
force. By the centrifugal force alone the earth would move from m to T
in a second, and by the sun’s attraction alone it would fall through T n
in the same time. Hence the length of T n, in miles, is the space the
earth would fall through in a second by the sun’s attraction. Now, as
the earth’s orbit is very nearly a circle, if 360 degrees be divided by
the number of seconds in a sidereal year of 365-1/4 days, it will give m
n, the arc which the earth moves through in a second, and then the
tables will give the length of the line C T in numbers corresponding to
that angle; but, as the radius C n is assumed to be unity in the tables,
if 1 be subtracted from the number representing C T, the length of T n
will be obtained; and, when multiplied by 95,000,000, to reduce it to
miles, the space which the earth falls through, by the sun’s attraction,
will be obtained in miles. By this simple process it is found that, if
the sun were placed in one scale of a balance, it would require 354,936
earths to form a counterpoise.


NOTE 137, p. 59. The sum of the greatest and least distances S P, S A,
fig. 12, is equal to P A, the major axis; and their difference is equal
to twice the excentricity C S. The longitude ♈ S P of the planet, when
in the point P, at its least distance from the sun, is the longitude of
the perihelion. The greatest height of the planet above the plane of the
ecliptic E N e n, is equal to the inclination of the orbit P N A n to
that plane. The longitude of the planet, when in the plane of the
ecliptic, can only be the longitude of one of the points N or n; and,
when one of these points is known, the other is given, being 180°
distant from it. Lastly, the time included between two consecutive
passages of the planet through the same node N or n, is its periodic
time, allowance being made for the recess of the node in the interval.


NOTE 138, p. 60. Suppose that it were required to find the position of a
point in space, as of a planet, and that one observation places it in n,
fig. 34, another observation places it in nʹ, another in nʺ, and so on;
all the points n, nʹ, nʺ, nʹʹʹ, &c., being very near to one another. The
true place of the planet P will not differ much from any of these
positions. It is evident, from this view of the subject, that P n, P nʹ,
P nʺ, &c., are the errors of observation. The true position of the
planet P is found by this property, that the squares of the numbers
representing the lines P n, P nʹ, &c., when added together, is the least
possible. Each line P n, P nʹ, &c., being the whole error in the place
of the planet, is made up of the errors of all the elements; and, when
compared with the errors obtained from theory, it affords the means of
finding each. The principle of least squares is of very general
application; its demonstration cannot find a place here; but the reader
is referred to Biot’s Astronomy, vol. ii. p. 203.

[Illustration: _Fig. 34._]


NOTE 139, p. 61. The true longitude of Uranus was in advance of the
tables previous to 1795, and continued to advance till 1822, after which
it diminished rapidly till 1830-1, when the observed and calculated
longitudes agreed, but then the planet fell behind the calculated place
so rapidly that it was clear the tables could no longer represent its
motion.


NOTE 140, p. 65. _An axis that, &c._ Fig. 20 represents the earth
revolving in its orbit about the sun in S, the axis of rotation P p
being everywhere parallel to itself.


NOTE 141, p. 65. _Angular velocities that are sensibly uniform._ The
earth and planets revolve about their axis with an equable motion, which
is never either faster or slower. For example, the length of the day is
never more nor less than twenty-four hours.


NOTE 142, p. 68. If fig. 1 be the moon, her polar diameter N S is the
shortest; and of those in the plane of the equator, Q E q, that which
points to the earth is greater than all the others.


NOTE 143, p. 73. _Inversely proportional, &c._ That is, the total amount
of solar radiation becomes less as the minor axis C Cʹ, fig. 20, of the
earth’s orbit becomes greater.


NOTE 144, p. 75. Fig. 35 represents the position of the apparent orbit
of the sun as it is at present, the earth being in E. The sun is nearer
to the earth in moving through ♎ P ♈ than in moving through ♈ A ♎, but
its motion through ♎ P ♈ is more rapid than its motion through ♈ A ♎;
and, as the swiftness of the motion and the quantity of heat received
vary in the same proportion, a compensation takes place.

[Illustration: _Fig. 35._]


NOTE 145, p. 76. _In an ellipsoid of revolution_, fig. 1, the polar
diameter N S, and every diameter in the equator q E Q e, are permanent
axes of rotation, but the rotation would be unstable about any other.
Were the earth to begin to rotate about C a, the angular distance from a
to the equator at q would no longer be ninety degrees, which would be
immediately detected by the change it would occasion in the latitudes.


NOTE 146, pp. 50, 80. Let q ♈ Q, and E ♎ e, fig. 11, be the planes of
the equator and ecliptic. The angle e ♈ Q, which separates them, called
the obliquity of the ecliptic, varies in consequence of the action of
the sun and moon upon the protuberant matter at the earth’s equator.
That action brings the point Q towards e, and tends to make the plane q
♈ Q coincide with the ecliptic E ♈ e, which causes the equinoctial
points ♈ and ♎ to move slowly backwards on the plane e ♈ E, at the rate
of 50ʺ·41 annually. This part of the motion, which depends upon the form
of the earth, is called luni-solar precession. Another part, totally
independent of the form of the earth, arises from the mutual action of
the earth, planets, and sun, which, altering the position of the plane
of the ecliptic e ♈ E, causes the equinoctial points ♈ and ♎ to advance
at the rate of Oʺ·31 annually; but, as this motion is much less than the
former, the equinoctial points recede on the plane of the ecliptic at
the rate of 50ʺ·1 annually. This motion is called the precession of the
equinoxes.


NOTE 147, p. 81. Let q ♈ Q, e ♈ E, fig. 36, be the planes of the
equinoctial or celestial equator and ecliptic, and p, P, their poles.
Then suppose p, the pole of the equator, to revolve with a tremulous or
wavy motion in the little ellipse p c d b in about 19 years, both
motions being very small, while the point a is carried round in the
circle a A B in 25,868 years. The tremulous motion may represent the
half-yearly variation, the motion in the ellipse gives an idea of the
nutation discovered by Bradley, and the motion in the circle a A B
arises from the precession of the equinoxes. The greater axis p d of the
small ellipse is 18ʺ·5, its minor axis b c is 13ʺ·74. These motions are
so small that they have very little effect on the parallelism of the
axis of the earth’s rotation during its revolution round the sun, as
represented in fig. 20. As the stars are fixed, this real motion in the
pole of the earth must cause an apparent change in their places.

[Illustration: _Fig. 36._]

[Illustration: figure: equidistant wires in an eye-piece]


NOTE 148, p. 83. By means of a transit instrument, which is a telescope
mounted so as to revolve only in the plane of the meridian, the instant
of the transit or passage of a celestial body across the meridian can be
determined. The transits of the principal stars are used to ascertain
the time, or, which is the same thing, the amount of the error of
clocks. A system of equidistant wires, as represented in the figure, is
placed in the focus of the eye-piece, so that the middle wire is
perpendicular and at right angles to the axis of the telescope. It
consequently represents a portion of the celestial meridian; and when a
star is seen to cross that wire it then crosses the celestial meridian
of the place of observation. A clock beating seconds being close at
hand, the duty of an observer is to note the exact second and part of a
second at which a star crosses each wire successively in consequence of
the rotation of the earth. Then the mean of all these observations will
give the time at which the star crosses the celestial meridian of the
place of observation to the tenth of a second, provided the observations
are accurate. Now it happens that the simultaneous impression on the eye
and ear is estimated differently by different observers, so that one
person will note the transit of a star, for example, as happening the
fraction of a second sooner or later than another person; and as that is
the case in every observation he makes, it is called his _personal
equation_, that is to say, it is a correction that must be applied to
all the observations of the individual, and a curious instance of
individuality it is. For instance, M. Otto Struve notes every
observation Oʺ·11 too soon, M. Peters Oʺ·13 too late; M. Struve noted
every observation one second later than M. Bessel, and M. Argelander
estimated the transit of a star 1ʺ·2 later than M. Bessel. All these
gentlemen were or are first-rate observers; and when the personal
equation is known it is easy to correct the observations. However, to
avoid that inconvenience Mr. Bond has introduced a method in the
Observatory at Cambridge in the United States in which touch is combined
with sight instead of hearing, which is now used also at Greenwich. The
observer at the moment of the observation presses his fingers on a
machine which by means of a galvanic battery conveys the impression to
where time is measured and marked, so that the observation is at once
recorded and the personal equation avoided.


NOTE 149, p. 84. _Let_ N be the pole, fig. 11, e E the ecliptic, and Q q
the equator. Then, N n m S being a meridian, and at right angles to the
equator, the arc ♈ m is less than the arc ♈ n.


NOTE 150, p. 85. _Heliacal rising of Sirius._ When the star appears in
the morning, in the horizon, a little before the rising of the sun.


NOTE 151, p. 87. Let P ♈ A ♎, fig. 35, be the apparent orbit or path of
the sun, the earth being in E. Its major axis, A P, is at present
situate as in the figure, where the solar perigee P is between the
solstice of winter and the equinox of spring. So that the time of the
sun’s passage through the arc ♈ A ♎ is greater than the time he takes to
go through the arc ♎ P ♈. The major axis A P coincided with ♎ ♈, the
line of the equinoxes, 4000 years before the Christian era; at that time
P was in the point ♈. In 6468 of the Christian era the perigee P will
coincide with ♎. In 1234 A.D. the major axis was perpendicular to ♈ ♎,
and then P was in the winter solstice.


NOTE 152, p. 88. _At the solstices, &c._ Since the declination of a
celestial object is its angular distance from the equinoctial, the
declination of the sun at the solstice is equal to the arc Q e, fig. 11,
which measures the obliquity of the ecliptic, or angular distance of the
plane ♈ e ♎ from the plane ♈ Q ♎.


NOTE 153, p. 88. _Zenith distance_ is the angular distance of a
celestial object from the point immediately over the head of an
observer.


NOTE 154, p. 89. _Reduced to the level of the sea._ The force of
gravitation decreases as the square of the height above the surface of
the earth increases, so that a pendulum vibrates slower on high ground;
and, in order to have a standard independent of local circumstances, it
is necessary to reduce it to the length that would exactly make 86,400
vibrations in a mean solar day at the level of the sea.


NOTE 155, p. 90. _A quadrant of the meridian_ is a fourth part of a
meridian, or an arc of a meridian containing 90°, as N Q, fig. 11.


NOTE 156, p. 93. _Moon’s southing._ The time when the moon is on the
meridian of any place, which happens about forty-eight minutes later
every day.


NOTE 157, p. 96. _The angular velocity of the earth’s rotation_ is at
the rate of 180° in twelve hours, which is the time included between the
passages of the moon at the upper and under meridian.


NOTE 158, p. 96. If S be the earth, fig. 14, d the sun, and C Q O D the
orbit of the moon, then C and O are the syzygies. When the moon is new,
she is at C, and when full she is at O; and, as both sun and moon are
then on the same meridian, it occasions the spring-tides, it being high
water at places under C and O, while it is low water at those under Q
and D. The neap-tides happen when the moon is in quadrature at Q or D,
for then she is distant from the sun by the angle d S Q, or d S D, each
of which is 90°.


NOTE 159, p. 97. _Declination._ If the earth be in C, fig. 11, and if q
♈ Q be the equinoctial, and N m S a meridian, then m C n is the
declination of a body at n. Therefore the cosine of that angle is the
cosine of the declination.


NOTE 160, pp. 99, 131. Fig 37 shows the propagation of waves from two
points C and Cʹ, where stones are supposed to have fallen. Those points
in which the waves cross each other are the places where they counteract
each other’s effects, so that the water is smooth there, while it is
agitated in the intermediate spaces.


NOTE 161, p. 100. _The centrifugal force may, &c._ The centrifugal force
acts in a direction at right angles to N S, the axis of rotation, fig.
30. Its effects are equivalent to two forces, one of which is in the
direction b m perpendicular to the surface Q m n of the earth, and
diminishes the force of gravity at m. The other acts in the direction of
the tangent m T, which makes the fluid particles tend towards the
equator.

[Illustration: _Fig. 37._]


NOTE 162, p. 106. _Analytical formula or expression._ A combination of
symbols or signs expressing or representing a series of calculation, and
including every particular case that can arise from a general law.


NOTE 163, p. 106. _Fig. 38 is a perfect octahedron._ Sometimes its
angles, A, X, a, a, &c., are truncated, or cut off. Sometimes a slice is
cut off its edges A a, X a, a a, &c. Occasionally both these
modifications take place.

[Illustration: _Fig. 38._]


NOTE 164, p. 107. Prismatic crystals of sulphate of nickel are somewhat
like fig. 62, only that they are thin, like a hair.


NOTE 165, p. 108. _Zinc_, a metal either found as an ore or mixed with
other metals. It is used in making brass.


NOTE 166, p. 108. _A cube_ is a solid contained by six plane square
surfaces, as fig. 39.

[Illustration: _Fig. 39._]


NOTE 167, p. 108. _A tetrahedron_ is a solid contained by four
triangular surfaces, as fig. 40: of this solid there are many varieties.

[Illustration: _Fig. 40._]


NOTE 168, p. 108. There are many varieties of the octahedron. In that
mentioned in the text, the base a a a a, fig. 38, is a square, but the
base may be a rhomb; this solid may also be elongated in the direction
of its axis A X, or it may be depressed.


NOTE 169, pp. 109, 192, 273. _A rhombohedron_ is a solid contained by
six plane surfaces, as in fig. 63, the opposite planes being equal and
similar rhombs parallel to one another; but all the planes are not
necessarily equal or similar, nor are its angles right angles. In
carbonate of lime the angle C A B is 105°·55, and the angle B or C is
75°·05.


NOTE 170, p. 109. _Sublimation._ Bodies raised into vapour which is
again condensed into a solid state.


NOTE 171, p. 112. _Platinum._ The heaviest of metals; its colour is
between that of silver and lead.


NOTE 172, p. 113. The surface of a column of water, or spirit of wine,
in a capillary tube, is hollow; and that of a column of quicksilver is
convex, or rounded, as in fig. 41.


NOTE 173, p. 113. _Inverse ratio, &c._ The elevation of the liquid is
greater in proportion as the internal diameter of the tube is less.


NOTE 174, p. 114. In fig. 41 the line c d shows the direction of the
resulting force in the two cases.

[Illustration: _Fig. 41._]


NOTE 175, p. 115. When two plates of glass are brought near to one
another in water, the liquid rises between them; and, if the plates
touch each other at one of their upright edges, the outline of the water
will become an hyperbola.


NOTE 176, p. 115. Let A Aʹ, fig. 42, be two plates, both of which are
wet, and B Bʹ two that are dry. When partly immersed in a liquid, its
surface will be curved close to them, but will be of its usual level for
the rest of the distance. At such a distance they will neither attract
nor repel one another. But, as soon as they are brought near enough to
have the whole of the liquid surface between them curved, as in a aʹ, b
bʹ, they will rush together. If one be wet and another dry, as C Cʹ,
they will repel one another at a certain distance; but, as soon as they
are brought very near, they will rush together, as in the former cases.

[Illustration: _Fig. 42._]


NOTE 177, p. 123. In a paper on the atmospheric changes that produce
rain and wind, by Thomas Hopkins, Esq., in the Geographical Journal, it
is shown that, when vapour is condensed and falls in rain, a partial
vacuum is formed, and that heavier air presses in as a current of wind.
Thus the vacuum arising from the great precipitation at the tropics
causes the polar winds to descend from the upper regions of the
atmosphere and blow along the surface to the equator as trade winds to
supply the place of the hot currents that are continually raising them
into the higher regions. This circumstance removes the only difficulty
in Lieutenant Maury’s theory of the winds.


NOTE 178, p. 134. _Latent or absorbed heat._ There is a certain quantity
of heat in all bodies, which cannot be detected by the thermometer, but
which may become sensible by compression.


NOTE 179, p. 137. _Reflected waves._ A series of waves of light, sound,
or water, diverge in all directions from their origin I, fig. 43, as
from a centre. When they meet with an obstacle S S, they strike against
it, and are reflected or turned back by it in the same form as if they
had proceeded from the centre C, at an equal distance on the other side
of the surface S S.

[Illustration: _Fig. 43._]


NOTE 180, p. 138. _Elliptical shell._ If fig. 6 be a section of an
elliptical shell, then all sounds coming from the focus S to different
points on the surface, as m, are reflected back to F, because the angle
T m S is equal to t m F. In a spherical hollow shell, a sound diverging
from the centre is reflected back to the centre again.


NOTE 181, p. 142. Fig. 44 represents musical strings in vibration; the
straight lines are the strings when at rest. The first figure of the
four would give the fundamental note, as, for example, the low C. The
second and third figures would give the first and second harmonics; that
is, the octave and the 12th above C, n n n being the points at rest; the
fourth figure shows the real motion when compounded of all three.

[Illustration: _Fig. 44._]


NOTE 182, p. 143. Fig. 45 represents sections of an open and of a shut
pipe, and of a pipe open at one end. When sounded, the air spontaneously
divides itself into segments. It remains at rest in the divisions or
nodes n nʹ, &c., but vibrates between them in the direction of the
arrow-heads. The undulations of the whole column of air give the
fundamental note, while the vibrations of the divisions give the
harmonics.

[Illustration: _Fig. 45._]


NOTE 183, p. 144. Fig. 1, plate 1, shows the vibrating surface when the
sand divides it into squares, and fig. 2 represents the same when the
nodal lines divide it into triangles. The portions marked a a are in
different states of vibration from those marked b b.


NOTE 184, p. 145. Plates 1 and 2 contain a few of Chladni’s figures. The
white lines are the forms assumed by the sand, from different modes of
vibration, corresponding to musical notes of different degrees of pitch.
Plate 3 contains six of Chladni’s circular figures.


NOTE 185, p. 145. Mr. Wheatstone’s principle is, that when vibrations
producing the forms of figs. 1 and 2, plate 3, are united in the same
surface, they make the sand assume the form of fig. 3. In the same
manner, the vibrations which would separately cause the sand to take the
forms of figs. 4 and 5, would make it assume the form in fig. 6 when
united. The figure 9 results from the modes of vibration of 7 and 8
combined. The parts marked a a are in different states of vibration from
those marked b b. Figs. 1, 2, and 3, plate 4, represent forms which the
sand takes in consequence of simple modes of vibration; 4 and 5 are
those arising from two combined modes of vibration; and the last six
figures arise from four superimposed simple modes of vibration. These
complicated figures are determined by computation independent of
experiment.


NOTE 186, p. 146. The long cross-lines of fig. 46 show the two systems
of nodal lines given by M. Savart’s laminæ.

[Illustration: _Fig. 46._]


NOTE 187, p. 146. The short lines on fig. 46 show the positions of the
nodal lines on the other sides of the same laminæ.


NOTE 188, p. 146. Fig. 47 gives the nodal lines on a cylinder, with the
paper rings that mark the quiescent points.

[Illustration: _Fig. 47._]

[Illustration: _Fig. 48._]


NOTE 189, pp. 138, 153, 156. _Reflection and Refraction._ Let P C p,
fig. 48, be perpendicular to a surface of glass or water A B. When a ray
of light, passing through the air, falls on this surface in any
direction I C, part of it is reflected in the direction C S, and the
other part is bent at C, and passes through the glass or water in the
direction C R. I C is called the incident ray, and I C P the angle of
incidence; C S is the reflected ray, and P C S the angle of reflection;
C R is the refracted ray, and p C R the angle of refraction. The plane
passing through S C and I C is the plane of reflection, and the plane
passing through I C and C R is the plane of refraction. In ordinary
cases, C I, C S, C R, are all in the same plane. We see the surface by
means of the reflected light, which would otherwise be invisible.
Whatever the reflecting surface may be, and however obliquely the light
may fall upon it, the angle of reflection is always equal to the angle
of incidence. Thus I C, Iʹ C, being rays incident on the surface at C,
they will be reflected into C S, C Sʹ, so that the angle S C P will be
equal to the angle I C P, and Sʹ C P equal to Iʹ C P. That is by no
means the case with the refracted rays. The incident rays I C, Iʹ C, are
bent at C towards the perpendicular, in the direction C R, C Rʹ; and the
law of refraction is such, that the sine of the angle of incidence has a
constant ratio to the sine of the angle of refraction; that is to say,
the number expressing the length of I m, the sine of I C P, divided by
the number expressing the length of R n, the sine of R C p, is the same
for all the rays of light that can fall upon the surface of any one
substance, and is called its index of refraction. Though the index of
refraction be the same for any one substance, it is not the same for all
substances. For water it is 1·336; for crown-glass it is 1·535; for
flint-glass, 1·6; for diamond, 2·487; and for chromate of lead it is 3,
which substance has a higher refractive power than any other known.
Light falling perpendicularly on a surface passes through it without
being refracted. If the light be now supposed to pass from a dense into
a rare medium, as from glass or water into air, then R C, Rʹ C, become
the incident rays; and in this case the refracted rays, C I, C Iʹ, are
bent from the perpendicular instead of towards it. When the incidence is
very oblique, as r C, the light never passes into the air at all, but it
is _totally_ reflected in the direction C rʹ, so that the angle p C r is
equal to p C rʹ; that frequently happens at the second surface of glass.
When a ray I C falls from air upon a piece of glass A B, it is in
general refracted at each surface. At C it is bent towards the
perpendicular, and at R from it, and the ray emerges parallel to I C;
but, when the ray is very oblique to the second surface, it is totally
reflected. An object seen by total reflection is nearly as vivid as when
seen by direct vision, because no part of the light is refracted. When
light falls upon a plate of crown-glass, at an angle of 4° 32ʹ counted
from the surface, the glass reflects 4 times more light than it
transmits. At an angle of 7° 1ʹ the reflected light is double of the
transmitted; at an angle of 11° 8ʹ the light reflected is equal to that
transmitted; at 17° 17ʹ the reflected is equal to 1/2 the transmitted
light; at 26° 38ʹ it is equal to 1/4, the variation, according to Arago,
being as the square of the cosine.


NOTE 189, p. 154. _Atmospheric refraction._ Let a b, a b, &c., fig. 49,
be strata, or extremely thin layers, of the atmosphere, which increase
in density towards m n, the surface of the earth. A ray coming from a
star meeting the surface of the atmosphere at S would be refracted at
the surface of each layer, and would consequently move in the curved
line S v v v A; and as an object is seen in the direction of the ray
that meets the eye, the star, which really is in the direction A S,
would seem to a person at A to be in s. So that refraction, which always
acts in a vertical direction, raises objects above their true place. For
that reason, a body at Sʹ, below the horizon H A O, would be raised, and
would be seen in sʹ. The sun is frequently visible by refraction after
he is set, or before he is risen. There is no refraction in the zenith
at Z. It increases all the way to the horizon, where it is greatest, the
variation being proportional to the tangent of the angles Z A S, Z A Sʹ,
the distances of the bodies S Sʹ from the zenith. The more obliquely the
rays fall, the greater the refraction.

[Illustration: _Fig. 49._]

[Illustration: _Fig. 50._]


NOTE 190, p. 154. _Bradley’s method of ascertaining the amount of
refraction._ Let Z, fig. 50, be the zenith or point immediately above an
observer at A; let H O be his horizon, and P the pole of the equinoctial
A Q. Hence P A Q is a right angle. A star as near to the pole as s would
appear to revolve about it, in consequence of the rotation of the earth.
At noon, for example, it would be at s above the pole, and at midnight
it would be in sʹ below it. The sum of the true zenith distances, Z A s,
Z A sʹ, is equal to twice the angle Z A P. Again, S and Sʹ being the sun
at his greatest distances from the equinoctial A Q when in the
solstices, the sum of his true zenith distances, Z A S, Z A Sʹ, is equal
to twice the angle Z A Q. Consequently, the four true zenith distances,
when added together, are equal to twice the right angle Q A P; that is,
they are equal to 180°. But the observed or apparent zenith distances
are less than the true on account of refraction; therefore the sum of
the four apparent zenith distances is less than 180° by the whole amount
of the four refractions.


NOTE 191, p. 155. _Terrestrial refraction._ Let C, fig. 51, be the
centre of the earth, A an observer at its surface, A H his horizon, and
B some distant point, as the top of a hill. Let the arc B A be the path
of a ray coming from B to A; E B, E A, tangents to its extremities; and
A G, B F, perpendicular to C B. However high the hill B may be, it is
nothing when compared with C A, the radius of the earth; consequently, A
B differs so little from A D that the angles A E B and A C B are
supplementary to one another; that is, the two taken together are equal
to 180°. A C B is called the horizontal angle. Now B A H is the real
height of B, and E A H its apparent height; hence refraction raises the
object B, by the angle E A B, above its real place. Again, the real
depression of A, when viewed from B, is F B A, whereas its apparent
depression is F B E, so E B A is due to refraction. The angle F B A is
equal to the sum of the angles B A H and A C B; that is, the true
elevation is equal to the true depression and the horizontal angle. But
the true elevation is equal to the apparent elevation diminished by the
refraction; and the true depression is equal to the apparent depression
increased by refraction. Hence twice the refraction is equal to the
horizontal angle augmented by the difference between the apparent
elevation and the apparent depression.

[Illustration: _Fig. 51._]


NOTE 192, p. 155. Fig. 52 represents the phenomenon in question. S P is
the real ship, with its inverted and direct images seen in the air. Were
there no refraction, the rays would come from the ship S P to the eye E
in the direction of the straight lines; but, on account of the variable
density of the inferior strata of the atmosphere, the rays are bent in
the curved lines P c E, P d E, S m E, S n E. Since an object is seen in
the direction of the tangent to that point of the ray which meets the
eye, the point P of the real ship is seen at p and pʹ, and the point S
seems to be in s and sʹ; and, as all the other points are transferred in
the same manner, direct and inverted images of the ship are formed in
the air above it.

[Illustration: _Fig. 52._]


NOTE 193, p. 156. Fig. 53 represents the section of a poker, with the
refraction produced by the hot air surrounding it.

[Illustration: _Fig. 53._]


NOTE 194, p. 156. _The solar spectrum._ A ray from the sun at S, fig.
54, admitted into a dark room, through a small round hole H in a
window-shutter, proceeds in a straight line to a screen D, on which it
forms a bright circular spot of white light, of nearly the same diameter
with the hole H. But when the refracting angle B A C of a glass prism is
interposed, so that the sunbeam falls on A C the first surface of the
prism, and emerges from the second surface A B at equal angles, it
causes the rays to deviate from the straight path S D, and bends them to
the screen M N, where they form a coloured image V R of the sun, of the
same breadth with the diameter of the hole H, but much longer. The space
V R consists of seven colours—violet, indigo, blue, green, yellow,
orange, and red. The violet and red, being the most and least
refrangible rays, are at the extremities, and the green occupy the
middle part at G. The angle D g G is called the mean _deviation_, and
the spreading of the coloured rays over the angle V g R the
_dispersion_. The deviation and dispersion vary with the refracting
angle B A C of the prism, and with the substance of which it is made.

[Illustration: _Fig. 54._]


NOTE 195, pp. 159, 164. Under the same circumstances, and where the
refracting angles of the two prisms are equal, the angles D g G and V g
R, fig. 54, are greater for flint-glass than for crown-glass. But, as
they vary with the angle of the prism, it is only necessary to augment
the refracting angle of the crown-glass prism by a certain quantity, to
produce nearly the same deviation and dispersion with the flint-glass
prism. Hence, when the two prisms are placed with their refracting
angles in opposite directions, as in fig. 54, they nearly neutralize
each other’s effects, and refract a beam of light without resolving it
into its elementary coloured rays. Sir David Brewster has come to the
conclusion that there may be refraction without colour by means of two
prisms, or two lenses, when properly adjusted, even though they be made
of the same kind of glass.


NOTE 196, p. 165. The object glass of the achromatic telescope consists
of a convex lens A B, fig. 55, of crown-glass placed on the outside,
towards the object, and of a concave-convex lens C D of flint-glass,
placed towards the eye. The focal length of a lens is the distance of
its centre from the point in which the rays converge, as F, fig. 60. If,
then, the lenses A B and C D be so constructed that their focal lengths
are in the same proportion as their dispersive powers, they will refract
rays of light without colour.

[Illustration: _Fig. 55._]


NOTE 197, p. 165. If the mean refracting angle of the prism D g G, fig.
54, were the same for all substances, then the difference D g V - D g R
would be the dispersion. But the angle of the prism being the same, all
these angles are different in each substance, so that in order to obtain
the dispersion of any substance the angle D g V - D g R must be divided
by the angle D g G or its excess above unity, to which the mean
refraction is always proportional. According to Mr. Fraunhofer the
refraction of the extreme violet and red rays in crown-glass is 1·5466
and 1·5258; so D g V - D g R = 1·5466 - 1·5258 = ·0208, and half the sum
of the excess of each above unity is = ·5362; consequently

       (D g V - D g R)/D g G = ·0208/·5362 = 0·03879; for diamond

       (D g V - D g R)/D g G = (2·467 - 2·411)/1·439 = 0·0389;

so that the dispersive power of diamond is a little less than that of
crown-glass; hence the splendid refracted colours which distinguish
diamond from every other precious stone are not owing to its high
dispersive power, but to its great mean refraction.—SIR DAVID BREWSTER.


NOTE 198, p. 168. When a sunbeam, after having passed through a coloured
glass V Vʹ, fig. 56, enters a dark room by two small slits O Oʹ in a
card, or piece of tin, they produce alternate bright and black bands on
a screen S Sʹ at a little distance. When either one or other of the
slits O or Oʹ is stopped, the dark bands vanish, and the screen is
illuminated by a uniform light, proving that the dark bands are produced
by the interference of the two sets of rays. Again, let H m, fig. 57, be
a beam of white light passing through a hole at H, made with a fine
needle in a piece of lead or a card, and received on a screen S Sʹ. When
a hair, or a small slip of card h hʹ, about the 30th of an inch in
breadth, is held in the beam, the rays bend round on each side of it,
and, arriving at the screen in different states of vibration, interfere
and form a series of coloured fringes on each side of a central white
band m. When a piece of card is interposed at C, so as to intercept the
light which passes on one side of the hair, the coloured fringes vanish.
When homogeneous light is used, the fringes are broadest in red, and
become narrower for each colour of the spectrum progressively to the
violet, which gives the narrowest and most crowded fringes. These very
elegant experiments are due to Dr. Thomas Young.

[Illustration: _Fig. 56._]

[Illustration: _Fig. 57._]

[Illustration: _Fig. 58._]


NOTE 199, pp. 171, 200. Fig. 58 shows Newton’s rings, of which there are
seven, formed by screwing two lenses of glass together. Provided the
incident light be white, they always succeed each other in the following
order:—

1st ring, or 1st order of colours: Black, very faint blue, brilliant
white, yellow, orange, red.

2nd ring: Dark purple, or rather violet, blue, a very imperfect yellow
green, vivid yellow, crimson red.

3rd ring: Purple, blue, rich grass green, fine yellow, pink, crimson.

4th ring: Dull blueish green, pale yellowish pink, red.

5th ring: Pale blueish green, white, pink.

6th ring: Pale blue green, pale pink.

7th ring: Very pale blueish green, very pale pink.

After the seventh order the colours become too faint to be
distinguished. The rings decrease in breadth, and the colours become
more crowded together, as they recede from the centre. When the light is
homogeneous, the rings are broadest in the red, and decrease in breadth
with every successive colour of the spectrum to the violet.


NOTE 200, p. 172. The absolute thickness of the film of air between the
glasses is found as follows:—Let A F B C, fig. 59, be the section of a
lens lying on a plane surface or plate of glass P Pʹ, seen edgewise, and
let E C be the diameter of the sphere of which the lens is a segment. If
A B be the diameter of any one of Newton’s rings, and B D parallel to C
E, then B D or C F is the thickness of the air producing it. E C is a
known quantity; and when A B, the diameter, is measured with compasses,
B D or F C can be computed. Newton found that the length of B D,
corresponding to the darkest part of the first ring, is the 98,000th
part of an inch when the rays fall perpendicularly on the lens, and from
this he deduced the thickness corresponding to each colour in the system
of rings. By passing each colour of the solar spectrum in succession
over the lenses, Newton also determined the thickness of the film of air
corresponding to each colour, from the breadth of the rings, which are
always of the same colour with the homogeneous light.

[Illustration: _Fig. 59._]


NOTE 201, p. 174. The focal length or distance of a lens is the distance
from its centre to the point F, fig. 60, in which the refracted rays
meet. Let L Lʹ be a lens of very short focal distance fixed in the
window-shutter of a dark room. A sunbeam S L Lʹ passing through the lens
will be brought to a focus in F, whence it will diverge in lines F C, F
D, and will form a circular image of light on the opposite wall. Suppose
a sheet of lead, having a small pin-hole pierced through it, to be
placed in this beam; when the pin-hole is viewed from behind with a lens
at E, it is surrounded with a series of coloured rings, which vary in
appearance with the relative positions of the pin-hole and eye with
regard to the point F. When the hole is the 30th of an inch in diameter
and at the distance of 6-1/2 feet from F, when viewed at the distance of
24 inches, there are seven rings of the following colours:—

1st order: White, pale yellow, yellow, orange, dull red.

2nd order: Violet, blue, whitish, greenish yellow, fine yellow, orange
red.

3rd order: Purple, indigo blue, greenish blue, brilliant green, yellow
green, red.

4th order: Blueish green, blueish white, red.

5th order: Dull green, faint blueish white, faint red.

6th order: Very faint green, very faint red.

7th order: A trace of green and red.

[Illustration: _Fig. 60._]

[Illustration: _Fig. 61._]

[Illustration: _Fig. 62._]


NOTE 202, p. 175. Let L Lʹ, fig. 61, be the section of a lens placed in
a window-shutter, through which a very small beam of light S L Lʹ passes
into a dark room, and comes to a focus in F. If the edge of a knife K N
be held in the beam, the rays bend away from it in hyperbolic curves K
r, K rʹ, &c., instead of coming directly to the screen in the straight
line K E, which is the boundary of the shadow. As these bending rays
arrive at the screen in different states of undulation, they interfere,
and form a series of coloured fringes, r rʹ, &c., along the edge of the
shadow K E S N of the knife. The fringes vary in breadth with the
relative distances of the knife-edge and screen from F.


NOTE 203, p. 177. Fig. 43 represents the phenomena in question, where S
S is the surface, and I the centre of incident waves. The reflected
waves are the dark lines returning towards I, which are the same as if
they had originated in C on the other side of the surface.


NOTE 204, p. 180. Fig. 62 represents a prismatic crystal of tourmaline,
whose axis is A X. The slices that are used for polarising light are cut
parallel to A X.


NOTE 205, p. 181. _Double refraction._ If a pencil of light R r, fig.
63, falls upon a rhombohedron of Iceland spar A B X C, it is separated
into two equal pencils of light at r, which are refracted in the
directions r O, r E: when these arrive at O and E they are again
refracted, and pass into the air in the directions O o, E o, parallel to
one another and to the incident ray R r. The ray r O is refracted
according to the ordinary law, which is, that the sines of the angles of
incidence and refraction bear a constant ratio to one another (see Note
184), and the rays R r, r O, O o, are all in the same plane. The pencil
r E, on the contrary, is bent aside out of that plane, and its
refraction does not follow the constant ratio of the sines; r E is
therefore called the extraordinary ray, and r O the ordinary ray. In
consequence of this bisection of the light, a spot of ink at O is seen
double at O and E, when viewed from r I; and when the crystal is turned
round, the image E revolves about O, which remains stationary.

[Illustration: _Fig. 63._]


NOTE 206, p. 182. Both of the parallel rays O o and E o, fig. 63, are
polarised on leaving the doubly refracting crystal, and in both the
particles of light make their vibrations at right angles to the lines O
o, E o. In the one, however, these vibrations lie, for example, in the
plane of the horizon, while the vibrations of the other lie in the
vertical plane perpendicular to the horizon.


NOTE 207, p. 183. If light be made to fall in various directions on the
natural faces of a crystal of Iceland spar, or on faces cut and polished
artificially, one direction A X, fig. 63, will be found, along which the
light passes without being separated into two pencils. A X is the optic
axis. In some substances there are two optic axes forming an angle with
each other. The optic axis is not a fixed line, it only has a fixed
direction; for if a crystal of Iceland spar be divided into smaller
crystals, each will have its optic axis; but if all these pieces be put
together again, their optic axes will be parallel to A X. Every line,
therefore, within the crystal parallel to A X is an optic axis; but as
these lines have all the same direction, the crystal is still said to
have but one optic axis.


NOTE 208, p. 184. If I C, fig. 48, be the incident and C S the reflected
rays, then the particles of polarised light make their vibrations at
right angles to the plane of the paper.


NOTE 209, p. 184. Let A A, fig. 48, be the surface of the reflector, I C
the incident and C S the reflected rays; then, when the angle S C B is
57°, and consequently the angle P C S equal to 33°, the black spot will
be seen at C by an eye at S.


NOTE 210, p. 185. Let A B, fig. 48, be a reflecting surface, I C the
incident and C S the reflected rays; then, if the surface be
plate-glass, the angle S C B must be 57°, in order that C S may be
polarised. If the surface be crown-glass or water, the angle S C B must
be 56° 55ʹ for the first, and 53° 11ʹ for the second, in order to give a
polarised ray.


NOTE 211, p. 186. A polarising apparatus is represented in fig. 64,
where R r is a ray of light falling on a piece of glass r at an angle of
57°: the reflected ray r s is then polarised, and may be viewed through
a piece of tourmaline in s, or it may be received on another plate of
glass, B, whose surface is at right angles to the surface of r. The ray
r s is again reflected in s, and comes to the eye in the direction s E.
The plate of mica, M I, or of any substance that is to be examined, is
placed between the points r and s.

[Illustration: _Fig. 64._]


NOTE 212, p. 187. In order to see these figures, the polarised ray r s,
fig. 64, must pass through the optic axis of the crystal, which must be
held as near as possible to s on one side, and the eye placed as near as
possible to s on the other. Fig. 65 shows the image formed by a crystal
of Iceland spar which has one optic axis. The colours in the rings are
exactly the same with those of Newton’s rings given in Note 199, and the
cross is black. If the spar be turned round its axis, the rings suffer
no change; but if the tourmaline through which it is viewed, or the
plate of glass, B, be turned round, this figure will be seen at the
angles 0°, 90°, 180°, and 270° of its revolution. But in the
intermediate points, that is, at the angles 45°, 135°, 225°, and 315°,
another system will appear, such as represented in fig. 66, where all
the colours of the rings are complementary to those of fig. 65, and the
cross is white. The two systems of rings, if superposed, would produce
white light.

[Illustration: _Fig. 65._]

[Illustration: _Fig. 66._]


NOTE 213, p. 188. Saltpetre, or nitre, crystallises in six-sided prisms
having two optic axes inclined to one another at an angle of 5°. A slice
of this substance about the 6th or 8th of an inch thick, cut
perpendicularly to the axis of the prism, and placed very near to s,
fig. 64, so that the polarised ray r s may pass through it, exhibits the
system of rings represented in fig. 67, where the points C and C mark
the position of the optic axes. When the plate B, fig. 64, is turned
round, the image changes successively to those given in figs. 68, 69,
and 70. The colours of the rings are the same with those of thin plates,
but they vary with the thickness of the nitre. Their breadth enlarges or
diminishes also with the colour, when homogeneous light is used.

[Illustration: _Fig. 67._]

[Illustration: _Fig. 68._]

[Illustration: _Fig. 69._]

[Illustration: _Fig. 70._]

[Illustration: _Fig. 71._]


NOTE 214, p. 189. Fig. 71 represents the appearance produced by placing
a slice of rock crystal in the polarised ray r s, fig. 64. The uniform
colour in the interior of the image depends upon the thickness of the
slice; but whatever that colour may be, it will alternately attain a
maximum brightness and vanish with the revolution of the glass B. It may
be observed, that the two kinds of quartz, or rock crystal, mentioned in
the text, are combined in the amethyst, which consists of alternate
layers of right-handed and left-handed quartz, whose planes are parallel
to the axis of the crystal.


NOTE 215, p. 193. Suppose the major axis A P of an ellipse, fig. 18, to
be invariable, but the excentricity C S continually to diminish, the
ellipse would bulge more and more; and when C S vanished, it would
become a circle whose diameter is A P. Again, if the excentricity were
continually to increase, the ellipse would be more and more flattened
till C S was equal to C P, when it would become a straight line A P. The
circle and straight line are therefore the limits of the ellipse.


NOTE 216, p. 194. The coloured rings are produced by the interference of
two polarised rays in different states of undulation, on the principle
explained for common light.


NOTE 217, p. 225. According to Mr. Joule, that heat is produced by
motion, and that it is equivalent to it, Mr. Thompson of Glasgow
investigates from whence the sun derives his heat, since he shows that
neither combustion nor his primitive heat could have supplied the waste
during 6000 years. He concludes that the solar heat is maintained by
myriads of minute bodies that are revolving at the edge of his dense
nebulosity or atmosphere, some of which are often seen by us as falling
stars. These, vaporized by his heat, and drawn by his attraction, meet
with intense resistance on entering the solar atmosphere as a shower of
meteoric rain; through it they descend in spiral lines to the sun’s
surface, producing enormous heat by friction during their fall, and
serving for fuel on their arrival.


NOTE 218, p. 252. The class Cryptogamia contains the ferns, mosses,
funguses, and sea-weeds; in all of which the parts of the flowers are in
general too minute to be evident.


NOTE 219, p. 254. Zoophytes are the animals which form madrepores,
corals, sponges, &c.


NOTE 220, p. 254. The Saurian tribe are creatures of the crocodile and
lizard kind.


NOTE 221, p. 266. If heat from a non-luminous source be polarised by
reflection or refraction at r, fig. 64, the polarised ray r s will be
stopped or transmitted by a plate of mica M I, under the same
circumstances that it would stop or transmit light; and if heat were
visible, images analogous to those of figs. 65, 67, &c., would be seen
at the point s.


NOTE 222, pp. 275, 329, 357. The foot-pound, or unit of mechanical force
established by Mr. Joule, is the force that would raise one pound weight
of matter to the height of one foot; or it is the impetus or force
generated by a body of one pound weight falling by its gravitation
through the height of one foot.

Impetus, vis viva, or living force, is equal to the mass of a body
multiplied by the square of the velocity with which it is moving, and is
the true measure of work or labour. For if a weight be raised 10 feet,
it will require four times the labour to raise an equal weight 40 feet.
If both these weights be allowed to descend freely by their gravitation,
at the end of their fall their velocities will be as 1 to 2; that is, as
the square roots of their heights; but the _effect produced_ will be as
their masses multiplied by 1 and 4; but these are the squares of their
velocities: hence the impetus or vis viva is as the mass into the square
of the velocity.

Thus impetus is the true measure of the labour employed to raise the
weights, and of the _effect_ of their descent, and is entirely
independent of time. Now heat is proportional to impetus, and impetus is
the true measure of labour. In percussion the heat evolved is in
proportion to the force of the impetus, and is thus measured by labour.

Travail is a word used in mechanics, to express that _work done_ is
equal to the labouring force employed. The work done may be resistance
overcome or any other effect produced, while the labouring force may be
a horse, a steam-engine, wind, falling water, &c.


NOTE 223, p. 313. When a stream of positive electricity descends from P
to n, fig. 72, in a vertical wire at right angles to the plane of the
horizontal circle A B, the negative electricity ascends from n to P, and
the force exerted by the current makes the north pole of a magnet
revolve about the wire in the direction of the arrow-heads in the
circumference, and it makes the south pole revolve in the opposite
direction. When the current of positive electricity flows upwards from n
to P, these effects are reversed.

[Illustration: _Fig. 72._]

[Illustration: _Fig. 73._]


NOTE 224, p. 314. Fig. 73 represents a helix or coil of copper wire,
terminated by two cups containing a little quicksilver. When the
positive wire of a Voltaic battery is immersed in the cup p, and the
negative wire in the cup n, the circuit is completed. The quicksilver
ensures the connection between the battery and the helix, by conveying
the electricity from the one to the other. While the electricity flows
through the helix, the magnet S N remains suspended within it, but falls
down the moment it ceases. The magnet always turns its south pole S
towards P, the positive wire of the battery, and its north pole towards
the negative wire.


NOTE 225, p. 316. A copper wire coiled in the form represented in fig.
73 was the first and most simple form of the electro-dynamic cylinder.
When its extremities P and n are connected with the positive and
negative poles of a Voltaic battery, it becomes a perfect magnet during
the time that a current of electricity is flowing through it, P and n
being its north and south poles.


NOTE 226, p. 344. It is to Halley we are indebted for the first
declination chart and the theory of 4 poles of maximum magnetic
intensity, since confirmed by observation, as well as the earliest
authentic values of the magnetic elements in London and St. Helena,
where he went on purpose to make observations on terrestrial magnetism.
Since that time M. Gauss has formed charts of the magnetic lines, and
published a theory which very nearly represents the magnetic state of
the globe. The mass of observations daily making by our cruizers and our
Government surveys in every part of the earth is enormous.


NOTE 227, p. 360. In fig. 74 the hyperbola H P Y, the parabola p P R,
and the ellipse A E P L, have the focal distance S P, and coincide
through a small space on each side of the perihelion P; and, as a comet
is only visible when near P, it is difficult to ascertain which of the
three curves it moves in.

[Illustration: _Fig. 74._]


NOTE 228, p. 363. In fig. 75, E A represents the orbit of Halley’s
comet, E T the orbit of the earth, and S the sun. The proportions are
very nearly exact.

[Illustration: _Fig. 75._]


NOTE 229, p. 382. Fig. 74 represents the curves in question. It is
evident that, for the same focal distance S P, there can be but one
circle and one parabola p P R, but that there may be an infinity of
ellipses between the circle and the parabola, and an infinity of
hyperbolas H P Y exterior to the parabola p P R.


NOTE 230, p. 387. Let A B, fig. 26, be the diameter of the earth’s
orbit, and suppose a star to be seen in the direction A Sʹ from the
earth when at A. Six months afterwards, the earth, having moved through
half of its orbit, would arrive at B, and then the star would appear in
the direction B Sʹ, if the diameter A B, as seen from Sʹ, had any
sensible magnitude. But A B, which is 190,000,000 of miles, does not
appear to be greater than the thickness of a spider’s thread, as seen
from 61 Cygni, supposed to be the nearest of the fixed stars.


NOTE 231, p. 389. Stars whose parallax and proper motions are known.

 Name of Star.   Proper Motion.   Parallax.   Observers and Computers.

 α Centauri      3ʺ·764           0ʺ·92       Maclear.
    „              ..             1ʺ          Henderson.
 61 Cygni        5ʺ·123           0ʺ·374      Bessel.
 α Lyræ          0ʺ·364           0ʺ·207      Peters.
 Sirius          1ʺ·234           0ʺ·230      Henderson.
 Arcturus        2ʺ·269           0ʺ·127      Peters.
 Pole Star       0ʺ·035           0ʺ·106      Peters.
 Capella           ..             0ʺ·046      Peters.
 La Chevre       0ʺ·461           0ʺ·046      Peters.
 ι Great Bear    0ʺ·746           0ʺ·133      Peters.

The space run through in one second by these stars is therefore—

           α Centauri      5 leagues Henderson and Maclear.
           61 Cygni       10 leagues Bessel.
           α Lyræ          2 leagues Struve and Peters.
           Sirius          6 leagues Henderson and Maclear.
           Arcturus       22 leagues Peters.
           Pole Star       ½ league  Lindenau and Struve.
           La Chevre      12 leagues Peters.
           ι Great Bear    7 leagues Peters.

There are three great discrepancies in the parallax of the star
Argelander or 1830 Groombridge. M. Otto Struve makes it 0ʺ·034, which
gives it a velocity of 251 leagues per second, while M. Faye finds the
parallax to be between 0ʺ·03 and 0ʺ·01, which makes its velocity from 30
to 85 leagues per second.

These are all minimum velocities, because we can only determine on the
celestial vault a projection perhaps much foreshortened of the real
motions of the stars.


NOTE 232, pp. 398, 401. The following are the binary systems whose
orbits have been accurately determined:—

     Name of Star.    Period in  Perihelion     By whom Computed.
                       Years.    Passage.

     ζ Herculis         30·216   1831·41        Madler.

     η Coronæ           42·500   1807·21        Madler.

     ζ Cancri           58·910   1853·37        Madler.

     ξ Ursæ Majoris     58·262   1817·25        Savary.

     ω Leonis           82·533   1849·76        Villarceaux.

     ρ Ophiuchi         73·862   1806·83        Encke.

     3062 in Dorpat     94·765   1837·41        Madler.
     Catalogue

     ξ Bootis          117·140   1779·88        Sir J. Herschel.

     δ Cygni           178·700   1862·87        Hind.

     γ Virginis        182·120   1836·43        Sir J. Herschel.

     Castor            252·660   1855·83        Sir J. Herschel.

     ς Coronæ          736·880   1826·48        Hind.

     γ Virginis        632·270   1699           Hind.

     α Centauri         77·000   1851·50        Jacob.


                          Orbit of γ Virginis.

           Perihelion passage                         1836·40

           Inclination                                27° 36ʹ

           Position of ascending Node                    19 7

           Angle between line of Nodes   and          295° 13
           Apsides

           Excentricity                                0·8794

           Period in years                             184·53


                          Orbit of ζ Herculis.

           Perihelion passage                         1830·56
           Inclination                               140° 39ʹ
           Position of ascending Node                217° 14ʹ
           Angle between line of Nodes and Apsides     266·53
           Eccentricity                                0·4381
           Period in years                              37·21

                                  _Computed by J. Fletcher, Esq._, 1853.


NOTE 233, p. 403. The mass is found in the manner explained in the text;
but the method of computing the distance of the star may be made more
clear by what follows. Though the orbit of the satellite star is really
and apparently elliptical, let it be represented by C D O, fig. 14, for
the sake of illustration, the earth being in d. It is clear that, when
the star moves through C D O, its light will take longer in coming to
the earth from O than from C, by the whole time it employs in passing
through O C, the breadth of its orbit. When that time is known by
observation, reduced to seconds, and multiplied by 190,000, which is the
number of miles light darts through in a second, the product will be the
breadth of the orbit in miles. From this the dimensions of the ellipse
will be obtained by the aid of observation; the length and position of
any diameter as S p may be found; and as all the angles of the triangle
d S p can be determined by observation, the distance of the star from
the earth may be computed.


NOTE 234, p. 405. The mean results of MM. Argelander, Otto Struve, and
Luhndahl for stars in the northern hemisphere and the epoch 1790, places
the point to which the sun is tending in 259° 5ʹ of right ascension and
55° 23ʹ of north polar distance. Mr. Gallaway computed from stars in the
southern hemisphere, at the same epoch, the point to have been in 260°
1ʹ right ascension and 55° 37ʹ north polar distance, results nearly
identical, though from very different data.


NOTE 235, p. 414. One of the globular clusters mentioned in the text is
represented in fig. 1, plate 8. The stars are gradually condensed
towards the centre, where they run together in a blaze. The more
condensed part is projected on a ground of irregularly scattered stars,
which fills the whole field of the telescope. There are few stars near
this cluster.


NOTE 236, p. 420. Plate 8 shows five nebulæ as seen in Sir John
Herschel’s 20-feet telescope.

1. An enormous ring seen obliquely with a dark centre and a small star
at each extremity.

2. The ring in the constellation Lyra.

3. The dumb-bell nebula in Vulpicula.

4. The spiral nebula or brother system in the 20-feet telescope.

5. A spindle-shaped nebula.

Plate 9 represents some of the same objects as seen by Lord Rosse.

1. Nebula in the girdle of Andromeda.

2. The circular nebula of Lyra.

3. The dumb-bell nebula in Vulpicula.

The spiral nebulæ of 51 Messier, as seen by Lord Rosse, 1 in plate 10,
represents fig. 4 of plate 8; and fig. 2 in the same plate is part of
the great nebula in Orion, for the whole has never been seen, on account
of extreme remoteness.


NOTE 237, pp. 32, 427. The motion of the earth is visibly proved by M.
Foucault’s experiments. If a pendulum be left to oscillate quite freely,
the forces producing the oscillations being in the vertical plane, there
is no cause that can produce an absolute change in its position with
regard to space; but the motion of the earth changes the position of a
spectator with respect to the vertical plane, and he refers his own
motion to it, which seems gradually to turn away from its position,
precisely as a person in a boat refers his own motion to that of the
land, and thus the motion of the earth is truly and visibly proved.




                                 INDEX.

 Aberdeen, high water at, 94.

 Absorption, influence of, on temperature, 239;
   difference of sea and land in power of, 242;
   gradually decreasing, in transmission of radiant heat, 259;
   of radiant heat, varying with substances, 268;
   a transfer of force, 275, 276.

 Acceleration of the moon’s mean motion, 37, 38.

 Adams, Mr., perturbation in Uranus’s motion computed by, 22;
   discovery of Neptune, 62.

 Aërolites, theory of, 420, 423.

 Africa, tidal wave passing, 94;
   mean annual equatorial temperature in, 245;
   indigenous productions of, 249, 250.

 Air, comparative velocity of light in water and, 202.
   _See_ Atmosphere.

 Airy, Professor, periodic inequality in the solar system worked out by,
    26;
   phenomenon observed by, during an eclipse, 41;
   mass of Jupiter ascertained by, 55;
   experiments ascertaining its density, 57;
   astronomical tables improved by, 63;
   discoveries in polarization of light, 192, 193.

 Aldebaran, an optically double star, 401.

 Aleutian Islands, the, vegetation of, 252.

 Alexandria, arc of the meridian measured between Syene and, 49.

 Algæ, districts of distinct species of, 252;
   banks of, in the Atlantic, 253.

 Algol, fluctuations in lustre of, 390, 391.

 Alhazen, effects of refraction observed by, 155.

 Alkalies, resolved into metallic oxides, 307.

 Alpha Antaris, “Coal Sacks” between α Centauri and, 386.

 Alpha Aquilæ, an optically double star, 401.

 —— Centauri, the parallax of, 54;
   its rank, 384;
   the Milky Way near, 386;
   parallax, as determined by Henderson and Maclear, 387;
   distance from the sun, 388;
   orbit and mass of, 399, 400;
   colour, 401;
   amount of light emitted by, 404;
   rate of its proper motion, 404, 405;
   globular nebulous cluster, 414.

 —— Crucis, zone of stars passing through, 385;
   zone between η Argûs and, 390;
   nebulous cluster round, 415.

 —— Lyræ, the polar star of the northern hemisphere, 82;
   parallax of, 388;
   distance from the sun, 389;
   an optically double star, 400;
   amount of light emitted by, 404.

 —— Orionis, a variable star, 393, 394.

 Alum, experiments on the crystallization of, 106, 107;
   heat transmitted through, 261, 262.

 Amazons, the river of, distance from its mouth where tides are
    perceptible, 98;
   area occupied by forests on, 243.

 America, course of the tidal wave along its coasts, 93, 94;
   mean annual equatorial temperature in, 245;
   separation of isothermal lines in high latitudes, _ib._;
   number of known species of plants indigenous in, 249;
   number of species of trees, 252;
   shooting stars over the continent of, 421.

 ——, South, area of country raised by an earthquake in, 234.

 Ampère, M., his discovery in electricity, 316;
   theory of magnetism, 317, 318;
   experiment testing his theory, 319, 320.

 Analysis, boundless dominion of, 427, 428.

 Andes, the, proportion of, to the earth’s mass, 6;
   increasing rarity of the air experienced in ascending, 118.

 Andromeda, nebula in, 413;
   nebulous region of, 417.

 Angström, the electric spark defined by, 303.

 Animals, specific diversity of, laws regulating their distribution,
    254, 255.

 Annual equation, the, of the moon, 35, 36.

 —— variations in mean values of the magnetic elements, 343.

 Annular nebulæ, 409;
   in the northern hemisphere, 410, 411.

 Antarctic Ocean, tidal wave rising in 93;
   period of its passage to the Thames, 94;
   depth of the stratum of constant temperature in, 101;
   depression of the barometer observed in, 120.

 Antilles Islands, hurricanes beginning at, 126.

 Antinori, Cav., experiments of, in electricity, 333.

 Antinous, comet observed in the constellation of, 372;
   the Milky Way between Orion and, 386.

 Antithesis, the general character of magnetism, 339.

 Aphelion of a planet’s path defined, 16.

 Apogee, solar, its coincidence with the solstices, 86, 87.

 April, 1833, disappearance of Saturn’s rings, 67;
   apparent and mean time coinciding in, 84.

 Apsides of an axis defined, 9;
   direct, variable motion of, 14;
   cause of their advance, or recession, 16.

 Apures, the mission of the, Humboldt’s observations on sound at, 135.

 Aqueous vapour, proportion of, in the atmosphere, 117.

 Ara, nebula in, 414.

 Arabian Gulf, the, monsoons blowing over, 124.

 Arabs, the, their observations on planetary irregularities, 26;
   lunar eclipses observed by, 38;
   their division of time, 85;
   the pendulum used as a measure of time by, 90.

 Arago, François, experiment by, in proof of the undulatory theory of
    light, 200;
   decisive experiment suggested by, 202;
   observations in photography, 213;
   observations on the moon’s atmosphere, 226;
   increase of temperature below the earth’s surface calculated by, 230;
   slow communication of temperature from the earth, observed, 244;
   source of magnetism discovered, 330;
   theory of his magnetic experiments, 332;
   divergent flames of a comet described by, 364;
   his treatise on comets, 368;
   nature of comet’s light determined by, 380, 381;
   numbers of comets computed, 381, 382;
   remark of, on _fixed_ stars, 405.

 Arc, the Voltaic, 303-305.

 Arcet, M. d’, vibration of fibres of the retina according to, 178.

 Archer, Scott, stimulus given to photography by, 207.

 Arcs of the meridian, mode of measuring, 47.

 Arctic Sea, depth of the zone of constant temperature, 101.

 —— regions, vegetation found in, 249.

 Arcturus, comet bearing comparison with, 379;
   rank of, 384.

 Areas, described by the radii vectores of planets, a test of disturbing
    forces, 10;
   unequable description of, 15.

 Argelander, M., period of a comet calculated by, 370;
   his mode of estimating distance of fixed stars, 389;
   periods of fluctuation in stars computed by, 390, 391;
   sun’s motion proved, 405.

 Argentine preparations in photography, chemical energy varying with,
    207, 208;
   changes effected by washing with alkalies, 210, 211.

 Argo, variable star in, 393.

 Aries, season of the sun’s entrance into, in Hipparchus’ age, 80.

 Arseniate of soda, its crystals, 109.

 Artesian wells, mode of sinking, origin of the name, 230.

 Asia, indigenous productions of, 249.

 Assyrians, the, division of time by, 85.

 Astronomers, fruits of their labours, 3;
   question still to be resolved by, 24;
   terrestrial orbit differently measured by, 36.

 Astronomical distances, method of measuring, 43;
   tables, method of forming, 58-64.

 Astronomy, its rank in the physical sciences, an important office of,
    1;
   studies necessary to the study of, 2;
   the key to divers problems in physical science, 3;
   the two greatest discoveries in, 23;
   the three departments of, 58;
   standards for measurement afforded by, 83;
   application of, to chronology, 87-89;
   furnishing standards of weights and measures, 89, 90;
   atmospheric effects connecting the laws of molecular attraction with,
      102;
   progress lately made by, 419, 420.

 Atalanta, diameter of, 56.

 Atlantic Ocean, direction of tidal waves in, 93;
   conditions modifying tides, 94;
   depth of, 96;
   currents, 100;
   origin of hurricanes, 126;
   superficial temperature of, 244;
   distinct vegetation of the polar basin, 252;
   beds of algæ in, 253;
   meteors falling in, 421.

 —— telegraph, 325, 326;
   terrestrial magnetism disturbing, 346.

 Atmosphere of nebulous stars, 411, 412.

 —— of planets, 226, 227.

 —— of the sun, its constitution, 42;
   indications of an absorptive surrounding the luminous, 213;
   the true, 224.

 —— terrestrial, solar rays bent by, in lunar eclipses, 40;
   influence of, in solar eclipses, 41;
   its analysis, pressure on the surface of the globe, 117;
   form of, gradual decrease in density of its strata, 117, 118;
   influence of temperature on its density, 119;
   mean pressure of, variable, 120;
   the medium conveying sound, 129;
   sympathetic vibrations transmitted by, 147, 148;
   its action on light, falsifying vision, 153;
   phenomena produced by accidental
   changes in its strata, 155-156;
   effects of increased density in the stratum in the horizon, 157, 158;
   lunar heat absorbed by, 227;
   cause of the cooler air in higher regions of, 240, 241;
   sun’s heat modified by, 244;
   action of electricity in, 284;
   transmission of electricity by induction, 286;
   periodical variations of electricity in, 291;
   accidental developments of electricity, 291, 292;
   cause of variations in its magnetism, 344, 345;
   nebulous bodies made visible by, 421-423.

 Atmospheric air, extreme elasticity of, 105.

 —— pressure, effect of, on electricity, 288.

 Atomic constitution determining crystalline forms, 109.

 Atoms, qualities of, determining the nature of substances, 110;
   differences in weight of, 111.

 Attraction, modes of, in spheres, in the celestial bodies, 4;
   determining the forms of planets, 6;
   determining the motions of planets, 7;
   solar, compelling the elliptical revolutions of planets, 8;
   mutual, of planets, complicating their motions, 10;
   interference of, disturbing the motions of heavenly bodies, 11;
   disturbances from the operation of reciprocal, 13;
   disturbances from inequality of, 14;
   of satellites to primaries, little disturbed, 26;
   disturbing force of, in spheroids, 27;
   its effects on Jupiter’s satellites, 28;
   sun’s, of the moon, 34;
   principle modifying the earth’s, 37;
   local, affecting the plumb-line, 48;
   comparative force of the sun’s, 57;
   of an external body affecting a spheroid, 79;
   producing tides, 91, 92;
   of particles of matter, 103;
   capillary, 113;
   producing annual atmospheric undulations, 121;
   the lunar atmosphere affected by, 226;
   expansive force of heat overcoming, 271;
   of electricities, 283;
   destruction of, producing electricity, 284;
   laws of electrical, 286-288;
   modes of, in static and in voltaic electricity, 317;
   action of planetary, on comet’s orbits, 361-363;
   range of solar, 365.

 Aurora, the, affecting the compass, 312.

 Australia, evidence of deserts in the interior of, 124;
   species of plants common to Europe and, 251.

 Auvergne, temperature of hot springs in, 231.

 Axes, change in form of masses revolving round, 6.

 ——, major, length of, in orbits, invariable, 20;
   of the orbits of Jupiter’s satellites, cause of the direct motion
      observed in, 28;
   position of, in the solar system, 65;
   a nutation in planetary, 66;
   of the moon, 68, 69;
   mechanical law affecting, 76.

 ——, optic, of crystals, 183.

 Axis, greater, of the earth’s orbit, period of its revolution, 38;
   period of the earth’s revolution, 58;
   excess of Jupiter’s equatorial over his polar, 66;
   of rotation, proof of its being invariable, 76, 77.

 ——, major, of a planet’s orbit, distance from the sun measured by, 8;
   designation of its extremities, 9;
   length of, determining the form of the orbit, 10;
   periods of its revolutions, 17;
   length of, not permanently changed, 20;
   Jupiter’s periodically diminished, Saturn’s increased, 26;
   of the solar ellipse, period of its revolution, 86.

 ——, magnecrystallic, 349.

 Azores, the, icebergs reaching, 100.


 Babbage, Charles, his theory of volcanic action, 235-237;
   quotation from, on the nature of force, 353.

 Babinet, M., his theory of dark lines observed in the solar spectrum,
    163;
   comet’s light computed by, 359.

 Babylon, eclipse observed at, 36.

 Bacon, Francis, anticipation of discovery by, 32.

 Baily, Mr., compression of the terrestrial spheroid calculated by, 50;
   density of the earth determined, 57;
   fictitious antiquity ascribed to Indian astronomical observations,
      88.

 Bali, volcanic eruption in, 233.

 Balloon, rarity of the air felt in a, 118;
   observations made from, 119.

 Baltic, the, a tideless sea, 98;
   decreased atmospheric pressure on the shores of, 120.

 Barlow, Mr., observations supporting his theory of electric currents,
    346.

 Barometer, the, principles of cohesion and attraction applied to the
    construction of, 113;
   density of the atmosphere measured by, 117;
   mean heights of, varying with atmospheric densities, 118;
   mountain heights measured by, 119, 120;
   atmospheric phenomena affecting, 120;
   used to trace the course of atmospheric waves, 121;
   cause of sudden fall in, before hurricanes, 127;
   refraction varying with, 154.

 Barrow, Cape, observations on magnetic storms at, 345, 346.

 Battery, voltaic, construction of, 298, 299;
   Professor Daniell’s improvements, 299, 300;
   action of, charged with water, 300;
   constant flow of electricity obtained by means of, 312.

 ——, magnetic, constructed by Dr. Faraday, 324, 325;
   Mr. Henley’s magneto-electric, 325;
   Atlantic telegraph, 326;
   structure of, for land telegraphs, 328;
   relation of heat to power of, 329;
   thermo-electric, 333.

 Batsha, port of, tides neutralised in, 99.

 Bayle, comparative density of the atmosphere in interplanetary space
    according to his law, 356.

 Bear, Little, the, the polar star in, 82.

 Becquerel, M. E., unexplained photographic phenomenon observed by, 213;
   phosphorescent property in the solar spectrum discovered, 216;
   cause of phosphorescence, 217;
   electricity excited by pressure, 283;
   light attributed to electricity by, 284;
   cause of phosphorescence investigated, 296;
   instrument comparing intensities of electricities invented, 300;
   crystals formed by agency of electricity, 308;
   thermo-electric battery constructed by, 333;
   effect of atmospheric on terrestrial magnetism estimated, 345.

 Beehive, the, a nebulous star, 415.

 Berard, M., experiments of, in polarizing heat, 264.

 Berlin, line of coincidence in temperature passing through, 238.

 Berne, increasing temperature of a deserted mine in, 230.

 Berre, Dr., photographic pictures perfected by, 205.

 Bessel, M., his calculations from measurements of arcs of the meridian,
    48;
   calculation of the sun’s mean apparent diameter, 56;
   his computation of the mass of Saturn’s ring, 68;
   diminished obliquity of the ecliptic observed by, 81;
   parallax calculated, 389;
   his theory of Sirius’s irregular motions, 392;
   catalogue of double stars, 396;
   mass of 61 Cygni found by, 404.

 Beta Lyræ, a variable star, 391;
   nebula between γ Lyræ and, 410.

 Benzenberg, M., velocities of falling stars computed by, 423.

 Biela, M., date of the discovery of his comet, 367;
   possibility of collision with the earth, 368;
   present and prospective planetary influence on, 369;
   becoming two distinct bodies, 369, 370.

 Binary systems of stars, 395-406.
   _See_ Double stars.

 Biot, M., his ascent in a balloon, 118;
   experiments of, on the transmission of sounds through pipes, 137;
   liquids possessing the power of circular polarization discovered by,
      190;
   his theory of circular polarization, 191;
   cause of phosphorescence in the solar spectrum investigated by, 217.

 Birds, distribution of distinct species of, 255.

 Birt, Mr., atmospheric waves measured by, 121, 122.

 Bise, in Switzerland, cause of, 242.

 Bismuth, its magnetic and electric properties, 347.

 Black Sea, the, scarcely affected by tides, 98.

 Bode, Baron, law of, assumed in computing Neptune’s position, 61;
   failing in the case of Neptune, 63.

 Bond, Mr., satellite of Saturn discovered by, 32;
   elliptical nebula resolved, 413.

 Bonnycastle, Captain, phosphorescent phenomenon observed by, 295, 296.

 Bonpland, M., identical productions of the Old and New World found by,
    251.

 Boötes, nebulous system in, 417.

 Bore, the, of the Hoogly, its origin, 94.

 Botanical districts, distinct, of the globe, 251, 252.

 Botto, M., thermo-electricity used in decomposition by, 333.

 Bouguer, degrees of the meridian measured by, 48.

 Boussingault, M., depth of the underground stratum of constant heat
    calculated by, 228.

 Bouvard, M., atmospheric undulations estimated by, 121.

 Bradley, Dr., motion of the pole of the equator discovered by, 84;
   his tables of refraction, 155.

 Brahmins, measurement of time by, 85.

 Brand, M., observation of, on meteors, 423.

 Brewster, Sir David, his analysis of the solar spectrum, 161;
   experiments on rayless lines, 163;
   experiments on spectra of flames, 164;
   law discovered by, determining angles of polarization for light, 183;
   experiments on fluorescence of light, 197;
   line of coincidence in temperature of springs and of the atmosphere
      determined by, 238;
   temperature of a pole of maximum cold determined, 245;
   isogeothermal lines determined by, 246;
   observations on the light of fixed stars, 402.

 Brighton, phenomenon caused by reflection observed from, 157.

 Brinkley, Bishop, mass of the moon determined by, 56.

 British Channel, height of tides in, 98.

 —— Isles, atmospheric wave passing over, 121.

 Brorsen, M., periods of comets discovered by, 370.

 Brown, Dr. Robert, peculiar vegetation found by, in Australia, 251.

 Buchan, Dr., phenomenon caused by reflection observed by, 157.


 Cæsar, Julius, era computed from his reign, 85.

 Cagniard de la Tour, M., instrument designed by, measuring musical
    notes, 143.

 Calms produced by the trade-winds, 122, 123.

 Calorific rays.
   _See_ Rays of heat.

 Calotype, the invention of, 204.

 Camelopard, nebulous system in, 417.

 Canaries, the, vegetation of, 252.

 Canary-glass, fluorescence of light in, 196.

 Cancer, the calms of, 123;
   the tropic of, marking the limit of the trade-winds, 126;
   nebulous cluster in, 415.

 Canis Major, position of, 390.

 —— Venatica, nebulous system in, 417.

 Capillarity, theory of, 113;
   forces producing, 114;
   familiar examples of, 115;
   curious phenomena, 115, 116.

 Capricorn, the calms of, 123;
   the tropic of, hurricanes changing their direction at, 126.

 Carbon, its powers contrasted as a crystal and as an opaque amorphous
    substance, 302, 303.

 Carbonate of lime.
   _See_ Lime.

 Carbonic oxide, its constituent parts, 111.

 —— acid, proportion of, in the atmosphere, 117.

 Cardinal points, the, position of continental masses with regard to,
    influencing temperature, 244.

 Caribbean Islands, hurricanes beginning at, 126.

 Castor, discovered by Sir William Herschel, 396.

 Cassiopeia, star appearing and vanishing in, 392, 393.

 Categat, the, consequence of its narrowness, 98.

 Cauchy, M., data furnished by, for investigation of the theory of
    light, 201.

 Cayenne, variation in length of the pendulum between Paris and, 51.

 Celestial bodies:
   law of their mutual attraction, 4;
   of the solar system:
     law determining their attraction to the sun, 5;
     problem to fix the positions of, on occurrence of disturbance in
        their motions through counteracting attractions, 11;
     theory of their mutual connection and dependence, 24;
     mode of finding the absolute distances of, 43;
     distances of, computed from their parallax, 52, 54;
   apparent position of, affected by refraction, 153, 154;
   apparent infinity of, 420.

 Centaur, position of, 390;
   brilliant double star in, 399.

 Central Asia, the mountains of, their ascent by Marco Polo, 118.

 Centre of gravity.
   _See_ Gravity.

 Centrifugal force, moon’s motions modified by, 5;
   influence of, on planet-forms, 6;
   retarding oscillations of the pendulum, 32;
   action of, in determining the figure of the earth, 44, 45;
   measurement of its intensity, 49;
   resolved into two forces, its action on the sea, 100.

 Ceres, astronomical tables of, 63;
   height of her atmosphere, 226;
   comet of 1770 revolving beyond the orbit of, 361.

 Cetus, nebulous patches crossing, 417.

 Chaldeans, the, mean longitude found from observations of, 36;
   result of comparison of their observations with modern, 38.

 Challis, Professor, Brewster’s analysis of light questioned by, 161.

 Charcoal, light produced by electricity from, 302-303.

 Charles V., the Emperor, observations on comets, made in his reign,
    370.

 Chaudes Aigues, temperature of, 231.

 Chemical action of rays of the solar spectrum, 203, 207;
   varying maximum of energy, 208;
   action varying with refrangibility, 209-212;
   action in luminous spectrum not continuous, 213;
   energy an independent property of rays, 214;
   properties of the parathermic rays, 219;
   action of light maintaining vegetation, 249;
   affinities the source of the power of steam, 278;
   of electricity on oxygen, 284;
   eliciting voltaic electricity, 297, 300;
   voltaic electricity, an agent in, analysis, 307, 308.

 —— combinations, theory of, 110;
   invariable proportions of, 111;
   cohesive force inducing, 112;
   producing combustion, 270.

 —— force, the power of, 112.

 —— rays, causing the deposition of dew, 269.

 Chile, elevation of land by an earthquake in, 234.

 China, distinct flora of, 251.

 —— Sea, the, monsoons blowing over, 124.

 —— ink, polarized light reflected from, 193.

 Chinese, the, observations of, on the mean motions of Jupiter and
    Saturn, 25;
   proof of their early study of astronomy, 88;
   decimal divisions used by, 90;
   elements of comets computed from their observation, 365;
   comet of 1264 recorded by, 370.

 —— Tartary, herbarium collected in, 250, 251.

 Chladni, discovery of, in musical science, 145.

 Christian era, traces of astronomical records before, 365.

 Chromatype, the invention of, 206.

 Chronology, dependent on astronomy, 87-89.

 Chrysotype, the, coloured photographs obtained from, 206.

 Circuit, galvanic, modes of obtaining, 332.

 Circular arcs, principle with regard to their sines and cosines, a
    pledge for the stability of the solar system, 20.

 —— motion, ratio of forces procuring, 382.

 —— orbits of planets distinguished from elliptical, 8;
   of satellites, 27.

 —— polarization of light, 189-192;
   of heat, 266.

 Circumference of the earth, 49.

 Civil time, measure of its periods, 83;
   not precisely adjusted to solar revolutions, 85.

 Clairaut, periodic time of Halley’s comet computed by, 362, 363.

 Cleavages of crystals, 109;
   position of, affecting the intensity of magnetic action, 350.

 Climates, planetary, 225, 226;
   cause of the different terrestrial, 237;
   phenomena affecting, 239, 240;
   causes of variety of, 243, 244;
   milder, of the Polar Ocean, 245, 246;
   like mean annual temperatures not ensuring like, 246;
   compensations of irregularities, 247.

 Clocks, showing apparent sidereal time, 83;
   regulated to show decimal time, 84;
   irregular action of, corrected by the laws of unequal expansion, 272.

 Clouds, circling the belt of equatorial calms, 123;
   region of, 124;
   electricity evolved from, 291-292.

 Cloyne, Bishop of, his calculation of the moon’s mass, 56.

 Coal-measures, tropical plants in, 72, 73;
   age of their formation, 75.

 Coal, chemical force evolved from, by combustion, 278;
   source of its combustible qualities, 279, 280.

 “Coal Sacks” in the Milky Way, 386.

 Cohesion, influence of, on matter, 105;
   phenomena arising from its force, 106;
   attraction of, overcome by the expansive power of heat, 271.

 Cohesive force, properties of material molecules constituting, 103;
   effectual only to unite particles of like nature, 110;
   inducing chemical combination, 112;
   capillary attraction, an action of, 113.

 Coins, impressions taken from, by contact, 220;
   by electricity, 221.

 Cold, contraction caused by, 271, 272;
   mitigated by slow propagation of heat in air, 273;
   generated by voltaic electricity, 302;
   increasing the conducting power of the air, 345.

 Colladon, M., experiments of, testing the velocity of sound, 135.

 Collision between the earth and comets, possibilities, possible effects
    of, 367, 369.

 Collodion, sensitiveness of, to light, 203;
   properties of, as an agent in photography, 207.

 Colours, seven primary, 159;
   theory of the decomposition of white light into, 160;
   degree of refrangibility not invariable, 161;
   three primary, _ib._;
   new, discovered by Sir John Herschel, 162;
   rays refracted without, 164;
   rarely homogeneous, 165;
   experiments on accidental and complementary, 165, 166;
   determined by undulations of ether, experiments, 170-175;
   of material substances, whence derived, 175;
   produced by analyzing polarized light, 186-188;
   varying with refrangibility of rays, 198;
   obtained in photography, 206;
   images of the solar spectrum imitating the prismatic, 208-209;
   of seaweeds, 253;
   not invariably dependent on light, _ib._;
   affected by absorption and reflection, 268;
   of the electric spark, affected by the atmosphere, 289;
   of the voltaic spectrum, 303;
   of the electric spark, 304;
   produced by oxidation on silver, 305;
   of the fixed stars, 401, 402;
   of planetary nebulæ, 412;
   of nebulous clusters, 415.

 Columbus, beds of algæ found by, 253.

 Column, capillary, forces producing changes in its form, 114, 115.

 Coma Berenices, a nebulous cluster, 415;
   nebulous zone passing, 416, 417.

 Combustion, cause of, 270;
   defined, 304.

 Comets, attraction by the sun of, 5;
   disturbances in the motion of, a key to the nature of the ethereal
      medium, 22;
   retrograde motion in, 33;
   passing through Jupiter’s satellites, 69;
   return of, to their perihelia, furnishing historical data, 88;
   existence of the luminous ether demonstrated by, 168, 169;
   terrestrial atmosphere unaffected by, 358;
   amount of their light computed, 358, 359;
   passages of, through the solar system, 359;
   velocity, paths of, 359, 360;
   proof of the return of, 360;
   disturbing action of planets on their orbits, 361;
   of 1770, an example, 361, 362;
   computed return of Halley’s, 362, 363;
   aspects, records of Halley’s, 363-365;
   discoveries made by the revolutions of, 365;
   of the solar system, Encke’s, 365, 366;
   Biela’s, possibility of collision with, 367, 370;
   periods of various, 370;
   cause of their brilliancy, 371;
   velocity, sun’s influence on, 371, 372;
   of 1843, 372, 373;
   their constitution, 373, 374;
   of 1811, its luminous envelopes, 374, 375;
   sudden convulsions in, 375;
   tails, 375-377;
   causes assigned for contraction of diameter in, 377, 378;
   Donati’s, 378, 379;
   nature of their light, 379-381;
   computations of their numbers, 381, 382;
   orbits of, 383;
   nebula resembling, 413.

 Compass, mariner’s, phenomena disturbing, 312;
   intensity of a galvanic current measured by, 315.

 Compression of the terrestrial spheroid, calculations of, 48-51;
   cause of the great, in Jupiter, 66;
   measures of, from pressure of superincumbent mass, 78;
   effect of, on magnetic action, 351.

 Concord, a, in music, 142.

 Conductors of electricity, 284, 285;
   lightning, 293;
   molecular structure determining the power of, 303.

 Conic sections, conditions compelling bodies in space to move in, 5;
   principle determining their nature, 11.

 Constellations, nearest the sun, 390;
   where the orbit of the solar system lies, 406;
   occupied by the nebulous system, 417.

 Contraction caused by cold, 271, 272.

 Cook, Captain, object of his first voyage, 53.

 Cooper, Mr., list of missing stars drawn up by, 395.

 Copper, electricity communicated to plates of, 220;
   lightning-conductors of, 293;
   action of an electro-magnet on, 351, 352.

 Cordier, temperature of mines observed by, 228.

 Cordilleras, effect on temperature of their table-lands, 241.

 Corn, a, field used to illustrate the propagation of sound, 129, 130.

 Cornwall, hot-springs in mines of, 229.

 Corona Australis, nebula in, 414.

 Corpuscular theory of light, 167;
   phenomena disproving, 171, 175, 176.

 Coseguina, volcanic irruption of, 233.

 Coulomb, instrument measuring electrical intensity, invented by, 287.

 Creation, vastness and magnificence of, 2.

 Crimea, cause of the great storm in the, 122.

 Cross, Mr., voltaic battery with constant action invented by, 300.

 Cross, the Southern, vacant patches of the Milky Way near, 386.

 Crystallization defined, 106;
   forms of, their variety affected by temperature, 107, 108;
   permanent and variable forms, 108, 109;
   cleavages in, 109;
   common to all substances, _ib._;
   by the agency of electricity, 308, 309.

 Crystals, conditions determining their forms, 107-109;
   optic axes of, 183;
   used in polarizing light, 186, 188;
   changes in, effected by compression, 189;
   transmission of rays of heat by, 258;
   expansion of, by heat, 272, 273;
   formed by electricity, 308;
   action of magnetism in, 349, 350;
   circumstances determining the set of, 350, 351;
   effect of temperature on magnetized, 352.

 Cumming, Professor, experiments of, in thermo-electricity, 333.

 Currents, two great, setting from each pole towards the equator, 100;
   proving the rotation of winds, 124, 125.

 ——, electric, flow of, regulated by Volta, 297-299;
   characteristics of Voltaic, 301;
   conductors, non-conductors of, 309;
   continuous flow of Voltaic, 312;
   action of, on magnets, 313-315;
   reciprocal and mutual action of magnetic and electric, 316, 317;
   Ampère’s theory of, unsolved difficulties, 317, 318;
   effect of, on polarized rays, 319;
   electric, evolved by magnets, 322, 323;
   their power of producing induction, 324;
   direction of, produced by rotation, 330-332;
   evolved by application of heat, 332, 333;
   produced by intersecting magnetic curves, 339;
   induced by crossing terrestrial lines of magnetic force, 342.

 Curves, described by bodies projected in space, 5.

 ——, magnetic, 338;
   electricity produced by intersecting, 339;
   nature of, proved by Dr. Faraday, 339, 340;
   terrestrial, 341, 342;
   extent of the range of terrestrial, 344;
   complete connected system of the terrestrial, 345;
   inductive effect on the Atlantic telegraph, 346;
   diamagnetic, 348.

 Cyanite, changes effected in, by magnetism, 349.

 Cyanotypes, coloured photographs obtained by, 206.

 Cygni 61, distance from the sun of, 389;
   orbit and mass of, 398, 399;
   colours, 401;
   mass, 404;
   proper motion, 405.

 Cygnus, portion of the Milky Way lying between α Centauri and, 386.

 Cylinders, rotating by electricity, 313;
   electro-dynamic, 316.


 Dalcoath copper-mine, its temperature, 228.

 Daguerre, M., his inventions in photography, 205;
   action of light on the iodide of silver explained by, 219.

 Daguerreotype, the, invention of, 205.

 Dalton, Dr., law of definite proportion established by, 111;
   law of the wind’s rotation observed by, 125.

 Damoiseau, M., perturbations of a comet computed by, 367.

 Daniell, Professor, Voltaic battery improved by, 299.

 Daubuisson, M., observations of, in mines, 228.

 Davy, Sir Humphry, his first attempts to produce photographic pictures,
    203-204;
   experiment of, proving identity of heat and motion, 275;
   experiments on the electric spectrum, 289;
   alkalies, earths decomposed by, 307.

 Days, law determining the length of, 71;
   period of the mean sidereal and solar, 83;
   varying with the seasons, 84;
   decimal division of, 84;
   seven, the most permanent division of time, 85.

 Deccan, the, wheat ripening in, 250.

 December, 1832, disappearance of Saturn’s rings in, 67;
   coincidence of mean and apparent time in, 84;
   date of Christ’s nativity, 85;
   the astronomical year beginning in, 86.

 Decimal division of time, 84.

 Declinations of the moon, 97.

 Decomposition, effected by electricity, 307-308;
   by magnetism, 323;
   by thermo-electricity, 333.

 Delambre, his computations of the length of the year, 359.

 Delta Cephei, a variable star, 391.

 Denmark, course of the tidal wave to, 94.

 Density, variable, impeding sound, 135, 136:
   of media, modifying refraction, 153.

 Densities of heavenly bodies, formula finding, 56;
   experiments, 57, 58;
   comparative of the terrestrial globe, 77, 78.

 Deserts, causing monsoons, 124;
   influence of, on temperature, 243.

 Dew, cause of its deposition, 269.

 Diamagnetic substances, 335, 336.

 Diamagnetism defined, 335;
   substances it is resident in, 336;
   discovery, characteristics of, 347;
   neutral substances obtained by proportionate combination of, with
      paramagnetism, _ib._;
   polarity of, 348;
   connected with arrangement of molecules, 350-351;
   affected by division and compression, 351;
   possibly identical with paramagnetism, 356, 357.

 Diameter of the earth, 21;
   Jupiter’s polar, 27;
   excess of his equatorial, 39;
   apparent, of the sun and moon, nearly equal, 40;
   of the earth, 49;
   of bodies composing the solar system, 56;
   of Neptune, 63;
   comets lacking a sensible, 373;
   contraction of, in comets, 377;
   causes assigned for, 377, 378.

 —— of an annular nebula, 410;
   sensible, of a planetary nebula, 412.

 Diamond, the, polarized light reflected from, 193.

 Dielectrics in electricity, 286.

 Dieppe, seen from Hastings, 157.

 Differential telescope, the, experiments to be made by, 227.

 Discord, a, in music, 142.

 Diurnal tides of the atmosphere, their duration, 121.

 —— variations in mean values of the magnetic elements, 343.

 Dœbereiner, M., spontaneous combustion discovered by, 112.

 Doldrums, region of the, 123.

 Dollond, Mr., achromatic telescope perfected by, 165.

 Donati, Signore, discovery of his comet, 378;
   changes in, its irregularities, 379.

 Doradus, nebulous patches on, 417.

 Dorpat, occultation of a star observed from, 364.

 Double nebulæ, 411.

 Double stars, catalogues of, 395, 396;
   formulæ obtaining the relative position and motions, 396, 397;
   eclipse in γ Virginis, 397;
   orbit of, determined, 398;
   eclipse in ζ Herculis, _ib._;
   orbits and periodic times of, 398, 399;
   anomalies in motions, 400;
   optically double, 400, 401;
   colours of, 401;
   rays composing the light of, 401, 402;
   passage of light from, furnishing data to ascertaining their actual
      distance, 402, 403;
   data for finding their masses, 403, 404;
   calculations founded on the quantity of light emitted from, 404;
   real and apparent motions of, 404-406;
   apparent periodic time, 406, 407;
   connection of elliptical nebulæ with, 411.

 Dove, Professor, law of the wind’s rotation developed by, 125;
   average temperature of the earth’s surface estimated by, 237.

 Draco, nebulous system in, 417.

 Draper, Professor, experiments of, on fluorescence of light, 198;
   experiments in photography, 213;
   properties of parathermic rays discovered by, 219;
   spectrum produced from diffracted light, 223;
   theory of heat propagated by undulations, 267.

 Dunlop, Mr., revolution of a double star calculated by, 400.

 Dusejour, M., distances of comets computed by, 359.

 Dynamic electricity, 297.
   _See_ Voltaic.

 —— theory of heat, fundamental principle of, 357.

 Dynamic equator of the earth, 343.

 Dynamical theory of heat, 274, 275;
   illustrated by liquefaction and condensation, 278;
   by generation of steam, 276, 277;
   power of nature, 279-281.

 Dynamics, principle in, a law, with regard to the earth’s rotation, 72;
   electro, discovery of action of currents in, 316;
   the theory of, universal application of, 426, 427.


 Earth, the, influence of its form on attraction, 4;
   square of the moon’s distance from, 5;
   form of, 6, 7;
   moon’s influence on its rotations, 7;
   diameter of, 21;
   mean distance from the sun, _ib. note_;
   permanence of revolution in its times and seasons, 23;
   perturbation in the mean motion of Venus and, 26;
   proof of the motion of, in its orbit, of its rotation, 32;
   variations in its attraction of the moon, 37;
   compression of its spheroid, 38;
   internal structure of, 39;
   its mean distance from the sun, 43;
   theoretical investigation of its figure, 44-46;
   dimensions of, determined, 48, 49;
   figure of, found by calculating its variations in gravitation, 49-51;
   density compared with the sun, 56;
   experiments finding its mean density, 57, 58;
   rate of revolution round its axis, 58;
   its diurnal rotation immutable, 71, 72;
   changes in temperature and their causes, 73, 74;
   nature of the revolutions producing geological changes, 76, 77;
   conjectures touching its internal structure, 78;
   effects produced by solar and lunar attraction affecting its equator,
      79-81;
   its form furnishing standards of weight and measure, 89;
   rotation of, acting on tides, 92;
   attraction of, affecting the lunar atmosphere, 226;
   conjectured constitution of its interior, 231, 232;
   principles regulating the diffusion of solar heat, 237-247;
   distribution of known species of plants over, 249-252;
   electric tension of, 291;
   lines of magnetic force issuing from, 341;
   magnetic properties of, 342, 343;
   effect of its collision with a comet, 368;
   nearest approach of comets to, 369;
   passage of light from α Centauri to, 388;
   theories of meteors falling on, 421-423.

 Earthquakes in South America, 234.

 Earths, decomposed by voltaic electricity, 307.

 Eastern coasts, cause of their colder climates, 244.

 Ebb, _see_ Tides.

 Éboulemens of mountains in Switzerland, cause of, 271.

 Echoes, theory of their origin, 137, 138.

 Eclipses, lunar, accelerated revolutions proved by observations of, 36;
   observations of, confirming results of analysis, 38;
   principle regulating their return, 39;
   refraction of rays by the terrestrial atmosphere, 40.

 ——, solar, 40;
   effects of light in, 41.

 ——, planetary, 42;
   the solar atmosphere visible in, 224;
   of double stars, 397, 398.

 Ecliptic, the, forming the equinoxes, 9;
   latitude reckoned from the plane of, _ib._;
   deviations of planetary orbits from, 10;
   forces affecting their position towards, 15;
   their compensated and uncompensated variations to the plane of, 18,
      19;
   secular variation in the plane of, 23;
   orbits of satellites, nearly perpendicular to, 33;
   lunar motions towards, 35;
   inclination of the sun’s plane of rotation to, 65;
   inclination of the plane of Saturn’s rings, 67;
   inclination of the plane of the terrestrial equator, 79;
   tendency of its plane to coincide with the equatorial, _ib._;
   retrograde motion of the equinoctial points on, 80;
   obliquity of, affecting the duration of time, 84.

 Edinburgh, comparatively equal mean annual temperature of, 246.

 Egypt, hieroglyphic manuscript from, interpreted by astronomy, 89.

 Egyptians, the civil year of, 85.

 Elastic impact, the foundation of dynamical theories, 357.

 Elasticity, property of, resisting compression, 105.

 Electric telegraphs, experiment suggesting the principle of, 323;
   construction of, 325-328.

 Electricity assumed as the medium attracting particles of matter, 103,
    104;
   identical with chemical affinity, 110;
   in composition and decomposition, subject to laws of definite
      proportion, 112;
   influencing winds, 125;
   its comparative velocity, 138;
   producing phosphorescence, 217;
   communicated to metal plates by juxtaposition, 220;
   impressions traced on glass by, 221;
   rays exciting, 223;
   a dual power, 282;
   modes of exciting by disturbing equilibrium, 282-284;
   transmission of, 284, 285;
   transmission by induction, 285, 286;
   laws of attraction and repulsion determining intensity of, 286-288;
   heat and light produced by, 288;
   velocity of, 289;
   experiment determining its velocity, 290;
   development of, in the atmosphere, 291, 292;
   phosphorescence excited by, 294;
   Voltaic, _see_ Voltaic;
   conduction of static, contrasted with Voltaic, 309;
   laws of action in, distinguishing it from Voltaic, 317;
   relation between 322, 323;
   telegraphs working by, 323-328;
   produced by rotation, 330, 331;
   thermo, 332, 333;
   exact balance of its dual force, 334;
   points of analogy between magnetism and, 340, 341;
   causing convulsions in comets, 375.

 Electro-dynamics, _see_ Dynamics.

 —— magnetism, _see_ Magnetism.

 Elements, the three terrestrial magnetic, 343;
   variations in, _ib._;
   storms affecting, 344.

 Elevation, effect of, on temperature, 240-242;
   on vegetation, 250.

 Ellipses, described by planets, 5;
   paths of planets describing, 10;
   preventing compensation of disturbance, 15;
   cause and measures of variation in, 17;
   described by comets, 363, 366.

 Ellipsoid, an, of revolution, mass assuming the form of, 45;
   its equatorial and its polar radius, 48;
   permanent axes of rotation, 76.

 Elliptic motion, ratio of forces procuring, 382.

 Elliptical polarization of light, 192, 193;
   of heat, 267.

 —— nebulæ, 409;
   their connection with double stars, 411;
   frequency, 413;
   difficult of resolution, 415.

 Encke, Professor, sun’s parallax found by, 53;
   his comet, 169;
   aspects, period of his comet, 365, 366;
   cause of acceleration in its revolution, 366, 367;
   crossing the terrestrial orbit, 368;
   prospective and present planetary influence on, 369;
   disappearance of its tail and nucleus, 369;
   referred to, 377;
   contraction of diameter, _ib._

 England, arcs of the meridian measured in, 48;
   course of the tidal wave towards its west coast, 94;
   peculiarities of photography in, 213;
   meteors falling in, 421.

 Engravings copied by photography, 204;
   impressions taken by contact with iodized silver, 221;
   impressions taken from, by galvanism, 309.

 Epipolic light, 197.

 Epsilon Orionis, zone of stars passing through, 385.

 Equation of the centre, defined, 9;
   lunar, 35.

 Equator, the, forces compelling the wider circle of, 6;
   inclination of the terrestrial to the plane of the ecliptic, 23;
   of the solar system, 24;
   measure of the centrifugal force at, 49;
   calculation from lunar action on the terrestrial, 55;
   effects produced by external attraction influencing the direction of
      its plane, 79, 80;
   inequality in its polar motion, 81;
   cause of the calms at, 122;
   depth of the underground stratum of constant temperature at, 228;
   maximum of solar heating influence, 238;
   superficial extent of land, 244;
   mean annual temperature, 245.

 Equator of the sun, maximum of solar heat attained in, 225.

 ——, dynamic, surrounding the terrestrial globe, 343.

 ——, magnetic, of the earth, 343.

 Equinoctial circle, the, defined, 9.

 —— points, effects of solar and lunar attraction on, 79;
   period of their revolution, 80;
   measuring time, 83.

 Equinoxes, the, defined, 9;
   venial, a point whence planetary motions are estimated, _ib._;
   of the planets, cause of a precession in, 66;
   causes preventing their invariable correspondence with points of the
      ecliptic, 79;
   precession affecting the seasons, 80;
   secular motion of, periodic variations, 80, 81;
   eras depending on the precession of, 86, 87;
   tides augmented in, 97.

 Eras, astronomical, determined by the position of the major axis of the
    solar ellipse, 86, 87.

 Eratosthenes, the earth’s circumference measured by, 49.

 Eridanus, nebulous patches crossing, 417.

 Erman, M., depression of the barometer observed by, 120.

 Eruptions, volcanic, recorded, 234.

 Eta Aquilæ, a variable star, 391.

 —— Argûs, zone stretching from, 390;
   nebula round, 418, 419.

 —— Coronæ, periodic time of, 398.

 Etna, measurements of, 120.

 Ethereal medium, undulations of, propagating heat, 267;
   permeable to lines of magnetic force, 344;
   its density, 356;
   transmitting gravity, _ib._;
   magnetic, 356, 357;
   offices discharged by, 357;
   pervading the visible creation, 358;
   influence of, on comet motion, 365;
   astral revolutions accelerated by, 366;
   probable increase in density of, 367.

 Europe, atmospheric wave passing over, 121;
   causes of variation of climate in, 244;
   separation of isothermal lines in high latitudes of, 245;
   differences of latitude enjoying the same mean temperature, 246;
   indigenous productions of, 249;
   number of indigenous productions common to Australia and, 251;
   number of species of forest trees, 252.

 Eudoxus, Plato’s contemporary, astronomical observation of, 88.

 Evaporation, conditions affecting, 269, 270.

 Everest, Colonel, arc of the meridian measured by, 48.

 Excentricity of planetary orbits measured, 17.

 Expansion, universal law of, 271;
   accuracy in measurement ensured by laws of unequal, 272;
   of crystals, 272, 273;
   theory of, 275, 277;
   of steam, 278;
   by electricity, 285.

 Extra-tropical winds, 124.


 Fabricius, the comet of 1556 observed by, 370;
   variable star, 390.

 Fahrenheit, mode of ascertaining heights proposed by, 120.

 Falling stars, 420;
   theories of, 422, 423.

 Faraday, Dr., gases reduced to liquids by, 105;
   experiments testing chemical affinity, 111;
   instance of cohesive force inducing chemical combination, 112;
   experiments on vibrations producing colour, 173;
   influence of dialectrics, 286;
   chemical origin of electricity defended by, 300;
   electro-chemical decomposition defined by, 308;
   remarks of, on conduction of voltaic electricity, 309;
   experiments on magnetic rotation, 313;
   experiment magnetizing polarized light, 318, 319;
   importance of his experiment, 320;
   experiment establishing the identity of magnetism and electricity,
      322, 323;
   his magnetic battery, 324, 325;
   aid given by, in construction of telegraphs, 326, 328;
   electricity produced by rotatory motion explained, 330;
   his classification of substances according to magnetic qualities,
      332;
   quotation from, on conservation of force in electricity, 334;
   magnetism raised to a new science by, 335;
   the magnet as represented by, 338;
   experiment determining the forms of magnetic lines of force, 339,
      340;
   accidental electro-magnetic combinations pointed out by, 342;
   his discovery of diamagnetism, 347;
   experiments on magnetic action in crystals, 349;
   observations on influence of heat in magnetism, 352;
   definition of gravity questioned by, 354, 355;
   magnetism of the ethereal medium tested, 356.

 Fauna, distinct, of separate regions, 254, 255.

 Faye, M., his conception of the sun’s constitution, 41;
   his theory of phenomena observed in eclipses, 42;
   comet of 1843 discovered by, 361.

 Fiedler, Dr., fulgorites exhibited by, 293.

 Fire, chemical combination producing, 270.

 —— balls, theory of, 421.

 Fires, central, subterranean, 231-237.

 Fish, phosphorescent, 294, 295;
   electric, 310.

 Fixed stars.
   _See_ Stars.

 Fizeau, M., decisive experiment in proof of the undulatory theory of
    light accomplished by, 202.

 Flame, chemical combination evolving, 270, 271.

 Flames, lambent, caused by electricity, 294.

 —— divergent from the nucleus of a comet, 364.

 Fletcher, Mr., periodic time of γ Virginis determined by, 398.

 Flora of the Himalaya, 250;
   distinct, in separate regions, 251;
   condition establishing distinct, in islands, 252.

 Florence, comet discovered from, 378.

 Fluor-spar, its property of diminishing refrangibility of light, 196.

 Fluorescence of light, definition of, 195;
   vibrations of the substance producing, 196;
   experiments, 197, 198.

 Focus of a meteoric shower, 422.

 Fog, yellow, excluding the chemical action of rays, 214.

 Forbes, Professor, temperature of the boiling point ascertained by,
    120;
   observations of, on rayless lines, 163;
   lunar heat tested by, 227;
   experiments of, in polarization of heat, 264, 267.

 Force, relation of, to heat, 275;
   transforming solids to liquids and to vapour, 275, 277;
   a power of nature, 279;
   light and heat modes of, 219, 220;
   heat a living, 329;
   lines of magnetic, 338, 340;
   conservation of, maintained in periodic variation of atmospheric
      magnetism, 345;
   increatable, indestructible, 353;
   examples of conservation of, 354;
   fundamental principle of conservation, 357;
   influence and action of the gravitating, 424, 426.

 Forces, the unknown cause of motion, 5 _et passim_;
   counteraction of solar and tangential, in planetary motion, 8;
   adjustment of, ensuring the permanence of the solar system, 11, 12;
   three partial, causing perturbation in planetary motion, 14, 15;
   excess of equatorial diameter the origin of, 27, 28;
   three, disturbing lunar motions, 34, 35;
   determining planet forms, 44, 45;
   producing tides, 91, 92;
   combining to form the centrifugal, 100;
   acting on molecules of matter, 102, 105;
   producing capillary phenomena, 114;
   latent, in nature, 279, 280;
   one universal power, the root of all, 321;
   exact balance of, in electricity, 334;
   kindred and convertible, 353;
   developing comets’ tails, 375;
   determining the forms of orbits, 382, 383;
   maintaining the stability of the solar system, 426;
   mutual relations of, 427.

 Forests, change produced in the atmosphere by, 241, 243;
   number of species of trees found in American and European, 252.

 Formentera, quadrant of the meridian passing through, furnishing a unit
    of linear measure, 89.

 Fornix, nebulous patches crossing, 417.

 Forster, Lieutenant, conversation carried on by, across Port Bowen
    Harbour, 136.

 Fossil plants, an evidence of change in temperature, 74.

 Fourier, mean temperature of space according to, 119;
   rate of decrease in the earth’s central heat computed by, 232.

 Fox, Mr., temperatures in mines tested by, 228, 229;
   law of paramagnetic force ascertained by, 338;
   observations in mines, proving agency of electro-magnetism, 346.

 France, arcs of the meridian measured in, 48;
   unit of linear measure in, 89;
   mode of arithmetical computation, 90;
   atmospheric pressure in, 120;
   cliffs of, seen from Hastings, 157.

 Fraunhofer, M., discovery of rayless lines in the solar spectrum, 162;
   comparative refrangibility of rays ascertained by, 163;
   data furnished by, to determine the dispersive power of rays, 165;
   his discovery determining the length of waves independently of
      refraction, 201;
   spectrum of an electric spark observed by, 289.

 Freezing, temperature required for, under pressure, 271;
   theory of, 276.

 Fresnel, M., his testimony in favour of the undulatory theory of light,
    171;
   theory of refraction, 183;
   discoveries in polarization of light, 191, 193.

 Freyberg, green plants found in mines at, 253.

 Friction evolving heat, 274, 275;
   electricity, 282, 283.

 Fringes of coloured light bordering shadows, 174, 175;
   produced by interference of polarized rays, 194.

 Fulgorites, found in Silesia, 293.

 Fundy, the Gulf of, cross tides pouring into, 94.


 Gage, Mr., experiments of, on magnetism, 315.

 Gales.
   _See_ Winds.

 Galileo, laws affecting music discovered by, 145;
   his method of finding distances of fixed stars, 388.

 Galle, Dr., Neptune’s place communicated to, by Le Verrier, 62.

 Galloway, Mr., sun’s motion proved by, 405.

 Galvani, Professor, peculiar effects of electricity suggested to, 297.

 Galvanism, phenomenon suggesting the theory of, 297;
   batteries, 298, 300;
   heat and light evolved by currents of, 300, 304;
   decomposition and composition, 307, 308;
   applied to plating and gilding, 309;
   effect of heat on, 310;
   effect of, on the senses, _ib._;
   fish exhibiting analogous phenomena, 310, 311;
   phenomena exhibited by currents of, on magnets, 312, 314:
   intensity of a current measured, 315;
   conditions obtaining a circuit in, 332.

 Galvanometer, the principle of its construction, 315;
   experiment by means of, identifying magnetism and electricity, 322,
      323.

 Gambart, M., parabolic elements of a comet computed by, 367.

 Gamma Andromeda, colours of, 401.

 —— Aquarii, planetary nebula near, 412.

 —— Hydræ, a variable star, 391.

 —— Leonis, focus of a meteoric shower in, 422.

 —— Sagittarii, cluster of the Milky Way round, 387.

 —— Virginis, eclipse in, 397;
   orbit of the revolving star determined, 398.

 Ganges, the, tidal wave at the mouths of, 94.

 Gardner, Mr., extent of diametrically opposite lands estimated by, 244.

 Gases, conditions retaining matter in the form of, 104, 105;
   combinations of, 111;
   transmission of radiant heat through, 258;
   expansion of, 271;
   voltaic spectrum modified by, 303;
   effect of heat on the conducting powers of, 309.

 Gassiot, Mr., experiments of, on the electric discharge, 306;
   connexion between magnetism and light discovered by, 321;
   electric apparatus improved, 328.

 Geneva, the Lake of, experiment on the velocity of sound in, 135.

 Gensanne, M., increasing temperature of mines tested by, 228.

 Geographers, lunar motions important to, 42.

 Geological changes, probable cause of, 77.

 Geology, the lessons of, 326.

 Georgia Island, S., excess of cold in, over corresponding latitudes,
    241.

 Germany, shooting stars seen from, 421.

 Gibraltar, the Straits of, turning aside the tidal wave, 98.

 Giromagny, temperature of the lead-mines of, 228.

 Glass, effect of cohesion on plates of, 106;
   musical notes elicited from rods and plates of, 144-147;
   transmission of waves of light in, 177;
   polarizing light, 184, 185;
   elliptical polarization produced by, 193, 194;
   used in photography, 207;
   impressions on, from bodies in contact with, 220;
   impressions on, traced by electricity, 221;
   transmission of radiant heat by, 259;
   by coloured, 261, 262;
   its temper altered by magnetism, 352, 353.

 Globular clusters of nebulæ, 413-415.

 Glow-discharge observed by Captain Bonnycastle, 295, 296.

 Gold, action of, on light, 173.

 Good Hope, the Cape of, icebergs drifted to, 101.

 Goodricke, Mr., variable stars discovered by, 391;
   opaque bodies represented as revolving round fixed stars by, 394.

 Graham, Mrs., account of an earthquake by, 234.

 Graham’s compensation pendulum, 272.

 Gravitating force of the sun, 365, 424, 425.

 Gravitation, offices of, in the material creation, 1, 2;
   process of reasoning in ascertaining the law of, 3;
   law determining its intensity in the solar system, 5;
   complex action of, by attraction in mass and in particles, 6;
   increase of, towards the poles of the earth, 45;
   calculations founded on its increase, 49-51;
   in a mine, its excess over surface, 57;
   action of, modifying tides, 92, 93;
   law, universally acting on matter, 105;
   the air subject to, 117;
   influence of, in motions of the heavenly bodies, 382, 383;
   double stars revolving by, 398;
   stellar systems subject to, 400;
   influence of, on nebulæ, 416;
   a general law of the visible creation, 424;
   mode of its action, 425, 426.

 Gravity, centre of, in spheres, effect of impulses passing through, 7;
   of the solar system, invariable plane passing through, 23;
   straight line described by, 24;
   action of, in determining the figure of the earth, 44, 45;
   definition irreconcilable with the conservation of force, 354, 355;
   question of its transmission, 355, 356.

 Great Bear, the nebulous zone passing, 416.

 —— Gobi, the, effect of the expansion of air over, 124.

 Greeks, astronomical observations of, confirming results of analysis,
    38.

 Greenland, ocean on the northern coast of, 94.

 Greenwich, lunar distances computed for, 43;
   quadrant of the meridian passing through, furnishing a unit of linear
      measure, 89;
   periodic circuits of winds, 125.

 Grimaldi, coloured fringes bordering shadows described by, 175.

 Groombridge, velocity of his proper motion, 404.

 Grotthus, the transmission of voltaic electricity investigated by, 298.

 Grove, Mr., copper and zinc plates electrified by, 220;
   substances radiating heat of different refrangibilities enumerated
      by, 257;
   the transmission of voltaic electricity investigated by, 298;
   electric heat tested by, 301, 302;
   remarks of, on carbon, 302, 303;
   on the voltaic arc, 304, 305;
   remarks of, on light and heat, 319;
   electric apparatus improved by, 328;
   his definition of the ethereal medium, 355.

 Grylli, supposed delicate sense of hearing in, 132.

 Guanaxato, temperature of the silver-mine of, 228.

 Gulfs separating stars, 390.

 Gum-guaiacum, chemically affected by rays of the solar spectrum, 203;
   condition of its sensibility to light, 206;
   effect of red rays on, 209;
   used in experiments on parathermic rays, 217, 218.

 Gum-lac, electrical intensity measured by means of, 286, 287.

 Gymnotus electricus, the, 310.


 Haidinger, M., experiments of, proving water an essential part of
    crystals, 107.

 Hail, formation of, 270.

 Hales, his calculation of the amount of surface exposed by the leaves
    of a helianthus, 243.

 Hall, Mr., achromatic telescope constructed by, 165.

 Halley, elements of a comet’s orbit computed by, 362;
   return of his comet, 363;
   changes in its aspect, 363, 364;
   records of, 365;
   no solid nucleus in, 374;
   cause of its luminous sectors, 376;
   Sir John Herschel’s observations on, 378.

 Hare, the, comet observed near, 372, 373.

 Harmonics of the fundamental note in music, 140, 141.

 Harmony, property of sound regulating, 131;
   definition of, vibrations producing, 142.

 Harris, Sir William Snow, experiments of, in electricity, 287, 288;
   lightning-conductors invented by, 293.

 Harrison, pendulum invented by, 272.

 Hastings, coast of France distinctly seen from, 157.

 Heat affecting the form of crystals, 107;
   evolved in chemical combinations, 110;
   irregular decrease of, in the atmosphere, 119;
   maxima of, in the solar spectrum, 215;
   peculiar chemical quality of, in parathermic rays, 218;
   impressions traced by, 220-222;
   periodical variations in the sun’s, 225;
   different proportions of solar, reaching the planets, 225, 226;
   effect of the terrestrial atmosphere on lunar, 227;
   mode of its development in opaque bodies, _ib._;
   sources of terrestrial, 228-238;
   irregular distribution of, 239-247;
   laws affecting its radiation, 257;
   its transmission, 258-262;
   polarization of, 264-267;
   undulatory theory, 267;
   absorption and reflection of radiant, 268;
   phenomena caused by radiation of, 269;
   accumulation of, producing light, 270;
   expansive force of, 271, 272;
   modes of propagation, 273, 274;
   produced by motion and equivalent to it, 274-277;
   laws regulating the force of artificial, 279, 280;
   power evolved by application of, 280;
   identical in nature with sound, 281;
   electrical, 288;
   sheet-lightning caused by, 294;
   phosphorescence, 294;
   developed by voltaic electricity, 301, 302;
   effect of, on electrical conductors, 309;
   connexion between the production of electricity and, 310;
   its direct relation to magnetism and electricity, 319, 320;
   mechanical power and convertible forces, 329;
   terrestrial magnetism attributed to the action of, 333;
   measured by electric currents, 334;
   affecting atmospheric magnetism, 344;
   fundamental principle of the dynamic theory, 357.

 Helena, St., distinct flora of, 252.

 Helix, circular and elliptical, described in polarization of light,
    192, 193;
   electrical experiments by means of, 314;
   induction of, increasing electric power, 322, 323.

 Heller, his observations on the comet of 1556, 370, 371.

 Helmholtz, Professor, power of chemical force estimated by, 112;
   his calculation of the chemical force developed by combustion, 278;
   of the amount of latent force in our system, 280.

 Hemisphere, cause of excess of cold in the southern, 241;
   superficial extent of land in northern and southern, 244.

 Henley, Mr., magneto-electric machine constructed by, 325.

 Henderson, Professor, parallax of α Centauri calculated by, 387;
   of Sirius, 389.

 Henry, Professor, experiments of, on magnetism, 315.

 Herapath, Mr., his view of elastic force preferred to Sir Humphry
    Davy’s, 276.

 Hercules, eclipse of a double star in, 398;
   globular nebulous cluster, 414.

 Herschel, Sir William, observations of Saturn’s and Uranus’s satellites
    by, 32, 33;
   theory of, regarding the solar constitution, 41;
   cause of effects of light in eclipses according to, 42;
   rotation of Jupiter’s satellites determined by, 70;
   mutual independence of light and heat, 214, 215;
   influence of the sun’s spots on heat, 225;
   point of maximum heat in the solar spectrum, 263;
   comet of 1811 observed by, 374;
   its luminous envelopes examined, 375;
   the Milky Way examined by, 385;
   his discovery of the orbital motions of double stars, 388;
   catalogue of double stars by, 395, 396;
   periodic time of γ Virginis determined by, 398;
   eclipse of a double star observed, _ib._;
   binary system discovered, 400;
   remarks on the motions of the stars, 405;
   nebulæ resolvable into stars, 507.

 Herschel, Sir John, approximate periods of satellites ascertained by,
    33;
   thickness of Saturn’s ring computed, 67;
   observations of, on seasons, 74;
   difficulty of varying time, in observations at distances, obviated
      by, 86;
   tenuity of atmospheric air demonstrated, 110;
   rapid decrease of density in the atmosphere, 118;
   mean temperature of space computed by, 119;
   height of Etna measured, 120;
   his explanation of anomalies in atmospheric phenomena, _ib._;
   quotation from, on the transmission of sound, 136;
   observations of, on thunder, 138;
   remarks on the absorption of light by coloured media, 175, 176;
   on polarization of light, 179;
   experimentalising apparatus, 188;
   discovery of epipolic light, 197;
   discoveries in photography, 205, 206;
   analysis of the solar spectrum, discovery of its chemical properties,
      207-219;
   his theory of volcanic action, 235-237;
   observations showing the maximum of heating influence of the solar
      rays, 238;
   theory of the original distribution of plants, 254;
   divergent flame of a comet observed by, 364;
   remarks on the possible destruction of the solar system, 372;
   causes assigned by, for contraction of diameter in comets, 378;
   comparative lustre of stars measured by, 384, 385;
   the Milky Way described, 385, 386;
   number of stars in a group of the Milky Way computed, 387;
   variable star discovered, 391;
   remarks of, on the nature of the fixed stars, 392;
   variable stars discovered by, 393;
   remarks on variable stars, 394;
   star missed by, 395;
   double stars discovered, 396;
   eclipse of a double star observed, 397;
   orbits determined, 398, 399;
   observations on colours of double stars, 401;
   light of α Centauri compared with the moon’s by, 404;
   light of the fixed stars calculated, _ib._;
   observations on nebulæ corrected, 407;
   catalogues of nebulæ, 408;
   nebulæ discovered by, 409;
   annular nebula described, 410;
   magnitude of planetary nebulæ computed, 412;
   globular nebulous cluster described, 413;
   law of gravitation ascribed to nebulæ, 416;
   nebula round η Argus described, 418;
   his work on Nebulæ, 419.

 Herschel, Miss, Encke’s comet seen by, 365;
   catalogue of nebulæ, 407.

 Hevelius, divergent flames of a comet described by, 364;
   contraction in diameter of comets observed, 377;
   phases in comets observed, 380.

 Hieroglyphics interpreted by astronomy, 89.

 Himalaya, the, inappreciable effect of, on the globe’s surface, 6;
   singular effect of refraction on, 156;
   cause of greater elevation of the snow-line on the northern side of,
      241;
   flora of, 250.

 Hind, Mr., comet’s orbit computed by, 370, 371;
   observations of, on Donati’s comet, 379;
   variable stars discovered by, 391;
   vanishing star discovered, 393;
   his belief in planetary systems, 394.

 Hindostan, the tidal wave striking on its coasts, 94.

 Hipparchus, precession discovered by, change of seasons since his age,
    80;
   phenomenon suggesting his catalogue of the stars, 392.

 History corroborated and corrected by astronomy, 87, 89.

 Hoar-frost, cause of, 269.

 Holtzmann, M., opinion of, with regard to the vibrations of polarized
    light, 223.

 Hoogly, the, bore of, 94.

 Horizon, effects produced by the denser stratum of air in, 157, 158.

 Horologium, nebulous patches in, 417.

 Horton coal-mine, experiments with the pendulum in, 57.

 Hours, cause of their mal-correspondence over the globe, 86.

 Hudson’s Bay, tide in, 98.

 Humboldt, his sufferings from rarity of the atmosphere, 118;
   his explanation of the apparent greater acuteness of hearing observed
      at night, 135;
   observations of, in mines, 228;
   causes of disturbance in the equal diffusion of heat enumerated by,
      240;
   identical productions of the Old and New World found by, 251;
   his distribution of palms and grasses, 252;
   green plants found growing in mines by, 253.

 Hunt, Mr., coloured image of the solar spectrum obtained by, 209;
   image obtained in England, 213;
   his experiments in tracing images by juxtaposition of bodies, 220,
      221;
   experiments on the condensing power of rays, 223.

 Hurricanes, origin and cause of, 125, 126;
   curve described by the axis of, _ib._;
   their extent and velocity, 126,127;
   phenomena resulting from their revolving motion, 127;
   laws of, making avoidance possible, 128.

 Huygens, theory originated by, 169.

 Hydrogen, proportion of, in water and gases, 111;
   spectrum from, 303;
   separated from water by electricity, 307.

 Hygrometer, dew-point measured by, 269.

 Hyperbolic motion, ratio of forces procuring, 382.


 Iapetus, seen by Mr. Lassell, 33.

 Ibn Junis, progress of science in his time, 90.

 Ice, formation of, 271;
   force acting in its formation, 276;
   stopping the current of voltaic electricity, 309.

 Icebergs, drifting of, 100, 101;
   farthest range of northern and southern, 241;
   effect of electricity in collisions, 284.

 Iceland spar, its property of double refraction, 181;
   polarized ray analyzed by, 187;
   transmission of radiant heat by, 258;
   electricity elicited from, 284.

 Illumination, comparative, of objects, experiments determining, 227.

 Images, coloured, of the solar spectrum, 208-211;
   traced by contact and juxtaposition of bodies, 219, 220;
   by electricity, 221;
   by media absorbing hot rays, 222.

 India, arcs of the meridian measured in, 48;
   discovery of Saturn’s ring, 66;
   ancient monument of astronomical knowledge, 85;
   observations confirming the antiquity of astronomical science in, 88.

 Indian Ocean, the tidal wave in, 94;
   monsoons blowing over, 124.

 Induction, law of, in electricity, 285, 286;
   magnetic, 314, 315;
   phenomena of, produced by electric currents, 324;
   illustrated by the Atlantic telegraph, 325, 326;
   velocity of electricity modified by power of, 327;
   possibility of electro, furnishing a motive power, 328;
   of electricity by rotation of magnets, 330-332;
   as possessed by magnets, 336;
   paramagnetism evolved by, 337;
   means of accelerating, _ib._;
   subject to the laws of mechanics, 338;
   analogy between electric and magnetic, 341;
   of heavenly bodies, affecting terrestrial magnetism, 346, 347;
   diamagnetic substances capable of, 348.

 Indus, comet passing through the constellation of, 379.

 Inequality, the, of Jupiter and Saturn marking historical epochs, 88.

 Insects, law of their dispersion, 255.

 Instruments, musical, 143, 149, 150;
   imitating articulation of letters, 151, 152.

 Insulation in electricity, 285.

 Interference, laws of, neutralizing undulations, 138, 139;
   the theory of, referred to a general law, 169.

 Iota Cetæ, comet observed near, 372.

 —— Orionis, a nebulous star, 411.

 Ireland, progress of the tidal wave towards, 94.

 Iron, distilled, 305;
   rotation of its particles, _ib._;
   magnetized by electricity, 314, 315;
   magnetic properties of, 332;
   rendered paramagnetic, 336, 337;
   magnetic and electric properties of, 347;
   elasticity of, affected by magnetism, 352.

 Islands, character of their floras, 252.

 Isogeothermal lines of temperature defined, 238, 239;
   parallel with the isothermal lines, 246.

 Isomorphous crystals, 109.

 Isothermal lines of temperature defined, 240;
   latitudes of, deviation from the line of the equator, 245;
   formula determining, 246;
   similarity of vegetation in the same, 253.

 Italy, local attraction, occasioning inaccuracy in measurement, 48.

 Ivory, M., his method of computing heights, 120;
   his theoretical investigation of planet forms, 44;
   deduction from measurement of arcs of the meridian, 48.


 Jacob, Mr., discovery of Saturn’s ring by, 66;
   periodic time of α Centauri determined by, 399;
   periodic time of 70 Ophiuchi, 400.

 James, Colonel, measurements of, in the General Survey of Great
    Britain, 47;
   density of the earth determined by, 58.

 Jamin, M., remarks of, on substances producing elliptical polarization,
    193.

 January, epoch of its beginning the year, 85.

 Jews, denominations of time in their calendars, 85.

 Josephstadt, discovery of a comet from, 367.

 Joule, Mr., heat considered a mechanical force by, 275;
   his view of elastic force, 276;
   amount of latent force in a pound of coal, computed by, 278;
   furnishing data to Professor Thomson, 279;
   quantity of heat generated in a unit of time by electricity computed
      by, 302;
   powerful magnet obtained by electricity, 315;
   electric machines constructed by, 328;
   experiments proving heat and mechanical power convertible, 329.

 Jovial system, mass of the whole, 55.

 Julian Calendar, year of, the first of our era, 86.

 June, 1833, reappearance of Saturn’s rings, 67;
   coincidence of times in, 84.

 Juno, the diameter of, 56;
   astronomical tables of, 63.

 Jupiter, rotation of, distinguished from the other planets, 7;
   periodical inequality in his motions, 15;
   discovery of telescopic planets between Mars and, 20, 21;
   diameter of, 21;
   his position with respect to the equator of the solar system, 24;
   inequalities in the motion of, apparently anomalous, 25, 26;
   his mass proved not homogeneous, 29;
   eclipses, 30, 31;
   compression of his spheroid computed, 39;
   eclipsed by Mars, 42;
   mass of, compared with the sun, 55;
   his diameter, 56;
   increase of density in, 58;
   astronomical tables of, 60;
   rapid rotation, 66;
   period of a year in, _ib._;
   effect of his disturbing energy, 81;
   photographic images of, 226;
   light reflected by his atmosphere, 227;
   action of, on the comet of 1770, 361, 362;
   on Halley’s comet, 362, 363;
   comet revolving between the orbits of the earth and, 367;
   future influence of, on comets, 369;
   comet nearly approaching his fourth satellite, 370;
   comets having their perihelia in his orbit, 381.

 ——, orbit of, revolutions of its major axis, source of variation in
    excentricity, 17;
   slow revolution of its nodes, decrease in its inclination to the
      ecliptic, 19.

 —— with his satellites, an epitome of the solar system, 27;
   effect of his excessive equatorial diameter on their orbits, 28;
   satellites, libration in, 69;
   rotation of, 70.


 Kane, Dr., Polar Sea discovered by, 94;
   cold of Northern Greenland marked by, 247.

 Kappa Crucis, cluster of coloured stars round, 419.

 —— Draconis, seen in the pole of the equator, 88, 89.

 Karsten, Mr., impressions made on glass by electricity, 221.

 Kasan, summer and winter mean temperature of, compared with Edinburgh,
    246, 247.

 Kater, Captain, approximate length of the pendulum, determined by, 89.

 Kempelen, M., speaking-machine invented by, 151.

 Kepler, paths, revolutions of planets discovered by, 5;
   his law regarding the mean distances of planets from the sun, 19;
   law of, applied to calculating distances, 53, 54;
   rapidity of planetary revolutions determined by his law, 66;
   his law finding areas described by heavenly bodies, referred to, 360.

 Kew, balloon ascent from, 119.

 Knoblauch, position of the magnecrystallic axis proved by, 349.

 Knowledge, limited nature of human, 2.

 Kotzebue, stratum in the ocean discovered by, 101.

 Kratzenstein, M., instrument invented by, articulating words, 151.

 Kupffer, M., observations of, on temperature, 246.


 La Basilicata, earthquake in, 234.

 Lacaille, his globular nebulous cluster, 414;
   nebula, 418.

 La Grange, his investigations into the stability of the solar system,
    20, 21;
   greatest discovery of, 23.

 La Hire, phases in comets observed by, 380.

 La Place, stability of the solar system proved by, 20;
   principle in astronomical calculations established, 23;
   angle of inclination fixed, 24;
   his theory accounting for acceleration in the moon’s mean motion, 36,
      37;
   result of observations compared with his theory of Jupiter’s
      satellites, 55;
   theory of planetary motion, 65, 66;
   universal epoch proposed by, 87;
   scientific observations complementing historical records, 87;
   date fixed by, for the lunar tables of the Indians, 88;
   justifies Newton’s theory of tides, 96;
   density of a liquid column estimated by, 114;
   action of the earth on a comet, 359;
   change in a comet’s orbit, 361;
   cause of error in Clairaut’s calculation pointed out by, 363;
   opinion of, as to the comet of 1682, 378.

 “Lake of the Gazelles” ascribed to an effect of reflection, 157.

 Lalande, epochs of conjunctions computed by, 42.

 Lambda Herculis, general motion of the stars determined by, 405.

 Land, dry, comparative extent of, on the globe, 242, 244;
   extent of, in diametrical opposition, 244.

 Landscapes in chiaroscuro, produced by photography, 207.

 Languages, resemblances and analogies between, 255, 256.

 Lapland, arcs of the meridian measured in, 48;
   transit of Venus observed in, 53.

 Laroche, M., his experiments on transmission of radiant heat, 259, 261.

 Lassell, Mr., satellite of Saturn discovered by, 32;
   observations of, on Uranus’ satellites, 33;
   his discovery of Neptune’s satellite, _ib._;
   observations on Saturn’s rings, 66.

 Latent heat, energetic action of, on matter, 275-277.

 Latitude, the, of a planet defined, mode of obtaining, 9, 10;
   cause of periodical inequalities in, 15;
   perturbations from action of the perpendicular force, 18;
   moon’s motion in, disturbed, 35;
   effects of disturbance, 38;
   data of, used in computing a planet’s place in the heavens, 58-60;
   conditions ensuring the invariability of geographical, 76, 77;
   change effected by nutation in, 81;
   climate not invariable in the same, 239;
   degrees of, where diminution of mean heat is most rapid, 244, 245;
   the same mean temperature in different, 246, 247;
   of wine-growing, 250;
   magnetic storms varying with, 345.

 Layang, observations made at, 1100 years before the Christian era, 88.

 Le Sueur, specific diversity of marine animals observed by, 254.

 Le Verrier, M., principle of La Grange applied by, 21;
   zone of instability found, _ib._;
   discovery of Neptune, 62;
   his observations on atmospheric waves, 122;
   comets identified by, 362;
   his table of comets’ orbits, _ib._

 Lenticular nebulæ, 409;
   haze surrounding the sun, 412.

 Leo, nebulous system in, 417.

 Léon-Faucault, M., velocity of light in air and water ascertained by,
    202.

 Lerius, banks of algæ found by, 253.

 Leslie, Professor, compression of air calculated by, 78;
   experiments on radiation of heat, 257.

 Lexel, observations of, on the comet of 1770, 361, 362.

 Libra, the five great planets in conjunction near, 42.

 Librations of the moon, of Jupiter’s satellites, 69;
   of α Centauri, 399.

 Lichen, red, growing on snow, 249.

 Light, rate of its velocity, 31;
   truth deduced from the uniformity of its velocity, 32;
   from the aberration of, _ib._;
   period required to reach the earth from α Centauri, 54;
   action of the atmosphere on, 153;
   conditions regulating the transmission and reflection of, 156;
   loss of, transmitted by the horizontal stratum, 157;
   effects of transmission through the atmosphere, 158;
   Newton’s analysis of, 159;
   Brewster’s, 161;
   phenomena disproving Newton’s theory, 167, 168;
   undulatory theory, 168-170;
   conditions affecting its intensity and colour, 170;
   experiments testing the mutual relations of colour and, 171-175;
   law of its absorption identical with a law of motion, 175-177;
   repeated vibrations producing the sensation of, 178;
   polarized, defined, 179;
   modes of polarization, substances polarizing, 179-185;
   accidental polarization of, 195;
   degraded, or fluorescence, 196;
   objections to the undulatory theory analyzed and disproved, 199-202;
   comparative velocity of, in air and water, 202;
   pictures produced by reflected, 203-207;
   rays of, independent of heat, 214, 215;
   comparative amounts of solar and lunar, 225;
   different measures of illumination from, 227;
   influence of, on vegetation, 249;
   colour developed without the influence of, 253;
   separated from heat by Melloni, 265;
   produced by accumulation of heat, 270;
   law regulating the force of artificial, 279, 280;
   electrical, 288, 289;
   produced by voltaic electricity, 302;
   stratifications of the electric, 306;
   influence of magnetism and electricity on, 319, 320;
   of comets, 379-381;
   of the fixed stars, 401-404.

 Lightning, development of heat exhibited by, 276, 277;
   experiment showing the velocity of, 289;
   theory of, 292;
   the back stroke, _ib._;
   force of the direct stroke, 293;
   sheet, 294;
   effect of, on the compass, 312.

 Lime, carbonate of, variety of form in its crystals, 107;
   invariable form ultimately assumed by, 109.

 Lines of magnetic force, 338, 339;
   experiment ascertaining the form of, 339, 340;
   terrestrial, 341, 342;
   extensive courses of, 344;
   a connected system, 345;
   diamagnetic, 348.

 Lion, the, conjunction of planets in, 42.

 Liquids, balance of forces constituting, 104, 105;
   action of capillary attraction on, 113-116.

 —— possessing the property of circular polarization of light, 190,
    191-193.

 Liquids, conditions affecting the transmission of radiant heat by, 263;
   evaporation from, 269;
   expansion of, by heat, 271;
   propagation of heat in, 273;
   action of heat as a mechanical force on, 275-277.

 London, retarding of the tidal wave between Aberdeen and, 94.

 ——, pendulum vibrating in its latitude, a standard of measurement, 89;
   fulgorites exhibited in, 293.

 Long, Dr., his attempt to measure distances of fixed stars, 388.

 Longitude, mode of reckoning mean and true, 9;
   of the perihelion and of the epoch defined, 10;
   cause of periodical perturbations in, 14;
   calculation from the moon’s influence on the sun’s, 55;
   data of, used in computing a planet’s place in the heavens, 58-60;
   change effected by precession and nutation in, 81.

 Lloyd, experiments of, in polarization of heat, 264.

 Lubbock, Sir John, theory of planetary motion completed by, 64;
   his theory of shooting stars, 423.

 Lumière cendré, definition of, 227.

 Lunar distance, defined, 43.

 —— theory, mean distances obtained from, 43.

 —— tides of the terrestrial atmosphere, 121.

 Lundahles, M., motions of heavenly bodies investigated by, 405.

 Lupus, position of, 390.

 Lussac, Gay, M., uniting of gases by volumes discovered by, 111;
   ascent of, in a balloon, 118;
   course of a lightning flash ascertained by, 292.

 Lutetia, diameter of, 56.

 Lyell, Sir Charles, his theory of changes of temperature in the
    northern hemisphere, 75;
   annual number of volcanic eruptions computed by, 233;
   volcanic phenomena related by, 234.

 Lyncis 12, a triple star, 395.

 Lyra, a variable star in, 391;
   a double star, 395;
   nebula, 410.


 Machinery, relations of, to force, 353.

 Mackintosh, Sir James, quotation from, illustrating the essential
    advantages of study, 1.

 Maclear, Mr., parallax calculated by, 387.

 Madeira, vegetation of, 252.

 Madras, Saturn’s ring discovered from, 66.

 Magellanic clouds, the, 417, 418.

 Magnecrystallic action, 349;
   temperature affecting, 352.

 Magnetic bodies, difference in power of, 347.

 —— elements, the three terrestrial, 343.

 —— equator of the earth, 343.

 —— meridian, the, mean action of forces determining, 343.

 —— poles of the earth, 343.

 —— storms, 344;
   varying with latitude, 345, 346.

 Magnetism, source of, 318;
   producing electrical phenomena, 322, 323;
   rotatory motion a source of, 330;
   classification of substances, with regard to their susceptibility of,
      332;
   residing in substances after two manners, 335;
   experiment illustrating the forces of, 338;
   antithesis, its general character, 339;
   form of its lines of force, 339, 340;
   analogous properties of electricity and of, 340, 341;
   terrestrial, 342-347;
   connexion between solar and terrestrial, 344;
   action of, in crystals, 349-351;
   influence of temperature in, 352;
   affecting elasticity of matter, 352, 353;
   a property of the ethereal medium (?), 356, 357.

 ——, electro, discovery, importance of the science, 312;
   rotation effected by, 313, 314;
   electric intensity measured, 315;
   action of currents in, defined, 316;
   Ampère’s theory of, 317, 318;
   causing rotation of polarized rays, 319;
   action of, on light, 320;
   accidental combinations, 342;
   influencing metalliferous deposits, 346.

 Magneto-electricity, principle suggesting, 322;
   machine constructed on the principle of, 325;
   relation of heat to, 329.

 Magnets, influence of, on electric light, 307;
   fish possessing the power of making, 311;
   effect of an electric stream on, 312-314;
   obtained by electricity, 315;
   power of electro, measured, 315;
   cylinders acting as, 316, 317;
   producing electrical effects, 322, 323;
   evolving electricity by rotation, 330;
   classification of substances in relation to, 332;
   polarity a property of, 336;
   effect on themselves of imparting paramagnetism, 337;
   experiment showing the lines of force of, 338;
   properties of, indestructible by subdivision, 338, 339;
   the earth reckoned among, 342;
   planets reckoned among, 346;
   action of an electro, on copper, 351.

 Maguire, Captain, his observations on magnetic storms, 345, 346.

 Malo, St., rising of the tide at, 98.

 Malus, M., discovery of polarization of light by, 195;
   attempts of, to polarize heat, 264.

 Malta, observations on Saturn’s rings made at, 66.

 Manchester, thunderstorm near, in 1835, 292.

 Mankind, distinct tribes of, 255;
   limited perceptions of, 267.

 Marcet, M., rate of increase in temperature below the earth’s surface
    calculated by, 230.

 Marco Polo, atmospheric effects observed by, in ascending mountains,
    118.

 Marine plants, laws regulating their distribution, 252, 253;
   animals, specific localities of, 254.

 Mariner’s compass.
   _See_ Compass.

 Mars, used in illustrating the possible effects of the radial
    distributing force, 19;
   telescopic planets between Jupiter and, 20, 21;
   diameter of, 21;
   mean distance from the sun, _ib. note_;
   eclipse of Jupiter by, 42;
   parallax found by observing his oppositions, parallax of, 53;
   internal structure, 58;
   astronomical tables of, 63;
   climate of, 225;
   approach of the comet of 1770 to, 362;
   comets having their perihelia in his orbit, 381.

 Marseilles, transit of a comet across the sun observed from, 374.

 Masses, of the sun, of planets and their satellites, computations
    finding, 55, 56.

 Mathematics, use of, in the study of astronomy, 2.

 Matter, theory of its constitution, 102;
   hypotheses as to forces uniting its particles, 103, 104;
   counterbalancing action of elasticity and cohesion, 105;
   crystallization common to all forms of, 109;
   indestructibility of its particles, 110;
   composition of unorganised bodies, subject to permanent law, 110,
      111;
   agent composing or decomposing, 112;
   mode of ascertaining the magnetism of, 335;
   increatable, indestructible, 353;
   proportion of, to spare, 424.

 Matteucci, M., effect of electricity on polished silver observed by,
    221;
   experiment showing polarization by electricity, 286;
   doubts of, on the polarity of diamagnetism, 348 _note_;
   experiments on magnetic action in crystals, 350;
   observation on the action of compression, 352.

 Maury, Lieutenant, calms named by, 123.

 Measurement of astronomical distances, formula assisting, 43.

 Mechain, M., Encke’s comet seen by, 365.

 Mechanical equivalent of heat, 275.

 —— engines, incapable of generating force, 279.

 Mediterranean, the, conditions of, shutting out the tidal wave, 98;
   hurricane in, divided into two storms, 126;
   vegetation of, 252.

 Medium, ethereal, transmitting magnetism, 344;
   density of, 356;
   probable relations of, to gravity, _ib._;
   experiment testing its magnetic properties, 356, 357;
   functions of, 357;
   pervading the visible creation, 358;
   unsolved question touching, 365;
   a cause of accelerated revolutions of comets, 366, 367;
   direction of its increase in density, 367.

 Medium occupying space, 424.

 Medusa tribes, the, phosphorescent brilliancy of, 295.

 Melloni, M., experiments of, in photography, 214;
   his application of the principle of thermo-electricity, 333;
   experiments of, in transmission of heat, 258-263;
   fixing the maximum of heat in the solar spectrum, 264;
   in polarization of heat, 264-266;
   light separated from heat by, 265.

 Melville Island, height of the thermometer in, in January, 247.

 Mercury, inclination of his orbit to the plane of the ecliptic, 21;
   eclipse of, 42;
   cause of his rotation unknown, 65;
   ellipticity of his orbit compared with the terrestrial, 74;
   climate of, 226;
   comet revolving between the orbits of Pallas and, 367;
   attraction of, determining a comet’s orbit, 369;
   comets revolving in his orbit, 381;
   velocity of, 400.

 ——, propagation of heat in, 273;
   rotating by electricity, 314.

 Meridian, constant, of high water, 92.

 ——, mode of determining the magnetic, 343.

 Meridians, size and form of the earth determined from, 46;
   measurement of arcs, 47;
   anomalies from local attraction, 48;
   result of the computations, 48, 49;
   permanent, of the moon, 69, 70.

 ——, magnetic, influencing the direction of metallic veins, 346.

 Messier, comet of 1770 observed by, 361;
   Encke’s comet seen by, 365;
   nebula described by, 409.

 Metallic salts, action of the rays of the solar spectrum on, 203.

 —— springs used in construction of musical instruments, 143;
   rods giving musical notes, 144.

 Metallic surfaces, polarized light reflected from, 193;
   plates, impressions on, from bodies in contact with, 220.

 Metals, expansion of, by heat, 271;
   propagation of heat in, 274;
   transmission of electricity by, 284;
   electricity developed by oxidation of, 298;
   determining the appearance of a spectrum of voltaic flame, 303;
   distilled in the voltaic arc, 304, 305;
   electro-plating of, 309;
   properties of, modifying electric susceptibility, 333;
   magnetism an agent in the formation of, 346.

 Meteor, the bursting of a, 118.

 Meteors, 420;
   theory of, 421-423.

 Meteoric stones, proofs of their foreign origin, 420, 421;
   shower of, 421, 422.

 Mètre, adopted by the French as their unit of linear measure, 89.

 Mica, polarization by induction effected with, 286.

 Milky Way, the, described, 385;
   Sir John Herschel’s description, 385, 386;
   “Coal Sacks,” 386;
   stars composing, 286, 287;
   zone of stars crossing, 390;
   position of variable stars with regard to, 395;
   crowding in, apparent only, 405;
   orbit in the plane of, 406;
   relation of, to the stellar universe, 407;
   nebula resembling, 409;
   its quarter of the heavens, 414, 415;
   dividing the nebulous system, 416, 417;
   great nebula in, 418;
   remote branches of, 419.

 Minerals, possessing the phosphorescent property, 294.

 Mines, cause of increased temperature in, 229;
   green plants growing in, 253.

 Mira, periods of its fluctuations in lustre, 390.

 Mirage, supposed cause of, 157.

 Miraldi, rotation of Jupiter’s satellite determined by, 70.

 Mitscherlich, M., his experiments on crystals, 107;
   discoveries, 108;
   experiments of, in expansions of crystals, 272.

 Mocha, meteors falling at, 421.

 Moignot, M., crystals compressed by, 189.

 Moisture, an indispensable requisite for vegetation, 248;
   transmission of electricity effected by, 284, 288.

 Molecular polarity, produced by electricity, 282;
   attraction, electricity developed by destruction of, 284.

 —— structure affecting transmission of electricity, 303.

 —— vortices, hypothesis of, accounting for the absorption of light,
    177.

 Molecules, material, attraction and repulsion of, 103;
   effect of elasticity and cohesion on, 104-106;
   uniting to form crystals, 107-109;
   extreme minuteness of ultimate, 110;
   of ether, modes of their vibration in natural and polarized light,
      193;
   in fluorescent light, 196, 197;
   images traced by the mutual action of, 219-222;
   arrangement of, connected with magnetism, 350-352.

 Mollusks, distinct species of, 254.

 Monocerotis 11, a triple star, 395.

 Monsoons, theory of the, 123, 124.

 Months, antiquity of, as a measure of time, 85.

 Moon, the, force restraining, 4, 5;
   mean distance of, from the earth, 4;
   results effected by her nearness to the earth, 7;
   annual rate of decrease in her orbit’s excentricity, 17;
   average distance of, from the earth’s centre, period of her circuit
      of the heavens, 34;
   her periodic perturbations, 35-38;
   causes assigned for acceleration of her mean motion, 36, 37;
   eclipses of, 39, 40;
   longitudes determined by observations of, 42, 43;
   her mean horizontal parallax, 52;
   sources whence her mass may be determined, 55, 56;
   her diameter, 56;
   rotation of, 68;
   librations, 69;
   mountains, 70;
   precession resulting from her attraction, 79-81;
   influence of, producing tides, 91, 92, 96-98;
   period of her declinations, 97;
   atmospheric equilibrium disturbed by her attraction, 121;
   cause of her apparent increased magnitude in the horizon, 158;
   photographic image of, 214;
   comparative amount of light emitted by, 225;
   cause of the rarity of her atmosphere, 226;
   increased intensity of light at full, _ib._;
   effect of the terrestrial atmosphere on heat radiated from, 227;
   cause of acceleration in the mean motion of, 366;
   light reaching the earth from, 404.

 Moorcroft, herbarium collected by, 250, 251.

 Moser, Professor, mutual influence of bodies in contact tested by, 219,
    220.

 Mossotti, Professor, his analysis to prove the identity of the cohesive
    force with gravitation, 103, 104;
   his definition of gravity, 355.

 Motion, a law of the universe, 274;
   perpetual, impossible, 279.

 Mountains, anomalies in measurement caused by, 48;
   rarity of atmosphere on, 118;
   cause of perpetual snow, 119;
   modes of determining heights of, 120;
   becoming new centres of motion in hurricanes, 126;
   influence of chains on temperature, 241, 242;
   cause of éboulemens in, 271;
   tops of, fused by lightning, 293.

 ——, lunar, effect of solar rays passing between, in eclipses, 41;
   influence of, on the moon’s motions, 96;
   three classes of, 70.

 Mu Herculis, direction of solar motion with regard to, 406.

 Multiple systems of stars, 395.

 Mundy, Captain, mirage described by, 157.

 Music, comparison instituted of sympathetic notes in, 2;
   regulated undulations of sound producing, 142;
   instruments of, 143;
   experiments by means of vibrating plates, 144-146;
   sympathetic vibrations, 147, 148;
   experiments showing, 148, 149.

 Musical instruments constructed by Professor Wheatstone, 143.


 Naples, comet discovered from, 370.

 Nautical Almanac, computations for calculating longitudes, 43;
   time calculated by, 84.

 Navigation, importance of lunar motions in, 42;
   laws of storms to be observed in, 127, 128.

 Neap-tides, 96, 99.

 Nebulæ, number and general aspect of, 407;
   catalogues, 407, 408;
   classes, 408;
   irregular, 408, 409;
   of definite form, 409;
   spiral, 409, 410;
   annular, 410, 411;
   elliptical, double, 411;
   distance of a nebulous star discoverable, 411, 412;
   aspect and colour of planetary, 412;
   elliptical common, 413;
   globular clusters, 413-415;
   resolution of, 415;
   star clusters, 415, 416;
   probable law of motion, 416;
   distribution of, 416, 417;
   the Magellanic clouds, 417, 418;
   round η Argûs, 418, 419;
   remote systems, 419;
   invisible solar, 421;
   meteors falling from, 422.

 Nebulous appearances of a comet, 364;
   extent of, matter surrounding a comet, 373;
   its variable brilliancy, 374;
   appearances round the sun, 412.

 —— stars, 411, 412.

 Needle, magnetized, effect of Voltaic electricity on a, 312, 313;
   suspended by means of electricity, 314;
   condition of its deviation by an electric current, 317.

 Negative electricity defined, 282;
   mode of exciting, 283.

 —— impressions in photography, 204.

 Neptune, periodical variations in his orbit, 22;
   revolution of his satellite from east to west, 33;
   remoteness of, 54;
   anticipation of discovery, 61;
   orbit and motions of, determined, 62;
   his diameter, mean distance from the sun, 63;
   temperature of, 225;
   action of, on Halley’s comet, 363.

 Neutral phosphate of soda, its crystals, 109.

 New Mexico, monsoons occasioned by its deserts, 124.

 Newton, Sir Isaac, steps of his argument for the universal influence of
    gravitation, 3;
   his discoveries of modes of attraction, 4;
   motions of bodies projected in space, ascertained by, 5;
   form of a fluid mass in rotation ascertained, 45;
   problem occupying astronomers since, 64;
   discrepancy between his theory of tides and observations, 96;
   compound nature of white light proved by, 159;
   his analysis of the solar spectrum disputed, 161;
   his theory of light disproved, 167;
   measurements of coloured rays, 172, 173;
   scale of colours, 174;
   decisive experiment disproving the theory of light, 202;
   remarks on the transmission of gravity, 355.

 Niagara, the falls of, not independent of the influence of astronomy,
    1.

 Nickel, sulphate of, change in its crystals, when exposed to the sun,
    107.

 Niepcé, M., photographic pictures rendered permanent by, 204;
   discovery in photography suggested, 207;
   colours of images of the sun taken, 213;
   experiments by, on saturation of substances with light, 296.

 Nimes, discovery of a telescopic planet at, 21.

 Nitrogen, proportion of, in the atmosphere, 117;
   spectrum from, 303;
   iron volatilized by the Voltaic arc in, 304;
   unaffected by magnetism, 344.

 Nobili, M., direction of electric currents ascertained by, 333.

 Nodes, ascending and descending, of a planet defined, 9;
   movement of their lines in secular disturbances, 14;
   advance and recession of, 18;
   supposed recession of, on the equator of the solar system, 24;
   of the moon, period of their sidereal revolution, 37;
   secular inequality affecting, 38;
   influence of, on eclipses, 39;
   cause of their rapid motion, 55;
   points of rest on a vibrating string, 141;
   in the vibrations of an undulating column of air, 142;
   in vibrations of solids, 147.

 Non-conductors of electricity, 284, 285.

 Non-electrics, 285.

 North Atlantic, the, winds in, 124.

 —— Polar Ocean, tide in the, 94.

 Norway, course of the tidal wave to, 94.

 Notes in music, 142, 143.

 Nubecula, Major and Minor, 417, 418.

 Nucleus, of Halley’s comet, changes in its aspect, 364;
   disappearance of, in Encke’s, 369;
   division, in Biela’s, 369, 370;
   diaphanous, 373;
   solidity of, tested, 374;
   of a spiral nebula, 409.

 Nuremburg, observations on a comet from, 370.

 Nutations produced by the moon’s nearness to the earth, 7;
   in Jupiter’s equator, 29;
   in the planetary axes, 66;
   effect of, on the pole of the equator, longitudes and latitudes
      altered by, 81.

 Nysa, nearness of its orbit to the earth, 21.


 Oaks, range of, near the equator, 250.

 Occultation, central, by Halley’s comet, 364;
   geographical position ascertained by, 384;
   prospective, by a sun of α Centauri, 400.

 Occultations of stars, 42, 43.

 Ocean, the, density and mean depth of, 51;
   mean density, compared with the earth’s, 77;
   its form in equilibrio, when revolving round an axis, 92;
   solar and lunar attraction disturbing its equilibrium, _ib._;
   inequalities in periodic motions, 93;
   motions of the tidal wave in 95;
   stability of its equilibrium, 100;
   circulation of currents in, _ib._;
   stratum of constant temperature in, 101;
   zones of, _ib._;
   decrease and increase of temperature with depth, 231;
   absorption and radiation of heat by, 242;
   electricity evolved from, 291.

 Oceans of light and heat, processes producing, 225.

 Ochotzk, the sea of, depression of the barometer observed in, 120.

 October, 1832, position of Saturn’s rings in, 67.

 Olbers, M., computations for a comet by, 367;
   period of his comet, 370;
   comet of 1811 observed by, 374.

 Opaque bodies, mode in which heat is developed in, 227.

 Ophiuchi 70, anomalies in the motions of, 400.

 Ophiuchus, clusters of the Milky Way between the Shield and, 387;
   new star disappearing from, 393.

 Optic axis, the, of crystals, 183;
   phenomena exhibited by transmission of a polarized ray along, 187,
      188;
   affected by compression, 189.

 Orbit, the, of the earth, attraction intensified by its diminished
    excentricity, 37;
   excentricity of, affecting temperature, 74, 75;
   crossed by comets, 368.

 —— of the moon, force ruling, 4;
   its excentricity, 34;
   changes in, 35;
   its inclination to the plane of the ecliptic, 79.

 —— of a nebula, 415.

 —— of the solar system, 405, 406.

 Orbits of comets, subject to variation, 361;
   examples, 361-363;
   prospective changes in, 369, 370;
   of Donati’s, 379;
   forces determining their forms, 382, 383.

 —— of double stars, 396-400.

 —— of planets, force regulating a planet’s velocity in, 8;
   measurement of their excentricity, 9;
   seven elements of, determining their position in space, 10;
   unequal movements in, 15;
   variation from elliptical to circular, 17;
   secular variations of, in inclination to the plane of the ecliptic,
      18, 19;
   stable and unstable in form, 21, 22;
   influence of the ethereal medium on, 22;
   principle facilitating observations on secular inequalities, 23, 24;
   revolutions of Saturn compared with Jupiter, 25;
   periodic inequality increased by secular variations in their
      elements, 26;
   comets revolving in, 381, 382;
   cause of diversity in form of, 382.

 Orbits of satellites, forms of Jupiter’s, 27;
   their inclinations, 28;
   inclinations of Saturn’s, 32;
   positions of Uranus’s, 33;
   forms of data in computing a planet’s place in the heavens, 59.

 Orinoco, the cataracts of the, heard by day and by night, 135;
   area occupied by forests on, 243.

 Orion, the Milky Way between Antinous and, 385, 386;
   position of, 390;
   variable star in, 393, 394;
   multiple system in, 395;
   nebula in, 408.

 Oersted, Professor, discovery of, suggesting the theory of
    electro-magnetism, 312;
   science founding the reputation of, 316.

 Oscillations, wide-spreading, produced by gravitation, 2;
   mechanical principle affecting small, 11;
   of the sines and cosines of circular arcs, 20;
   invariable plane whence they may be estimated, 24;
   of the pendulum retarded, 32;
   of the pendulum, experiments founded on, 50, 51;
   experiments testing the earth’s density, 57;
   a measure of time, 83;
   produced by tides, 95, 96;
   instruments measuring atmospheric, 113;
   barometer affected by periodic atmospheric, 120, 122;
   of ears of corn, 129, 130;
   producing musical notes, 140-142;
   instances of forced sympathetic, 148;
   causing vicissitudes in climates, 247;
   of the pendulum, disturbed by effects of temperature, 272;
   measuring variation of electrical intensity, 287.

 Otto, M., motions of the heavenly bodies observed by, 405.

 Oxidation of metals, electricity developed by, 298;
   by the Voltaic discharge on polished silver, 305.

 Oxides decomposed by electricity, 307;
   alkalies resolved into metallic, 307.

 Oxygen, in crystals, 109;
   proportion of, in water and carbonic oxide, 111;
   in the atmosphere, 117;
   chemical combination with, evolving light and heat, 270;
   action of electricity on, 284;
   electricity afforded by combination of metals with, 298;
   spectrum from, 303;
   separated from water by electricity, 307;
   paramagnetic, 344.

 Ozone, produced by electricity, 284.


 Pacific Ocean, mean depth of, 77;
   course of tidal waves down, 93;
   mean depth of, 96;
   currents, 100.

 Paderborn, fulgorites from, 293.

 Pallas, inclination of its orbit to the ecliptic, 10;
   diameter of, 21;
   astronomical tables, 63;
   ellipticity of its orbit compared with the terrestrial, 74;
   height of its atmosphere, 226;
   comet revolving between the orbits of Mercury and, 367.

 Pan’s pipes, vibrations in the air passing over, 142.

 Parabolic motion, ratio of forces procuring, 382.

 Parallax of the sun, circumstance favourable to its correction, 21.

 —— of an object defined, 43.

 ——, definition, mode of ascertaining, 52;
   distances computed from, 52-54;
   calculation from the moon’s horizontal, 55.

 —— of fixed stars, 387-390.

 —— of meteors, 421, 422.

 Paramagnetic substances, 335, 336.

 Paramagnetism defined, 335;
   substances it is resident in, 336;
   modes of imparting, _ib._;
   a dual power, _ib._;
   imparted by induction, 337;
   law of its intensity, 338;
   a property of oxygen, 344;
   in antithesis to diamagnetism, 347;
   neutral substances obtained by combinations of diamagnetism and,
      _ib._;
   Dr. Tyndall’s experiments on polarity of, 348;
   dependent on arrangement of molecules, 350, 351;
   affected by compression, 351;
   truth establishing its identity with diamagnetism, 356, 357.

 Parathermic rays, analyzed by Sir John Herschel, 217-219.

 Paris, variation in length of the pendulum at, 51;
   mean annual temperature, 228;
   temperature of an Artesian well in, 230.

 Paths of comets, 359, 360;
   secrets disclosed by their excentricities, 365.

 Parry, Sir Edward, turned back by the Polar current, 101;
   mean temperature calculated from observations of, 245;
   thermometer at Melville Island marked by, 247.

 Pauxis, the Straits of, ebb and flow of the sea in, 98.

 Peel, Sir William, thunderstorm experienced by, 293, 294.

 Pegasus, nebulous region of, 417.

 Pendulum, the, principle equalizing its oscillations, 50;
   the earth’s figure calculated by, 50, 51;
   experiments ascertaining the earth’s density, 57;
   isochronous, a measure of time, 83;
   a standard of the measure of extension, 89;
   the, a connecting link between time and force, 94;
   inventions to neutralise the effects of temperature, 272.

 Penumbra, in lunar eclipse, breadth of space occupied by, 40.

 Perigee, of the lunar orbit, period of its revolution, 37, 38;
   cause of its rapid motion, 55.

 ——, solar, periods of its coincidence with the equinoxes, 86.

 Perihelion of a planet’s path defined, 16.

 —— of the earth’s orbit, its position regulating the length of seasons,
    74.

 Periodic inequalities of planets, 13, 14;
   law from which they are deduced, 24, 25;
   of Jupiter’s satellites, 28, 29;
   lunar, 35.

 Perkins, Mr., experiments of, testing the laws of compression, 78.

 Peron, M., specific diversity of marine animals asserted by, 254.

 Perpendicular force, the source of periodic inequalities, 15;
   effects produced by, 18.

 Perpetual motion, invariable proportion between heat and force
    precluding, 279.

 Perseus, variable star in, 390, 391.

 Peters, Mr., comet discovered by, 370;
   parallax of α Lyræ, 388, 389;
   distances of fixed stars calculated, 389;
   his theory of Sirius’ irregular motions, 392;
   sun’s motion proved by, 405.

 Petit, M., observations of, on meteoric satellites, 423.

 Peru, arcs of the meridian measured in, 48.

 Phases of the moon, regulating returns of eclipses, 39.

 Phenomena, of effects of light in eclipses, 41, 42;
   applied to computing longitudes, 43;
   caused by tidal oscillation, 96;
   from force of cohesion, 106, 107;
   of capillary attraction, 115;
   produced by refraction and reflection, 155-157;
   by polarization of light, 186-190;
   exhibited in fluorescence of light, 196, 197;
   resulting from interaction of rays and molecules, analogous to
      effects of photography, 219-222;
   phosphorescent, 295, 296;
   of galvanism, 310;
   of magnetism, 335, 345-348;
   magnecrystallic, 349, 350;
   exhibited by comets, 363, 364, 369, 370, 372-376;
   by the Milky Way, 385-387;
   by variable stars, 390-393;
   by double stars, 397-401;
   by nebulæ, 409-415, 417-419;
   by meteoric showers, 421, 422.

 Phosphorescence, rays of the solar spectrum exciting, 216;
   cause of, in the solar spectrum, 217;
   excited by electricity, 294;
   fish possessing the property of, 295;
   the glow discharge, 295, 296;
   experiments investigating the nature of, 296.

 Photo-galvanic engraving, 309.

 Photography, first suggestions, 203;
   discoveries and improvements in, 204-207;
   conditions affecting the chemical properties of rays producing, 207,
      208;
   images of the solar spectrum obtained by, 208-210;
   coloured copy of an engraving, 211;
   phenomena in, suggesting an absorptive action in the solar
      atmosphere, 212, 213;
   chemical energy producing, distinct from light and heat, 214;
   experiments by means of, testing the properties of rays, 218, 219;
   experiments on action of light, heat, electricity, producing results
      analogous to effects of, 219-223.

 Photosphere, the, of the sun described, 224.

 Physical Sciences, the most extensive example of their connection, mode
    of its operation, 1.

 Pi Herculis, direction of solar motion with regard to, 406.

 Pisces, nebulous region of, 417.

 Planetary motion, representation of, 14.

 —— nebulæ, 409;
   appearance of, 412.

 Planets, paths round the sun described by, 5;
   law determining their revolutions, _ib._;
   forces adjusting their forms, 6;
   their motions in elliptical orbits, mean distance from the sun, 8;
   mode of obtaining the place of, in their orbits, 9;
   computations giving the place of, in space, 10;
   disturbances from reciprocal attraction affecting, compensations,
      13-19;
   telescopic, 20, 21;
   perturbations in the mean motions of, 25, 26;
   influence of, on lunar motions, 36;
   eclipses and conjunctions of, 42;
   formula finding their masses, 55;
   their diameters, 56;
   mass of the telescopic, compared with the moon, _ib._;
   comparative density, 58;
   method of computing their places, 58-64;
   discovery of, 61-63;
   exploded theory touching telescopic, 63;
   periods of their rotations, 66;
   variation and position of the plane of the ecliptic produced by, 79;
   its effect on the equinoctial points, 80;
   climates of, 225, 226;
   probably magnets, 346;
   constant velocity of their mean motions, 366.

 Plants, distribution of known species over the globe, 249, 250.

 Plates, vibrating, experiments by means of, 144-146.

 Plateau, M., experiments of, on colour, 165, 166.

 Platina, incandescent, used as a source of heat, 260.

 Platinum, experiment producing spontaneous combustion of, 112, 113.

 Playfair, Professor, quoted in reference to La Grange’s discovery, 23.

 Pleiades, the, nebulous stars, 415.

 Plücker, Professor, discoveries of, in the action of magnetism in
    crystals, 349.

 Plumb-line, deviations of, from local attraction, 48;
   earth’s density calculated from a deviation of, 58.

 Poinsot, M., La Place’s discovery extended by, 23;
   comparison by, 24.

 Point, ready escape of electricity from a, 288.

 Poisson, M., decisions of, on the phenomena of capillary attraction,
    114.

 Polar basin, probable temperature of, 245, 246.

 —— star, change of position in the, 81, 82.

 —— vegetation, contrasted with tropical, 248.

 Polarity, produced by electricity, 282;
   of magnets defined, 336;
   induced in iron, 337;
   its antithetical manifestations of, 339;
   invariably dual, 341;
   of diamagnetic substances, 347, 348.

 Polarization of light, definition of, 179;
   refracted by various substances, 180-183;
   by reflection, 184;
   angles of, 185;
   phenomena exhibited by transmission through analyzing media, 186-188;
   circular, 189-191;
   theory of circular and elliptical, 192, 193;
   substances producing, 193, 194;
   theory of coloured images formed by, 194;
   accidental, 195;
   discovery of, _ib._;
   degraded light incapable of, 198;
   communicating electricity, 220;
   plane of motion of vibrations in, 223.

 Polarization of heat, first attempts, 264;
   successful experiments, 265-267.

 —— of electricity by induction, 286.

 ——, experiment showing the action of magnetism on, 319;
   affected by mechanical compression, 352.

 Poldice mine, the, temperature of the water pumped from, 229.

 Poles, the, cause of the flattening of a spheroidal mass at, 6;
   diameter of Jupiter at, 27;
   experiment determining the increase of gravitation towards, 49, 50;
   the, drifting of ice from, 100, 101;
   of maximum cold, centres of the isothermal lines, 245, 246;
   nature of magnetic force distinguished by, 332;
   four terrestrial, of maximum magnetic force, two magnetic, 343.

 Pollux, an optically double star, 401.

 Port Bowen Harbour, transmission of sound across, when frozen, 136.

 Positive electricity, defined, 282;
   mode of exciting, 283.

 —— impressions in photography, 204.

 Pouillet, M., his estimate of the mean temperature of space, 119;
   quantity of solar heat received by the earth computed by, 238;
   data furnished by, to Professor Thomson, 279;
   development of electricity investigated by, 291.

 Powell, Baden, substances producing elliptical polarization enumerated
    by, 193;
   dispersion of light accounted for by the undulatory theory, 200, 201;
   experiments in transmission of radiant heat, 262;
   attempts to polarise heat, 264.

 Power, Mr., undulations producing fluorescent light computed by, 197;
   law of solar rays acting on media, 198.

 Præsepe, the, in Cancer, 415.

 Precession, a, in the equinoxes of planets, its cause, 66;
   mean, of the equinoctial points, defined and calculated, 80;
   influence of, on the pole of the equator, on longitudes, 81.

 Pressure, electricity elicited by, 283, 284;
   law of electrical, 288.

 Principato Citeriore, earthquake in, 234.

 Prisms, solar spectrum formed by, 159;
   neutralizing effects of colour, 164;
   of brown tourmaline, light polarized by, 180;
   resolution of the pure white sunbeam by, 222;
   substance of, determining the point of maximum heat in the solar
      spectrum, 263, 264;
   electrical light analysed by, 288.

 Problem determining the motions of translation of the celestial bodies,
    11;
   of the three bodies, 58;
   the hardest astronomical, 92.

 Procyon, light of, 402.

 Proportion, definite, the law of, in mixing substances, 111, 112.

 Protoxides of metals, their crystals, 109.

 Prussia, Eastern, fulgorites from, 293.

 Ptolemy, decrease in the inclination of Jupiter’s orbit since the age
    of, 19;
   discovery of the Evection by, 35;
   Indian lunar tables calculated in his time, 88;
   horoscope ascribed to the age of, 89;
   effects of refraction observed by, 155;
   colour of Sirius in his time, 401.


 Quadratures, the equation of the centre in, 9;
   lunar orbit augmented in, 35;
   tides affected by the moon in, 96.

 Quadrupeds, distribution of distinct species of, 255.

 Quartz, crystallised, light polarized circularly by, 189, 190;
   varieties of polarization exhibited by, 193.

 Quebec, extremes of temperature found in, 247.

 Quinine, sulphate of, producing fluorescence of light, 197.


 Radial force producing periodical changes in relative positions of the
    heavenly bodies, 15;
   effects produced by, 16, 17;
   principle neutralising its ultimate result, 19, 20.

 Radiation of heat, laws regulating, 257;
   universal from substances, 268;
   natural phenomena resulting from, 269;
   slow decrease of the earth’s central heat from, 232;
   influence of, on temperature, 239;
   power of, in water compared with dry land, 242;
   of heat, a transfer of motion, 277.

 Radii vectores, signification of, 8;
   areas described by, 10;
   force disturbing in the direction of, 14, 15.

 Ragona-Scina, M., his theory of rayless lines in the spectrum, 163.

 Rain, force shaping drops, 106;
   cause of periodic tropical, 123;
   region of, 124;
   theory of its formation, 270;
   an electric conductor, 292.

 Rankine, Mr., his theory of the structure of matter, 104;
   his theory of the absorption of light, 177.

 Rays, common nature and common properties of, 268.

 —— of heat, existing independently of luminous, 257;
   laws of transmission of, 258;
   analogy between transmission of luminous rays and, 259;
   temperature of their source affecting transmission, 260;
   varying in nature with their origin, 261;
   transmitted through coloured glass, 262;
   traversing various media, _ib._;
   subject to refraction and reflection, 263;
   polarized, 265-267;
   absorption and reflection of, 268;
   rotation of polarized, caused by magnetism, 319.

 —— of light, bent by passing from rare into dense media, 153;
   partial and total reflection of, 156;
   loss of, by obliquity of incidence, 158;
   theory of their transmission and absorption, 159-161;
   comparative refrangibility of, 163;
   experiments on dispersion of, 164;
   principle determining their colour, 170, 171;
   transmission of, in glass or water, 177, 178;
   conditions of polarized, 179;
   double refraction, 181-183;
   polarized by reflection, 184, 185;
   coloured images produced by interference of, 194, 195;
   internal dispersion of, 195-198;
   heat, light, chemical action, independent properties of, 214, 215;
   undulations constituting, 223;
   conditions modifying the power of solar, to produce heat, 237;
   transmitted independently of calorific rays, 258;
   magnetizing of polarized, 318, 319.

 Rays, solar, effect produced by their refraction in lunar eclipse, 40;
   passing between lunar mountains in solar eclipse, 41.

 —— of the solar spectrum, their chemical properties, 203;
   varying chemical energy, 207, 208;
   varying nature of their action, 208;
   peculiar chemical action of the red, 209-211;
   deoxydating and oxydating action of, 211, 212;
   experiments detailed, 212-215;
   new, obscure, detected by Sir John Herschel, 217.

 Red Sea, the, tide in, 98.

 Reflection of waves of sound, 137, 138;
   of rays at surfaces of strata differing in density, phenomena
      occasioned by, 156, 157;
   affecting colour, 160;
   motion of a ray of light in, 177;
   light polarized by, 184, 185;
   elliptical polarization produced by, 193;
   heat polarized by, 266;
   of radiant heat from surfaces, 268.

 Refraction of the sun’s rays in lunar eclipses, 40;
   of waves of sound, 138;
   of light by the atmosphere, 153, 154;
   mode of estimating, in case of celestial bodies, 155;
   formulæ obtaining in case of terrestrial objects, _ib._;
   phenomena occasioned by, 155, 156;
   colours decomposed by, 159, 160;
   produced without colour, 164, 165;
   power of, in media affecting the elasticity of the luminous ether,
      177;
   of a polarized ray, 180;
   double, 181, 182;
   Fresnel’s theory of, 183;
   diminished capability of producing fluorescence, 196;
   capability of, in rays, affecting their chemical action, 209-212;
   effect of, on the lunar atmosphere, 226;
   influence of, on transmission of heat, 258;
   of rays of heat, 261-264;
   heat polarized by, 266.

 Refrangibility, substances diminishing, of light, 196;
   affecting the chemical action of rays, 209-212;
   affecting radiation of heat, 257;
   affecting transmission of radiant heat, 261-263.

 Reich, Professor, temperature of mines observed by, 228;
   mean increase calculated by, 230.

 Reptiles, distribution of distinct species of, 254.

 Repulsion of electricities, 283;
   experiments determining the laws of electrical, 286, 287;
   modes of, in static and in Voltaic electricity, 317;
   developing comets’ tails, 375-377.

 Resistance, a cause of accelerated motion, 367.

 Retina, the, action of, in receiving impressions, 166;
   comparative sensibility of its fibres to light, 178.

 Retrograde motion of comets, 359, 368, 373, 379.

 Rhodiola rosea, identical species of, found in Tartary and in Scotland,
    251.

 Rhombohedrons of carbonate of lime, 109.

 Richman, Professor, killed by lightning, 293.

 Richter, variation in length of the pendulum observed by, 51.

 Rings of Saturn, 66-68;
   Saturn’s, diamagnetic, 347;
   luminous, surrounding comets, 374, 375;
   surrounding Donati’s, 379.

 Ritchie, Professor, electrical experiments of, 314.

 Ritter, M., chemical properties of the solar spectrum observed by, 203;
   oxydizing effect of red rays, 209.

 Rive, M. Auguste de la, rate of increase of temperature in wells
    observed by, 230.

 Rivers, curvature of the land proved by, 46;
   influence of, on the earth’s rotation, 71;
   rising of tides in, 98;
   effect of, in cooling the atmosphere, 243.

 Roget, Dr., phenomena of electro-magnetism explained by, 313.

 Rome, observations on lunar mountains made at, 70;
   era fixed at, 85;
   comet discovered from, 370.

 Ross, Sir James, stratum in the ocean discovered by, 101;
   depressure of the barometer observed by, 120;
   volcanic region discovered, 232.

 Rosse, Lord, nebulæ resolved by his telescope, 407, 408;
   spiral nebula, 409, 410;
   annular nebulæ discovered by, 410;
   nebulous star, 411;
   planetary nebulæ, 412;
   nebulæ resolved by, 415.

 Rotation affecting winds, 122-127;
   of winds, 124, 125;
   of hurricanes, 125, 126;
   produced by the Voltaic current acting on iron, 305;
   of stratifications of electrical light, 307;
   caused by electricity, 313, 314;
   of light caused by an electric current, 319;
   of magnets producing electricity, 330-332;
   changes produced in comets by, 376.

 Rotations of the solar system, 7;
   of the sun, 65;
   of the planets, 66;
   of satellites, 68;
   of Jupiter’s satellites, 70;
   of the earth, a measure of time, 71;
   influence of temperature on, 72;
   axis of, invariable, 76, 77.

 Rotatory motion, form indicating, 65;
   of Donati’s comet, 379.

 Roux, M. le, observations on magnetic action in crystals, 350.

 Rudberg, M., refrangibility of substances ascertained by, 201, 202.

 Ruhmkorff, M., improvements on his electro-inductive apparatus, 328.

 Russell, Scott, Mr., velocity of the tidal wave estimated by, 95.

 Russia, arc of the meridian measured in, 48;
   climates of, 244.


 Sabine, General, variations in the magnetic elements investigated by,
    343, 344.

 Sagittarius, comet traversing the constellation of, 379;
   the Milky Way in, 386;
   nebula, 414.

 Sahara, the, causing monsoons, 124.

 —— desert, extent, influence of, on the atmosphere, 243.

 Salt, Mr., papyrus sent from Egypt by, 89.

 Sand, tubes in, formed by lightning, 293.

 Sandy deserts influencing temperature, 243.

 Sandwich Land, excess of cold in, over corresponding latitudes, 241.

 Sargassa, or grassy sea, found in the Atlantic, 253.

 Satellites, intensified action of attraction upon, 7;
   intimate union of, with their primaries, 26;
   exceptions to a general law of the solar system, 65, _note_;
   rotations equal to the times of their revolutions, 68;
   comet passing through, 69.

 ——, Jupiter’s, proportion of their mass to that of their primary, 27;
   disturbing force of attraction affecting their orbits, 28;
   periodic and secular inequalities, 28, 29;
   eclipses, 30;
   rotation, 70;
   passage of a comet through, 359;
   comet nearly approaching, 370.

 —— of Saturn, 32;
   of Uranus and Neptune, 33.

 ——, mode of computing their masses, 55;
   comparative density of, 58.

 —— of Neptune, 63.

 —— of the earth, shooting stars, 423.

 Saturn, unequally occurring compensations of disturbance in its
    motions, 15;
   disturbing influence of, on Jupiter, excentricity of its orbit
      compared with Jupiter’s, 17;
   retarding the revolution of Jupiter’s nodes, 19;
   invariable plane passing between Jupiter and, 24;
   observations on the mean motions of Jupiter and, 25, 26;
   eclipse of, 42;
   internal structure, 58;
   astronomical tables of, 60;
   period of his year, 66;
   the rings of, described, 66-68;
   his ring probably diamagnetic, 347;
   action of, on Halley’s comet, 362, 363;
   comets having their perihelia in his orbit, 381.

 Saurian reptiles, distinct tribes of, 254.

 Saussure, M., temperature of mines observed by, 228, 229;
   lichen discovered by, 249.

 Savart, M., his researches and experiments in acoustics, 132, 133;
   experiments on vibrations of glass rulers, 145-147;
   experiments showing sympathetic undulations, 148, 149;
   discoveries on the nature of voice, 152.

 Savary, M., orbital elements of a double star determined by, 396;
   his mode of ascertaining the actual distances of fixed stars, 402,
      403.

 Scheele, M., chemical changes effected by the solar spectrum observed
    by, 203.

 Schroëter, height of planetary atmospheres calculated by, 226.

 Schwabe, M., periodic variation in the solar spots observed by, 344.

 Science, its value regarded as the pursuit of truth, 1;
   errors of the senses corrected by, 32;
   evidence of its antiquity, 87.

 Sciences, mutual relations of forces proving the connexion between,
    319-321;
   analysis proving the whole circle of, kin, 427, 428.

 Scoresby, Captain, phenomenon occasioned by refraction observed by,
    156.

 Scorpio, vacant patch of the Milky Way in, 386;
   position of, 390;
   a double star in, 395;
   nebula in, 414.

 Scotland, progress of the tidal wave round, 94.

 Sea, the, inappreciable influence of, on the direction of gravity, 77;
   mean height of snow-line above the level of, 241;
   comparative extent of, 242.

 Seasons, conditions determining the duration of, 74;
   cause of their unequal periods, 87;
   theory of the tropical dry and rainy, 123.

 Seaweeds, photographic impressions of, 205, 206;
   luxuriance, deep colours of, 253.

 Secchi, Professor, mountains of the moon observed by, 70;
   photographic image of the moon obtained, 214;
   temperatures of the sun’s surface estimated, 225;
   experiments of, in photographing the moon and Jupiter, 226, 227.

 Secular inequalities of planets, 13, 14;
   means of discovering, 24, 25;
   effect of, on the mean motion of the moon, 36, 37.

 —— variations in mean values of the magnetic elements, 343.

 Seebeck, point of maximum heat in solar spectrum fixed by, 263;
   discovery of, 264;
   relations of heat to electricity discovered by, 332, 333.

 Seed-lobes, proportion in the distribution of plants having one or two,
    252.

 Seleniate of zinc, crystals of, 107.

 Senarmont, M., experiments of, in expansion of crystals, 273.

 Senses, necessarily inaccurate testimony of the, 281.

 September, times coinciding in, 84.

 Serpentarius, star in, vanishing, 392.

 Shell-fish, their mode of clinging to rocks, 117.

 Shield, the, clusters of the Milky Way between Ophiuchus and, 387.

 Shooting stars, phenomena of, described, 421, 422;
   theories of, 423.

 Siberia, Eastern, depression of the barometer observed in, 120.

 Sidereal times, mean, periods of, 83;
   measurement of apparent, _ib._

 Sigma Eridani, period of revolution in, 400.

 Silesia, fulgorites from, 293.

 Silver iodized, its sensitiveness to impressions, 221.

 Sirius, the Egyptian year estimated from, 85;
   comet’s tail extending from the Hare to, 373;
   rank of, 384;
   comparative magnitude, 385;
   parallax, 389;
   cause of his irregular motion, 392;
   change in colour, 401;
   light, 402;
   extent of surface, 404.

 Smyth, Admiral, his measurement of Etna compared with Sir John
    Herschel’s, 120;
   eclipse of a double star observed by, 397;
   its periodic time determined, 398.

 ——, Piazzi, heat of the moon felt by, 227.

 Snow, cause of perpetual, on summits of alpine chains, 119;
   causes modifying the height of the line of perpetual, 241;
   protecting vegetation, 249;
   radiation of heat by, 257.

 Soda, sulphate of, change of form in its crystals, 107;
   crystals of the neutral phosphate and the arseniate of, 109.

 Soil, the, dependence of temperature on the nature of its products,
    243.

 Solar gravitation, 424, 425.

 —— magnetism, its connexion with terrestrial, 344.

 —— spectrum, cause of the point of maximum heat varying in, 263, 264.

 —— system, the, gravitation of the bodies composing, 5;
   conditions securing the stability of, 11, 12;
   proof of its stability, 20;
   equilibrium of, underanged by the ethereal medium, 22;
   invariable plane, forming the equator of, 23, 24;
   question of its revolution round a common centre, 24;
   properties of its medium, 32;
   masses of bodies composing, 55, 56;
   their diameters, 56;
   uniform direction of rotation in, 65;
   comparative apparent importance of, in creation, 226;
   probably magnetic throughout, 346;
   comets forming part of, 365;
   possible ultimate destruction of, 372;
   computations of comets revolving within, 381, 382;
   paths described by heavenly bodies in, 382, 383;
   position of, relative to the Milky Way, 385;
   direction of its motion, 405.

 Soleil, M., crystals compressed by, 189.

 Solids, conditions reducing molecular particles to, 104, 105;
   distinctive forms taken by matter in, 106;
   velocity of sound passing through, 135;
   change of shape in, accompanying ringing sound, 147;
   expansion of, by heat, 271.

 Solstices, the, solar motion at, affecting the duration of time, 84;
   the year estimated from the winter, 85;
   periodical coincidence of the solar perigee and apogee with, 86, 87.

 Sothaic period, the, of the Egyptians, 85.

 Sound, medium conveying, 129;
   its propagation by undulations illustrated, 129, 130;
   conditions modifying the intensity of, musical notes, 131;
   experiments testing the compass of audible, 132, 133;
   media modifying the velocity of, 133-137;
   laws of its reflection from surfaces, 137, 138;
   undulations of, subject to the laws of interference, 138, 139;
   laws of the foundation of musical science, 140-143;
   reinforced by resonance of cavities, 150, 151;
   repeated vibrations required to produce, 178;
   different modes of action in undulations producing light and, 199,
      200;
   identical nature of heat and, 280, 281;
   measuring velocity, 290, 291.

 Sounding boards, intensifying musical vibrations, 149;
   action of, in musical instruments, 150.

 South, Sir James, positions of stellar systems measured by, 396.

 South pole, the, excess of cold at, 241.

 —— Sea islands, height of tides at, 98.

 Southern Ocean, rise of the tidal wave in, 93;
   velocity of the wave, 94.

 Spain, meteoric showers off the coast of, 421.

 Specific heat defined, 275.

 Spectra of gases and flames, their characteristic peculiarities, 163,
    164;
   three superposed, of the pure white sunbeam, 222.

 Spectrum, the solar, decomposed into seven colours, 159;
   colours of, modified by thickness of the medium absorbing, 160;
   decomposed into three colours, 161;
   rayless lines in, 162;
   observations and experiments on rayless lines, 163, 164;
   experiment of fluorescent light, 197;
   obtained independently of prismatic refraction, 201;
   energetic action of, on matter, 203;
   photographic coloured images of, 208-210;
   analysis, properties of, experiments, 211-219;
   complex nature of, 222;
   produced from diffracted light, 223.

 —— of an electric spark, 289.

 —— of the Voltaic arc, 303.

 Spheres, mode of attraction in hollow and solid, 4;
   planets partaking the nature of, 7;
   impulses regulating rotations, _ib._;
   conditions procuring the figure of, 44;
   formula finding the density, 56;
   force giving the form of, 106;
   power of retaining electricity, 288.

 Spherical form, the result of cohesion, 106.

 Spheroids, influencing attraction differently from spheres, 4;
   force disturbing attraction in, 27;
   compression of the terrestrial and of Jupiter’s, computed, 38, 39;
   of elliptical strata, quantities invariable in, 46;
   of the sun, 65;
   effect produced by the attraction of an external body on, 79;
   power of retaining electricity, 288.

 Spiral nebula, 409, 410.

 Spots on the sun’s surface, periods of their vicissitudes, 224;
   amount of heat varying with, 225.

 Spring tides, 96-99.

 Springs, hot, rising in mines, 229;
   mean heat of the earth determined from, 238.

 Standards of weights and measures, whence derived, 89, 90.

 Stars, fixed, the, the solar system probably not independent of, 24;
   velocity of light deduced from aberration of, 31;
   vast distances of, 54;
   precession affecting their longitudes, 80;
   computations of their positions furnishing historical data, 88, 89;
   made visible by refraction, 154;
   peculiar law of light demonstrated by the aberration of, 202;
   magnitude of the solar system seen from, 226;
   numbers, classification of, 384;
   positions, 385;
   the Milky Way, 385-387;
   parallaxes and distances of, 387-389;
   variable, 390-395;
   missing, 395;
   systems of multiple, classified, _ib._;
   binary, 395-406 (_see_ Double stars);
   nebulous, 406-419 (_see_ Nebulæ);
   seemingly innumerable, 420;
   meteors, 420-423.

 Static electricity, 282:
   _see_ Electricity.

 Steam, formation of, 269;
   force converting liquids into, 277;
   measure of its elasticity, 278;
   question of its being superseded by electricity, 328.

 Steel, paramagnetism induced in, 336;
   conditions of magnetic power remaining permanently in, 337, 338;
   its elasticity affected by magnetism, 352.

 Stephenson, George, quotation from, 279-280.

 Stokes, Professor, remarks of, on gradation of colours, 161;
   experiments on fluorescence of light, 197;
   his decision with regard to vibrations of polarised light, 223.

 Storms, magnetic, 344;
   varying with latitude, 345, 346.

 Strata of the earth, position and comparative density of, 77.

 Stratifications, experiments showing, in electric light, 306, 307.

 Struve, M., measurement by, 48;
   his observations on Saturn’s rings, 68;
   occultation by a comet observed by, 364;
   comet’s nucleus described, _ib._;
   distance of a fixed star measured by, 388, 389;
   catalogue of double stars, 396;
   remarks on colour and light of double stars, 401;
   sun’s motion proved by, 405.

 Stutgardt, natural hot springs used in manufactories near, 231.

 Submarine telegraph, 325-327.

 Sulphate of magnesia, its crystals boiled in alcohol, 108.

 —— of nickel, effect of exposure to the sun, on its crystals, 107.

 —— of soda, its crystals, 107.

 —— of zinc, experiment on its crystals, 108.

 Sulphuretted hydrogen gas, its constituent parts, 111.

 Sumbawa, volcanic eruption of, 233.

 Summer, mean temperature of, varying in the same latitude, 246, 247;
   atmospheric electricity in, 291.

 Sun, the, law regulating his attraction of heavenly bodies, 5;
   effect of his attraction on planetary orbits, mean distance of
      planets from, 8;
   importance of his magnitude in the solar system, 12;
   disturbances in the relative positions of planets and, 14;
   force modifying his intensity of attraction, 16;
   resistance offered by, to the power of disturbing forces, 20;
   periods of conjunctions of Jupiter, Saturn, and, 25;
   influence of, on lunar motions, 34, 35;
   action of the planets reflected by, 37;
   eclipses of, 40, 41;
   supposed constitution of, 41;
   his atmosphere, 42;
   mode of finding his parallax, 52, 53;
   mean distance from the earth, 53;
   mass of, 55;
   diameter, 56;
   comparative density, attractive force, 56, 57;
   astronomical tables of, 63;
   deductions from his rotation about an axis, period of, 65;
   attraction of, producing a precession of the equinoxes, 79, 81;
   returns of, a measure of time, 83-85;
   divisions of time, dependent on revolutions of the major axis of his
      orbit, 86, 87;
   action on tides, 92, 97;
   disturbing the equilibrium of the atmosphere, 121;
   dry and rainy seasons regulated by, 123;
   cause of decreased light and heat in horizontal rays, 157, 158;
   distance of, falsely estimated, 158;
   light polarized by, 195;
   indications of an absorptive atmosphere surrounding, 212, 213;
   his diameter, 224;
   appearance of, through his atmospheres, _ib._;
   variations in heat and light emitted from, 225, 226;
   amount of heat annually received by the earth from, 238;
   effect of his brilliancy on the heat emitted by, 259;
   his position affecting variations in the magnetic elements, 343, 344;
   connexion between periodic variation in his spots and in the magnetic
      elements, 344;
   vast sweep of his gravitating force, 365;
   increased attraction of, for comets, 372;
   gulfs separating stars from, 390;
   possibility of change in his lustre, 394;
   spot on, measured by Sir John Herschel, 394, 395;
   proportion of his light to the moon’s, 404;
   rate and orbit of motion with his system, 405, 406;
   a nebulous star, 412;
   meteoric nebula revolving round, 422;
   gravitating force of, 424, 425.

 Sunbeams, resolved into their component colours, 159-162;
   law prevailing in the phenomena of, 198;
   light a distinct property of, 214;
   resolved into three spectra, 222;
   undulations constituting, 223;
   their influence on vegetation, 249.

 Swan, the, vanishing star in, 393.

 Switzerland, meteors falling in, 421.

 Syene, arc of the meridian measured between Alexandria and, 49.

 Sykes, Colonel, extensive range of cultivation of wheat observed by,
    250.

 Sympathetic vibrations in musical instruments, 147-149.

 Syren, the, an instrument ascertaining the number of musical pulsations
    in a second, 143.

 Syzygies, tides increased in the, 96.


 Table-lands, high, influence of, on the atmosphere, 241.

 Tahiti, transit of Venus observed at, 53.

 Tail of comets, sudden development of, 372;
   forces producing, 375;
   unequal illumination of, 375, 376;
   change in position of, 376;
   divided, _ib._;
   constitution of, 377.

 Talbot, Fox, his inventions in photography, 204.

 Tangent, a, to planetary orbits, planets impelled in the direction of,
    8;
   force, disturbing, in the direction of, 14, 15;
   deflection from, a measurement of centrifugal force, 49.

 Tangential force, occasioning secular inequalities, 14;
   effects produced by, 15;
   producing the variation of the moon, 35;
   force acting on the sea, 100.

 —— velocity, effects produced by modifications of, 16;
   undiminished by the ethereal medium, 22.

 Telegraph, the electric, discovery leading to the invention of, 323,
    324;
   the Atlantic, 325;
   principles of its construction, 326, 327;
   date of its completion, 327.

 Telegraphs, land, principle of their construction, 328.

 Telescope, the achromatic, principle of its construction, 164.

 ——, the differential, differences in illumination determined by, 227.

 ——, Lord Rosse’s, nebulæ resolved by, 407, 415.

 Telescopium, comet traversing the constellation of, 379;
   nebula in, 414.

 Temperature, a decrease in, affecting the earth’s rotation, 72;
   excentricity of the terrestrial orbit, a cause of decreasing, 73;
   law equalising, 74;
   geological changes affecting, 75.

 ——, varying in the terrestrial atmosphere, zone of constant, 119;
   affecting atmospheric undulations, 121;
   modifying the velocity of sound, 134;
   chemical action of light affected by, 218-222;
   of the ethereal medium, 227, 228;
   underground stratum of constant, 228;
   rate of increase in, below the earth’s crust, 228, 231;
   of the ocean, 231;
   mode of finding annual average, 239;
   causes of disturbance in regular variation of, 240-245;
   variations in the same latitude, 246, 247;
   influence of, on vegetation, 248;
   affecting transmission of heat, 259, 260;
   of solid bodies, caused by absorption of rays, 268;
   affecting the length of the pendulum, 272;
   causes of perpetual variations in, 274;
   transmission of electricity affected by, 284;
   affecting magnetism, 352.

 Teneriffe, the Peak of, prevailing winds on, 124;
   lunar heat on, 227;
   zones of vegetation, 250;
   character of its flora, 252.

 Terrestrial globe, the, a magnet, 336.

 —— magnetism, 341-343;
   the three elements and their variations, 343, 344;
   storms, period of their variation, 344;
   its connexion with solar magnetism, _ib._;
   effect of atmospheric magnetism on, 345;
   probable cause of, 346;
   effect of planetary magnetism on, 346, 347.

 —— meridian, a, defined, 46.

 Tessular system of crystallization, 108.

 Texas, monsoons occasioned by its deserts, 124.

 Thames, the, period occupied by the tidal wave in reaching, 94.

 Thaw, cause of the sensible chilliness of, 276.

 Theory of probabilities, use of, in determining astronomical data, 60.

 Thermo-electric currents, discovery of, 332;
   phenomena exhibited by, 333;
   principle of, applied to measuring heat, 333, 334.

 Thermography, examples of, 219-221.

 Thermometer, the, principles applied to the construction of, 113;
   consulted in determining mountain heights, 119, 120;
   refraction varying with, 154;
   heat measured by motion in, 274.

 Thermomultiplier, use of, in experiments, 264;
   principle of its construction, 333, 334.

 Theta Orionis, the multiple system of, 395.

 Thomas, St., the island of, hurricane with pauses at, 127.

 Thomson, W., Professor, experiments of, in freezing water, 271;
   dynamical theory of heat maintained by, 275 _note_;
   his calculation of the force exerted in vibrations of light, 279;
   investigation into the relations of light and magnetism, 320;
   density of the ethereal medium computed by, 356;
   magnetic property of the ethereal medium pleaded for, 357.

 Thunder, theory of prolonged peals of, 138.

 Tibet, wheat ripening in, 250.

 Tidal wave, theory of, 92;
   its birthplace, 93;
   course of, 93, 94;
   velocity, 94;
   effect of depth on its motion, 95.

 Tides, calculation from the moon’s action on, 55;
   theory of forces producing, 91, 92;
   circumstances occasioning irregularities, 93;
   rising, progress of, 93, 94;
   three kinds of oscillations in, 95, 96;
   variations in, from lunar and solar influence, 96-98;
   effect of interference of waves on, 99;
   the sea’s equilibrium underanged by, 100.

 ——, lunar and diurnal, of the terrestrial atmosphere, 121;
   examples of sympathetic undulation, 148.

 Time, a measure of motion, 58;
   a measure of angular motion, 83;
   difference between mean and apparent solar, 84;
   mean equinoctial, mode of computing its object, 86;
   estimation of, corrected by means of laws of unequal expansion, 272.

 Timocharis, comparison of his observations with Hipparchus, 80.

 Tomboro, submerged in a volcanic eruption, 233.

 Toronto, observations on magnetic storms at, 346.

 Torpedo, the, electrical action of, 310, 311.

 Torricellian vacuum, experiment on the electric discharge in the, 306;
   lines of magnetic force passing through, 344.

 Toucan, comet approaching the constellation of, 379;
   a nebula in, 414.

 Toucani, 47;
   globular nebulous cluster, 414.

 Tourmaline, brown, light polarized by prisms of, 180;
   property qualifying it to analyze polarized light, 182;
   coloured images produced by, 186, 187;
   changed by compression, 189;
   heat polarized by, 265;
   electricity communicated to, 284.

 Trade winds, friction of, not affecting the earth’s velocity, 72;
   action on the general motion of the sea, 100;
   system of, accounting for atmospheric anomalies, 120;
   theory of their origin, phenomena connected with, 122, 123;
   becoming monsoons, 124.

 Transits of Venus, 52, 53.

 ——, two consecutive, of any star, a measure of time, 83.

 Transmission of radiant heat, 258, 262;
   of electricity, 284, 285;
   of voltaic electricity, 298;
   molecular structure affecting, 303;
   method of, determining the influence of electric currents, 317;
   of gravity, an unsolved question, 355;
   probable agent, 356;
   medium of, in space, 424.

 Transparent bodies, temperature of, unaffected by the sun’s rays, 227.

 Trees, number of species of forest, found in America and Europe, 252.

 Tribes, apparently distinct, of the human race, 255.

 Triple stars, 395;
   periods of revolution in, 400.

 Tropical year, change in its length, 80;
   period of, 83;
   difficulty of adjusting its estimation, 85.

 —— revolution of the major axis of the solar ellipse, its period, 86.

 —— vegetation, the luxuriance of, 248.

 Tuileries, clock in the, showing decimal time, 84.

 Twilight, caused by refraction, 154;
   effect of reflection, 158.

 Tyndall, Professor, his experiments proving diamagnetic polarity, 348;
   on magnetic action in crystals, 349.


 Undulations, theory of, 99;
   of the atmosphere, 121, 122;
   of the waves of sound, 129, 130;
   intervals produced by interference, 139;
   giving musical notes, 142, 143;
   sympathetic, 147, 149;
   of the luminous ether, 169, 170;
   in refraction and reflection, 177;
   producing fluorescence, 197;
   different, in light and sound, 199, 200;
   constituting a sunbeam, 223;
   heat propagated by, 267;
   of light, evolution of latent force in extinguished, 279, 280;
   of natural forces identical, 281.

 Undulatory theory of light, 168-170;
   law of motion affecting, 176, 177;
   phenomena proving, 198;
   objection, from the different action of light and sound, refuted,
      199;
   proving the existence of the ethereal medium, 358;
   acceleration in comet’s motion proving, 367.

 —— theory, experiments determining in favour of, 200, 201;
   final and decisive experiment, 202;
   of heat, 267.

 Unison, note in, 142.

 United States, astronomical observations made in, 371, 373.

 Uranium, phosphorescent property of, 296;
   peculiar luminous properties of, 296.

 Uranus, effect of reciprocal attraction between Neptune and, 22;
   periods of the revolutions of his satellites, 33;
   distance from the sun, 54;
   astronomical tables of, 60;
   discovery suggested by his perturbations, 61;
   observations on, leading to Neptune’s discovery, 62;
   sun’s influence in, 225;
   action of, on Halley’s comet, 363;
   appearance of the sun to, 380, 381;
   comets in his orbit, 381, 382.

 Ursa Major, periodic time of a double star in, 398;
   nebulous region of, 417.

 Utah, deserts of, causing monsoons, 124.


 Vacuum produced by shell-fish, 117;
   existing in the air, 118.

 Valz, M., telescopic planet discovered by, 21;
   comet observed by, 358;
   observations on a comet’s approach to the sun, 364;
   cause assigned by, for contraction in diameter of comets, 377, 378.

 Vapour, formation and dispersion of, 269, 270;
   force developing, 277.

 Variable stars, periodic fluctuation of lustre in, 390, 391;
   new, appearing and vanishing, 392, 394;
   missing, 395.

 Variables, region of the, 122.

 Vegetation, effect of, in lowering temperature, 243;
   the two requisites for, 248;
   strength and vitality of, 249;
   chemical action of light influencing, _ib._;
   laws of its distribution, 249-252;
   distribution of marine, 252, 253;
   theories of specific diversity of original distribution of, 253, 254.

 Venus, zone of instability between the sun and, 21;
   perturbation in the mean motion of the earth and, 26;
   eclipsing Mercury, 42;
   transits of, parallaxes calculated from, 52, 53;
   astronomical tables of, 63;
   climate, 226.

 Vernal equinox, planetary motions estimated from, 9.

 Vesta, astronomical tables of, 63;
   no atmosphere surrounding, 226.

 Vesuvius, revived volcanic action of, 234.

 Vibrating plates used in experiments on musical sound, 144, 147.

 Vibrations of the air producing sound, 129;
   in music, 131;
   number made by the human voice in a second, 132.

 —— of the ether in natural and polarized light, 193;
   in fluorescence of light, 196;
   plane of, in polarized light, 223.

 Vico, Padre de, comet discovered by, 370.

 Vienna, observations on comets from, 370.

 Vietch, James, comet with luminous rings discovered by, 374, 375.

 Vincent, St., revival of an extinct volcano in, 234.

 Virginia, daguerreotyped spectral image obtained in, 213.

 Virgo, planetary conjunction between Libra and, 42;
   variable star in, 392;
   star vanished from, 395;
   nebulous zone passing, 416, 417.

 Viviers, transit of a comet across the sun observed from, 374.

 Volcanic regions of the globe, 232;
   annual number of eruptions, 233;
   celebrated eruptions, _ib._;
   earthquakes caused by, 234;
   supposed causes of action, 235;
   Sir John Herschel’s theory, 235-237.

 Volta, Professor, electricity rendered manageable by, 297;
   the world’s debt to, 328.

 Voltaic electricity, first suggestions of, 297;
   theory of the transmission of, 298;
   construction of the battery, 298, 299;
   theory of its production, 300;
   characteristic properties, 300, 301;
   action of, generating heat and light, 301-303;
   arc, experiments, 303-305;
   the, discharge oxidizing silver, 305, 306;
   stratified light, 306, 307;
   chemical decomposition effected by agency of, 307, 308;
   crystallization, 308;
   an agent in the fine arts, 309;
   conductors of, _ib._;
   relations of heat and, 310;
   fish producing effects of, 310, 311;
   science suggested by its influence on a magnetized needle, 312;
   rotation effected by, 313, 314;
   inducing magnetism, 314, 315;
   distinction between static electricity and, 317;
   unvarying dual force of, 334.

 Voltaic pile, the, invention of, 297;
   perfected, 298-300.

 Vortices, molecular, theory of, 104.

 Vosges mountains, temperature of mines in the, 228.

 Vulpecula, nebula in, 409.


 Wardhus, transit of Venus observed at, 53.

 Watches, irregular action of, corrected by the laws of unequal
    expansion, 272.

 Water, constituent parts of, 111;
   boiling point of, an estimate of mountain heights, 120;
   as a medium for sound, 135;
   light polarized circularly by, 194;
   experiment deciding the velocity of light in, 202;
   law of expansion of, 271;
   process of congelation, 276;
   boiling points of, 277;
   decomposed by electric agency, 307;
   as an electric conductor, 309;
   rotating by electricity, 314.

 Waterspouts, origin and cause of, 128.

 Waterstone, Mr., magnetic property of the ethereal medium maintained
    by, 357.

 Waves neutralized by interference, 99.

 ——, atmospheric, over local districts, periods, dimensions of, 121,
    122.

 —— of sound, 131;
   furnishing an illustration of reflections of sound and light, 137;
   interference of, producing calm, 139.

 Wedgwood, Dr., attempts of, to trace objects by means of light, 203,
    204.

 Week, the, of seven days, the most ancient and universal division of
    time, 85.

 Wells, increase of temperature in, 230, 231.

 Welsh, Mr., observations made by, in a balloon ascent, 119.

 West Indies, the, cause of hurricanes in, 126.

 Wheels invented to test intensity of sound, 132, 133.

 Wheat, range of its cultivation, 250.

 Wheatstone, Professor, experiments in acoustics of, 132;
   musical instruments invented by, 143;
   paper on musical vibrations read by, 145;
   experiments on sounding boards of, 150;
   experiments on sound reinforced by resonance, 151;
   instrument measuring velocities of electricity and light invented by,
      202;
   spectrum of an electric spark observed, 289;
   speed of electricity measured, 289, 290;
   experiments on the spectrum of Voltaic flame, 303.

 Willis, Mr., articulating machine invented by, 151;
   investigations of, into the mechanism of the larynx, 152.

 Winds, trade, 122, 123;
   monsoons, 124;
   extra-tropical, in the North Atlantic, _ib._;
   currents above the trade winds, 124, 125;
   phenomena of rotatory motion, 125;
   hurricanes, 125, 128;
   agency of, influencing temperature, 244, 245.

 Wines, range of cultivation of the best, 250.

 Winter, atmospheric electricity in, 291.

 ——, mean temperature of, varying in the same latitude, 246, 247.

 Wolf, Professor, periods of variation in solar heat computed by, 225.

 Wollaston, Dr., experiments of, on sensitiveness to sound, quotation
    from, 132;
   experiment of, to show the effect of variable media on refraction,
      156;
   discovery of rayless lines in the solar spectrum, 162;
   observations of, on the chemical properties of the solar spectrum,
      203, 209;
   magnetic rotation suggested by, 313;
   light emitted by the heavenly bodies calculated, 404.


 Xi Ursæ Majoris, periodic time of, 398;
   velocity of the revolving star, 400.


 Year, a, in Jupiter and Saturn, 66;
   tropical change in its length, 80;
   length of the sidereal, _ib._;
   period of the mean, 83;
   estimation of the Egyptian, 85;
   first of our era, 86;
   length of the, affected by a comet’s passage, 359.

 Young, Dr., his calculation of the possible compression of solids, 78;
   date of a horoscope determined by, 89;
   density of a liquid column estimated by, 114;
   exception adduced by, to a general law in acoustics, 137;
   his theory of the pleasures of harmony, 142;
   undulatory theory established by, 169;
   data used by, to test his theory of light, 175;
   illustration of, proving sound and heat kindred forces, 280, 281.


 Zeta Cancri, a triple star, 395;
   periodic time of, 398;
   revolution, 400;
   colours, 401.

 Zeta Herculis, periodic time, eclipse of, 398;
   light, 402.

 Zinc, seleniate of, effect of temperature on its crystals, 107;
   sulphate of, its crystals boiled in alcohol, 108.

 ——, electricity communicated to plates of, 220.

 Zodiac, the, signs of, change in their positions, 80.

 Zone of constant temperature in the atmosphere, 119;
   laws of storms in the temperate and torrid, 127, 128;
   of spots on the sun’s surface, its breadth, 224;
   of constant temperature below the earth’s crust, 228;
   comparative unequal distribution of land in temperate and torrid,
      244;
   of fixed stars, 385;
   of stars nearest the sun, 390;
   nebulous, 416;
   of nebulous patches, 417;
   of meteoric nebulæ, 423.

 Zones of instability of planetary orbits, 21.

 —— of temperature in the ocean, 101.

 —— of vegetation on the Peak of Teneriffe, 250.

 Zoophytes, specific distribution of, 254.


                                THE END.


        LONDON: PRINTED BY W. CLOWES AND SONS, STAMFORD STREET,
                           AND CHARING CROSS.

[Illustration: PLATE 1.]

[Illustration: PLATE 2.]

[Illustration: PLATE 3.]

[Illustration: PLATE 4.]

[Illustration: PLATE 5.]

[Illustration: PLATE 6.]

[Illustration: PLATE 7.]

These correspond to No. 1, 6, and 7 of Faraday’s plate in his 29th
Series of Experimental Researches in Electricity.

[Illustration: PLATE 8.]

[Illustration: PLATE 9.]

[Illustration: PLATE 10.

  Fig. 1.
  Spiral nebulæ of 51 Messier, as seen by Lord Rosse.

  Fig. 2.
  Great nebula of Orion.
  ]




                               Footnotes

Footnote 1:

  The mean distance of the earth from the sun is 95,000,000 miles, but
  to avoid the inconvenience of large numbers, it is assumed to be the
  unit of distance; hence the mean distance of Mars is 1·52369, or 1·5
  nearly, that of the earth being = 1.

Footnote 2:

  The obliquity given in the text is for the year 1858.

Footnote 3:

  Sir John Herschel remarks that there are just as many thousands of
  feet in a degree of the meridian in our latitude as there are days in
  the year, viz. 365,000.

  The Greenwich Observatory is in N. lat. 51° 28ʹ40ʺ.

Footnote 4:

  Or more correctly 3422ʺ·325 and 238,793 miles, as deduced from Mr.
  Adams’ more accurate calculations.

Footnote 5:

  Neptune was discovered in the year 1846.

Footnote 6:

  The satellites of the two great planets on the farthest verge of the
  solar system form a singular exception to this law.

Footnote 7:

  See the chapter on the Tides and Currents in the ‘Physical Geography,’
  by the author, 4th edition.

Footnote 8:

  Sir John Herschel on Meteorology.

Footnote 9:

  Bakerian Lecture, by Michael Faraday, Esq. Phil. Trans. 1857.

Footnote 10:

  See page 104.

Footnote 11:

  M. Marbach of Breslau.

Footnote 12:

  ‘Meteorology,’ by Sir J. Herschel.

Footnote 13:

  This theory of heat and motion originated with Mr. Joule, of
  Manchester, who has maintained it with the greatest talent, both by
  experiment and analysis; and it has had an able advocate in Professor
  W. Thomson, of Glasgow.

Footnote 14:

  To this remarkable man the world is indebted for the locomotive
  railway system, which is rapidly advancing the civilization of
  mankind. Britain may well be proud of its working classes, which can
  produce such men; and Mr. George Stephenson is not the only one; there
  are many others; but no man has ever had greater influence by his
  labours and discoveries on human affairs.

Footnote 15:

  ‘Correlation of the Physical Forces, by W. R. Grove, Esq.,’ one of the
  most remarkable and talented works that has appeared, to which the
  author with pleasure acknowledges her obligations.

Footnote 16:

  “Eripuit fulmen Cœlo, sceptrumque tyrannis,” is the inscription on a
  medal struck in honour of Franklin.

Footnote 17:

  Faraday.

Footnote 18:

  Professor Matteucci still expresses doubts on this subject, but has
  not yet finished his experiments.

Footnote 19:

  Babbage.

Footnote 20:

  Phil. Mag. for May 1858.




                          Transcriber's Notes


Some corrections were made to the original text. In particular,
punctuation was corrected without further note. Inconsistent spelling
and hyphenation was retained unless noted otherwise. There were two
Notes 189 in the original; this was retained as printed. Spelling of
Index entries was changed to reflect the body text where inconsistencies
were found. Index page numbers were corrected where errors were found.
Further corrections are noted below:

             p. 50 0·005·1449 ->  0·0051449
             p. 61 24,000 -> 240,000
             p. 62 M. Leverrier -> M. Le Verrier
             p. 84 in mean solar day -> in a mean solar day
             p. 96  syzigies -> syzygies
             p. 115 arrising -> arising
             p. 120 Herchel -> Herschel
             p. 123 generally know -> generally known
             p. 159 Fraunhoffer’s -> Fraunhofer’s
             p. 168 contaary -> contrary
             p. 214 oxyde -> oxide
             p. 216 aperature -> aperture
             p. 296 M Niepce -> M. Niepcé
             p. 306 torrecelian -> Torricellian
             p. 307 potass -> potash
             p. 350 de Roux -> le Roux
             p. 423 Β -> β
             p. 447 areal -> aërial
             p. 456 perigree -> perigee
             p. 471 108° -> 180°
             p. 478 Meissier -> Messier