Produced by Jonathan Ingram, Dave Maddock, Charles Franks
and the Online Distributed Proofreading Team.










[Illustration: SIR ISAAC NEWTON (From the bust by Roubiliac In Trinity
College, Cambridge.)]

HISTORY OF ASTRONOMY

BY

GEORGE FORBES,
M.A., F.R.S., M. INST. C. E.,

(FORMERLY PROFESSOR OF NATURAL PHILOSOPHY, ANDERSON'S COLLEGE, GLASGOW)

AUTHOR OF "THE TRANSIT OF VENUS," RENDU'S "THEORY OF THE GLACIERS OF
SAVOY," ETC., ETC.




CONTENTS

  PREFACE

  BOOK I. THE GEOMETRICAL PERIOD

     1. PRIMITIVE ASTRONOMY AND ASTROLOGY

     2. ANCIENT ASTRONOMY--CHINESE AND CHALDÆANS

     3. ANCIENT GREEK ASTRONOMY

     4. THE REIGN OF EPICYCLES--FROM PTOLEMY TO COPERNICUS

  BOOK II. THE DYNAMICAL PERIOD

     5. DISCOVERY OF THE TRUE SOLAR SYSTEM--TYCHO BRAHE--KEPLER

     6. GALILEO AND THE TELESCOPE--NOTIONS OF GRAVITY BY HORROCKS, ETC.

     7. SIR ISAAC NEWTON--LAW OF UNIVERSAL GRAVITATION

     8. NEWTON'S SUCCESSORS--HALLEY, EULER, LAGRANGE, LAPLACE, ETC.

     9. DISCOVERY OF NEW PLANETS--HERSCHEL, PIAZZI, ADAMS, AND LE
        VERRIER

  BOOK III. OBSERVATION


    10. INSTRUMENTS OF PRECISION--SIZE OF THE SOLAR SYSTEM

    11. HISTORY OF THE TELESCOPE--SPECTROSCOPE

  BOOK IV. THE PHYSICAL PERIOD

    12. THE SUN

    13. THE MOON AND PLANETS

    14. COMETS AND METEORS

    15. THE STARS AND NEBULÆ

  INDEX



PREFACE


An attempt has been made in these pages to trace the evolution of
intellectual thought in the progress of astronomical discovery, and,
by recognising the different points of view of the different ages, to
give due credit even to the ancients. No one can expect, in a history
of astronomy of limited size, to find a treatise on "practical" or on
"theoretical astronomy," nor a complete "descriptive astronomy," and
still less a book on "speculative astronomy." Something of each of
these is essential, however, for tracing the progress of thought and
knowledge which it is the object of this History to describe.

The progress of human knowledge is measured by the increased habit of
looking at facts from new points of view, as much as by the
accumulation of facts. The mental capacity of one age does not seem to
differ from that of other ages; but it is the imagination of new
points of view that gives a wider scope to that capacity. And this is
cumulative, and therefore progressive. Aristotle viewed the solar
system as a geometrical problem; Kepler and Newton converted the point
of view into a dynamical one. Aristotle's mental capacity to
understand the meaning of facts or to criticise a train of reasoning
may have been equal to that of Kepler or Newton, but the point of view
was different.

Then, again, new points of view are provided by the invention of new
methods in that system of logic which we call mathematics. All that
mathematics can do is to assure us that a statement A is equivalent to
statements B, C, D, or is one of the facts expressed by the statements
B, C, D; so that we may know, if B, C, and D are true, then A is true.
To many people our inability to understand all that is contained in
statements B, C, and D, without the cumbrous process of a mathematical
demonstration, proves the feebleness of the human mind as a logical
machine. For it required the new point of view imagined by Newton's
analysis to enable people to see that, so far as planetary orbits are
concerned, Kepler's three laws (B, C, D) were identical with Newton's
law of gravitation (A). No one recognises more than the mathematical
astronomer this feebleness of the human intellect, and no one is more
conscious of the limitations of the logical process called
mathematics, which even now has not solved directly the problem of
only three bodies.

These reflections, arising from the writing of this History, go to
explain the invariable humility of the great mathematical astronomers.
Newton's comparison of himself to the child on the seashore applies to
them all. As each new discovery opens up, it may be, boundless oceans
for investigation, for wonder, and for admiration, the great
astronomers, refusing to accept mere hypotheses as true, have founded
upon these discoveries a science as exact in its observation of facts
as in theories. So it is that these men, who have built up the most
sure and most solid of all the sciences, refuse to invite others to
join them in vain speculation. The writer has, therefore, in this
short History, tried to follow that great master, Airy, whose pupil he
was, and the key to whose character was exactness and accuracy; and he
recognises that Science is impotent except in her own limited sphere.

It has been necessary to curtail many parts of the History in the
attempt--perhaps a hopeless one--to lay before the reader in a limited
space enough about each age to illustrate its tone and spirit, the
ideals of the workers, the gradual addition of new points of view and
of new means of investigation.

It would, indeed, be a pleasure to entertain the hope that these pages
might, among new recruits, arouse an interest in the greatest of all
the sciences, or that those who have handled the theoretical or
practical side might be led by them to read in the original some of
the classics of astronomy. Many students have much compassion for the
schoolboy of to-day, who is not allowed the luxury of learning the art
of reasoning from him who still remains pre-eminently its greatest
exponent, Euclid. These students pity also the man of to-morrow, who
is not to be allowed to read, in the original Latin of the brilliant
Kepler, how he was able--by observations taken from a moving platform,
the earth, of the directions of a moving object, Mars--to deduce the
exact shape of the path of each of these planets, and their actual
positions on these paths at any time. Kepler's masterpiece is one of
the most interesting books that was ever written, combining wit,
imagination, ingenuity, and certainty.

Lastly, it must be noted that, as a History of England cannot deal
with the present Parliament, so also the unfinished researches and
untested hypotheses of many well-known astronomers of to-day cannot be
included among the records of the History of Astronomy. The writer
regrets the necessity that thus arises of leaving without mention the
names of many who are now making history in astronomical work.

G. F.
_August 1st, 1909._




BOOK I.  THE GEOMETRICAL PERIOD



1. PRIMITIVE ASTRONOMY AND ASTROLOGY.


The growth of intelligence in the human race has its counterpart in
that of the individual, especially in the earliest stages.
Intellectual activity and the development of reasoning powers are in
both cases based upon the accumulation of experiences, and on the
comparison, classification, arrangement, and nomenclature of these
experiences. During the infancy of each the succession of events can
be watched, but there can be no _à priori_ anticipations.
Experience alone, in both cases, leads to the idea of cause and effect
as a principle that seems to dominate our present universe, as a rule
for predicting the course of events, and as a guide to the choice of a
course of action. This idea of cause and effect is the most potent
factor in developing the history of the human race, as of the
individual.

In no realm of nature is the principle of cause and effect more
conspicuous than in astronomy; and we fall into the habit of thinking
of its laws as not only being unchangeable in our universe, but
necessary to the conception of any universe that might have been
substituted in its place. The first inhabitants of the world were
compelled to accommodate their acts to the daily and annual
alternations of light and darkness and of heat and cold, as much as to
the irregular changes of weather, attacks of disease, and the fortune
of war.  They soon came to regard the influence of the sun, in
connection with light and heat, as a cause. This led to a search for
other signs in the heavens. If the appearance of a comet was sometimes
noted simultaneously with the death of a great ruler, or an eclipse
with a scourge of plague, these might well be looked upon as causes in
the same sense that the veering or backing of the wind is regarded as
a cause of fine or foul weather.

For these reasons we find that the earnest men of all ages have
recorded the occurrence of comets, eclipses, new stars, meteor
showers, and remarkable conjunctions of the planets, as well as
plagues and famines, floods and droughts, wars and the deaths of great
rulers. Sometimes they thought they could trace connections which
might lead them to say that a comet presaged famine, or an eclipse
war.

Even if these men were sometimes led to evolve laws of cause and
effect which now seem to us absurd, let us be tolerant, and gratefully
acknowledge that these astrologers, when they suggested such "working
hypotheses," were laying the foundations of observation and deduction.

If the ancient Chaldæans gave to the planetary conjunctions an
influence over terrestrial events, let us remember that in our own
time people have searched for connection between terrestrial
conditions and periods of unusual prevalence of sun spots; while De la
Rue, Loewy, and Balfour Stewart[1] thought they found a connection
between sun-spot displays and the planetary positions. Thus we find
scientific men, even in our own time, responsible for the belief that
storms in the Indian Ocean, the fertility of German vines, famines in
India, and high or low Nile-floods in Egypt follow the planetary
positions.

And, again, the desire to foretell the weather is so laudable that we
cannot blame the ancient Greeks for announcing the influence of the
moon with as much confidence as it is affirmed in Lord Wolseley's
_Soldier's Pocket Book_.

Even if the scientific spirit of observation and deduction (astronomy)
has sometimes led to erroneous systems for predicting terrestrial
events (astrology), we owe to the old astronomer and astrologer alike
the deepest gratitude for their diligence in recording astronomical
events. For, out of the scanty records which have survived the
destructive acts of fire and flood, of monarchs and mobs, we have
found much that has helped to a fuller knowledge of the heavenly
motions than was possible without these records.

So Hipparchus, about 150 B.C., and Ptolemy a little later, were able
to use the observations of Chaldæan astrologers, as well as those of
Alexandrian astronomers, and to make some discoveries which have
helped the progress of astronomy in all ages.  So, also, Mr. Cowell[2]
has examined the marks made on the baked bricks used by the Chaldæans
for recording the eclipses of 1062 B.C. and 762 B.C.; and has thereby
been enabled, in the last few years, to correct the lunar tables of
Hansen, and to find a more accurate value for the secular acceleration
of the moon's longitude and the node of her orbit than any that could
be obtained from modern observations made with instruments of the
highest precision.

So again, Mr. Hind [3] was enabled to trace back the period during
which Halley's comet has been a member of the solar system, and to
identify it in the Chinese observations of comets as far back as 12
B.C. Cowell and Cromellin extended the date to 240 B.C. In the same
way the comet 1861.i. has been traced back in the Chinese records to
617 A.D. [4]

The theoretical views founded on Newton's great law of universal
gravitation led to the conclusion that the inclination of the earth's
equator to the plane of her orbit (the obliquity of the ecliptic) has
been diminishing slowly since prehistoric times; and this fact has
been confirmed by Egyptian and Chinese observations on the length of
the shadow of a vertical pillar, made thousands of years before the
Christian era, in summer and winter.

There are other reasons why we must be tolerant of the crude notions
of the ancients. The historian, wishing to give credit wherever it may
be due, is met by two difficulties. Firstly, only a few records of
very ancient astronomy are extant, and the authenticity of many of
these is open to doubt. Secondly, it is very difficult to divest
ourselves of present knowledge, and to appreciate the originality of
thought required to make the first beginnings.

With regard to the first point, we are generally dependent upon
histories written long after the events.  The astronomy of Egyptians,
Babylonians, and Assyrians is known to us mainly through the Greek
historians, and for information about the Chinese we rely upon the
researches of travellers and missionaries in comparatively recent
times. The testimony of the Greek writers has fortunately been
confirmed, and we now have in addition a mass of facts translated from
the original sculptures, papyri, and inscribed bricks, dating back
thousands of years.

In attempting to appraise the efforts of the beginners we must
remember that it was natural to look upon the earth (as all the first
astronomers did) as a circular plane, surrounded and bounded by the
heaven, which was a solid vault, or hemisphere, with its concavity
turned downwards. The stars seemed to be fixed on this vault; the
moon, and later the planets, were seen to crawl over it. It was a
great step to look on the vault as a hollow sphere carrying the sun
too. It must have been difficult to believe that at midday the stars
are shining as brightly in the blue sky as they do at night. It must
have been difficult to explain how the sun, having set in the west,
could get back to rise in the east without being seen _if_ it was
always the same sun. It was a great step to suppose the earth to be
spherical, and to ascribe the diurnal motions to its rotation.
Probably the greatest step ever made in astronomical theory was the
placing of the sun, moon, and planets at different distances from the
earth instead of having them stuck on the vault of heaven. It was a
transition from "flatland" to a space of three dimensions.

Great progress was made when systematic observations began, such as
following the motion of the moon and planets among the stars, and the
inferred motion of the sun among the stars, by observing their
_heliacal risings_--i.e., the times of year when a star
would first be seen to rise at sunrise, and when it could last be seen
to rise at sunset. The grouping of the stars into constellations and
recording their places was a useful observation. The theoretical
prediction of eclipses of the sun and moon, and of the motions of the
planets among the stars, became later the highest goal in astronomy.

To not one of the above important steps in the progress of astronomy
can we assign the author with certainty. Probably many of them were
independently taken by Chinese, Indian, Persian, Tartar, Egyptian,
Babylonian, Assyrian, Phoenician, and Greek astronomers.  And we have
not a particle of information about the discoveries, which may have
been great, by other peoples--by the Druids, the Mexicans, and the
Peruvians, for example.

We do know this, that all nations required to have a calendar. The
solar year, the lunar month, and the day were the units, and it is
owing to their incommensurability that we find so many calendars
proposed and in use at different times. The only object to be attained
by comparing the chronologies of ancient races is to fix the actual
dates of observations recorded, and this is not a part of a history of
astronomy.

In conclusion, let us bear in mind the limited point of view of the
ancients when we try to estimate their merit. Let us remember that the
first astronomy was of two dimensions; the second astronomy was of
three dimensions, but still purely geometrical. Since Kepler's day we
have had a dynamical astronomy.


FOOTNOTES:

[1] Trans. R. S. E., xxiii. 1864, p. 499, _On Sun Spots_, etc., by
B. Stewart. Also Trans. R. S. 1860-70. Also Prof. Ernest Brown, in
_R. A. S. Monthly Notices_, 1900.

[2] _R. A. S. Monthly Notices_, Sup.; 1905.

[Illustration: CHALDÆAN BAKED BRICK OR TABLET, _Obverse and reverse
sides_, Containing record of solar eclipse, 1062 B.C., used lately by
Cowell for rendering the lunar theory more accurate than was possible
by finest modern observations. (British Museum collection,
No. 35908.)]

[3] _R. A. S. Monthly Notices_, vol. x., p. 65.

[4] R. S. E. Proc., vol. x., 1880.



2. ANCIENT ASTRONOMY--THE CHINESE AND CHALDÆANS.


The last section must have made clear the difficulties the way of
assigning to the ancient nations their proper place in the development
of primitive notions about astronomy. The fact that some alleged
observations date back to a period before the Chinese had invented the
art of writing leads immediately to the question how far tradition can
be trusted.

Our first detailed knowledge was gathered in the far East by
travellers, and by the Jesuit priests, and was published in the
eighteenth century. The Asiatic Society of Bengal contributed
translations of Brahmin literature. The two principal sources of
knowledge about Chinese astronomy were supplied, first by Father
Souciet, who in 1729 published _Observations Astronomical,
Geographical, Chronological, and Physical_, drawn from ancient
Chinese books; and later by Father Moyriac-de-Mailla, who in 1777-1785
published _Annals of the Chinese Empire, translated from
Tong-Kien-Kang-Mou_.

Bailly, in his _Astronomie Ancienne_ (1781), drew, from these and
other sources, the conclusion that all we know of the astronomical
learning of the Chinese, Indians, Chaldæans, Assyrians, and Egyptians
is but the remnant of a far more complete astronomy of which no trace
can be found.

Delambre, in his _Histoire de l'Astronomie Ancienne_ (1817),
ridicules the opinion of Bailly, and considers that the progress made
by all of these nations is insignificant.

It will be well now to give an idea of some of the astronomy of the
ancients not yet entirely discredited.  China and Babylon may be taken
as typical examples.

_China_.--It would appear that Fohi, the first emperor, reigned
about 2952 B.C., and shortly afterwards Yu-Chi made a sphere to
represent the motions of the celestial bodies. It is also mentioned,
in the book called Chu-King, supposed to have been written in 2205
B.C., that a similar sphere was made in the time of Yao (2357
B.C.).[1] It is said that the Emperor Chueni (2513 B.C.) saw five
planets in conjunction the same day that the sun and moon were in
conjunction. This is discussed by Father Martin (MSS. of De Lisle);
also by M. Desvignolles (Mem. Acad. Berlin, vol. iii., p. 193), and by
M. Kirsch (ditto, vol. v., p. 19), who both found that Mars, Jupiter,
Saturn, and Mercury were all between the eleventh and eighteenth
degrees of Pisces, all visible together in the evening on February
28th 2446 B.C., while on the same day the sun and moon were in
conjunction at 9 a.m., and that on March 1st the moon was in
conjunction with the other four planets. But this needs confirmation.

Yao, referred to above, gave instructions to his astronomers to
determine the positions of the solstices and equinoxes, and they
reported the names of the stars in the places occupied by the sun at
these seasons, and in 2285 B.C. he gave them further orders. If this
account be true, it shows a knowledge that the vault of heaven is a
complete sphere, and that stars are shining at mid-day, although
eclipsed by the sun's brightness.

It is also asserted, in the book called _Chu-King_, that in the
time of Yao the year was known to have 3651/4 days, and that he
adopted 365 days and added an intercalary day every four years (as in
the Julian Calendar). This may be true or not, but the ancient Chinese
certainly seem to have divided the circle into 365 degrees. To learn
the length of the year needed only patient observation--a
characteristic of the Chinese; but many younger nations got into a
terrible mess with their calendar from ignorance of the year's length.

It is stated that in 2159 B.C. the royal astronomers Hi and Ho failed
to predict an eclipse. It probably created great terror, for they were
executed in punishment for their neglect. If this account be true, it
means that in the twenty-second century B.C. some rule for calculating
eclipses was in use. Here, again, patient observation would easily
lead to the detection of the eighteen-year cycle known to the
Chaldeans as the _Saros_. It consists of 235 lunations, and in
that time the pole of the moon's orbit revolves just once round the
pole of the ecliptic, and for this reason the eclipses in one cycle
are repeated with very slight modification in the next cycle, and so
on for many centuries.

It may be that the neglect of their duties by Hi and Ho, and their
punishment, influenced Chinese astronomy; or that the succeeding
records have not been available to later scholars; but the fact
remains that--although at long intervals observations were made of
eclipses, comets, and falling stars, and of the position of the
solstices, and of the obliquity of the ecliptic--records become rare,
until 776 B.C., when eclipses began to be recorded once more with some
approach to continuity. Shortly afterwards notices of comets were
added. Biot gave a list of these, and Mr. John Williams, in 1871,
published _Observations of Comets from 611 B.C. to 1640 A.D.,
Extracted from the Chinese Annals_.

With regard to those centuries concerning which we have no
astronomical Chinese records, it is fair to state that it is recorded
that some centuries before the Christian era, in the reign of
Tsin-Chi-Hoang, all the classical and scientific books that could be
found were ordered to be destroyed. If true, our loss therefrom is as
great as from the burning of the Alexandrian library by the Caliph
Omar. He burnt all the books because he held that they must be either
consistent or inconsistent with the Koran, and in the one case they
were superfluous, in the other case objectionable.

_Chaldæans_.--Until the last half century historians were
accustomed to look back upon the Greeks, who led the world from the
fifth to the third century B.C., as the pioneers of art, literature,
and science. But the excavations and researches of later years make us
more ready to grant that in science as in art the Greeks only
developed what they derived from the Egyptians, Babylonians, and
Assyrians. The Greek historians said as much, in fact; and modern
commentators used to attribute the assertion to undue modesty. Since,
however, the records of the libraries have been unearthed it has been
recognised that the Babylonians were in no way inferior in the matter
of original scientific investigation to other races of the same era.

The Chaldæans, being the most ancient Babylonians, held the same
station and dignity in the State as did the priests in Egypt, and
spent all their time in the study of philosophy and astronomy, and the
arts of divination and astrology. They held that the world of which we
have a conception is an eternal world without any beginning or ending,
in which all things are ordered by rules supported by a divine
providence, and that the heavenly bodies do not move by chance, nor by
their own will, but by the determinate will and appointment of the
gods. They recorded these movements, but mainly in the hope of tracing
the will of the gods in mundane affairs. Ptolemy (about 130 A.D.)
made use of Babylonian eclipses in the eighth century B.C. for
improving his solar and lunar tables.

Fragments of a library at Agade have been preserved at Nineveh, from
which we learn that the star-charts were even then divided into
constellations, which were known by the names which they bear to this
day, and that the signs of the zodiac were used for determining the
courses of the sun, moon, and of the five planets Mercury, Venus,
Mars, Jupiter, and Saturn.

We have records of observations carried on under Asshurbanapal, who
sent astronomers to different parts to study celestial phenomena. Here
is one:--

To the Director of Observations,--My Lord, his humble servant
Nabushum-iddin, Great Astronomer of Nineveh, writes thus: "May Nabu
and Marduk be propitious to the Director of these Observations, my
Lord. The fifteenth day we observed the Node of the moon, and the moon
was eclipsed."

The Phoenicians are supposed to have used the stars for navigation,
but there are no records. The Egyptian priests tried to keep such
astronomical knowledge as they possessed to themselves. It is probable
that they had arbitrary rules for predicting eclipses. All that was
known to the Greeks about Egyptian science is to be found in the
writings of Diodorus Siculus. But confirmatory and more authentic
facts have been derived from late explorations. Thus we learn from
E. B. Knobel[2] about the Jewish calendar dates, on records of land
sales in Aramaic papyri at Assuan, translated by Professor A. H. Sayce
and A. E. Cowley, (1) that the lunar cycle of nineteen years was used
by the Jews in the fifth century B.C. [the present reformed Jewish
calendar dating from the fourth century A.D.], a date a "little more
than a century after the grandfathers and great-grandfathers of those
whose business is recorded had fled into Egypt with Jeremiah" (Sayce);
and (2) that the order of intercalation at that time was not
dissimilar to that in use at the present day.

Then again, Knobel reminds us of "the most interesting discovery a few
years ago by Father Strassmeier of a Babylonian tablet recording a
partial lunar eclipse at Babylon in the seventh year of Cambyses, on
the fourteenth day of the Jewish month Tammuz."  Ptolemy, in the
Almagest (Suntaxis), says it occurred in the seventh year of Cambyses,
on the night of the seventeenth and eighteenth of the Egyptian month
Phamenoth.  Pingré and Oppolzer fix the date July 16th, 533 B.C. Thus
are the relations of the chronologies of Jews and Egyptians
established by these explorations.


FOOTNOTES:

[1] These ancient dates are uncertain.

[2] _R. A. S. Monthly Notices_, vol. lxviii., No. 5, March, 1908.



3. ANCIENT GREEK ASTRONOMY.


We have our information about the earliest Greek astronomy from
Herodotus (born 480 B.C.). He put the traditions into writing. Thales
(639-546 B.C.) is said to have predicted an eclipse, which caused much
alarm, and ended the battle between the Medes and Lydians. Airy fixed
the date May 28th, 585 B.C. But other modern astronomers give
different dates. Thales went to Egypt to study science, and learnt
from its priests the length of the year (which was kept a profound
secret!), and the signs of the zodiac, and the positions of the
solstices. He held that the sun, moon, and stars are not mere spots on
the heavenly vault, but solids; that the moon derives her light from
the sun, and that this fact explains her phases; that an eclipse of
the moon happens when the earth cuts off the sun's light from her. He
supposed the earth to be flat, and to float upon water. He determined
the ratio of the sun's diameter to its orbit, and apparently made out
the diameter correctly as half a degree. He left nothing in writing.

His successors, Anaximander (610-547 B.C.) and Anaximenes (550-475
B.C.), held absurd notions about the sun, moon, and stars, while
Heraclitus (540-500 B.C.)  supposed that the stars were lighted each
night like lamps, and the sun each morning. Parmenides supposed the
earth to be a sphere.

Pythagoras (569-470 B.C.) visited Egypt to study science. He deduced
his system, in which the earth revolves in an orbit, from fantastic
first principles, of which the following are examples: "The circular
motion is the most perfect motion," "Fire is more worthy than earth,"
"Ten is the perfect number." He wrote nothing, but is supposed to have
said that the earth, moon, five planets, and fixed stars all revolve
round the sun, which itself revolves round an imaginary central fire
called the Antichthon. Copernicus in the sixteenth century claimed
Pythagoras as the founder of the system which he, Copernicus, revived.

Anaxagoras (born 499 B.C.) studied astronomy in Egypt. He explained
the return of the sun to the east each morning by its going under the
flat earth in the night. He held that in a solar eclipse the moon
hides the sun, and in a lunar eclipse the moon enters the earth's
shadow--both excellent opinions. But he entertained absurd ideas of
the vortical motion of the heavens whisking stones into the sky, there
to be ignited by the fiery firmament to form stars. He was prosecuted
for this unsettling opinion, and for maintaining that the moon is an
inhabited earth. He was defended by Pericles (432 B.C.).

Solon dabbled, like many others, in reforms of the calendar. The
common year of the Greeks originally had 360 days--twelve months of
thirty days. Solon's year was 354 days. It is obvious that these
erroneous years would, before long, remove the summer to January and
the winter to July. To prevent this it was customary at regular
intervals to intercalate days or months. Meton (432 B.C.) introduced a
reform based on the nineteen-year cycle. This is not the same as the
Egyptian and Chaldean eclipse cycle called _Saros_ of 223
lunations, or a little over eighteen years.  The Metonic cycle is 235
lunations or nineteen years, after which period the sun and moon
occupy the same position relative to the stars. It is still used for
fixing the date of Easter, the number of the year in Melon's cycle
being the golden number of our prayer-books.  Melon's system divided
the 235 lunations into months of thirty days and omitted every
sixty-third day. Of the nineteen years, twelve had twelve months and
seven had thirteen months.

Callippus (330 B.C.) used a cycle four times as long, 940 lunations,
but one day short of Melon's seventy-six years. This was more correct.

Eudoxus (406-350 B.C.) is said to have travelled with Plato in
Egypt. He made astronomical observations in Asia Minor, Sicily, and
Italy, and described the starry heavens divided into constellations.
His name is connected with a planetary theory which as generally
stated sounds most fanciful. He imagined the fixed stars to be on a
vault of heaven; and the sun, moon, and planets to be upon similar
vaults or spheres, twenty-six revolving spheres in all, the motion of
each planet being resolved into its components, and a separate sphere
being assigned for each component motion. Callippus (330 B.C.)
increased the number to thirty-three. It is now generally accepted
that the real existence of these spheres was not suggested, but the
idea was only a mathematical conception to facilitate the construction
of tables for predicting the places of the heavenly bodies.

Aristotle (384-322 B.C.) summed up the state of astronomical knowledge
in his time, and held the earth to be fixed in the centre of the
world.

Nicetas, Heraclides, and Ecphantes supposed the earth to revolve on
its axis, but to have no orbital motion.

The short epitome so far given illustrates the extraordinary deductive
methods adopted by the ancient Greeks. But they went much farther in
the same direction. They seem to have been in great difficulty to
explain how the earth is supported, just as were those who invented
the myth of Atlas, or the Indians with the tortoise. Thales thought
that the flat earth floated on water. Anaxagoras thought that, being
flat, it would be buoyed up and supported on the air like a kite.
Democritus thought it remained fixed, like the donkey between two
bundles of hay, because it was equidistant from all parts of the
containing sphere, and there was no reason why it should incline one
way rather than another. Empedocles attributed its state of rest to
centrifugal force by the rapid circular movement of the heavens, as
water is stationary in a pail when whirled round by a string.
Democritus further supposed that the inclination of the flat earth to
the ecliptic was due to the greater weight of the southern parts owing
to the exuberant vegetation.

For further references to similar efforts of imagination the reader is
referred to Sir George Cornwall Lewis's _Historical Survey of the
Astronomy of the Ancients_; London, 1862. His list of authorities
is very complete, but some of his conclusions are doubtful.  At p. 113
of that work he records the real opinions of Socrates as set forth by
Xenophon; and the reader will, perhaps, sympathise with Socrates in
his views on contemporary astronomy:--

With regard to astronomy he [Socrates] considered a knowledge of it
desirable to the extent of determining the day of the year or month,
and the hour of the night, ... but as to learning the courses of the
stars, to be occupied with the planets, and to inquire about their
distances from the earth, and their orbits, and the causes of their
motions, he strongly objected to such a waste of valuable time. He
dwelt on the contradictions and conflicting opinions of the physical
philosophers, ... and, in fine, he held that the speculators on the
universe and on the laws of the heavenly bodies were no better than
madmen (_Xen. Mem_, i. 1, 11-15).

Plato (born 429 B.C.), the pupil of Socrates, the fellow-student of
Euclid, and a follower of Pythagoras, studied science in his travels
in Egypt and elsewhere.  He was held in so great reverence by all
learned men that a problem which he set to the astronomers was the
keynote to all astronomical investigation from this date till the time
of Kepler in the sixteenth century. He proposed to astronomers _the
problem of representing the courses of the planets by circular and
uniform motions_.

Systematic observation among the Greeks began with the rise of the
Alexandrian school. Aristillus and Timocharis set up instruments and
fixed the positions of the zodiacal stars, near to which all the
planets in their orbits pass, thus facilitating the determination of
planetary motions. Aristarchus (320-250 B.C.) showed that the sun must
be at least nineteen times as far off as the moon, which is far short
of the mark. He also found the sun's diameter, correctly, to be half a
degree.  Eratosthenes (276-196 B.C.) measured the inclination to the
equator of the sun's apparent path in the heavens--i.e., he
measured the obliquity of the ecliptic, making it 23° 51', confirming
our knowledge of its continuous diminution during historical times. He
measured an arc of meridian, from Alexandria to Syene (Assuan), and
found the difference of latitude by the length of a shadow at noon,
summer solstice. He deduced the diameter of the earth, 250,000
stadia. Unfortunately, we do not know the length of the stadium he
used.

Hipparchus (190-120 B.C.) may be regarded as the founder of
observational astronomy. He measured the obliquity of the ecliptic,
and agreed with Eratosthenes.  He altered the length of the tropical
year from 365 days, 6 hours to 365 days, 5 hours, 53 minutes--still
four minutes too much. He measured the equation of time and the
irregular motion of the sun; and allowed for this in his calculations
by supposing that the centre, about which the sun moves uniformly, is
situated a little distance from the fixed earth. He called this point
the _excentric_. The line from the earth to the "excentric" was
called the _line of apses_. A circle having this centre was
called the _equant_, and he supposed that a radius drawn to the
sun from the excentric passes over equal arcs on the equant in equal
times. He then computed tables for predicting the place of the sun.

He proceeded in the same way to compute Lunar tables. Making use of
Chaldæan eclipses, he was able to get an accurate value of the moon's
mean motion.  [Halley, in 1693, compared this value with his own
measurements, and so discovered the acceleration of the moon's mean
motion. This was conclusively established, but could not be explained
by the Newtonian theory for quite a long time.] He determined the
plane of the moon's orbit and its inclination to the ecliptic. The
motion of this plane round the pole of the ecliptic once in eighteen
years complicated the problem. He located the moon's excentric as he
had done the sun's.  He also discovered some of the minor
irregularities of the moon's motion, due, as Newton's theory proves,
to the disturbing action of the sun's attraction.

In the year 134 B.C. Hipparchus observed a new star.  This upset every
notion about the permanence of the fixed stars. He then set to work to
catalogue all the principal stars so as to know if any others appeared
or disappeared. Here his experiences resembled those of several later
astronomers, who, when in search of some special object, have been
rewarded by a discovery in a totally different direction. On comparing
his star positions with those of Timocharis and Aristillus he found no
stars that had appeared or disappeared in the interval of 150 years;
but he found that all the stars seemed to have changed their places
with reference to that point in the heavens where the ecliptic is 90°
from the poles of the earth--i.e., the equinox. He found that this
could be explained by a motion of the equinox in the direction of the
apparent diurnal motion of the stars. This discovery of _precession of
the equinoxes_, which takes place at the rate of 52".1 every year, was
necessary for the progress of accurate astronomical observations. It
is due to a steady revolution of the earth's pole round the pole of
the ecliptic once in 26,000 years in the opposite direction to the
planetary revolutions.

Hipparchus was also the inventor of trigonometry, both plane and
spherical. He explained the method of using eclipses for determining
the longitude.

In connection with Hipparchus' great discovery it may be mentioned
that modern astronomers have often attempted to fix dates in history
by the effects of precession of the equinoxes. (1) At about the date
when the Great Pyramid may have been built gamma Draconis was near to the
pole, and must have been used as the pole-star. In the north face of
the Great Pyramid is the entrance to an inclined passage, and six of
the nine pyramids at Gizeh possess the same feature; all the passages
being inclined at an angle between 26° and 27° to the horizon and in
the plane of the meridian. It also appears that 4,000 years
ago--i.e., about 2100 B.C.--an observer at the lower end of the
passage would be able to see gamma Draconis, the then pole-star, at its
lower culmination.[1] It has been suggested that the passage was made
for this purpose. On other grounds the date assigned to the Great
Pyramid is 2123 B.C.

(2) The Chaldæans gave names to constellations now invisible from
Babylon which would have been visible in 2000 B.C., at which date it
is claimed that these people were studying astronomy.

(3) In the Odyssey, Calypso directs Odysseus, in accordance with
Phoenician rules for navigating the Mediterranean, to keep the Great
Bear "ever on the left as he traversed the deep" when sailing from the
pillars of Hercules (Gibraltar) to Corfu. Yet such a course taken now
would land the traveller in Africa.  Odysseus is said in his voyage in
springtime to have seen the Pleiades and Arcturus setting late, which
seemed to early commentators a proof of Homer's inaccuracy.  Likewise
Homer, both in the _Odyssey_ [2] (v. 272-5) and in the _Iliad_
(xviii. 489), asserts that the Great Bear never set in those
latitudes. Now it has been found that the precession of the equinoxes
explains all these puzzles; shows that in springtime on the
Mediterranean the Bear was just above the horizon, near the sea but
not touching it, between 750 B.C. and 1000 B.C.; and fixes the date of
the poems, thus confirming other evidence, and establishing Homer's
character for accuracy. [3]

(4) The orientation of Egyptian temples and Druidical stones is such
that possibly they were so placed as to assist in the observation of
the heliacal risings [4] of certain stars. If the star were known,
this would give an approximate date. Up to the present the results of
these investigations are far from being conclusive.

Ptolemy (130 A.D.) wrote the Suntaxis, or Almagest, which includes a
cyclopedia of astronomy, containing a summary of knowledge at that
date. We have no evidence beyond his own statement that he was a
practical observer. He theorised on the planetary motions, and held
that the earth is fixed in the centre of the universe. He adopted the
excentric and equant of Hipparchus to explain the unequal motions of
the sun and moon. He adopted the epicycles and deferents which had
been used by Apollonius and others to explain the retrograde motions
of the planets. We, who know that the earth revolves round the sun
once in a year, can understand that the apparent motion of a planet is
only its motion relative to the earth. If, then, we suppose the earth
fixed and the sun to revolve round it once a year, and the planets
each in its own period, it is only necessary to impose upon each of
these an additional _annual_ motion to enable us to represent truly
the apparent motions. This way of looking at the apparent motions
shows why each planet, when nearest to the earth, seems to move for a
time in a retrograde direction. The attempts of Ptolemy and others of
his time to explain the retrograde motion in this way were only
approximate. Let us suppose each planet to have a bar with one end
centred at the earth.  If at the other end of the bar one end of a
shorter bar is pivotted, having the planet at its other end, then the
planet is given an annual motion in the secondary circle (the
epicycle), whose centre revolves round the earth on the primary circle
(the _deferent_), at a uniform rate round the excentric. Ptolemy
supposed the centres of the epicycles of Mercury and Venus to be on a
bar passing through the sun, and to be between the earth and the
sun. The centres of the epicycles of Mars, Jupiter, and Saturn were
supposed to be further away than the sun.  Mercury and Venus were
supposed to revolve in their epicycles in their own periodic times and
in the deferent round the earth in a year. The major planets were
supposed to revolve in the deferent round the earth in their own
periodic times, and in their epicycles once in a year.

It did not occur to Ptolemy to place the centres of the epicycles of
Mercury and Venus at the sun, and to extend the same system to the
major planets. Something of this sort had been proposed by the
Egyptians (we are told by Cicero and others), and was accepted by
Tycho Brahe; and was as true a representation of the relative motions
in the solar system as when we suppose the sun to be fixed and the
earth to revolve.

The cumbrous system advocated by Ptolemy answered its purpose,
enabling him to predict astronomical events approximately. He improved
the lunar theory considerably, and discovered minor inequalities which
could be allowed for by the addition of new epicycles.  We may look
upon these epicycles of Apollonius, and the excentric of Hipparchus,
as the responses of these astronomers to the demand of Plato for
uniform circular motions. Their use became more and more confirmed,
until the seventeenth century, when the accurate observations of Tycho
Brahe enabled Kepler to abolish these purely geometrical makeshifts,
and to substitute a system in which the sun became physically its
controller.


FOOTNOTES:

[1] _Phil. Mag_., vol. xxiv., pp. 481-4.

[2]

Plaeiadas t' esoronte kai opse duonta bootaen
'Arkton th' aen kai amaxan epiklaesin kaleousin,
'Ae t' autou strephetai kai t' Oriona dokeuei,
Oin d'ammoros esti loetron Okeanoio.

"The Pleiades and Boötes that setteth late, and the Bear,
which they likewise call the Wain, which turneth ever in one
place, and keepeth watch upon Orion, and alone hath no part in
the baths of the ocean."

[3] See Pearson in the Camb. Phil. Soc. Proc., vol. iv., pt. ii., p.
93, on whose authority the above statements are made.

[4] See p. 6 for definition.



4. THE REIGN OF EPICYCLES--FROM PTOLEMY TO COPERNICUS.


After Ptolemy had published his book there seemed to be nothing more
to do for the solar system except to go on observing and finding more
and more accurate values for the constants involved--viz., the periods
of revolution, the diameter of the deferent,[1] and its ratio to that
of the epicycle,[2] the distance of the excentric[3] from the centre
of the deferent, and the position of the line of apses,[4] besides the
inclination and position of the plane of the planet's orbit. The only
object ever aimed at in those days was to prepare tables for
predicting the places of the planets. It was not a mechanical problem;
there was no notion of a governing law of forces.

From this time onwards all interest in astronomy seemed, in Europe at
least, to sink to a low ebb.  When the Caliph Omar, in the middle of
the seventh century, burnt the library of Alexandria, which had been
the centre of intellectual progress, that centre migrated to Baghdad,
and the Arabs became the leaders of science and philosophy. In
astronomy they made careful observations. In the middle of the ninth
century Albategnius, a Syrian prince, improved the value of
excentricity of the sun's orbit, observed the motion of the moon's
apse, and thought he detected a smaller progression of the sun's
apse. His tables were much more accurate than Ptolemy's. Abul Wefa, in
the tenth century, seems to have discovered the moon's "variation."
Meanwhile the Moors were leaders of science in the west, and Arzachel
of Toledo improved the solar tables very much. Ulugh Begh, grandson of
the great Tamerlane the Tartar, built a fine observatory at Samarcand
in the fifteenth century, and made a great catalogue of stars, the
first since the time of Hipparchus.

At the close of the fifteenth century King Alphonso of Spain employed
computers to produce the Alphonsine Tables (1488 A.D.), Purbach
translated Ptolemy's book, and observations were carried out in
Germany by Müller, known as Regiomontanus, and Waltherus.

Nicolai Copernicus, a Sclav, was born in 1473 at Thorn, in Polish
Prussia. He studied at Cracow and in Italy. He was a priest, and
settled at Frauenberg.  He did not undertake continuous observations,
but devoted himself to simplifying the planetary systems and devising
means for more accurately predicting the positions of the sun, moon,
and planets. He had no idea of framing a solar system on a dynamical
basis.  His great object was to increase the accuracy of the
calculations and the tables. The results of his cogitations were
printed just before his death in an interesting book, _De
Revolutionibus Orbium Celestium_. It is only by careful reading of
this book that the true position of Copernicus can be realised. He
noticed that Nicetas and others had ascribed the apparent diurnal
rotation of the heavens to a real daily rotation of the earth about
its axis, in the opposite direction to the apparent motion of the
stars. Also in the writings of Martianus Capella he learnt that the
Egyptians had supposed Mercury and Venus to revolve round the sun, and
to be carried with him in his annual motion round the earth. He
noticed that the same supposition, if extended to Mars, Jupiter, and
Saturn, would explain easily why they, and especially Mars, seem so
much brighter in opposition.  For Mars would then be a great deal
nearer to the earth than at other times. It would also explain the
retrograde motion of planets when in opposition.

We must here notice that at this stage Copernicus was actually
confronted with the system accepted later by Tycho Brahe, with the
earth fixed. But he now recalled and accepted the views of Pythagoras
and others, according to which the sun is fixed and the earth
revolves; and it must be noted that, geometrically, there is no
difference of any sort between the Egyptian or Tychonic system and
that of Pythagoras as revived by Copernicus, except that on the latter
theory the stars ought to seem to move when the earth changes its
position--a test which failed completely with the rough means of
observation then available. The radical defect of all solar systems
previous to the time of Kepler (1609 A.D.) was the slavish yielding to
Plato's dictum demanding uniform circular motion for the planets, and
the consequent evolution of the epicycle, which was fatal to any
conception of a dynamical theory.

Copernicus could not sever himself from this obnoxious tradition.[5]
It is true that neither the Pythagorean nor the Egypto-Tychonic system
required epicycles for explaining retrograde motion, as the Ptolemaic
theory did. Furthermore, either system could use the excentric of
Hipparchus to explain the irregular motion known as the equation of
the centre.  But Copernicus remarked that he could also use an
epicycle for this purpose, or that he could use both an excentric and
an epicycle for each planet, and so bring theory still closer into
accord with observation. And this he proceeded to do.[6] Moreover,
observers had found irregularities in the moon's motion, due, as we
now know, to the disturbing attraction of the sun.  To correct for
these irregularities Copernicus introduced epicycle on epicycle in the
lunar orbit.

This is in its main features the system propounded by Copernicus. But
attention must, to state the case fully, be drawn to two points to be
found in his first and sixth books respectively. The first point
relates to the seasons, and it shows a strange ignorance of the laws
of rotating bodies. To use the words of Delambre,[7] in drawing
attention to the strange conception,

  he imagined that the earth, revolving round the sun, ought always to
  show to it the same face; the contrary phenomena surprised him: to
  explain them he invented a third motion, and added it to the two
  real motions (rotation and orbital revolution). By this third motion
  the earth, he held, made a revolution on itself and on the poles of
  the ecliptic once a year ... Copernicus did not know that motion in
  a straight line is the natural motion, and that motion in a curve is
  the resultant of several movements. He believed, with Aristotle,
  that circular motion was the natural one.

Copernicus made this rotation of the earth's axis about the pole of
the ecliptic retrograde (i.e., opposite to the orbital revolution),
and by making it perform more than one complete revolution in a year,
the added part being 1/26000 of the whole, he was able to include the
precession of the equinoxes in his explanation of the seasons. His
explanation of the seasons is given on leaf 10 of his book (the pages
of this book are not all numbered, only alternate pages, or leaves).

In his sixth book he discusses the inclination of the planetary orbits
to the ecliptic. In regard to this the theory of Copernicus is unique;
and it will be best to explain this in the words of Grant in his great
work.[8] He says:--

  Copernicus, as we have already remarked, did not attack the
  principle of the epicyclical theory: he merely sought to make it
  more simple by placing the centre of the earth's orbit in the centre
  of the universe. This was the point to which the motions of the
  planets were referred, for the planes of their orbits were made to
  pass through it, and their points of least and greatest velocities
  were also determined with reference to it.  By this arrangement the
  sun was situate mathematically near the centre of the planetary
  system, but he did not appear to have any physical connexion with
  the planets as the centre of their motions.

According to Copernicus' sixth book, the planes of the planetary
orbits do not pass through the sun, and the lines of apses do not pass
through to the sun.

Such was the theory advanced by Copernicus: The earth moves in an
epicycle, on a deferent whose centre is a little distance from the
sun. The planets move in a similar way on epicycles, but their
deferents have no geometrical or physical relation to the sun. The
moon moves on an epicycle centred on a second epicycle, itself centred
on a deferent, excentric to the earth.  The earth's axis rotates about
the pole of the ecliptic, making one revolution and a twenty-six
thousandth part of a revolution in the sidereal year, in the opposite
direction to its orbital motion.

In view of this fanciful structure it must be noted, in fairness to
Copernicus, that he repeatedly states that the reader is not obliged
to accept his system as showing the real motions; that it does not
matter whether they be true, even approximately, or not, so long as
they enable us to compute tables from which the places of the planets
among the stars can be predicted.[9] He says that whoever is not
satisfied with this explanation must be contented by being told that
"mathematics are for mathematicians" (Mathematicis mathematica
scribuntur).

At the same time he expresses his conviction over and over again that
the earth is in motion. It is with him a pious belief, just as it was
with Pythagoras and his school and with Aristarchus. "But" (as Dreyer
says in his most interesting book, _Tycho Brahe_) "proofs of the
physical truth of his system Copernicus had given none, and could give
none," any more than Pythagoras or Aristarchus.

There was nothing so startlingly simple in his system as to lead the
cautious astronomer to accept it, as there was in the later Keplerian
system; and the absence of parallax in the stars seemed to condemn his
system, which had no physical basis to recommend it, and no
simplification at all over the Egypto-Tychonic system, to which
Copernicus himself drew attention. It has been necessary to devote
perhaps undue space to the interesting work of Copernicus, because by
a curious chance his name has become so widely known. He has been
spoken of very generally as the founder of the solar system that is
now accepted. This seems unfair, and on reading over what has been
written about him at different times it will be noticed that the
astronomers--those who have evidently read his great book--are very
cautious in the words with which they eulogise him, and refrain from
attributing to him the foundation of our solar system, which is
entirely due to Kepler.  It is only the more popular writers who give
the idea that a revolution had been effected when Pythagoras' system
was revived, and when Copernicus supported his view that the earth
moves and is not fixed.

It may be easy to explain the association of the name of Copernicus
with the Keplerian system. But the time has long passed when the
historian can support in any way this popular error, which was started
not by astronomers acquainted with Kepler's work, but by those who
desired to put the Church in the wrong by extolling Copernicus.

Copernicus dreaded much the abuse he expected to receive from
philosophers for opposing the authority of Aristotle, who had declared
that the earth was fixed.  So he sought and obtained the support of
the Church, dedicating his great work to Pope Paul III. in a lengthy
explanatory epistle. The Bishop of Cracow set up a memorial tablet in
his honour.

Copernicus was the most refined exponent, and almost the last
representative, of the Epicyclical School.  As has been already
stated, his successor, Tycho Brahe, supported the same use of
epicycles and excentrics as Copernicus, though he held the earth to be
fixed. But Tycho Brahe was eminently a practical observer, and took
little part in theory; and his observations formed so essential a
portion of the system of Kepler that it is only fair to include his
name among these who laid the foundations of the solar system which we
accept to-day.

In now taking leave of the system of epicycles let it be remarked that
it has been held up to ridicule more than it deserves. On reading
Airy's account of epicycles, in the beautifully clear language of his
_Six Lectures on Astronomy_, the impression is made that the
jointed bars there spoken of for describing the circles were supposed
to be real. This is no more the case than that the spheres of Eudoxus
and Callippus were supposed to be real. Both were introduced only to
illustrate the mathematical conception upon which the solar,
planetary, and lunar tables were constructed.  The epicycles
represented nothing more nor less than the first terms in the Fourier
series, which in the last century has become a basis of such
calculations, both in astronomy and physics generally.

[Illustration: "QUADRANS MURALIS SIVE TICHONICUS."  With portrait of
Tycho Brahe, instruments, etc., painted on the wall; showing
assistants using the sight, watching the clock, and recording.  (From
the author's copy of the _Astronomiæ Instauratæ Mechanica._)]


FOOTNOTES:

[1] For definition see p. 22.

[2] _Ibid_.

[3] For definition see p. 18.

[4] For definition see p. 18.

[5] In his great book Copernicus says: "The movement of the heavenly
bodies is uniform, circular, perpetual, or else composed of circular
movements." In this he proclaimed himself a follower of Pythagoras
(see p. 14), as also when he says: "The world is spherical because the
sphere is, of all figures, the most perfect" (Delambre,
_Ast. Mod. Hist_., pp. 86, 87).

[6] Kepler tells us that Tycho Brahe was pleased with this
device, and adapted it to his own system.

[7] _Hist. Ast._, vol. i., p. 354.

[8] _Hist. of Phys. Ast._, p. vii.

[9] "Est enim Astronomi proprium, historiam motuum coelestium
diligenti et artificiosa observatione colligere. Deinde causas
earundem, seu hypotheses, cum veras assequi nulla ratione possit
... Neque enim necesse est, eas hypotheses esse veras, imo ne
verisimiles quidem, sed sufficit hoc usum, si calculum observationibus
congruentem exhibeant."




BOOK II. THE DYNAMICAL PERIOD



5. DISCOVERY OF THE TRUE SOLAR SYSTEM--TYCHO BRAHE--KEPLER.


During the period of the intellectual and aesthetic revival, at the
beginning of the sixteenth century, the "spirit of the age" was
fostered by the invention of printing, by the downfall of the
Byzantine Empire, and the scattering of Greek fugitives, carrying the
treasures of literature through Western Europe, by the works of
Raphael and Michael Angelo, by the Reformation, and by the extension
of the known world through the voyages of Spaniards and Portuguese.
During that period there came to the front the founder of accurate
observational astronomy. Tycho Brahe, a Dane, born in 1546 of noble
parents, was the most distinguished, diligent, and accurate observer
of the heavens since the days of Hipparchus, 1,700 years before.

Tycho was devoted entirely to his science from childhood, and the
opposition of his parents only stimulated him in his efforts to
overcome difficulties.  He soon grasped the hopelessness of the old
deductive methods of reasoning, and decided that no theories ought to
be indulged in until preparations had been made by the accumulation of
accurate observations.  We may claim for him the title of founder of
the inductive method.

For a complete life of this great man the reader is referred to
Dreyer's _Tycho Brahe_, Edinburgh, 1890, containing a complete
bibliography. The present notice must be limited to noting the work
done, and the qualities of character which enabled him to attain his
scientific aims, and which have been conspicuous in many of his
successors.

He studied in Germany, but King Frederick of Denmark, appreciating his
great talents, invited him to carry out his life's work in that
country. He granted to him the island of Hveen, gave him a pension,
and made him a canon of the Cathedral of Roskilde. On that island
Tycho Brahe built the splendid observatory which he called Uraniborg,
and, later, a second one for his assistants and students, called
Stjerneborg. These he fitted up with the most perfect instruments, and
never lost a chance of adding to his stock of careful observations.[1]

The account of all these instruments and observations, printed at his
own press on the island, was published by Tycho Brahe himself, and the
admirable and numerous engravings bear witness to the excellence of
design and the stability of his instruments.

His mechanical skill was very great, and in his workmanship he was
satisfied with nothing but the best. He recognised the importance of
rigidity in the instruments, and, whereas these had generally been
made of wood, he designed them in metal. His instruments included
armillae like those which had been used in Alexandria, and other
armillae designed by himself--sextants, mural quadrants, large
celestial globes and various instruments for special purposes. He
lived before the days of telescopes and accurate clocks. He invented
the method of sub-dividing the degrees on the arc of an instrument by
transversals somewhat in the way that Pedro Nunez had proposed.

He originated the true system of observation and reduction of
observations, recognising the fact that the best instrument in the
world is not perfect; and with each of his instruments he set to work
to find out the errors of graduation and the errors of mounting, the
necessary correction being applied to each observation.

When he wanted to point his instrument exactly to a star he was
confronted with precisely the same difficulty as is met in gunnery and
rifle-shooting. The sights and the object aimed at cannot be in focus
together, and a great deal depends on the form of sight. Tycho Brahe
invented, and applied to the pointers of his instruments, an
aperture-sight of variable area, like the iris diaphragm used now in
photography. This enabled him to get the best result with stars of
different brightness.  The telescope not having been invented, he
could not use a telescopic-sight as we now do in gunnery.  This not
only removes the difficulty of focussing, but makes the minimum
visible angle smaller. Helmholtz has defined the minimum angle
measurable with the naked eye as being one minute of arc. In view of
this it is simply marvellous that, when the positions of Tycho's
standard stars are compared with the best modern catalogues, his
probable error in right ascension is only ± 24", 1, and in declination
only ± 25", 9.

Clocks of a sort had been made, but Tycho Brahe found them so
unreliable that he seldom used them, and many of his position-measurements
were made by measuring the angular distances from known stars.

Taking into consideration the absence of either a telescope or a
clock, and reading his account of the labour he bestowed upon each
observation, we must all agree that Kepler, who inherited these
observations in MS., was justified, under the conditions then
existing, in declaring that there was no hope of anyone ever improving
upon them.

In the year 1572, on November 11th, Tycho discovered in Cassiopeia a
new star of great brilliance, and continued to observe it until the
end of January, 1573. So incredible to him was such an event that he
refused to believe his own eyes until he got others to confirm what he
saw. He made accurate observations of its distance from the nine
principal stars in Casseiopeia, and proved that it had no measurable
parallax. Later he employed the same method with the comets of 1577,
1580, 1582, 1585, 1590, 1593, and 1596, and proved that they too had
no measurable parallax and must be very distant.

The startling discovery that stars are not necessarily permanent, that
new stars may appear, and possibly that old ones may disappear, had
upon him exactly the same effect that a similar occurrence had upon
Hipparchus 1,700 years before. He felt it his duty to catalogue all
the principal stars, so that there should be no mistake in the
future. During the construction of his catalogue of 1,000 stars he
prepared and used accurate tables of refraction deduced from his own
observations. Thus he eliminated (so far as naked eye observations
required) the effect of atmospheric refraction which makes the
altitude of a star seem greater than it really is.

Tycho Brahe was able to correct the lunar theory by his observations.
Copernicus had introduced two epicycles on the lunar orbit in the hope
of obtaining a better accordance between theory and observation; and
he was not too ambitious, as his desire was to get the tables accurate
to ten minutes. Tycho Brahe found that the tables of Copernicus were
in error as much as two degrees. He re-discovered the inequality
called "variation" by observing the moon in all phases--a thing which
had not been attended to. [It is remarkable that in the nineteenth
century Sir George Airy established an altazimuth at Greenwich
Observatory with this special object, to get observations of the moon
in all phases.] He also discovered other lunar equalities, and wanted
to add another epicycle to the moon's orbit, but he feared that these
would soon become unmanageable if further observations showed more new
inequalities.

But, as it turned out, the most fruitful work of Tycho Brahe was on
the motions of the planets, and especially of the planet Mars, for it
was by an examination of these results that Kepler was led to the
discovery of his immortal laws.

After the death of King Frederick the observatories of Tycho Brahe
were not supported. The gigantic power and industry displayed by this
determined man were accompanied, as often happens, by an overbearing
manner, intolerant of obstacles. This led to friction, and eventually
the observatories were dismantled, and Tycho Brahe was received by the
Emperor Rudolph II., who placed a house in Prague at his disposal.
Here he worked for a few years, with Kepler as one of his assistants,
and he died in the year 1601.

It is an interesting fact that Tycho Brahe had a firm conviction that
mundane events could be predicted by astrology, and that this belief
was supported by his own predictions.

It has already been stated that Tycho Brahe maintained that
observation must precede theory. He did not accept the Copernican
theory that the earth moves, but for a working hypothesis he used a
modification of an old Egyptian theory, mathematically identical with
that of Copernicus, but not involving a stellar parallax.  He says
(_De Mundi_, etc.) that

  the Ptolemean system was too complicated, and the new one which that
  great man Copernicus had proposed, following in the footsteps of
  Aristarchus of Samos, though there was nothing in it contrary to
  mathematical principles, was in opposition to those of physics, as
  the heavy and sluggish earth is unfit to move, and the system is
  even opposed to the authority of Scripture. The absence of annual
  parallax further involves an incredible distance between the
  outermost planet and the fixed stars.

We are bound to admit that in the circumstances of the case, so long
as there was no question of dynamical forces connecting the members of
the solar system, his reasoning, as we should expect from such a man,
is practical and sound. It is not surprising, then, that astronomers
generally did not readily accept the views of Copernicus, that Luther
(Luther's _Tischreden_, pp.  22, 60) derided him in his usual pithy
manner, that Melancthon (_Initia doctrinae physicae_) said that
Scripture, and also science, are against the earth's motion; and that
the men of science whose opinion was asked for by the cardinals (who
wished to know whether Galileo was right or wrong) looked upon
Copernicus as a weaver of fanciful theories.

Johann Kepler is the name of the man whose place, as is generally
agreed, would have been the most difficult to fill among all those who
have contributed to the advance of astronomical knowledge. He was born
at Wiel, in the Duchy of Wurtemberg, in 1571. He held an appointment
at Gratz, in Styria, and went to join Tycho Brahe in Prague, and to
assist in reducing his observations. These came into his possession
when Tycho Brahe died, the Emperor Rudolph entrusting to him the
preparation of new tables (called the Rudolphine tables) founded on
the new and accurate observations. He had the most profound respect
for the knowledge, skill, determination, and perseverance of the man
who had reaped such a harvest of most accurate data; and though Tycho
hardly recognised the transcendent genius of the man who was working
as his assistant, and although there were disagreements between them,
Kepler held to his post, sustained by the conviction that, with these
observations to test any theory, he would be in a position to settle
for ever the problem of the solar system.

[Illustration: PORTRAIT OF JOHANNES KEPLER.  By F. Wanderer, from
Reitlinger's "Johannes Kepler" (original in Strassburg).]

It has seemed to many that Plato's demand for uniform circular motion
(linear or angular) was responsible for a loss to astronomy of good
work during fifteen hundred years, for a hundred ill-considered
speculative cosmogonies, for dissatisfaction, amounting to disgust,
with these _à priori_ guesses, and for the relegation of the
science to less intellectual races than Greeks and other Europeans.
Nobody seemed to dare to depart from this fetish of uniform angular
motion and circular orbits until the insight, boldness, and
independence of Johann Kepler opened up a new world of thought and of
intellectual delight.

While at work on the Rudolphine tables he used the old epicycles and
deferents and excentrics, but he could not make theory agree with
observation. His instincts told him that these apologists for uniform
motion were a fraud; and he proved it to himself by trying every
possible variation of the elements and finding them fail.  The number
of hypotheses which he examined and rejected was almost incredible
(for example, that the planets turn round centres at a little distance
from the sun, that the epicycles have centres at a little distance
from the deferent, and so on). He says that, after using all these
devices to make theory agree with Tycho's observations, he still found
errors amounting to eight minutes of a degree. Then he said boldly
that it was impossible that so good an observer as Tycho could have
made a mistake of eight minutes, and added: "Out of these eight
minutes we will construct a new theory that will explain the motions
of all the planets." And he did it, with elliptic orbits having the
sun in a focus of each.[2]

It is often difficult to define the boundaries between fancies,
imagination, hypothesis, and sound theory.  This extraordinary genius
was a master in all these modes of attacking a problem. His analogy
between the spaces occupied by the five regular solids and the
distances of the planets from the sun, which filled him with so much
delight, was a display of pure fancy. His demonstration of the three
fundamental laws of planetary motion was the most strict and complete
theory that had ever been attempted.

It has been often suggested that the revival by Copernicus of the
notion of a moving earth was a help to Kepler. No one who reads
Kepler's great book could hold such an opinion for a moment. In fact,
the excellence of Copernicus's book helped to prolong the life of the
epicyclical theories in opposition to Kepler's teaching.

All of the best theories were compared by him with observation. These
were the Ptolemaic, the Copernican, and the Tychonic. The two latter
placed all of the planetary orbits concentric with one another, the
sun being placed a little away from their common centre, and having no
apparent relation to them, and being actually outside the planes in
which they move.  Kepler's first great discovery was that the planes
of all the orbits pass through the sun; his second was that the line
of apses of each planet passes through the sun; both were
contradictory to the Copernican theory.

He proceeds cautiously with his propositions until he arrives at his
great laws, and he concludes his book by comparing observations of
Mars, of all dates, with his theory.

His first law states that the planets describe ellipses with the sun
at a focus of each ellipse.

His second law (a far more difficult one to prove) states that a line
drawn from a planet to the sun sweeps over equal areas in equal
times. These two laws were published in his great work, _Astronomia
Nova, sen.  Physica Coelestis tradita commentariis de Motibus Stelloe;
Martis_, Prague, 1609.

It took him nine years more[3] to discover his third law, that the
squares of the periodic times are proportional to the cubes of the
mean distances from the sun.

These three laws contain implicitly the law of universal
gravitation. They are simply an alternative way of expressing that law
in dealing with planets, not particles. Only, the power of the
greatest human intellect is so utterly feeble that the meaning of the
words in Kepler's three laws could not be understood until expounded
by the logic of Newton's dynamics.

The joy with which Kepler contemplated the final demonstration of
these laws, the evolution of which had occupied twenty years, can
hardly be imagined by us.  He has given some idea of it in a passage
in his work on _Harmonics_, which is not now quoted, only lest
someone might say it was egotistical--a term which is simply grotesque
when applied to such a man with such a life's work accomplished.

The whole book, _Astronomia Nova_, is a pleasure to read; the
mass of observations that are used, and the ingenuity of the
propositions, contrast strongly with the loose and imperfectly
supported explanations of all his predecessors; and the indulgent
reader will excuse the devotion of a few lines to an example of the
ingenuity and beauty of his methods.

It may seem a hopeless task to find out the true paths of Mars and the
earth (at that time when their shape even was not known) from the
observations giving only the relative direction from night to
night. Now, Kepler had twenty years of observations of Mars to deal
with. This enabled him to use a new method, to find the earth's
orbit. Observe the date at any time when Mars is in opposition. The
earth's position E at that date gives the longitude of Mars M. His
period is 687 days. Now choose dates before and after the principal
date at intervals of 687 days and its multiples.  Mars is in each case
in the same position. Now for any date when Mars is at M and the earth
at E3 the date of the year gives the angle E3SM. And the
observation of Tycho gives the direction of Mars compared with the
sun, SE3M. So all the angles of the triangle SEM in any of these
positions of E are known, and also the ratios of SE1, SE2, SE3,
SE4 to SM and to each other.

For the orbit of Mars observations were chosen at intervals of a year,
when the earth was always in the same place.

[Illustration]

But Kepler saw much farther than the geometrical facts. He realised
that the orbits are followed owing to a force directed to the sun; and
he guessed that this is the same force as the gravity that makes a
stone fall. He saw the difficulty of gravitation acting through the
void space.  He compared universal gravitation to magnetism, and
speaks of the work of Gilbert of Colchester.  (Gilbert's book, _De
Mundo Nostro Sublunari, Philosophia Nova_, Amstelodami, 1651,
containing similar views, was published forty-eight years after
Gilbert's death, and forty-two years after Kepler's book and
reference.  His book _De Magnete_ was published in 1600.)

A few of Kepler's views on gravitation, extracted from the
Introduction to his _Astronomia Nova_, may now be mentioned:--

1. Every body at rest remains at rest if outside the attractive power
of other bodies.

2. Gravity is a property of masses mutually attracting in such manner
that the earth attracts a stone much more than a stone attracts the
earth.

3. Bodies are attracted to the earth's centre, not because it is the
centre of the universe, but because it is the centre of the attracting
particles of the earth.

4. If the earth be not round (but spheroidal?), then bodies at
different latitudes will not be attracted to its centre, but to
different points in the neighbourhood of that centre.

5. If the earth and moon were not retained in their orbits by vital
force (_aut alia aligua aequipollenti_), the earth and moon would come
together.

6. If the earth were to cease to attract its waters, the oceans would
all rise and flow to the moon.

7. He attributes the tides to lunar attraction.  Kepler had been
appointed Imperial Astronomer with a handsome salary (on paper), a
fraction of which was doled out to him very irregularly. He was led to
miserable makeshifts to earn enough to keep his family from
starvation; and proceeded to Ratisbon in 1630 to represent his claims
to the Diet. He arrived worn out and debilitated; he failed in his
appeal, and died from fever, contracted under, and fed upon,
disappointment and exhaustion. Those were not the days when men could
adopt as a profession the "research of endowment."

Before taking leave of Kepler, who was by no means a man of one idea,
it ought to be here recorded that he was the first to suggest that a
telescope made with both lenses convex (not a Galilean telescope) can
have cross wires in the focus, for use as a pointer to fix accurately
the positions of stars. An Englishman, Gascoigne, was the first to use
this in practice.

From the all too brief epitome here given of Kepler's greatest book,
it must be obvious that he had at that time some inkling of the
meaning of his laws--universal gravitation. From that moment the idea
of universal gravitation was in the air, and hints and guesses were
thrown out by many; and in time the law of gravitation would doubtless
have been discovered, though probably not by the work of one man, even
if Newton had not lived. But, if Kepler had not lived, who else could
have discovered his laws?


FOOTNOTES:

[1] When the writer visited M. D'Arrest, the astronomer, at
Copenhagen, in 1872, he was presented by D'Arrest with one of several
bricks collected from the ruins of Uraniborg. This was one of his most
cherished possessions until, on returning home after a prolonged
absence on astronomical work, he found that his treasure had been
tidied away from his study.

[2] An ellipse is one of the plane, sections of a cone. It is an oval
curve, which may be drawn by fixing two pins in a sheet of paper at S
and H, fastening a string, SPH, to the two pins, and stretching it
with a pencil point at P, and moving the pencil point, while the
string is kept taut, to trace the oval ellipse, APB. S and H are the
_foci_. Kepler found the sun to be in one focus, say S. AB is the
_major axis_. DE is the _minor axis_. C is the _centre_. The direction
of AB is the _line of apses_. The ratio of CS to CA is the
_excentricity_. The position of the planet at A is the _perihelion_
(nearest to the sun). The position of the planet at B is the
_aphelion_ (farthest from the sun). The angle ASP is the _anomaly_
when the planet is at P. CA or a line drawn from S to D is the _mean
distance_ of the planet from the sun.

[Illustration]

[3] The ruled logarithmic paper we now use was not then to be had by
going into a stationer's shop. Else he would have accomplished this in
five minutes.



6. GALILEO AND THE TELESCOPE--NOTIONS OF GRAVITY BY HORROCKS, ETC.


It is now necessary to leave the subject of dynamical astronomy for a
short time in order to give some account of work in a different
direction originated by a contemporary of Kepler's, his senior in fact
by seven years. Galileo Galilei was born at Pisa in 1564. The most
scientific part of his work dealt with terrestrial dynamics; but one
of those fortunate chances which happen only to really great men put
him in the way of originating a new branch of astronomy.

The laws of motion had not been correctly defined.  The only man of
Galileo's time who seems to have worked successfully in the same
direction as himself was that Admirable Crichton of the Italians,
Leonardo da Vinci. Galileo cleared the ground. It had always been
noticed that things tend to come to rest; a ball rolled on the ground,
a boat moved on the water, a shot fired in the air. Galileo realised
that in all of these cases a resisting force acts to stop the motion,
and he was the first to arrive at the not very obvious law that the
motion of a body will never stop, nor vary its speed, nor change its
direction, except by the action of some force.

It is not very obvious that a light body and a heavy one fall at the
same speed (except for the resistance of the air). Galileo proved this
on paper, but to convince the world he had to experiment from the
leaning tower of Pisa.

At an early age he discovered the principle of isochronism of the
pendulum, which, in the hands of Huyghens in the middle of the
seventeenth century, led to the invention of the pendulum clock,
perhaps the most valuable astronomical instrument ever produced.

These and other discoveries in dynamics may seem very obvious now; but
it is often the most every-day matters which have been found to elude
the inquiries of ordinary minds, and it required a high order of
intellect to unravel the truth and discard the stupid maxims scattered
through the works of Aristotle and accepted on his authority. A blind
worship of scientific authorities has often delayed the progress of
human knowledge, just as too much "instruction" of a youth often ruins
his "education." Grant, in his history of Physical Astronomy, has well
said that "the sagacity and skill which Galileo displays in resolving
the phenomena of motion into their constituent elements, and hence
deriving the original principles involved in them, will ever assure to
him a distinguished place among those who have extended the domains of
science."

But it was work of a different kind that established Galileo's popular
reputation. In 1609 Galileo heard that a Dutch spectacle-maker had
combined a pair of lenses so as to magnify distant objects. Working on
this hint, he solved the same problem, first on paper and then in
practice. So he came to make one of the first telescopes ever used in
astronomy. No sooner had he turned it on the heavenly bodies than he
was rewarded by such a shower of startling discoveries as forthwith
made his name the best known in Europe.  He found curious irregular
black spots on the sun, revolving round it in twenty-seven days; hills
and valleys on the moon; the planets showing discs of sensible size,
not points like the fixed stars; Venus showing phases according to her
position in relation to the sun; Jupiter accompanied by four moons;
Saturn with appendages that he could not explain, but unlike the other
planets; the Milky Way composed of a multitude of separate stars.

His fame flew over Europe like magic, and his discoveries were much
discussed--and there were many who refused to believe. Cosmo de Medici
induced him to migrate to Florence to carry on his observations.  He
was received by Paul V., the Pope, at Rome, to whom he explained his
discoveries.

He thought that these discoveries proved the truth of the Copernican
theory of the Earth's motion; and he urged this view on friends and
foes alike.  Although in frequent correspondence with Kepler, he never
alluded to the New Astronomy, and wrote to him extolling the virtue of
epicycles. He loved to argue, never shirked an encounter with any
number of disputants, and laughed as he broke down their arguments.

Through some strange course of events, not easy to follow, the
Copernican theory, whose birth was welcomed by the Church, had now
been taken up by certain anti-clerical agitators, and was opposed by
the cardinals as well as by the dignitaries of the Reformed
Church. Galileo--a good Catholic--got mixed up in these discussions,
although on excellent terms with the Pope and his entourage. At last
it came about that Galileo was summoned to appear at Rome, where he
was charged with holding and teaching heretical opinions about the
movement of the earth; and he then solemnly abjured these
opinions. There has been much exaggeration and misstatement about his
trial and punishment, and for a long time there was a great deal of
bitterness shown on both sides. But the general verdict of the present
day seems to be that, although Galileo himself was treated with
consideration, the hostility of the Church to the views of Copernicus
placed it in opposition also to the true Keplerian system, and this
led to unprofitable controversies.  From the time of Galileo onwards,
for some time, opponents of religion included the theory of the
Earth's motion in their disputations, not so much for the love, or
knowledge, of astronomy, as for the pleasure of putting the Church in
the wrong. This created a great deal of bitterness and intolerance on
both sides. Among the sufferers was Giordano Bruno, a learned
speculative philosopher, who was condemned to be burnt at the stake.

Galileo died on Christmas Day, 1642--the day of Newton's birth. The
further consideration of the grand field of discovery opened out by
Galileo with his telescopes must be now postponed, to avoid
discontinuity in the history of the intellectual development of this
period, which lay in the direction of dynamical, or physical,
astronomy.

Until the time of Kepler no one seems to have conceived the idea of
universal physical forces controlling terrestrial phenomena, and
equally applicable to the heavenly bodies. The grand discovery by
Kepler of the true relationship of the Sun to the Planets, and the
telescopic discoveries of Galileo and of those who followed him,
spread a spirit of inquiry and philosophic thought throughout Europe,
and once more did astronomy rise in estimation; and the irresistible
logic of its mathematical process of reasoning soon placed it in the
position it has ever since occupied as the foremost of the exact
sciences.

The practical application of this process of reasoning was enormously
facilitated by the invention of logarithms by Napier. He was born at
Merchistoun, near Edinburgh, in 1550, and died in 1617. By this system
the tedious arithmetical operations necessary in astronomical
calculations, especially those dealing with the trigonometrical
functions of angles, were so much simplified that Laplace declared
that by this invention the life-work of an astronomer was doubled.

Jeremiah Horrocks (born 1619, died 1641) was an ardent admirer of
Tycho Brahe and Kepler, and was able to improve the Rudolphine tables
so much that he foretold a transit of Venus, in 1639, which these
tables failed to indicate, and was the only observer of it. His life
was short, but he accomplished a great deal, and rightly ascribed the
lunar inequality called _evection_ to variations in the value of
the eccentricity and in the direction of the line of apses, at the
same time correctly assigning _the disturbing force of the Sun_
as the cause. He discovered the errors in Jupiter's calculated place,
due to what we now know as the long inequality of Jupiter and Saturn,
and measured with considerable accuracy the acceleration at that date
of Jupiter's mean motion, and indicated the retardation of Saturn's
mean motion.

Horrocks' investigations, so far as they could be collected, were
published posthumously in 1672, and seldom, if ever, has a man who
lived only twenty-two years originated so much scientific knowledge.

At this period British science received a lasting impetus by the wise
initiation of a much-abused man, Charles II., who founded the Royal
Society of London, and also the Royal Observatory of Greeenwich, where
he established Flamsteed as first Astronomer Royal, especially for
lunar and stellar observations likely to be useful for navigation. At
the same time the French Academy and the Paris Observatory were
founded. All this within fourteen years, 1662-1675.

Meanwhile gravitation in general terms was being discussed by Hooke,
Wren, Halley, and many others.  All of these men felt a repugnance to
accept the idea of a force acting across the empty void of space.
Descartes (1596-1650) proposed an ethereal medium whirling round the
sun with the planets, and having local whirls revolving with the
satellites. As Delambre and Grant have said, this fiction only
retarded the progress of pure science. It had no sort of relation to
the more modern, but equally misleading, "nebular hypothesis." While
many were talking and guessing, a giant mind was needed at this stage
to make things clear.



7. SIR ISAAC NEWTON--LAW OF UNIVERSAL GRAVITATION.


We now reach the period which is the culminating point of interest in
the history of dynamical astronomy.  Isaac Newton was born in
1642. Pemberton states that Newton, having quitted Cambridge to avoid
the plague, was residing at Wolsthorpe, in Lincolnshire, where he had
been born; that he was sitting one day in the garden, reflecting upon
the force which prevents a planet from flying off at a tangent and
which draws it to the sun, and upon the force which draws the moon to
the earth; and that he saw in the case of the planets that the sun's
force must clearly be unequal at different distances, for the pull out
of the tangential line in a minute is less for Jupiter than for
Mars. He then saw that the pull of the earth on the moon would be less
than for a nearer object. It is said that while thus meditating he saw
an apple fall from a tree to the ground, and that this fact suggested
the questions: Is the force that pulled that apple from the tree the
same as the force which draws the moon to the earth?  Does the
attraction for both of them follow the same law as to distance as is
given by the planetary motions round the sun? It has been stated that
in this way the first conception of universal gravitation arose.[1]

Quite the most important event in the whole history of physical
astronomy was the publication, in 1687, of Newton's _Principia
(Philosophiae Naturalis Principia Mathematica)_. In this great work
Newton started from the beginning of things, the laws of motion, and
carried his argument, step by step, into every branch of physical
astronomy; giving the physical meaning of Kepler's three laws, and
explaining, or indicating the explanation of, all the known heavenly
motions and their irregularities; showing that all of these were
included in his simple statement about the law of universal
gravitation; and proceeding to deduce from that law new irregularities
in the motions of the moon which had never been noticed, and to
discover the oblate figure of the earth and the cause of the
tides. These investigations occupied the best part of his life; but he
wrote the whole of his great book in fifteen months.

Having developed and enunciated the true laws of motion, he was able
to show that Kepler's second law (that equal areas are described by
the line from the planet to the sun in equal times) was only another
way of saying that the centripetal force on a planet is always
directed to the sun. Also that Kepler's first law (elliptic orbits
with the sun in one focus) was only another way of saying that the
force urging a planet to the sun varies inversely as the square of the
distance. Also (if these two be granted) it follows that Kepler's
third law is only another way of saying that the sun's force on
different planets (besides depending as above on distance) is
proportional to their masses.

Having further proved the, for that day, wonderful proposition that,
with the law of inverse squares, the attraction by the separate
particles of a sphere of uniform density (or one composed of
concentric spherical shells, each of uniform density) acts as if the
whole mass were collected at the centre, he was able to express the
meaning of Kepler's laws in propositions which have been summarised as
follows:--

The law of universal gravitation.--_Every particle of matter in the
universe attracts every other particle with a force varying inversely
as the square of the distance between them, and directly as the
product of the masses of the two particles_.[2]

But Newton did not commit himself to the law until he had answered
that question about the apple; and the above proposition now enabled
him to deal with the Moon and the apple. Gravity makes a stone fall
16.1 feet in a second. The moon is 60 times farther from the earth's
centre than the stone, so it ought to be drawn out of a straight
course through 16.1 feet in a minute. Newton found the distance
through which she is actually drawn as a fraction of the earth's
diameter.  But when he first examined this matter he proceeded to use
a wrong diameter for the earth, and he found a serious discrepancy.
This, for a time, seemed to condemn his theory, and regretfully he
laid that part of his work aside. Fortunately, before Newton wrote the
_Principia_ the French astronomer Picard made a new and correct
measure of an arc of the meridian, from which he obtained an accurate
value of the earth's diameter. Newton applied this value, and found,
to his great joy, that when the distance of the moon is 60 times the
radius of the earth she is attracted out of the straight course 16.1
feet per minute, and that the force acting on a stone or an apple
follows the same law as the force acting upon the heavenly bodies.[3]

The universality claimed for the law--if not by Newton, at least by
his commentators--was bold, and warranted only by the large number of
cases in which Newton had found it to apply. Its universality has been
under test ever since, and so far it has stood the test. There has
often been a suspicion of a doubt, when some inequality of motion in
the heavenly bodies has, for a time, foiled the astronomers in their
attempts to explain it. But improved mathematical methods have always
succeeded in the end, and so the seeming doubt has been converted into
a surer conviction of the universality of the law.

Having once established the law, Newton proceeded to trace some of its
consequences. He saw that the figure of the earth depends partly on
the mutual gravitation of its parts, and partly on the centrifugal
tendency due to the earth's rotation, and that these should cause a
flattening of the poles. He invented a mathematical method which he
used for computing the ratio of the polar to the equatorial diameter.

He then noticed that the consequent bulging of matter at the equator
would be attracted by the moon unequally, the nearest parts being most
attracted; and so the moon would tend to tilt the earth when in some
parts of her orbit; and the sun would do this to a less extent,
because of its great distance. Then he proved that the effect ought to
be a rotation of the earth's axis over a conical surface in space,
exactly as the axis of a top describes a cone, if the top has a sharp
point, and is set spinning and displaced from the vertical. He
actually calculated the amount; and so he explained the cause of the
precession of the equinoxes discovered by Hipparchus about 150 B.C.

One of his grandest discoveries was a method of weighing the heavenly
bodies by their action on each other. By means of this principle he
was able to compare the mass of the sun with the masses of those
planets that have moons, and also to compare the mass of our moon with
the mass of the earth.

Thus Newton, after having established his great principle, devoted his
splendid intellect to the calculation of its consequences. He proved
that if a body be projected with any velocity in free space, subject
only to a central force, varying inversely as the square of the
distance, the body must revolve in a curve which may be any one of the
sections of a cone--a circle, ellipse, parabola, or hyperbola; and he
found that those comets of which he had observations move in parabolae
round the Sun, and are thus subject to the universal law.

Newton realised that, while planets and satellites are chiefly
controlled by the central body about which they revolve, the new law
must involve irregularities, due to their mutual action--such, in
fact, as Horrocks had indicated. He determined to put this to a test
in the case of the moon, and to calculate the sun's effect, from its
mass compared with that of the earth, and from its distance. He proved
that the average effect upon the plane of the orbit would be to cause
the line in which it cuts the plane of the ecliptic (i.e., the line of
nodes) to revolve in the ecliptic once in about nineteen years. This
had been a known fact from the earliest ages. He also concluded that
the line of apses would revolve in the plane of the lunar orbit also
in about nineteen years; but the observed period is only ten
years. For a long time this was the one weak point in the Newtonian
theory. It was not till 1747 that Clairaut reconciled this with the
theory, and showed why Newton's calculation was not exact.

Newton proceeded to explain the other inequalities recognised by Tycho
Brahe and older observers, and to calculate their maximum amounts as
indicated by his theory. He further discovered from his calculations
two new inequalities, one of the apogee, the other of the nodes, and
assigned the maximum value. Grant has shown the values of some of
these as given by observation in the tables of Meyer and more modern
tables, and has compared them with the values assigned by Newton from
his theory; and the comparison is very remarkable.

                                     Newton.      Modern Tables.
                                      ° '  "         ° ' "
Mean monthly motion of Apses         1.31.28         3.4.0
Mean annual motion of nodes         19.18.1,23     19.21.22,50
Mean value of "variation"              36.10          35.47
Annual equation                        11.51          11.14
Inequality of mean motion of apogee    19.43          22.17
Inequality of mean motion of nodes      9.24           9.0

The only serious discrepancy is the first, which has been already
mentioned. Considering that some of these perturbations had never been
discovered, that the cause of none of them had ever been known, and
that he exhibited his results, if he did not also make the
discoveries, by the synthetic methods of geometry, it is simply
marvellous that he reached to such a degree of accuracy. He invented
the infinitesimal calculus which is more suited for such calculations,
but had he expressed his results in that language he would have been
unintelligible to many.

Newton's method of calculating the precession of the equinoxes,
already referred to, is as beautiful as anything in the _Principia_.
He had already proved the regression of the nodes of a satellite
moving in an orbit inclined to the ecliptic. He now said that the
nodes of a ring of satellites revolving round the earth's equator
would consequently all regress. And if joined into a solid ring its
node would regress; and it would do so, only more slowly, if
encumbered by the spherical part of the earth's mass. Therefore the
axis of the equatorial belt of the earth must revolve round the pole
of the ecliptic. Then he set to work and found the amount due to the
moon and that due to the sun, and so he solved the mystery of 2,000
years.

When Newton applied his law of gravitation to an explanation of the
tides he started a new field for the application of mathematics to
physical problems; and there can be little doubt that, if he could
have been furnished with complete tidal observations from different
parts of the world, his extraordinary powers of analysis would have
enabled him to reach a satisfactory theory.  He certainly opened up
many mines full of intellectual gems; and his successors have never
ceased in their explorations. This has led to improved mathematical
methods, which, combined with the greater accuracy of observation,
have rendered physical astronomy of to-day the most exact of the
sciences.

Laplace only expressed the universal opinion of posterity when he said
that to the _Principia_ is assured "a pre-eminence above all the
other productions of the human intellect."

The name of Flamsteed, First Astronomer Royal, must here be mentioned
as having supplied Newton with the accurate data required for
completing the theory.

The name of Edmund Halley, Second Astronomer Royal, must ever be held
in repute, not only for his own discoveries, but for the part he
played in urging Newton to commit to writing, and present to the Royal
Society, the results of his investigations. But for his friendly
insistence it is possible that the _Principia_ would never have
been written; and but for his generosity in supplying the means the
Royal Society could not have published the book.

[Illustration: DEATH MASK OF SIR ISAAC NEWTON.
Photographed specially for this work from the original, by kind
permission of the Royal Society, London.]

Sir Isaac Newton died in 1727, at the age of eighty-five.  His body
lay in state in the Jerusalem Chamber, and was buried in Westminster
Abbey.


FOOTNOTES:

[1] The writer inherited from his father (Professor J. D. Forbes) a
small box containing a bit of wood and a slip of paper, which had been
presented to him by Sir David Brewster. On the paper Sir David had
written these words: "If there be any truth in the story that Newton
was led to the theory of gravitation by the fall of an apple, this bit
of wood is probably a piece of the apple tree from which Newton saw
the apple fall. When I was on a pilgrimage to the house in which
Newton was born, I cut it off an ancient apple tree growing in his
garden." When lecturing in Glasgow, about 1875, the writer showed it
to his audience. The next morning, when removing his property from the
lecture table, he found that his precious relic had been stolen. It
would be interesting to know who has got it now!

[2] It must be noted that these words, in which the laws of
gravitation are always summarised in histories and text-books, do not
appear in the _Principia_; but, though they must have been composed by
some early commentator, it does not appear that their origin has been
traced. Nor does it appear that Newton ever extended the law beyond
the Solar System, and probably his caution would have led him to avoid
any statement of the kind until it should be proved.

With this exception the above statement of the law of universal
gravitation contains nothing that is not to be found in the
_Principia_; and the nearest approach to that statement occurs in the
Seventh Proposition of Book III.:--

Prop.: That gravitation occurs in all bodies, and that it is
proportional to the quantity of matter in each.

Cor. I.: The total attraction of gravitation on a planet arises, and
is composed, out of the attraction on the separate parts.

Cor. II.: The attraction on separate equal particles of a body is
reciprocally as the square of the distance from the particles.

[3] It is said that, when working out this final result, the
probability of its confirming that part of his theory which he had
reluctantly abandoned years before excited him so keenly that he was
forced to hand over his calculations to a friend, to be completed by
him.



8. NEWTON'S SUCCESSORS--HALLEY, EULER, LAGRANGE, LAPLACE, ETC.


Edmund Halley succeeded Flamsteed as Second Astronomer Royal in
1721. Although he did not contribute directly to the mathematical
proofs of Newton's theory, yet his name is closely associated with
some of its greatest successes.

He was the first to detect the acceleration of the moon's mean
motion. Hipparchus, having compared his own observations with those of
more ancient astronomers, supplied an accurate value of the moon's
mean motion in his time. Halley similarly deduced a value for modern
times, and found it sensibly greater.  He announced this in 1693, but
it was not until 1749 that Dunthorne used modern lunar tables to
compute a lunar eclipse observed in Babylon 721 B.C., another at
Alexandria 201 B.C., a solar eclipse observed by Theon 360 A.D., and
two later ones up to the tenth century.  He found that to explain
these eclipses Halley's suggestion must be adopted, the acceleration
being 10" in one century. In 1757 Lalande again fixed it at 10."

The Paris Academy, in 1770, offered their prize for an investigation
to see if this could be explained by the theory of gravitation. Euler
won the prize, but failed to explain the effect, and said: "It appears
to be established by indisputable evidence that the secular inequality
of the moon's mean motion cannot be produced by the forces of
gravitation."

The same subject was again proposed for a prize which was shared by
Lagrange [1] and Euler, neither finding a solution, while the latter
asserted the existence of a resisting medium in space.

Again, in 1774, the Academy submitted the same subject, a third time,
for the prize; and again Lagrange failed to detect a cause in
gravitation.

Laplace [2] now took the matter in hand. He tried the effect of a
non-instantaneous action of gravity, to no purpose. But in 1787 he
gave the true explanation.  The principal effect of the sun on the
moon's orbit is to diminish the earth's influence, thus lengthening
the period to a new value generally taken as constant. But Laplace's
calculations showed the new value to depend upon the excentricity of
the earth's orbit, which, according; to theory, has a periodical
variation of enormous period, and has been continually diminishing for
thousands of years. Thus the solar influence has been diminishing, and
the moon's mean motion increased. Laplace computed the amount at 10"
in one century, agreeing with observation. (Later on Adams showed that
Laplace's calculation was wrong, and that the value he found was too
large; so, part of the acceleration is now attributed by some
astronomers to a lengthening of the day by tidal friction.)

Another contribution by Halley to the verification of Newton's law was
made when he went to St. Helena to catalogue the southern stars. He
measured the change in length of the second's pendulum in different
latitudes due to the changes in gravity foretold by Newton.

Furthermore, he discovered the long inequality of Jupiter and Saturn,
whose period is 929 years. For an investigation of this also the
Academy of Sciences offered their prize. This led Euler to write a
valuable essay disclosing a new method of computing perturbations,
called the instantaneous ellipse with variable elements. The method
was much developed by Lagrange.

But again it was Laplace who solved the problem of the inequalities of
Jupiter and Saturn by the theory of gravitation, reducing the errors
of the tables from 20' down to 12", thus abolishing the use of
empirical corrections to the planetary tables, and providing another
glorious triumph for the law of gravitation.  As Laplace justly said:
"These inequalities appeared formerly to be inexplicable by the law of
gravitation--they now form one of its most striking proofs."

Let us take one more discovery of Halley, furnishing directly a new
triumph for the theory. He noticed that Newton ascribed parabolic
orbits to the comets which he studied, so that they come from
infinity, sweep round the sun, and go off to infinity for ever, after
having been visible a few weeks or months. He collected all the
reliable observations of comets he could find, to the number of
twenty-four, and computed their parabolic orbits by the rules laid
down by Newton. His object was to find out if any of them really
travelled in elongated ellipses, practically undistinguishable, in the
visible part of their paths, from parabolæ, in which case they would
be seen more than once. He found two old comets whose orbits, in shape
and position, resembled the orbit of a comet observed by himself in
1682.  Apian observed one in 1531; Kepler the other in 1607.  The
intervals between these appearances is seventy-five or seventy-six
years. He then examined and found old records of similar appearance in
1456, 1380, and 1305. It is true, he noticed, that the intervals
varied by a year and a-half, and the inclination of the orbit to the
ecliptic diminished with successive apparitions.  But he knew from
previous calculations that this might easily be due to planetary
perturbations. Finally, he arrived at the conclusion that all of these
comets were identical, travelling in an ellipse so elongated that the
part where the comet was seen seemed to be part of a parabolic
orbit. He then predicted its return at the end of 1758 or beginning of
1759, when he should be dead; but, as he said, "if it should return,
according to our prediction, about the year 1758, impartial posterity
will not refuse to acknowledge that this was first discovered by an
Englishman."[3] [_Synopsis Astronomiae Cometicae_, 1749.]

Once again Halley's suggestion became an inspiration for the
mathematical astronomer. Clairaut, assisted by Lalande, found that
Saturn would retard the comet 100 days, Jupiter 518 days, and
predicted its return to perihelion on April 13th, 1759. In his
communication to the French Academy, he said that a comet travelling
into such distant regions might be exposed to the influence of forces
totally unknown, and "even of some planet too far removed from the sun
to be ever perceived."

The excitement of astronomers towards the end of 1758 became intense;
and the honour of first catching sight of the traveller fell to an
amateur in Saxony, George Palitsch, on Christmas Day, 1758. It reached
perihelion on March 13th, 1759.

This fact was a startling confirmation of the Newtonian theory,
because it was a new kind of calculation of perturbations, and also it
added a new member to the solar system, and gave a prospect of adding
many more.

When Halley's comet reappeared in 1835, Pontecoulant's computations
for the date of perihelion passage were very exact, and afterwards he
showed that, with more exact values of the masses of Jupiter and
Saturn, his prediction was correct within two days, after an invisible
voyage of seventy-five years!

Hind afterwards searched out many old appearances of this comet, going
back to 11 B.C., and most of these have been identified as being
really Halley's comet by the calculations of Cowell and Cromellin[4]
(of Greenwich Observatory), who have also predicted its next
perihelion passage for April 8th to 16th, 1910, and have traced back
its history still farther, to 240 B.C.

Already, in November, 1907, the Astronomer Royal was trying to catch
it by the aid of photography.


FOOTNOTES:

[1] Born 1736; died 1813.

[2] Born 1749; died 1827.

[3] This sentence does not appear in the original memoir communicated
to the Royal Society, but was first published in a posthumous reprint.

[4] _R. A. S. Monthly Notices_, 1907-8.



9. DISCOVERY OF NEW PLANETS--HERSCHEL, PIAZZI, ADAMS, AND LE VERRIER.


It would be very interesting, but quite impossible in these pages, to
discuss all the exquisite researches of the mathematical astronomers,
and to inspire a reverence for the names connected with these
researches, which for two hundred years have been establishing the
universality of Newton's law. The lunar and planetary theories, the
beautiful theory of Jupiter's satellites, the figure of the earth, and
the tides, were mathematically treated by Maclaurin, D'Alembert,
Legendre, Clairaut, Euler, Lagrange, Laplace, Walmsley, Bailly,
Lalande, Delambre, Mayer, Hansen, Burchardt, Binet, Damoiseau, Plana,
Poisson, Gauss, Bessel, Bouvard, Airy, Ivory, Delaunay, Le Verrier,
Adams, and others of later date.

By passing over these important developments it is possible to trace
some of the steps in the crowning triumph of the Newtonian theory, by
which the planet Neptune was added to the known members of the solar
system by the independent researches of Professor J.C. Adams and of
M. Le Verrier, in 1846.

It will be best to introduce this subject by relating how the
eighteenth century increased the number of known planets, which was
then only six, including the earth.

On March 13th, 1781, Sir William Herschel was, as usual, engaged on
examining some small stars, and, noticing that one of them appeared to
be larger than the fixed stars, suspected that it might be a comet.
To test this he increased his magnifying power from 227 to 460 and
932, finding that, unlike the fixed stars near it, its definition was
impaired and its size increased.  This convinced him that the object
was a comet, and he was not surprised to find on succeeding nights
that the position was changed, the motion being in the ecliptic. He
gave the observations of five weeks to the Royal Society without a
suspicion that the object was a new planet.

For a long time people could not compute a satisfactory orbit for the
supposed comet, because it seemed to be near the perihelion, and no
comet had ever been observed with a perihelion distance from the sun
greater than four times the earth's distance. Lexell was the first to
suspect that this was a new planet eighteen times as far from the sun
as the earth is. In January, 1783, Laplace published the elliptic
elements. The discoverer of a planet has a right to name it, so
Herschel called it Georgium Sidus, after the king.  But Lalande urged
the adoption of the name Herschel.  Bode suggested Uranus, and this
was adopted. The new planet was found to rank in size next to Jupiter
and Saturn, being 4.3 times the diameter of the earth.

In 1787 Herschel discovered two satellites, both revolving in nearly
the same plane, inclined 80° to the ecliptic, and the motion of both
was retrograde.

In 1772, before Herschel's discovery, Bode[1] had discovered a curious
arbitrary law of planetary distances.  Opposite each planet's name
write the figure 4; and, in succession, add the numbers 0, 3, 6, 12,
24, 48, 96, etc., to the 4, always doubling the last numbers.  You
then get the planetary distances.

  Mercury, dist.-- 4  4 +   0 =   4
  Venus      "     7  4 +   3 =   7
  Earth      "    10  4 +   6 =  10
  Mars       "    15  4 +  12 =  16
   --                 4 +  24 =  28
  Jupiter  dist.  52  4 +  48 =  52
  Saturn     "    95  4 +  96 = 100
  (Uranus)   "   192  4 + 192 = 196
   --                 4 + 384 = 388

All the five planets, and the earth, fitted this rule, except that
there was a blank between Mars and Jupiter. When Uranus was
discovered, also fitting the rule, the conclusion was irresistible
that there is probably a planet between Mars and Jupiter. An
association of twenty-four astronomers was now formed in Germany to
search for the planet. Almost immediately afterwards the planet was
discovered, not by any member of the association, but by Piazzi, when
engaged upon his great catalogue of stars. On January 1st, 1801, he
observed a star which had changed its place the next night. Its motion
was retrograde till January 11th, direct after the 13th.  Piazzi fell
ill before he had enough observations for computing the orbit with
certainty, and the planet disappeared in the sun's rays. Gauss
published an approximate ephemeris of probable positions when the
planet should emerge from the sun's light. There was an exciting hunt,
and on December 31st (the day before its birthday) De Zach captured
the truant, and Piazzi christened it Ceres.


The mean distance from the sun was found to be 2.767, agreeing with
the 2.8 given by Bode's law. Its orbit was found to be inclined over
10° to the ecliptic, and its diameter was only 161 miles.

On March 28th, 1802, Olbers discovered a new seventh magnitude star,
which turned out to be a planet resembling Ceres. It was called
Pallas. Gauss found its orbit to be inclined 35° to the ecliptic, and
to cut the orbit of Ceres; whence Olbers considered that these might
be fragments of a broken-up planet. He then commenced a search for
other fragments. In 1804 Harding discovered Juno, and in 1807 Olbers
found Vesta. The next one was not discovered until 1845, from which
date asteroids, or minor planets (as these small planets are called),
have been found almost every year. They now number about 700.

It is impossible to give any idea of the interest with which the first
additions since prehistoric times to the planetary system were
received. All of those who showered congratulations upon the
discoverers regarded these discoveries in the light of rewards for
patient and continuous labours, the very highest rewards that could be
desired. And yet there remained still the most brilliant triumph of
all, the addition of another planet like Uranus, before it had ever
been seen, when the analysis of Adams and Le Verrier gave a final
proof of the powers of Newton's great law to explain any planetary
irregularity.

After Sir William Herschel discovered Uranus, in 1781, it was found
that astronomers had observed it on many previous occasions, mistaking
it for a fixed star of the sixth or seventh magnitude. Altogether,
nineteen observations of Uranus's position, from the time of
Flamsteed, in 1690, had been recorded.

In 1790 Delambre, using all these observations, prepared tables for
computing its position. These worked well enough for a time, but at
last the differences between the calculated and observed longitudes of
the planet became serious. In 1821 Bouvard undertook a revision of the
tables, but found it impossible to reconcile all the observations of
130 years (the period of revolution of Uranus is eighty-four years).
So he deliberately rejected the old ones, expressing the opinion that
the discrepancies might depend upon "some foreign and unperceived
cause which may have been acting upon the planet." In a few years the
errors even of these tables became intolerable. In 1835 the error of
longitude was 30"; in 1838, 50"; in 1841, 70"; and, by comparing the
errors derived from observations made before and after opposition, a
serious error of the distance (radius vector) became apparent.

In 1843 John Couch Adams came out Senior Wrangler at Cambridge, and
was free to undertake the research which as an undergraduate he had
set himself--to see whether the disturbances of Uranus could be
explained by assuming a certain orbit, and position in that orbit, of
a hypothetical planet even more distant than Uranus.  Such an
explanation had been suggested, but until 1843 no one had the boldness
to attack the problem.  Bessel had intended to try, but a fatal
illness overtook him.

Adams first recalculated all known causes of disturbance, using the
latest determinations of the planetary masses. Still the errors were
nearly as great as ever.  He could now, however, use these errors as
being actually due to the perturbations produced by the unknown
planet.

In 1844, assuming a circular orbit, and a mean distance agreeing with
Bode's law, he obtained a first approximation to the position of the
supposed planet.  He then asked Professor Challis, of Cambridge, to
procure the latest observations of Uranus from Greenwich, which Airy
immediately supplied. Then the whole work was recalculated from the
beginning, with more exactness, and assuming a smaller mean distance.

In September, 1845, he handed to Challis the elements of the
hypothetical planet, its mass, and its apparent position for September
30th, 1845. On September 22nd Challis wrote to Airy explaining the
matter, and declaring his belief in Adams's capabilities. When Adams
called on him Airy was away from home, but at the end of October,
1845, he called again, and left a paper with full particulars of his
results, which had, for the most part, reduced the discrepancies to
about 1". As a matter of fact, it has since been found that the
heliocentric place of the new planet then given was correct within
about 2°.

Airy wrote expressing his interest, and asked for particulars about
the radius vector. Adams did not then reply, as the answer to this
question could be seen to be satisfactory by looking at the data
already supplied.  He was a most unassuming man, and would not push
himself forward. He may have felt, after all the work he had done,
that Airy's very natural inquiry showed no proportionate desire to
search for the planet.  Anyway, the matter lay in embryo for nine
months.

Meanwhile, one of the ablest French astronomers, Le Verrier,
experienced in computing perturbations, was independently at work,
knowing nothing about Adams. He applied to his calculations every
possible refinement, and, considering the novelty of the problem, his
calculation was one of the most brilliant in the records of
astronomy. In criticism it has been said that these were exhibitions
of skill rather than helps to a solution of the particular problem,
and that, in claiming to find the elements of the orbit within certain
limits, he was claiming what was, under the circumstances, impossible,
as the result proved.

In June, 1846, Le Verrier announced, in the _Comptes Rendus de
l'Academie des Sciences_, that the longitude of the disturbing planet,
for January 1st, 1847, was 325, and that the probable error did not
exceed 10°.

This result agreed so well with Adams's (within 1°) that Airy urged
Challis to apply the splendid Northumberland equatoreal, at Cambridge,
to the search.  Challis, however, had already prepared an exhaustive
plan of attack which must in time settle the point.  His first work
was to observe, and make a catalogue, or chart, of all stars near
Adams's position.

On August 31st, 1846, Le Verrier published the concluding
part of his labours.

On September 18th, 1846, Le Verrier communicated his results to the
Astronomers at Berlin, and asked them to assist in searching for the
planet. By good luck Dr. Bremiker had just completed a star-chart of
the very part of the heavens including Le Verrier's position; thus
eliminating all of Challis's preliminary work. The letter was received
in Berlin on September 23rd; and the same evening Galle found the new
planet, of the eighth magnitude, the size of its disc agreeing with Le
Verrier's prediction, and the heliocentric longitude agreeing within
57'. By this time Challis had recorded, without reduction, the
observations of 3,150 stars, as a commencement for his search.  On
reducing these, he found a star, observed on August 12th, which was
not in the same place on July 30th. This was the planet, and he had
also observed it on August 4th.

The feeling of wonder, admiration, and enthusiasm aroused by this
intellectual triumph was overwhelming.  In the world of astronomy
reminders are met every day of the terrible limitations of human
reasoning powers; and every success that enables the mind's eye to see
a little more clearly the meaning of things has always been heartily
welcomed by those who have themselves been engaged in like
researches. But, since the publication of the _Principia_, in 1687,
there is probably no analytical success which has raised among
astronomers such a feeling of admiration and gratitude as when Adams
and Le Verrier showed the inequalities in Uranus's motion to mean that
an unknown planet was in a certain place in the heavens, where it was
found.

At the time there was an unpleasant display of international jealousy.
The British people thought that the earlier date of Adams's work, and
of the observation by Challis, entitled him to at least an equal share
of credit with Le Verrier. The French, on the other hand, who, on the
announcement of the discovery by Galle, glowed with pride in the new
proof of the great powers of their astronomer, Le Verrier, whose life
had a long record of successes in calculation, were incredulous on
being told that it had all been already done by a young man whom they
had never heard of.

These displays of jealousy have long since passed away, and there is
now universally an _entente cordiale_ that to each of these great men
belongs equally the merit of having so thoroughly calculated this
inverse problem of perturbations as to lead to the immediate discovery
of the unknown planet, since called Neptune.

It was soon found that the planet had been observed, and its position
recorded as a fixed star by Lalande, on May 8th and 10th, 1795.

Mr. Lassel, in the same year, 1846, with his two-feet reflector,
discovered a satellite, with retrograde motion, which gave the mass of
the planet about a twentieth of that of Jupiter.


FOOTNOTES:

[1] Bode's law, or something like it, had already been fore-shadowed
by Kepler and others, especially Titius (see _Monatliche
Correspondenz_, vol. vii., p. 72).




BOOK III. OBSERVATION



10. INSTRUMENTS OF PRECISION--STATE OF THE SOLAR SYSTEM.


Having now traced the progress of physical astronomy up to the time
when very striking proofs of the universality of the law of
gravitation convinced the most sceptical, it must still be borne in
mind that, while gravitation is certainly the principal force
governing the motions of the heavenly bodies, there may yet be a
resisting medium in space, and there may be electric and magnetic
forces to deal with. There may, further, be cases where the effects of
luminous radiative repulsion become apparent, and also Crookes'
vacuum-effects described as "radiant matter." Nor is it quite certain
that Laplace's proofs of the instantaneous propagation of gravity are
final.

And in the future, as in the past, Tycho Brahe's dictum must be
maintained, that all theory shall be preceded by accurate
observations. It is the pride of astronomers that their science stands
above all others in the accuracy of the facts observed, as well as in
the rigid logic of the mathematics used for interpreting these facts.

It is interesting to trace historically the invention of those
instruments of precision which have led to this result, and, without
entering on the details required in a practical handbook, to note the
guiding principles of construction in different ages.

It is very probable that the Chaldeans may have made spheres, like the
armillary sphere, for representing the poles of the heavens; and with
rings to show the ecliptic and zodiac, as well as the equinoctial and
solstitial colures; but we have no record. We only know that the tower
of Belus, on an eminence, was their observatory.  We have, however,
distinct records of two such spheres used by the Chinese about 2500
B.C.  Gnomons, or some kind of sundial, were used by the Egyptians and
others; and many of the ancient nations measured the obliquity of the
ecliptic by the shadows of a vertical column in summer and winter. The
natural horizon was the only instrument of precision used by those who
determined star positions by the directions of their risings and
settings; while in those days the clepsydra, or waterclock, was the
best instrument for comparing their times of rising and setting.

About 300 B.C. an observatory fitted with circular instruments for
star positions was set up at Alexandria, the then centre of
civilisation. We know almost nothing about the instruments used by
Hipparchus in preparing his star catalogues and his lunar and solar
tables; but the invention of the astrolabe is attributed to him.[1]

In more modern times Nuremberg became a centre of astronomical
culture. Waltherus, of that town, made really accurate observations of
star altitudes, and of the distances between stars; and in 1484
A.D. he used a kind of clock. Tycho Brahe tried these, but discarded
them as being inaccurate.

Tycho Brahe (1546-1601 A.D.) made great improvements in armillary
spheres, quadrants, sextants, and large celestial globes. With these
he measured the positions of stars, or the distance of a comet from
several known stars. He has left us full descriptions of them,
illustrated by excellent engravings. Previous to his time such
instruments were made of wood.  Tycho always used metal. He paid the
greatest attention to the stability of mounting, to the orientation of
his instruments, to the graduation of the arcs by the then new method
of transversals, and to the aperture sight used upon his
pointer. There were no telescopes in his day, and no pendulum
clocks. He recognised the fact that there must be instrumental
errors. He made these as small as was possible, measured their amount,
and corrected his observations.  His table of refractions enabled him
to abolish the error due to our atmosphere so far as it could affect
naked-eye observations. The azimuth circle of Tycho's largest quadrant
had a diameter of nine feet, and the quadrant a radius of six feet. He
introduced the mural quadrant for meridian observations.[2]

[Illustration: ANCIENT CHINESE INSTRUMENTS, Including quadrant, celestial
globe, and two armillae, in the Observatory at Peking. Photographed in
Peking by the author in 1875, and stolen by the Germans when the
Embassies were relieved by the allies in 1900.]

The French Jesuits at Peking, in the seventeenth century, helped the
Chinese in their astronomy. In 1875 the writer saw and photographed,
on that part of the wall of Peking used by the Mandarins as an
observatory, the six instruments handsomely designed by Father
Verbiest, copied from the instruments of Tycho Brahe, and embellished
with Chinese dragons and emblems cast on the supports. He also saw
there two old instruments (which he was told were Arabic) of date
1279, by Ko Show-King, astronomer to Koblai Khan, the grandson of
Chenghis Khan. One of these last is nearly identical with the armillae
of Tycho; and the other with his "armillae æquatoriæ maximæ," with
which he observed the comet of 1585, besides fixed stars and
planets.[3]

The discovery by Galileo of the isochronism of the pendulum, followed
by Huyghens's adaptation of that principle to clocks, has been one of
the greatest aids to accurate observation. About the same time an
equally beneficial step was the employment of the telescope as a
pointer; not the Galilean with concave eye-piece, but with a
magnifying glass to examine the focal image, at which also a fixed
mark could be placed.  Kepler was the first to suggest this. Gascoigne
was the first to use it. Huyghens used a metal strip of variable width
in the focus, as a micrometer to cover a planetary disc, and so to
measure the width covered by the planet. The Marquis Malvasia, in
1662, described the network of fine silver threads at right angles,
which he used in the focus, much as we do now.

In the hands of such a skilful man as Tycho Brahe, the old open
sights, even without clocks, served their purpose sufficiently well to
enable Kepler to discover the true theory of the solar system. But
telescopic sights and clocks were required for proving some of
Newton's theories of planetary perturbations. Picard's observations at
Paris from 1667 onwards seem to embody the first use of the telescope
as a pointer. He was also the first to introduce the use of Huyghens's
clocks for observing the right ascension of stars.  Olaus Romer was
born at Copenhagen in 1644. In 1675, by careful study of the times of
eclipses of Jupiter's satellites, he discovered that light took time
to traverse space. Its velocity is 186,000 miles per second. In 1681
he took up his duties as astronomer at Copenhagen, and built the first
transit circle on a window-sill of his house. The iron axis was five
feet long and one and a-half inches thick, and the telescope was fixed
near one end with a counterpoise. The telescope-tube was a double
cone, to prevent flexure. Three horizontal and three vertical wires
were used in the focus. These were illuminated by a speculum, near the
object-glass, reflecting the light from a lantern placed over the
axis, the upper part of the telescope-tube being partly cut away to
admit the light. A divided circle, with pointer and reading
microscope, was provided for reading the declination. He realised the
superiority of a circle with graduations over a much larger
quadrant. The collimation error was found by reversing the instrument
and using a terrestrial mark, the azimuth error by star observations.
The time was expressed in fractions of a second. He also constructed a
telescope with equatoreal mounting, to follow a star by one axial
motion. In 1728 his instruments and observation records were destroyed
by fire.

Hevelius had introduced the vernier and tangent screw in his
measurement of arc graduations. His observatory and records were burnt
to the ground in 1679. Though an old man, he started afresh, and left
behind him a catalogue of 1,500 stars.

Flamsteed began his duties at Greenwich Observatory, as first
Astronomer Royal, in 1676, with very poor instruments. In 1683 he put
up a mural arc of 140°, and in 1689 a better one, seventy-nine inches
radius.  He conducted his measurements with great skill, and
introduced new methods to attain accuracy, using certain stars for
determining the errors of his instruments; and he always reduced his
observations to a form in which they could be readily used. He
introduced new methods for determining the position of the equinox and
the right ascension of a fundamental star.  He produced a catalogue of
2,935 stars. He supplied Sir Isaac Newton with results of observation
required in his theoretical calculations. He died in 1719.

Halley succeeded Flamsteed to find that the whole place had been
gutted by the latter's executors. In 1721 he got a transit instrument,
and in 1726 a mural quadrant by Graham. His successor in 1742,
Bradley, replaced this by a fine brass quadrant, eight feet radius, by
Bird; and Bradley's zenith sector was purchased for the observatory.
An instrument like this, specially designed for zenith stars, is
capable of greater rigidity than a more universal instrument; and
there is no trouble with refraction in the zenith. For these reasons
Bradley had set up this instrument at Kew, to attempt the proof of the
earth's motion by observing the annual parallax of stars. He certainly
found an annual variation of zenith distance, but not at the times of
year required by the parallax. This led him to the discovery of the
"aberration" of light and of nutation. Bradley has been described as
the founder of the modern system of accurate observation. He died in
1762, leaving behind him thirteen folio volumes of valuable but
unreduced observations. Those relating to the stars were reduced by
Bessel and published in 1818, at Königsberg, in his well-known
standard work, _Fundamenta Astronomiae_. In it are results showing the
laws of refraction, with tables of its amount, the maximum value of
aberration, and other constants.

Bradley was succeeded by Bliss, and he by Maskelyne (1765), who
carried on excellent work, and laid the foundations of the Nautical
Almanac (1767).  Just before his death he induced the Government to
replace Bird's quadrant by a fine new mural _circle_, six feet in
diameter, by Troughton, the divisions being read off by microscopes
fixed on piers opposite to the divided circle. In this instrument the
micrometer screw, with a divided circle for turning it, was applied
for bringing the micrometer wire actually in line with a division on
the circle--a plan which is still always adopted.

Pond succeeded Maskelyne in 1811, and was the first to use this
instrument. From now onwards the places of stars were referred to the
pole, not to the zenith; the zero being obtained from measures on
circumpolar stars. Standard stars were used for giving the clock
error. In 1816 a new transit instrument, by Troughton, was added, and
from this date the Greenwich star places have maintained the very
highest accuracy.

George Biddell Airy, Seventh Astronomer Royal,[4] commenced his
Greenwich labours in 1835. His first and greatest reformation in the
work of the observatory was one he had already established at
Cambridge, and is now universally adopted. He held that an observation
is not completed until it has been reduced to a useful form; and in
the case of the sun, moon, and planets these results were, in every
case, compared with the tables, and the tabular error printed.

Airy was firmly impressed with the object for which Charles II. had
wisely founded the observatory in connection with navigation, and for
observations of the moon. Whenever a meridian transit of the moon
could be observed this was done. But, even so, there are periods in
the month when the moon is too near the sun for a transit to be well
observed. Also weather interferes with many meridian observations. To
render the lunar observations more continuous, Airy employed
Troughton's successor, James Simms, in conjunction with the engineers,
Ransome and May, to construct an altazimuth with three-foot circles,
and a five-foot telescope, in 1847. The result was that the number of
lunar observations was immediately increased threefold, many of them
being in a part of the moon's orbit which had previously been bare of
observations. From that date the Greenwich lunar observations have
been a model and a standard for the whole world.

Airy also undertook to superintend the reduction of all Greenwich
lunar observations from 1750 to 1830.  The value of this laborious
work, which was completed in 1848, cannot be over-estimated.

The demands of astronomy, especially in regard to small minor planets,
required a transit instrument and mural circle with a more powerful
telescope. Airy combined the functions of both, and employed the same
constructors as before to make a _transit-circle_ with a telescope of
eleven and a-half feet focus and a circle of six-feet diameter, the
object-glass being eight inches in diameter.

Airy, like Bradley, was impressed with the advantage of employing
stars in the zenith for determining the fundamental constants of
astronomy. He devised a _reflex zenith tube_, in which the zenith
point was determined by reflection from a surface of mercury. The
design was so simple, and seemed so perfect, that great expectations
were entertained. But unaccountable variations comparable with those
of the transit circle appeared, and the instrument was put out of use
until 1903, when the present Astronomer Royal noticed that the
irregularities could be allowed for, being due to that remarkable
variation in the position of the earth's axis included in circles of
about six yards diameter at the north and south poles, discovered at
the end of the nineteenth century. The instrument is now being used
for investigating these variations; and in the year 1907 as many as
1,545 observations of stars were made with the reflex zenith tube.

In connection with zenith telescopes it must be stated that Respighi,
at the Capitol Observatory at Rome, made use of a deep well with a
level mercury surface at the bottom and a telescope at the top
pointing downwards, which the writer saw in 1871. The reflection of
the micrometer wires and of a star very near the zenith (but not quite
in the zenith) can be observed together.  His mercury trough was a
circular plane surface with a shallow edge to retain the mercury. The
surface quickly came to rest after disturbance by street traffic.

Sir W. M. H. Christie, Eighth Astronomer Royal, took up his duties in
that capacity in 1881. Besides a larger altazimuth that he erected in
1898, he has widened the field of operations at Greenwich by the
extensive use of photography and the establishment of large
equatoreals.  From the point of view of instruments of precision, one
of the most important new features is the astrographic equatoreal, set
up in 1892 and used for the Greenwich section of the great
astrographic chart just completed. Photography has come to be of use,
not only for depicting the sun and moon, comets and nebulae, but also
to obtain accurate relative positions of neighbouring stars; to pick
up objects that are invisible in any telescope; and, most of all
perhaps, in fixing the positions of faint satellites. Thus Saturn's
distant satellite, Phoebe, and the sixth and seventh satellites of
Jupiter, have been followed regularly in their courses at Greenwich
ever since their discovery with the thirty-inch reflector (erected in
1897); and while doing so Mr. Melotte made, in 1908, the splendid
discovery on some of the photographic plates of an eighth satellite of
Jupiter, at an enormous distance from the planet. From observations in
the early part of 1908, over a limited arc of its orbit, before
Jupiter approached the sun, Mr. Cowell computed a retrograde orbit and
calculated the future positions of this satellite, which enabled
Mr. Melotte to find it again in the autumn--a great triumph both of
calculation and of photographic observation. This satellite has never
been seen, and has been photographed only at Greenwich, Heidelberg,
and the Lick Observatory.

Greenwich Observatory has been here selected for tracing the progress
of accurate measurement. But there is one instrument of great value,
the heliometer, which is not used at Greenwich. This serves the
purpose of a double image micrometer, and is made by dividing the
object-glass of a telescope along a diameter. Each half is mounted so
as to slide a distance of several inches each way on an arc whose
centre is the focus. The amount of the movement can be accurately
read. Thus two fields of view overlap, and the adjustment is made to
bring an image of one star over that of another star, and then to do
the same by a displacement in the opposite direction. The total
movement of the half-object glass is double the distance between the
star images in the focal plane. Such an instrument has long been
established at Oxford, and German astronomers have made great use of
it. But in the hands of Sir David Gill (late His Majesty's Astronomer
at the Cape of Good Hope), and especially in his great researches on
Solar and on Stellar parallax, it has been recognised as an instrument
of the very highest accuracy, measuring the distance between stars
correctly to less than a tenth of a second of arc.

The superiority of the heliometer over all other devices (except
photography) for measuring small angles has been specially brought
into prominence by Sir David Gill's researches on the distance of the
sun--_i.e.,_ the scale of the solar system. A measurement of the
distance of any planet fixes the scale, and, as Venus approaches the
earth most nearly of all the planets, it used to be supposed that a
Transit of Venus offered the best opportunity for such measurement,
especially as it was thought that, as Venus entered on the solar disc,
the sweep of light round the dark disc of Venus would enable a very
precise observation to be made.  The Transit of Venus in 1874, in
which the present writer assisted, overthrew this delusion.

In 1877 Sir David Gill used Lord Crawford's heliometer at the Island
of Ascension to measure the parallax of Mars in opposition, and found
the sun's distance 93,080,000 miles. He considered that, while the
superiority of the heliometer had been proved, the results would be
still better with the points of light shown by minor planets rather
than with the disc of Mars.

In 1888-9, at the Cape, he observed the minor planets Iris, Victoria,
and Sappho, and secured the co-operation of four other heliometers.
His final result was 92,870,000 miles, the parallax being 8",802
(_Cape Obs_., Vol. VI.).

So delicate were these measures that Gill detected a minute periodic
error of theory of twenty-seven days, owing to a periodically
erroneous position of the centre of gravity of the earth and moon to
which the position of the observer was referred. This led him to
correct the mass of the moon, and to fix its ratio to the earth's mass
= 0.012240.

Another method of getting the distance from the sun is to measure the
velocity of the earth's orbital motion, giving the circumference
traversed in a year, and so the radius of the orbit. This has been
done by comparing observation and experiment. The aberration of light
is an angle 20" 48, giving the ratio of the earth's velocity to the
velocity of light. The velocity of light is 186,000 miles a second;
whence the distance to the sun is 92,780,000 miles. There seems,
however, to be some uncertainty about the true value of the
aberration, any determination of which is subject to irregularities
due to the "seasonal errors." The velocity of light was experimentally
found, in 1862, by Fizeau and Foucault, each using an independent
method. These methods have been developed, and new values found, by
Cornu, Michaelson, Newcomb, and the present writer.

Quite lately Halm, at the Cape of Good Hope, measured
spectroscopically the velocity of the earth to and from a star by
observations taken six months apart.  Thence he obtained an accurate
value of the sun's distance.[5]

But the remarkably erratic minor planet, Eros, discovered by Witte in
1898, approaches the earth within 15,000,000 miles at rare intervals,
and, with the aid of photography, will certainly give us the best
result. A large number of observatories combined to observe the
opposition of 1900. Their results are not yet completely reduced, but
the best value deduced so far for the parallax[6] is 8".807 ±
0".0028.[7]


FOOTNOTES:

[1] In 1480 Martin Behaim, of Nuremberg, produced his _astrolabe_ for
measuring the latitude, by observation of the sun, at sea. It
consisted of a graduated metal circle, suspended by a ring which was
passed over the thumb, and hung vertically. A pointer was fixed to a
pin at the centre. This arm, called the _alhidada_, worked round the
graduated circle, and was pointed to the sun.  The altitude of the sun
was thus determined, and, by help of solar tables, the latitude could
be found from observations made at apparent noon.

[2] See illustration on p. 76.

[3] See Dreyer's article on these instruments in _Copernicus_,
Vol. I. They were stolen by the Germans after the relief of the
Embassies, in 1900. The best description of these instruments is
probably that contained in an interesting volume, which may be seen in
the library of the R. A. S., entitled _Chinese Researches_, by
Alexander Wyllie (Shanghai, 1897).

[4] Sir George Airy was very jealous of this honourable title. He
rightly held that there is only one Astronomer Royal at a time, as
there is only one Mikado, one Dalai Lama. He said that His Majesty's
Astronomer at the Cape of Good Hope, His Majesty's Astronomer for
Scotland, and His Majesty's Astronomer for Ireland are not called
Astronomers Royal.

[5] _Annals of the Cape Observatory_, vol. x., part 3.

[6] The parallax of the sun is the angle subtended by the earth's
radius at the sun's distance.

[7] A. R. Hinks, R.A.S.; _Monthly Notices_, June, 1909.



11. HISTORY OF THE TELESCOPE


Accounts of wonderful optical experiments by Roger Bacon (who died in
1292), and in the sixteenth century by Digges, Baptista Porta, and
Antonio de Dominis (Grant, _Hist. Ph. Ast_.), have led some to
suppose that they invented the telescope. The writer considers that it
is more likely that these notes refer to a kind of _camera
obscura_, in which a lens throws an inverted image of a landscape
on the wall.

The first telescopes were made in Holland, the originator being either
Henry Lipperhey,[1] Zacharias Jansen, or James Metius, and the date
1608 or earlier.

In 1609 Galileo, being in Venice, heard of the invention, went home
and worked out the theory, and made a similar telescope. These
telescopes were all made with a convex object-glass and a concave
eye-lens, and this type is spoken of as the Galilean telescope. Its
defects are that it has no real focus where cross-wires can be placed,
and that the field of view is very small.  Kepler suggested the convex
eye-lens in 1611, and Scheiner claimed to have used one in 1617. But
it was Huyghens who really introduced them. In the seventeenth century
telescopes were made of great length, going up to 300 feet. Huyghens
also invented the compound eye-piece that bears his name, made of two
convex lenses to diminish spherical aberration.

But the defects of colour remained, although their cause was unknown
until Newton carried out his experiments on dispersion and the solar
spectrum. To overcome the spherical aberration James Gregory,[2] of
Aberdeen and Edinburgh, in 1663, in his _Optica Promota_,
proposed a reflecting speculum of parabolic form. But it was Newton,
about 1666, who first made a reflecting telescope; and he did it with
the object of avoiding colour dispersion.

Some time elapsed before reflectors were much used.  Pound and Bradley
used one presented to the Royal Society by Hadley in 1723. Hawksbee,
Bradley, and Molyneaux made some. But James Short, of Edinburgh, made
many excellent Gregorian reflectors from 1732 till his death in 1768.

Newton's trouble with refractors, chromatic aberration, remained
insurmountable until John Dollond (born 1706, died 1761), after many
experiments, found out how to make an achromatic lens out of two
lenses--one of crown glass, the other of flint glass--to destroy the
colour, in a way originally suggested by Euler. He soon acquired a
great reputation for his telescopes of moderate size; but there was a
difficulty in making flint-glass lenses of large size. The first
actual inventor and constructor of an achromatic telescope was Chester
Moor Hall, who was not in trade, and did not patent it.  Towards the
close of the eighteenth century a Swiss named Guinand at last
succeeded in producing larger flint-glass discs free from
striae. Frauenhofer, of Munich, took him up in 1805, and soon
produced, among others, Struve's Dorpat refractor of 9.9 inches
diameter and 13.5 feet focal length, and another, of 12 inches
diameter and 18 feet focal length, for Lamont, of Munich.

In the nineteenth century gigantic _reflectors_ have been
made. Lassel's 2-foot reflector, made by himself, did much good work,
and discovered four new satellites.  But Lord Rosse's 6-foot
reflector, 54 feet focal length, constructed in 1845, is still the
largest ever made.  The imperfections of our atmosphere are against
the use of such large apertures, unless it be on high mountains.
During the last half century excellent specula have been made of
silvered glass, and Dr.  Common's 5-foot speculum (removed, since his
death, to Harvard) has done excellent work. Then there are the 5-foot
Yerkes reflector at Chicago, and the 4-foot by Grubb at Melbourne.

Passing now from these large reflectors to refractors, further
improvements have been made in the manufacture of glass by Chance, of
Birmingham, Feil and Mantois, of Paris, and Schott, of Jena; while
specialists in grinding lenses, like Alvan Clark, of the U.S.A., and
others, have produced many large refractors.

Cooke, of York, made an object-glass, 25-inch diameter, for Newall, of
Gateshead, which has done splendid work at Cambridge. We have the
Washington 26-inch by Clark, the Vienna 27-inch by Grubb, the Nice
291/2-inch by Gautier, the Pulkowa 30-inch by Clark. Then there was
the sensation of Clark's 36-inch for the Lick Observatory in
California, and finally his _tour de force_, the Yerkes 40-inch
refractor, for Chicago.

At Greenwich there is the 28-inch photographic refractor, and the
Thompson equatoreal by Grubb, carrying both the 26-inch photographic
refractor and the 30-inch reflector. At the Cape of Good Hope we find
Mr. Frank McClean's 24-inch refractor, with an object-glass prism for
spectroscopic work.

It would be out of place to describe here the practical adjuncts of a
modern equatoreal--the adjustments for pointing it, the clock for
driving it, the position-micrometer and various eye-pieces, the
photographic and spectroscopic attachments, the revolving domes,
observing seats, and rising floors and different forms of mounting,
the siderostats and coelostats, and other convenient adjuncts, besides
the registering chronograph and numerous facilities for aiding
observation.  On each of these a chapter might be written; but the
most important part of the whole outfit is the man behind the
telescope, and it is with him that a history is more especially
concerned.


SPECTROSCOPE.

Since the invention of the telescope no discovery has given so great
an impetus to astronomical physics as the spectroscope; and in giving
us information about the systems of stars and their proper motions it
rivals the telescope.

Frauenhofer, at the beginning of the nineteenth century, while
applying Dollond's discovery to make large achromatic telescopes,
studied the dispersion of light by a prism. Admitting the light of the
sun through a narrow slit in a window-shutter, an inverted image of
the slit can be thrown, by a lens of suitable focal length, on the
wall opposite. If a wedge or prism of glass be interposed, the image
is deflected to one side; but, as Newton had shown, the images formed
by the different colours of which white light is composed are
deflected to different extents--the violet most, the red least. The
number of colours forming images is so numerous as to form a
continuous spectrum on the wall with all the colours--red, orange,
yellow, green, blue, indigo, and violet. But Frauenhofer found with a
narrow slit, well focussed by the lens, that some colours were missing
in the white light of the sun, and these were shown by dark lines
across the spectrum.  These are the Frauenhofer lines, some of which
he named by the letters of the alphabet. The D line is a very marked
one in the yellow. These dark lines in the solar spectrum had already
been observed by Wollaston. [3]

On examining artificial lights it was found that incandescent solids
and liquids (including the carbon glowing in a white gas flame) give
continuous spectra; gases, except under enormous pressure, give bright
lines. If sodium or common salt be thrown on the colourless flame of a
spirit lamp, it gives it a yellow colour, and its spectrum is a bright
yellow line agreeing in position with line D of the solar spectrum.

In 1832 Sir David Brewster found some of the solar black lines
increased in strength towards sunset, and attributed them to
absorption in the earth's atmosphere.  He suggested that the others
were due to absorption in the sun's atmosphere. Thereupon Professor
J. D.  Forbes pointed out that during a nearly total eclipse the lines
ought to be strengthened in the same way; as that part of the sun's
light, coming from its edge, passes through a great distance in the
sun's atmosphere.  He tried this with the annular eclipse of 1836,
with a negative result which has never been accounted for, and which
seemed to condemn Brewster's view.

In 1859 Kirchoff, on repeating Frauenhofer's experiment, found that,
if a spirit lamp with salt in the flame were placed in the path of the
light, the black D line is intensified. He also found that, if he used
a limelight instead of the sunlight and passed it through the flame
with salt, the spectrum showed the D line black; or the vapour of
sodium absorbs the same light that it radiates. This proved to him the
existence of sodium in the sun's atmosphere.[4] Iron, calcium, and
other elements were soon detected in the same way.

Extensive laboratory researches (still incomplete) have been carried
out to catalogue (according to their wave-length on the undulatory
theory of light) all the lines of each chemical element, under all
conditions of temperature and pressure. At the same time, all the
lines have been catalogued in the light of the sun and the brighter of
the stars.

Another method of obtaining spectra had long been known, by
transmission through, or reflection from, a grating of equidistant
lines ruled upon glass or metal.  H. A. Rowland developed the art of
constructing these gratings, which requires great technical skill, and
for this astronomers owe him a debt of gratitude.

In 1842 Doppler[5] proved that the colour of a luminous body, like the
pitch or note of a sounding body, must be changed by velocity of
approach or recession. Everyone has noticed on a railway that, on
meeting a locomotive whistling, the note is lowered after the engine
has passed. The pitch of a sound or the colour of a light depends on
the number of waves striking the ear or eye in a second. This number
is increased by approach and lowered by recession.

Thus, by comparing the spectrum of a star alongside a spectrum of
hydrogen, we may see all the lines, and be sure that there is hydrogen
in the star; yet the lines in the star-spectrum may be all slightly
displaced to one side of the lines of the comparison spectrum. If
towards the violet end, it means mutual approach of the star and
earth; if to the red end, it means recession. The displacement of
lines does not tell us whether the motion is in the star, the earth,
or both.  The displacement of the lines being measured, we can
calculate the rate of approach or recession in miles per second.

In 1868 Huggins[6] succeeded in thus measuring the velocities of stars
in the direction of the line of sight.

In 1873 Vogel[7] compared the spectra of the sun's East (approaching)
limb and West (receding) limb, and the displacement of lines endorsed
the theory. This last observation was suggested by Zöllner.


FOOTNOTES:

[1] In the _Encyclopaedia Britannica_, article "Telescope," and in
Grant's _Physical Astronomy_, good reasons are given for awarding the
honour to Lipperhey.

[2] Will the indulgent reader excuse an anecdote which may encourage
some workers who may have found their mathematics defective through
want of use? James Gregory's nephew David had a heap of MS. notes by
Newton. These descended to a Miss Gregory, of Edinburgh, who handed
them to the present writer, when an undergraduate at Cambridge, to
examine. After perusal, he lent them to his kindest of friends,
J. C. Adams (the discoverer of Neptune), for his opinion. Adams's
final verdict was: "I fear they are of no value. It is pretty evident
that, when he wrote these notes, _Newton's mathematics were a little
rusty_."

[3] _R. S. Phil. Trans_.

[4] The experiment had been made before by one who did not understand
its meaning;. But Sir George G. Stokes had already given verbally the
true explanation of Frauenhofer lines.

[5] _Abh. d. Kön. Böhm. d. Wiss_., Bd. ii., 1841-42, p. 467. See
also Fizeau in the _Ann. de Chem. et de Phys_., 1870, p. 211.

[6] _R. S. Phil. Trans_., 1868.

[7] _Ast. Nach_., No. 1, 864.




BOOK IV. THE PHYSICAL PERIOD


We have seen how the theory of the solar system was slowly developed
by the constant efforts of the human mind to find out what are the
rules of cause and effect by which our conception of the present
universe and its development seems to be bound. In the primitive ages
a mere record of events in the heavens and on the earth gave the only
hope of detecting those uniform sequences from which to derive rules
or laws of cause and effect upon which to rely. Then came the
geometrical age, in which rules were sought by which to predict the
movements of heavenly bodies. Later, when the relation of the sun to
the courses of the planets was established, the sun came to be looked
upon as a cause; and finally, early in the seventeenth century, for
the first time in history, it began to be recognised that the laws of
dynamics, exactly as they had been established for our own terrestrial
world, hold good, with the same rigid invariability, at least as far
as the limits of the solar system.

Throughout this evolution of thought and conjecture there were two
types of astronomers--those who supplied the facts, and those who
supplied the interpretation through the logic of mathematics. So
Ptolemy was dependent upon Hipparchus, Kepler on Tycho Brahe, and
Newton in much of his work upon Flamsteed.

When Galileo directed his telescope to the heavens, when Secchi and
Huggins studied the chemistry of the stars by means of the
spectroscope, and when Warren De la Rue set up a photoheliograph at
Kew, we see that a progress in the same direction as before, in the
evolution of our conception of the universe, was being made. Without
definite expression at any particular date, it came to be an accepted
fact that not only do earthly dynamics apply to the heavenly bodies,
but that the laws we find established here, in geology, in chemistry,
and in the laws of heat, may be extended with confidence to the
heavenly bodies. Hence arose the branch of astronomy called
astronomical physics, a science which claims a large portion of the
work of the telescope, spectroscope, and photography. In this new
development it is more than ever essential to follow the dictum of
Tycho Brahe--not to make theories until all the necessary facts are
obtained. The great astronomers of to-day still hold to Sir Isaac
Newton's declaration, "Hypotheses non fingo." Each one may have his
suspicions of a theory to guide him in a course of observation, and
may call it a working hypothesis.  But the cautious astronomer does
not proclaim these to the world; and the historian is certainly not
justified in including in his record those vague speculations founded
on incomplete data which may be demolished to-morrow, and which,
however attractive they may be, often do more harm than good to the
progress of true science.  Meanwhile the accumulation of facts has
been prodigious, and the revelations of the telescope and spectroscope
entrancing.



12. THE SUN.


One of Galileo's most striking discoveries, when he pointed his
telescope to the heavenly bodies, was that of the irregularly shaped
spots on the sun, with the dark central _umbra_ and the less
dark, but more extensive, _penumbra_ surrounding it, sometimes
with several umbrae in one penumbra. He has left us many drawings of
these spots, and he fixed their period of rotation as a lunar month.

[Illustration: SOLAR SURFACE, As Photographed at the Royal
Observatory, Greenwich, showing sun-spots with umbrae, penumbrae, and
faculae.]

It is not certain whether Galileo, Fabricius, or Schemer was the first
to see the spots. They all did good work. The spots were found to be
ever varying in size and shape. Sometimes, when a spot disappears at
the western limb of the sun, it is never seen again.  In other cases,
after a fortnight, it reappears at the eastern limb. The faculae, or
bright areas, which are seen all over the sun's surface, but specially
in the neighbourhood of spots, and most distinctly near the sun's
edge, were discovered by Galileo. A high telescopic power resolves
their structure into an appearance like willow-leaves, or rice-grains,
fairly uniform in size, and more marked than on other parts of the
sun's surface.

Speculations as to the cause of sun-spots have never ceased from
Galileo's time to ours. He supposed them to be clouds. Scheiner[1]
said they were the indications of tumultuous movements occasionally
agitating the ocean of liquid fire of which he supposed the sun to be
composed.

A. Wilson, of Glasgow, in 1769,[2] noticed a movement of the umbra
relative to the penumbra in the transit of the spot over the sun's
surface; exactly as if the spot were a hollow, with a black base and
grey shelving sides. This was generally accepted, but later
investigations have contradicted its universality. Regarding the cause
of these hollows, Wilson said:--

  Whether their first production and subsequent numberless changes
  depend upon the eructation of elastic vapours from below, or upon
  eddies or whirlpools commencing at the surface, or upon the
  dissolving of the luminous matter in the solar atmosphere, as clouds
  are melted and again given out by our air; or, if the reader
  pleases, upon the annihilation and reproduction of parts of this
  resplendent covering, is left for theory to guess at.[3]

Ever since that date theory has been guessing at it.  The solar
astronomer is still applying all the instruments of modern research to
find out which of these suppositions, or what modification of any of
them, is nearest the truth. The obstacle--one that is perhaps fatal to
a real theory--lies in the impossibility of reproducing comparative
experiments in our laboratories or in our atmosphere.

Sir William Herschel propounded an explanation of Wilson's observation
which received much notice, but which, out of respect for his memory,
is not now described, as it violated the elementary laws of heat.

Sir John Herschel noticed that the spots are mostly confined to two
zones extending to about 35° on each side of the equator, and that a
zone of equatoreal calms is free from spots. But it was
R. C. Carrington[4] who, by his continuous observations at Redhill, in
Surrey, established the remarkable fact that, while the rotation
period in the highest latitudes, 50°, where spots are seen, is
twenty-seven-and-a-half days, near the equator the period is only
twenty-five days. His splendid volume of observations of the sun led
to much new information about the average distribution of spots at
different epochs.

Schwabe, of Dessau, began in 1826 to study the solar surface, and,
after many years of work, arrived at a law of frequency which has been
more fruitful of results than any discovery in solar physics.[5] In
1843 he announced a decennial period of maxima and minima of sun-spot
displays. In 1851 it was generally accepted, and, although a period of
eleven years has been found to be more exact, all later observations,
besides the earlier ones which have been hunted up for the purpose, go
to establish a true periodicity in the number of sun-spots. But quite
lately Schuster[6] has given reasons for admitting a number of
co-existent periods, of which the eleven-year period was predominant
in the nineteenth century.

In 1851 Lament, a Scotchman at Munich, found a decennial period in the
daily range of magnetic declination.  In 1852 Sir Edward Sabine
announced a similar period in the number of "magnetic storms"
affecting all of the three magnetic elements--declination, dip, and
intensity. Australian and Canadian observations both showed the
decennial period in all three elements. Wolf, of Zurich, and Gauthier,
of Geneva, each independently arrived at the same conclusion.

It took many years before this coincidence was accepted as certainly
more than an accident by the old-fashioned astronomers, who want rigid
proof for every new theory. But the last doubts have long vanished,
and a connection has been further traced between violent outbursts of
solar activity and simultaneous magnetic storms.

The frequency of the Aurora Borealis was found by Wolf to follow the
same period. In fact, it is closely allied in its cause to terrestrial
magnetism. Wolf also collected old observations tracing the
periodicity of sun-spots back to about 1700 A.D.

Spoerer deduced a law of dependence of the average latitude of
sun-spots on the phase of the sun-spot period.

All modern total solar eclipse observations seem to show that the
shape of the luminous corona surrounding the moon at the moment of
totality has a special distinct character during the time of a
sun-spot maximum, and another, totally different, during a sun-spot
minimum.

A suspicion is entertained that the total quantity of heat received by
the earth from the sun is subject to the same period. This would have
far-reaching effects on storms, harvests, vintages, floods, and
droughts; but it is not safe to draw conclusions of this kind except
from a very long period of observations.

Solar photography has deprived astronomers of the type of Carrington
of the delight in devoting a life's work to collecting data. It has
now become part of the routine work of an observatory.

In 1845 Foucault and Fizeau took a daguerreotype photograph of the
sun. In 1850 Bond produced one of the moon of great beauty, Draper
having made some attempts at an even earlier date. But astronomical
photography really owes its beginning to De la Rue, who used the
collodion process for the moon in 1853, and constructed the Kew
photoheliograph in 1857, from which date these instruments have been
multiplied, and have given us an accurate record of the sun's surface.
Gelatine dry plates were first used by Huggins in 1876.

It is noteworthy that from the outset De la Rue recognised the value
of stereoscopic vision, which is now known to be of supreme
accuracy. In 1853 he combined pairs of photographs of the moon in the
same phase, but under different conditions regarding libration,
showing the moon from slightly different points of view.  These in the
stereoscope exhibited all the relief resulting from binocular vision,
and looked like a solid globe.  In 1860 he used successive photographs
of the total solar eclipse stereoscopically, to prove that the red
prominences belong to the sun, and not to the moon.  In 1861 he
similarly combined two photographs of a sun-spot, the perspective
effect showing the umbra like a floor at the bottom of a hollow
penumbra; and in one case the faculæ were discovered to be sailing
over a spot apparently at some considerable height.  These appearances
may be partly due to a proper motion; but, so far as it went, this was
a beautiful confirmation of Wilson's discovery. Hewlett, however, in
1894, after thirty years of work, showed that the spots are not always
depressions, being very subject to disturbance.

The Kew photographs [7] contributed a vast amount of information about
sun-spots, and they showed that the faculæ generally follow the spots
in their rotation round the sun.

The constitution of the sun's photosphere, the layer which is the
principal light-source on the sun, has always been a subject of great
interest; and much was done by men with exceptionally keen eyesight,
like Mr. Dawes. But it was a difficult subject, owing to the rapidity
of the changes in appearance of the so-called rice-grains, about 1" in
diameter. The rapid transformations and circulations of these
rice-grains, if thoroughly studied, might lead to a much better
knowledge of solar physics. This seemed almost hopeless, as it was
found impossible to identify any "rice-grain" in the turmoil after a
few minutes. But M.  Hansky, of Pulkowa (whose recent death is
deplored), introduced successfully a scheme of photography, which
might almost be called a solar cinematograph. He took photographs of
the sun at intervals of fifteen or thirty seconds, and then enlarged
selected portions of these two hundred times, giving a picture
corresponding to a solar disc of six metres diameter. In these
enlarged pictures he was able to trace the movements, and changes of
shape and brightness, of individual rice-grains. Some granules become
larger or smaller. Some seem to rise out of a mist, as it were, and to
become clearer.  Others grow feebler. Some are split in two. Some are
rotated through a right angle in a minute or less, although each of
the grains may be the size of Great Britain. Generally they move
together in groups of very various velocities, up to forty kilometres
a second.  These movements seem to have definite relation to any
sun-spots in the neighbourhood. From the results already obtained it
seems certain that, if this method of observation be continued, it
cannot fail to supply facts of the greatest importance.

It is quite impossible to do justice here to the work of all those who
are engaged on astronomical physics.  The utmost that can be attempted
is to give a fair idea of the directions of human thought and
endeavour.  During the last half-century America has made splendid
progress, and an entirely new process of studying the photosphere has
been independently perfected by Professor Hale at Chicago, and
Deslandres at Paris.[8] They have succeeded in photographing the sun's
surface in monochromatic light, such as the light given off as one of
the bright lines of hydrogen or of calcium, by means of the
"Spectroheliograph." The spectroscope is placed with its slit in the
focus of an equatoreal telescope, pointed to the sun, so that the
circular image of the sun falls on the slit. At the other end of the
spectroscope is the photographic plate. Just in front of this plate
there is another slit parallel to the first, in the position where the
image of the first slit formed by the K line of calcium falls. Thus is
obtained a photograph of the section of the sun, made by the first
slit, only in K light. As the image of the sun passes over the first
slit the photographic plate is moved at the same rate and in the same
direction behind the second slit; and as successive sections of the
sun's image in the equatoreal enter the apparatus, so are these
sections successively thrown in their proper place on the photographic
plate, always in K light. By using a high dispersion the faculæ which
give off K light can be correctly photographed, not only at the sun's
edge, but all over his surface. The actual mechanical method of
carrying out the observation is not quite so simple as what is here
described.

By choosing another line of the spectrum instead of calcium K--for
example, the hydrogen line H(3)--we obtain two photographs, one
showing the appearance of the calcium floculi, and the other of the
hydrogen floculi, on the same part of the solar surface; and nothing
is more astonishing than to note the total want of resemblance in the
forms shown on the two. This mode of research promises to afford many
new and useful data.

The spectroscope has revealed the fact that, broadly speaking, the sun
is composed of the same materials as the earth. Ångstrom was the first
to map out all of the lines to be found in the solar spectrum. But
Rowland, of Baltimore, after having perfected the art of making true
gratings with equidistant lines ruled on metal for producing spectra,
then proceeded to make a map of the solar spectrum on a large scale.

In 1866 Lockyer[9] threw an image of the sun upon the slit of a
spectroscope, and was thus enabled to compare the spectrum of a spot
with that of the general solar surface. The observation proved the
darkness of a spot to be caused by increased absorption of light, not
only in the dark lines, which are widened, but over the entire
spectrum. In 1883 Young resolved this continuous obscurity into an
infinite number of fine lines, which have all been traced in a shadowy
way on to the general solar surface. Lockyer also detected
displacements of the spectrum lines in the spots, such as would be
produced by a rapid motion in the line of sight. It has been found
that both uprushes and downrushes occur, but there is no marked
predominance of either in a sun-spot. The velocity of motion thus
indicated in the line of sight sometimes appears to amount to 320
miles a second. But it must be remembered that pressure of a gas has
some effect in displacing the spectral lines.  So we must go on,
collecting data, until a time comes when the meaning of all the facts
can be made clear.

_Total Solar Eclipses_.--During total solar eclipses the time is so
short, and the circumstances so impressive, that drawings of the
appearance could not always be trusted. The red prominences of jagged
form that are seen round the moon's edge, and the corona with its
streamers radiating or interlacing, have much detail that can hardly
be recorded in a sketch. By the aid of photography a number of records
can be taken during the progress of totality. From a study of these
the extent of the corona is demonstrated in one case to extend to at
least six diameters of the moon, though the eye has traced it
farther. This corona is still one of the wonders of astronomy, and
leads to many questions. What is its consistency, if it extends many
million miles from the sun's surface? How is it that it opposed no
resistance to the motion of comets which have almost grazed the sun's
surface? Is this the origin of the zodiacal light?  The character of
the corona in photographic records has been shown to depend upon the
phase of the sun-spot period. During the sun-spot maximum the corona
seems most developed over the spot-zones--i.e., neither at the
equator nor the poles. The four great sheaves of light give it a
square appearance, and are made up of rays or plumes, delicate like
the petals of a flower.  During a minimum the nebulous ring seems to
be made of tufts of fine hairs with aigrettes or radiations from both
poles, and streamers from the equator.

[Illustration: SOLAR ECLIPSE, 1882.  From drawing by W. H. Wesley,
Secretary R.A.S.; showing the prominences, the corona, and an unknown
comet.]


On September 19th, 1868, eclipse spectroscopy began with the Indian
eclipse, in which all observers found that the red prominences showed
a bright line spectrum, indicating the presence of hydrogen and other
gases.  So bright was it that Jansen exclaimed: "_Je verrai ces
lignes-là en dehors des éclipses_." And the next day he observed the
lines at the edge of the uneclipsed sun.  Huggins had suggested this
observation in February, 1868, his idea being to use prisms of such
great dispersive power that the continuous spectrum reflected by our
atmosphere should be greatly weakened, while a bright line would
suffer no diminution by the high dispersion.  On October 20th
Lockyer,[10] having news of the eclipse, but not of Jansen's
observations the day after, was able to see these lines. This was a
splendid performance, for it enabled the prominences to be observed,
not only during eclipses, but every day. Moreover, the next year
Huggins was able, by using a wide slit, to see the whole of a
prominence and note its shape.  Prominences are classified, according
to their form, into "flame" and "cloud" prominences, the spectrum of
the latter showing calcium, hydrogen, and helium; that of the former
including a number of metals.

The D line of sodium is a double line, and in the same eclipse (1868)
an orange line was noticed which was afterwards found to lie close to
the two components of the D line. It did not correspond with any known
terrestrial element, and the unknown element was called "helium." It
was not until 1895 that Sir William Ramsay found this element as a gas
in the mineral cleavite.

The spectrum of the corona is partly continuous, indicating light
reflected from the sun's body. But it also shows a green line
corresponding with no known terrestrial element, and the name
"coronium" has been given to the substance causing it.

A vast number of facts have been added to our knowledge about the sun
by photography and the spectroscope. Speculations and hypotheses in
plenty have been offered, but it may be long before we have a complete
theory evolved to explain all the phenomena of the storm-swept
metallic atmosphere of the sun.

The proceedings of scientific societies teem with such facts and
"working hypotheses," and the best of them have been collected by Miss
Clerke in her _History of Astronomy during the Nineteenth Century_. As
to established facts, we learn from the spectroscopic researches (1)
that the continuous spectrum is derived from the _photosphere_ or
solar gaseous material compressed almost to liquid consistency; (2)
that the _reversing layer_ surrounds it and gives rise to black
lines in the spectrum; that the _chromosphere_ surrounds this, is
composed mainly of hydrogen, and is the cause of the red prominences
in eclipses; and that the gaseous _corona_ surrounds all of
these, and extends to vast distances outside the sun's visible
surface.


FOOTNOTES:

[1] _Rosa Ursina_, by C. Scheiner, _fol_.; Bracciani, 1630.

[2] _R. S. Phil. Trans_., 1774.

[3] _Ibid_, 1783.

[4] _Observations on the Spots on the Sun, etc.,_ 4°; London and
Edinburgh, 1863.

[5] _Periodicität der Sonnenflecken. Astron. Nach. XXI._, 1844,
P. 234.

[6] _R.S. Phil. Trans._ (ser. A), 1906, p. 69-100.

[7] "Researches on Solar Physics," by De la Rue, Stewart and Loewy;
_R. S. Phil. Trans_., 1869, 1870.

[8] "The Sun as Photographed on the K line"; _Knowledge_, London,
1903, p. 229.

[9] _R. S. Proc._, xv., 1867, p. 256.

[10] _Acad. des Sc._, Paris; _C. R._, lxvii., 1868, p. 121.



13. THE MOON AND PLANETS.


_The Moon_.--Telescopic discoveries about the moon commence with
Galileo's discovery that her surface has mountains and valleys, like
the earth. He also found that, while she always turns the same face to
us, there is periodically a slight twist to let us see a little round
the eastern or western edge. This was called _libration_, and the
explanation was clear when it was understood that in showing always
the same face to us she makes one revolution a month on her axis
_uniformly_, and that her revolution round the earth is not
uniform.

Galileo said that the mountains on the moon showed greater differences
of level than those on the earth.  Shröter supported this
opinion. W. Herschel opposed it. But Beer and Mädler measured the
heights of lunar mountains by their shadows, and found four of them
over 20,000 feet above the surrounding plains.

Langrenus [1] was the first to do serious work on selenography, and
named the lunar features after eminent men. Riccioli also made lunar
charts. In 1692 Cassini made a chart of the full moon. Since then we
have the charts of Schröter, Beer and Mädler (1837), and of Schmidt,
of Athens (1878); and, above all, the photographic atlas by Loewy and
Puiseux.

The details of the moon's surface require for their discussion a whole
book, like that of Neison or the one by Nasmyth and Carpenter. Here a
few words must suffice. Mountain ranges like our Andes or Himalayas
are rare. Instead of that, we see an immense number of circular
cavities, with rugged edges and flat interior, often with a cone in
the centre, reminding one of instantaneous photographs of the splash
of a drop of water falling into a pool. Many of these are fifty or
sixty miles across, some more. They are generally spoken of as
resembling craters of volcanoes, active or extinct, on the earth. But
some of those who have most fully studied the shapes of craters deny
altogether their resemblance to the circular objects on the moon.
These so-called craters, in many parts, are seen to be closely
grouped, especially in the snow-white parts of the moon. But there are
great smooth dark spaces, like the clear black ice on a pond, more
free from craters, to which the equally inappropriate name of seas has
been given. The most conspicuous crater, _Tycho_, is near the south
pole. At full moon there are seen to radiate from Tycho numerous
streaks of light, or "rays," cutting through all the mountain
formations, and extending over fully half the lunar disc, like the
star-shaped cracks made on a sheet of ice by a blow.  Similar cracks
radiate from other large craters. It must be mentioned that these
white rays are well seen only in full light of the sun at full moon,
just as the white snow in the crevasses of a glacier is seen bright
from a distance only when the sun is high, and disappears at
sunset. Then there are deep, narrow, crooked "rills" which may have
been water-courses; also "clefts" about half a mile wide, and often
hundreds of miles long, like deep cracks in the surface going straight
through mountain and valley.

The moon shares with the sun the advantage of being a good subject for
photography, though the planets are not. This is owing to her larger
apparent size, and the abundance of illumination. The consequence is
that the finest details of the moon, as seen in the largest telescope
in the world, may be reproduced at a cost within the reach of all.

No certain changes have ever been observed; but several suspicions
have been expressed, especially as to the small crater _Linné_, in the
_Mare Serenitatis_. It is now generally agreed that no certainty can
be expected from drawings, and that for real evidence we must await
the verdict of photography.

No trace of water or of an atmosphere has been found on the moon. It
is possible that the temperature is too low. In any case, no
displacement of a star by atmospheric refraction at occultation has
been surely recorded. The moon seems to be dead.

The distance of the moon from the earth is just now the subject of
re-measurement. The base line is from Greenwich to Cape of Good Hope,
and the new feature introduced is the selection of a definite point on
a crater (Mösting A), instead of the moon's edge, as the point whose
distance is to be measured.

_The Inferior Planets_.--When the telescope was invented, the phases
of Venus attracted much attention; but the brightness of this planet,
and her proximity to the sun, as with Mercury also, seemed to be a bar
to the discovery of markings by which the axis and period of rotation
could be fixed. Cassini gave the rotation as twenty-three hours, by
observing a bright spot on her surface. Shröter made it 23h. 21m. 19s.
This value was supported by others. In 1890 Schiaparelli[2] announced
that Venus rotates, like our moon, once in one of her revolutions, and
always directs the same face to the sun. This property has also been
ascribed to Mercury; but in neither case has the evidence been
generally accepted. Twenty-four hours is probably about the period of
rotation for each of these planets.

Several observers have claimed to have seen a planet within the orbit
of Mercury, either in transit over the sun's surface or during an
eclipse. It has even been named _Vulcan_. These announcements would
have received little attention but for the fact that the motion of
Mercury has irregularities which have not been accounted for by known
planets; and Le Verrier[3] has stated that an intra-Mercurial planet
or ring of asteroids would account for the unexplained part of the
motion of the line of apses of Mercury's orbit amounting to 38" per
century.

_Mars_.--The first study of the appearance of Mars by Miraldi led him
to believe that there were changes proceeding in the two white caps
which are seen at the planet's poles. W. Herschel attributed these
caps to ice and snow, and the dates of his observations indicated a
melting of these ice-caps in the Martian summer.

Schroter attributed the other markings on Mars to drifting clouds. But
Beer and Mädler, in 1830-39, identified the same dark spots as being
always in the same place, though sometimes blurred by mist in the
local winter. A spot sketched by Huyghens in 1672, one frequently seen
by W. Herschel in 1783, another by Arago in 1813, and nearly all the
markings recorded by Beer and Mädler in 1830, were seen and drawn by
F. Kaiser in Leyden during seventeen nights of the opposition of 1862
(_Ast. Nacht._, No. 1,468), whence he deduced the period of rotation
to be 24h. 37m. 22s.,62--or one-tenth of a second less than the period
deduced by R. A. Proctor from a drawing by Hooke in 1666.

It must be noted that, if the periods of rotation both of Mercury and
Venus be about twenty-four hours, as seems probable, all the four
planets nearest to the sun rotate in the same period, while the great
planets rotate in about ten hours (Uranus and Neptune being still
indeterminate).

The general surface of Mars is a deep yellow; but there are dark grey
or greenish patches. Sir John Herschel was the first to attribute the
ruddy colour of Mars to its soil rather than to its atmosphere.

The observations of that keen-sighted observer Dawes led to the first
good map of Mars, in 1869. In the 1877 opposition Schiaparelli revived
interest in the planet by the discovery of canals, uniformly about
sixty miles wide, running generally on great circles, some of them
being three or four thousand miles long. During the opposition of
1881-2 the same observer re-observed the canals, and in twenty of them
he found the canals duplicated,[4] the second canal being always 200
to 400 miles distant from its fellow.

The existence of these canals has been doubted.  Mr. Lowell has now
devoted years to the subject, has drawn them over and over again, and
has photographed them; and accepts the explanation that they are
artificial, and that vegetation grows on their banks.  Thus is revived
the old controversy between Whewell and Brewster as to the
habitability of the planets. The new arguments are not yet generally
accepted. Lowell believes he has, with the spectroscope, proved the
existence of water on Mars.

One of the most unexpected and interesting of all telescopic
discoveries took place in the opposition of 1877, when Mars was
unusually near to the earth. The Washington Observatory had acquired
the fine 26-inch refractor, and Asaph Hall searched for satellites,
concealing the planet's disc to avoid the glare. On August 11th he had
a suspicion of a satellite. This was confirmed on the 16th, and on the
following night a second one was added. They are exceedingly faint,
and can be seen only by the most powerful telescopes, and only at the
times of opposition. Their diameters are estimated at six or seven
miles. It was soon found that the first, Deimos, completes its orbit
in 30h. 18m.  But the other, Phobos, at first was a puzzle, owing to
its incredible velocity being unsuspected. Later it was found that the
period of revolution was only 7h. 39m. 22s. Since the Martian day is
twenty-four and a half hours, this leads to remarkable results.
Obviously the easterly motion of the satellite overwhelms the diurnal
rotation of the planet, and Phobos must appear to the inhabitants, if
they exist, to rise in the west and set in the east, showing two or
even three full moons in a day, so that, sufficiently well for the
ordinary purposes of life, the hour of the day can be told by its
phases.

The discovery of these two satellites is, perhaps, the most
interesting telescopic visual discovery made with the large telescopes
of the last half century; photography having been the means of
discovering all the other new satellites except Jupiter's fifth (in
order of discovery).

[Illustration: JUPITER.  From a drawing by E. M. Antoniadi, showing
transit of a satellite's shadow, the belts, and the "great red spot"
(_Monthly Notices_, R. A. S., vol. lix., pl. x.).]

_Jupiter._--Galileo's discovery of Jupiter's satellites was followed
by the discovery of his belts. Zucchi and Torricelli seem to have seen
them. Fontana, in 1633, reported three belts. In 1648 Grimaldi saw but
two, and noticed that they lay parallel to the ecliptic. Dusky spots
were also noticed as transient. Hooke[5] measured the motion of one in
1664. In 1665 Cassini, with a fine telescope, 35-feet focal length,
observed many spots moving from east to west, whence he concluded that
Jupiter rotates on an axis like the earth. He watched an unusually
permanent spot during twenty-nine rotations, and fixed the period at
9h. 56m. Later he inferred that spots near the equator rotate quicker
than those in higher latitudes (the same as Carrington found for the
sun); and W. Herschel confirmed this in 1778-9.

Jupiter's rapid rotation ought, according to Newton's theory, to be
accompanied by a great flattening at the poles. Cassini had noted an
oval form in 1691. This was confirmed by La Hire, Römer, and
Picard. Pound measured the ellipticity = 1/(13.25).

W. Herschel supposed the spots to be masses of cloud in the
atmosphere--an opinion still accepted.  Many of them were very
permanent. Cassini's great spot vanished and reappeared nine times
between 1665 and 1713. It was close to the northern margin of the
southern belt. Herschel supposed the belts to be the body of the
planet, and the lighter parts to be clouds confined to certain
latitudes.

In 1665 Cassini observed transits of the four satellites, and also saw
their shadows on the planet, and worked out a lunar theory for
Jupiter. Mathematical astronomers have taken great interest in the
perturbations of the satellites, because their relative periods
introduce peculiar effects. Airy, in his delightful book,
_Gravitation_, has reduced these investigations to simple
geometrical explanations.

In 1707 and 1713 Miraldi noticed that the fourth satellite varies much
in brightness. W. Herschel found this variation to depend upon its
position in its orbit, and concluded that in the positions of
feebleness it is always presenting to us a portion of its surface,
which does not well reflect the sun's light; proving that it always
turns the same face to Jupiter, as is the case with our moon. This
fact had also been established for Saturn's fifth satellite, and may
be true for all satellites.

In 1826 Struve measured the diameters of the four satellites, and
found them to be 2,429, 2,180, 3,561, and 3,046 miles.

In modern times much interest has been taken in watching a rival to
Cassini's famous spot. The "great red spot" was first observed by
Niesten, Pritchett, and Tempel, in 1878, as a rosy cloud attached to a
whitish zone beneath the dark southern equatorial band, shaped like
the new war balloons, 30,000 miles long and 7,000 miles across. The
next year it was brick-red. A white spot beside it completed a
rotation in less time by 51/2 minutes than the red spot--a difference
of 260 miles an hour. Thus they came together again every six weeks,
but the motions did not continue uniform.  The spot was feeble in
1882-4, brightened in 1886, and, after many changes, is still visible.

Galileo's great discovery of Jupiter's four moons was the last word in
this connection until September 9th, 1892, when Barnard, using the
36-inch refractor of the Lick Observatory, detected a tiny spot of
light closely following the planet. This proved to be a new satellite
(fifth), nearer to the planet than any other, and revolving round it
in 11h. 57m. 23s. Between its rising and setting there must be an
interval of 21/2 Jovian days, and two or three full moons. The sixth
and seventh satellites were found by the examination of photographic
plates at the Lick Observatory in 1905, since which time they have
been continuously photographed, and their orbits traced, at Greenwich.
On examining these plates in 1908 Mr. Melotte detected the eighth
satellite, which seems to be revolving in a retrograde orbit three
times as far from its planet as the next one (seventh), in these two
points agreeing with the outermost of Saturn's satellites (Phoebe).

_Saturn._--This planet, with its marvellous ring, was perhaps the most
wonderful object of those first examined by Galileo's telescope. He
was followed by Dominique Cassini, who detected bands like Jupiter's
belts. Herschel established the rotation of the planet in 1775-94.
From observations during one hundred rotations he found the period to
be 10h. 16m. 0s., 44. Herschel also measured the ratio of the polar to
the equatoreal diameter as 10:11.

The ring was a complete puzzle to Galileo, most of all when the planet
reached a position where the plane of the ring was in line with the
earth, and the ring disappeared (December 4th, 1612). It was not until
1656 that Huyghens, in his small pamphlet _De Saturni Luna Observatio
Nova_, was able to suggest in a cypher the ring form; and in 1659, in
his Systema Saturnium, he gave his reasons and translated the cypher:
"The planet is surrounded by a slender flat ring, everywhere distinct
from its surface, and inclined to the ecliptic." This theory explained
all the phases of the ring which had puzzled others. This ring was
then, and has remained ever since, a unique structure.  We in this age
have got accustomed to it. But Huyghens's discovery was received with
amazement.

In 1675 Cassini found the ring to be double, the concentric rings
being separated by a black band--a fact which was placed beyond
dispute by Herschel, who also found that the thickness of the ring
subtends an angle less than 0".3. Shröter estimated its thickness at
500 miles.

Many speculations have been advanced to explain the origin and
constitution of the ring. De Sejour said [6] that it was thrown off
from Saturn's equator as a liquid ring, and afterwards solidified. He
noticed that the outside would have a greater velocity, and be less
attracted to the planet, than the inner parts, and that equilibrium
would be impossible; so he supposed it to have solidified into a
number of concentric rings, the exterior ones having the least
velocity.

Clerk Maxwell, in the Adams prize essay, gave a physico-mathematical
demonstration that the rings must be composed of meteoritic matter
like gravel. Even so, there must be collisions absorbing the energy of
rotation, and tending to make the rings eventually fall into the
planet. The slower motion of the external parts has been proved by the
spectroscope in Keeler's hands, 1895.

Saturn has perhaps received more than its share of attention owing to
these rings. This led to other discoveries. Huyghens in 1655, and
J. D. Cassini in 1671, discovered the sixth and eighth satellites
(Titan and Japetus). Cassini lost his satellite, and in searching for
it found Rhea (the fifth) in 1672, besides his old friend, whom he
lost again. He added the third and fourth in 1684 (Tethys and
Dione). The first and second (Mimas and Encelades) were added by
Herschel in 1789, and the seventh (Hyperion) simultaneously by Lassel
and Bond in 1848. The ninth (Phoebe) was found on photographs, by
Pickering in 1898, with retrograde motion; and he has lately added a
tenth.

The occasional disappearance of Cassini's Japetus was found on
investigation to be due to the same causes as that of Jupiter's fourth
satellite, and proves that it always turns the same face to the
planet.

_Uranus and Neptune_.--The splendid discoveries of Uranus and two
satellites by Sir William Herschel in 1787, and of Neptune by Adams
and Le Verrier in 1846, have been already described. Lassel added two
more satellites to Uranus in 1851, and found Neptune's satellite in
1846. All of the satellites of Uranus have retrograde motion, and
their orbits are inclined about 80° to the ecliptic.

The spectroscope has shown the existence of an absorbing atmosphere on
Jupiter and Saturn, and there are suspicions that they partake
something of the character of the sun, and emit some light besides
reflecting solar light. On both planets some absorption lines seem to
agree with the aqueous vapour lines of our own atmosphere; while one,
which is a strong band in the red common to both planets, seems to
agree with a line in the spectrum of some reddish stars.

Uranus and Neptune are difficult to observe spectroscopically, but
appear to have peculiar spectra agreeing together. Sometimes Uranus
shows Frauenhofer lines, indicating reflected solar light. But
generally these are not seen, and six broad bands of absorption
appear.  One is the F. of hydrogen; another is the red-star line of
Jupiter and Saturn. Neptune is a very difficult object for the
spectroscope.

Quite lately [7] P. Lowell has announced that V. M.  Slipher, at
Flagstaff Observatory, succeeded in 1907 in rendering some plates
sensitive far into the red. A reproduction is given of photographed
spectra of the four outermost planets, showing (1) a great number of
new lines and bands; (2) intensification of hydrogen F.  and C. lines;
(3) a steady increase of effects (1) and (2) as we pass from Jupiter
and Saturn to Uranus, and a still greater increase in Neptune.

_Asteroids_.--The discovery of these new planets has been
described. At the beginning of the last century it was an immense
triumph to catch a new one. Since photography was called into the
service by Wolf, they have been caught every year in shoals. It is
like the difference between sea fishing with the line and using a
steam trawler. In the 1908 almanacs nearly seven hundred asteroids are
included. The computation of their perturbations and ephemerides by
Euler's and Lagrange's method of variable elements became so laborious
that Encke devised a special process for these, which can be applied
to many other disturbed orbits. [8]

When a photograph is taken of a region of the heavens including an
asteroid, the stars are photographed as points because the telescope
is made to follow their motion; but the asteroids, by their proper
motion, appear as short lines.

The discovery of Eros and the photographic attack upon its path have
been described in their relation to finding the sun's distance.

A group of four asteroids has lately been found, with a mean distance
and period equal to that of Jupiter. To three of these masculine names
have been given--Hector, Patroclus, Achilles; the other has not yet
been named.


FOOTNOTES:

[1] Langrenus (van Langren), F. Selenographia sive lumina austriae
philippica; Bruxelles, 1645.

[2] _Astr. Nach._, 2,944.

[3] _Acad. des Sc._, Paris; _C.R._, lxxxiii., 1876.

[4] _Mem. Spettr. Ital._, xi., p. 28.

[5] _R. S. Phil. Trans_., No. 1.

[6] Grant's _Hist. Ph. Ast_., p. 267.

[7] _Nature_, November 12th, 1908.

[8] _Ast. Nach_., Nos. 791, 792, 814, translated by G. B. Airy.
_Naut. Alm_., Appendix, 1856.



14. COMETS AND METEORS.


Ever since Halley discovered that the comet of 1682 was a member of
the solar system, these wonderful objects have had a new interest for
astronomers; and a comparison of orbits has often identified the
return of a comet, and led to the detection of an elliptic orbit where
the difference from a parabola was imperceptible in the small portion
of the orbit visible to us. A remarkable case in point was the comet
of 1556, of whose identity with the comet of 1264 there could be
little doubt.  Hind wanted to compute the orbit more exactly than
Halley had done. He knew that observations had been made, but they
were lost. Having expressed his desire for a search, all the
observations of Fabricius and of Heller, and also a map of the comet's
path among the stars, were eventually unearthed in the most unlikely
manner, after being lost nearly three hundred years.  Hind and others
were certain that this comet would return between 1844 and 1848, but
it never appeared.

When the spectroscope was first applied to finding the composition of
the heavenly bodies, there was a great desire to find out what comets
are made of. The first opportunity came in 1864, when Donati observed
the spectrum of a comet, and saw three bright bands, thus proving that
it was a gas and at least partly self-luminous.  In 1868 Huggins
compared the spectrum of Winnecke's comet with that of a Geissler tube
containing olefiant gas, and found exact agreement. Nearly all comets
have shown the same spectrum.[1] A very few comets have given bright
band spectra differing from the normal type. Also a certain kind of
continuous spectrum, as well as reflected solar light showing
Frauenhofer lines, have been seen.

[Illustration: COPY OF THE DRAWING MADE BY PAUL FABRICIUS.  To define
the path of comet 1556. After being lost for 300 years, this drawing
was recovered by the prolonged efforts of Mr. Hind and Professor
Littrow in 1856.]

When Wells's comet, in 1882, approached very close indeed to the sun,
the spectrum changed to a mono-chromatic yellow colour, due to sodium.

For a full account of the wonders of the cometary world the reader is
referred to books on descriptive astronomy, or to monographs on
comets.[2] Nor can the very uncertain speculations about the structure
of comets' tails be given here. A new explanation has been proposed
almost every time that a great discovery has been made in the theory
of light, heat, chemistry, or electricity.

Halley's comet remained the only one of which a prediction of the
return had been confirmed, until the orbit of the small, ill-defined
comet found by Pons in 1819 was computed by Encke, and found to have a
period of 3 1/3 years. It was predicted to return in 1822, and was
recognised by him as identical with many previous comets. This comet,
called after Encke, has showed in each of its returns an inexplicable
reduction of mean distance, which led to the assertion of a resisting
medium in space until a better explanation could be found.[3]

Since that date fourteen comets have been found with elliptic orbits,
whose aphelion distances are all about the same as Jupiter's mean
distance; and six have an aphelion distance about ten per cent,
greater than Neptune's mean distance. Other comets are similarly
associated with the planets Saturn and Uranus.

The physical transformations of comets are among the most wonderful of
unexplained phenomena in the heavens. But, for physical astronomers,
the greatest interest attaches to the reduction of radius vector of
Encke's comet, the splitting of Biela's comet into two comets in 1846,
and the somewhat similar behaviour of other comets. It must be noted,
however, that comets have a sensible size, that all their parts cannot
travel in exactly the same orbit under the sun's gravitation, and that
their mass is not sufficient to retain the parts together very
forcibly; also that the inevitable collision of particles, or else
fluid friction, is absorbing energy, and so reducing the comet's
velocity.

In 1770 Lexell discovered a comet which, as was afterwards proved by
investigations of Lexell, Burchardt, and Laplace, had in 1767 been
deflected by Jupiter out of an orbit in which it was invisible from
the earth into an orbit with a period of 51/2 years, enabling it to be
seen. In 1779 it again approached Jupiter closer than some of his
satellites, and was sent off in another orbit, never to be again
recognised.

But our interest in cometary orbits has been added to by the discovery
that, owing to the causes just cited, a comet, if it does not separate
into discrete parts like Biela's, must in time have its parts spread
out so as to cover a sensible part of the orbit, and that, when the
earth passes through such part of a comet's orbit, a meteor shower is
the result.

A magnificent meteor shower was seen in America on November 12th-13th,
1833, when the paths of the meteors all seemed to radiate from a point
in the constellation Leo. A similar display had been witnessed in
Mexico by Humboldt and Bonpland on November 12th, 1799. H. A. Newton
traced such records back to October 13th, A.D. 902. The orbital motion
of a cloud or stream of small particles was indicated. The period
favoured by H. A. Newton was 3541/2 days; another suggestion was 3751/2
days, and another 331/4 years.  He noticed that the advance of the date
of the shower between 902 and 1833, at the rate of one day in seventy
years, meant a progression of the node of the orbit.  Adams undertook
to calculate what the amount would be on all the five suppositions
that had been made about the period. After a laborious work, he found
that none gave one day in seventy years except the 331/4-year period,
which did so exactly. H. A. Newton predicted a return of the shower on
the night of November 13th-14th, 1866. He is now dead; but many of us
are alive to recall the wonder and enthusiasm with which we saw this
prediction being fulfilled by the grandest display of meteors ever
seen by anyone now alive.

The _progression_ of the nodes proved the path of the meteor
stream to be retrograde. The _radiant_ had almost the exact
longitude of the point towards which the earth was moving. This proved
that the meteor cluster was at perihelion. The period being known, the
eccentricity of the orbit was obtainable, also the orbital velocity of
the meteors in perihelion; and, by comparing this with the earth's
velocity, the latitude of the radiant enabled the inclination to be
determined, while the longitude of the earth that night was the
longitude of the node. In such a way Schiaparelli was able to find
first the elements of the orbit of the August meteor shower
(Perseids), and to show its identity with the orbit of Tuttle's comet
1862.iii. Then, in January 1867, Le Verrier gave the elements of the
November meteor shower (Leonids); and Peters, of Altona, identified
these with Oppolzer's elements for Tempel's comet 1866--Schiaparelli
having independently attained both of these results. Subsequently
Weiss, of Vienna, identified the meteor shower of April 20th (Lyrids)
with comet 1861. Finally, that indefatigable worker on meteors,
A. S. Herschel, added to the number, and in 1878 gave a list of
seventy-six coincidences between cometary and meteoric orbits.

Cometary astronomy is now largely indebted to photography, not merely
for accurate delineations of shape, but actually for the discovery of
most of them.  The art has also been applied to the observation of
comets at distances from their perihelia so great as to prevent their
visual observation. Thus has Wolf, of Heidelburg, found upon old
plates the position of comet 1905.v., as a star of the 15.5 magnitude,
783 days before the date of its discovery. From the point of view of
the importance of finding out the divergence of a cometary orbit from
a parabola, its period, and its aphelion distance, this increase of
range attains the very highest value.

The present Astronomer Royal, appreciating this possibility, has been
searching by photography for Halley's comet since November, 1907,
although its perihelion passage will not take place until April, 1910.


FOOTNOTES:

[1] In 1874, when the writer was crossing the Pacific Ocean in
H.M.S. "Scout," Coggia's comet unexpectedly appeared, and (while
Colonel Tupman got its positions with the sextant) he tried to use the
prism out of a portable direct-vision spectroscope, without success
until it was put in front of the object-glass of a binocular, when, to
his great joy, the three band images were clearly seen.

[2] Such as _The World of Comets_, by A. Guillemin; _History of
Comets_, by G. R. Hind, London, 1859; _Theatrum Cometicum_, by S. de
Lubienietz, 1667; _Cometographie_, by Pingré, Paris, 1783; _Donati's
Comet_, by Bond.

[3] The investigations by Von Asten (of St. Petersburg) seem to
support, and later ones, especially those by Backlund (also of
St. Petersburg), seem to discredit, the idea of a resisting medium.



15. THE FIXED STARS AND NEBULÆ.


Passing now from our solar system, which appears to be subject to the
action of the same forces as those we experience on our globe, there
remains an innumerable host of fixed stars, nebulas, and nebulous
clusters of stars. To these the attention of astronomers has been more
earnestly directed since telescopes have been so much enlarged.
Photography also has enabled a vast amount of work to be covered in a
comparatively short period, and the spectroscope has given them the
means, not only of studying the chemistry of the heavens, but also of
detecting any motion in the line of sight from less than a mile a
second and upwards in any star, however distant, provided it be bright
enough.

[Illustration: SIR WILLIAM HERSCHEL, F.R.S.--1738-1822.  Painted by
Lemuel F. Abbott; National Portrait Gallery, Room XX.]

In the field of telescopic discovery beyond our solar system there is
no one who has enlarged our knowledge so much as Sir William Herschel,
to whom we owe the greatest discovery in dynamical astronomy among the
stars--viz., that the law of gravitation extends to the most distant
stars, and that many of them describe elliptic orbits about each
other. W. Herschel was born at Hanover in 1738, came to England in
1758 as a trained musician, and died in 1822. He studied science when
he could, and hired a telescope, until he learnt to make his own
specula and telescopes. He made 430 parabolic specula in twenty-one
years. He discovered 2,500 nebulæ and 806 double stars, counted the
stars in 3,400 guage-fields, and compared the principal stars
photometrically.

Some of the things for which he is best known were results of those
accidents that happen only to the indefatigable enthusiast. Such was
the discovery of Uranus, which led to funds being provided for
constructing his 40-feet telescope, after which, in 1786, he settled
at Slough. In the same way, while trying to detect the annual parallax
of the stars, he failed in that quest, but discovered binary systems
of stars revolving in ellipses round each other; just as Bradley's
attack on stellar parallax failed, but led to the discovery of
aberration, nutation, and the true velocity of light.

_Parallax_.--The absence of stellar parallax was the great
objection to any theory of the earth's motion prior to Kepler's
time. It is true that Kepler's theory itself could have been
geometrically expressed equally well with the earth or any other point
fixed. But in Kepler's case the obviously implied physical theory of
the planetary motions, even before Newton explained the simplicity of
conception involved, made astronomers quite ready to waive the claim
for a rigid proof of the earth's motion by measurement of an annual
parallax of stars, which they had insisted on in respect of
Copernicus's revival of the idea of the earth's orbital motion.

Still, the desire to measure this parallax was only intensified by the
practical certainty of its existence, and by repeated failures. The
attempts of Bradley failed. The attempts of Piazzi and Brinkley,[1]
early in the nineteenth century, also failed. The first successes,
afterwards confirmed, were by Bessel and Henderson.  Both used stars
whose proper motion had been found to be large, as this argued
proximity. Henderson, at the Cape of Good Hope, observed alpha
Centauri, whose annual proper motion he found to amount to 3".6, in
1832-3; and a few years later deduced its parallax 1".16.  His
successor at the Cape, Maclear, reduced this to 0".92.

In 1835 Struve assigned a doubtful parallax of 0".261 to Vega (alpha
Lyræ). But Bessel's observations, between 1837 and 1840, of 61 Cygni,
a star with the large proper motion of over 5", established its annual
parallax to be 0".3483; and this was confirmed by Peters, who found
the value 0".349.

Later determinations for alpha2 Centauri, by Gill,[2] make its parallax
0".75--This is the nearest known fixed star; and its light takes 4 1/3
years to reach us. The light year is taken as the unit of measurement
in the starry heavens, as the earth's mean distance is "the
astronomical unit" for the solar system.[3] The proper motions and
parallaxes combined tell us the velocity of the motion of these stars
across the line of sight: alpha Centauri 14.4 miles a second=4.2
astronomical units a year; 61 Cygni 37.9 miles a second=11.2
astronomical units a year. These successes led to renewed zeal, and
now the distances of many stars are known more or less accurately.

Several of the brightest stars, which might be expected to be the
nearest, have not shown a parallax amounting to a twentieth of a
second of arc. Among these are Canopus, alpha Orionis, alpha Cygni, beta
Centauri, and gamma Cassiopeia. Oudemans has published a list of
parallaxes observed.[4]

_Proper Motion._--In 1718 Halley[5] detected the proper motions
of Arcturus and Sirius. In 1738 J. Cassinis[6] showed that the former
had moved five minutes of arc since Tycho Brahe fixed its position. In
1792 Piazzi noted the motion of 61 Cygni as given above. For a long
time the greatest observed proper motion was that of a small star 1830
Groombridge, nearly 7" a year; but others have since been found
reaching as much as 10".

Now the spectroscope enables the motion of stars to be detected at a
single observation, but only that part of the motion that is in the
line of sight. For a complete knowledge of a star's motion the proper
motion and parallax must also be known.

When Huggins first applied the Doppler principle to measure velocities
in the line of sight,[7] the faintness of star spectra diminished the
accuracy; but Vögel, in 1888, overcame this to a great extent by long
exposures of photographic plates.

It has often been noticed that stars which seem to belong to a group
of nearly uniform magnitude have the same proper motion. The
spectroscope has shown that these have also often the same velocity in
the line of sight. Thus in the Great Bear, beta, gamma, delta,
epsilon, zeta, all agree as to angular proper motion. delta was too
faint for a spectroscopic measurement, but all the others have been
shown to be approaching us at a rate of twelve to twenty miles a
second. The same has been proved for proper motion, and line of sight
motion, in the case of Pleiades and other groups.

Maskelyne measured many proper motions of stars, from which W.
Herschel[8] came to the conclusion that these apparent motions are for
the most part due to a motion of the solar system in space towards a
point in the constellation Hercules, R.A. 257°; N. Decl. 25°.  This
grand discovery has been amply confirmed, and, though opinions differ
as to the exact direction, it happens that the point first indicated
by Herschel, from totally insufficient data, agrees well with modern
estimates.

Comparing the proper motions and parallaxes to get the actual velocity
of each star relative to our system, C.L. Struve found the probable
velocity of the solar system in space to be fifteen miles a second, or
five astronomical units a year.

The work of Herschel in this matter has been checked by comparing
spectroscopic velocities in the line of sight which, so far as the
sun's motion is concerned, would give a maximum rate of approach for
stars near Hercules, a maximum rate of recession for stars in the
opposite part of the heavens, and no effect for stars half-way
between. In this way the spectroscope has confirmed generally
Herschel's view of the direction, and makes the velocity eleven miles
a second, or nearly four astronomical units a year.

The average proper motion of a first magnitude star has been found to
be 0".25 annually, and of a sixth magnitude star 0".04. But that all
bright stars are nearer than all small stars, or that they show
greater proper motion for that reason, is found to be far from the
truth. Many statistical studies have been made in this connection, and
interesting results may be expected from this treatment in the hands
of Kapteyn of Groningen, and others.[9]

On analysis of the directions of proper motions of stars in all parts
of the heavens, Kapteyn has shown[10] that these indicate, besides the
solar motion towards Hercules, two general drifts of stars in nearly
opposite directions, which can be detected in any part of the
heavens. This result has been confirmed from independent data by
Eddington (_R.A.S., M.N._) and Dyson (_R.S.E. Proc._).

Photography promises to assist in the measurement of parallax and
proper motions. Herr Pulfrich, of the firm of Carl Zeiss, has vastly
extended the applications of stereoscopic vision to astronomy--a
subject which De la Rue took up in the early days of photography.  He
has made a stereo-comparator of great beauty and convenience for
comparing stereoscopically two star photographs taken at different
dates. Wolf of Heidelberg has used this for many purposes. His
investigations depending on the solar motion in space are remarkable.
He photographs stars in a direction at right angles to the line of the
sun's motion. He has taken photographs of the same region fourteen
years apart, the two positions of his camera being at the two ends of
a base-line over 5,000,000,000 miles apart, or fifty-six astronomical
units. On examining these stereoscopically, some of the stars rise out
of the general plane of the stars, and seem to be much nearer. Many of
the stars are thus seen to be suspended in space at different
distances corresponding exactly to their real distances from our solar
system, except when their proper motion interferes. The effect is most
striking; the accuracy of measurement exceeds that of any other method
of measuring such displacements, and it seems that with a long
interval of time the advantage of the method increases.

_Double Stars._--The large class of double stars has always been much
studied by amateurs, partly for their beauty and colour, and partly as
a test for telescopic definition. Among the many unexplained stellar
problems there is one noticed in double stars that is thought by some
to be likely to throw light on stellar evolution. It is this: There
are many instances where one star of the pair is comparatively faint,
and the two stars are contrasted in colour; and in every single case
the general colour of the faint companion is invariably to be classed
with colours more near to the blue end of the spectrum than that of
the principal star.

_Binary Stars._--Sir William Herschel began his observations of double
stars in the hope of discovering an annual parallax of the stars. In
this he was following a suggestion of Galileo's. The presumption is
that, if there be no physical connection between the stars of a pair,
the largest is the nearest, and has the greatest parallax. So, by
noting the distance between the pair at different times of the year, a
delicate test of parallax is provided, unaffected by major
instrumental errors.

Herschel did, indeed, discover changes of distance, but not of the
character to indicate parallax. Following this by further observation,
he found that the motions were not uniform nor rectilinear, and by a
clear analysis of the movements he established the remarkable and
wholly unexpected fact that in all these cases the motion is due to a
revolution about their common centre of gravity.[11] He gave the
approximate period of revolution of some of these: Castor, 342 years;
delta Serpentis, 375 years; gamma Leonis, 1,200 years; epsilon Bootis,
1,681 years.

Twenty years later Sir John Herschel and Sir James South, after
re-examination of these stars, confirmed[12] and extended the results,
one pair of Coronæ having in the interval completed more than a whole
revolution.

It is, then, to Sir William Herschel that we owe the extension of the
law of gravitation, beyond the limits of the solar system, to the
whole universe. His observations were confirmed by F.G.W. Struve (born
1793, died 1864), who carried on the work at Dorpat. But it was first
to Savary,[13] and later to Encke and Sir John Herschel, that we owe
the computation of the elliptic elements of these stars; also the
resulting identification of their law of force with Newton's force of
gravitation applied to the solar system, and the force that makes an
apple fall to the ground. As Grant well says in his _History_:
"This may be justly asserted to be one of the most sublime truths
which astronomical science has hitherto disclosed to the researches of
the human mind."

Latterly the best work on double stars has been done by
S. W. Burnham,[14] at the Lick Observatory. The shortest period he
found was eleven years (kappa Pegasi).  In the case of some of
these binaries the parallax has been measured, from which it appears
that in four of the surest cases the orbits are about the size of the
orbit of Uranus, these being probably among the smallest stellar
orbits.

The law of gravitation having been proved to extend to the stars, a
discovery (like that of Neptune in its origin, though unlike it in the
labour and originality involved in the calculation) that entrances the
imagination became possible, and was realised by Bessel--the discovery
of an unknown body by its gravitational disturbance on one that was
visible. In 1834 and 1840 he began to suspect a want of uniformity in
the proper motion of Sirius and Procyon respectively. In 1844, in a
letter to Sir John Herschel,[15] he attributed these irregularities in
each case to the attraction of an invisible companion, the period of
revolution of Sirius being about half a century. Later he said: "I
adhere to the conviction that Procyon and Sirius form real binary
systems, consisting of a visible and an invisible star.  There is no
reason to suppose luminosity an essential quality of cosmical
bodies. The visibility of countless stars is no argument against the
invisibility of countless others." This grand conception led Peters to
compute more accurately the orbit, and to assign the place of the
invisible companion of Sirius. In 1862 Alvan G. Clark was testing a
new 18-inch object-glass (now at Chicago) upon Sirius, and, knowing
nothing of these predictions, actually found the companion in the very
place assigned to it. In 1896 the companion of Procyon was discovered
by Professor Schaeberle at the Lick Observatory.

Now, by the refined parallax determinations of Gill at the Cape, we
know that of Sirius to be 0".38. From this it has been calculated that
the mass of Sirius equals two of our suns, and its intrinsic
brightness equals twenty suns; but the companion, having a mass equal
to our sun, has only a five-hundredth part of the sun's brightness.

_Spectroscopic Binaries_.--On measuring the velocity of a star in the
line of sight at frequent intervals, periodic variations have been
found, leading to a belief in motion round an invisible
companion. Vogel, in 1889, discovered this in the case of Spica (alpha
Virginis), whose period is 4d. 0h. 19m., and the diameter of whose
orbit is six million miles. Great numbers of binaries of this type
have since then been discovered, all of short period.

Also, in 1889, Pickering found that at regular intervals of fifty-two
days the lines in the spectrum of zeta of the Great Bear are
duplicated, indicating a relative velocity, equal to one hundred miles
a second, of two components revolving round each other, of which that
apparently single star must be composed.

It would be interesting, no doubt, to follow in detail the
accumulating knowledge about the distances, proper motions, and orbits
of the stars; but this must be done elsewhere. Enough has been said to
show how results are accumulating which must in time unfold to us the
various stellar systems and their mutual relationships.

_Variable Stars._--It has often happened in the history of different
branches of physical science that observation and experiment were so
far ahead of theory that hopeless confusion appeared to reign; and
then one chance result has given a clue, and from that time all
differences and difficulties in the previous researches have stood
forth as natural consequences, explaining one another in a rational
sequence. So we find parallax, proper motion, double stars, binary
systems, variable stars, and new stars all bound together.

The logical and necessary explanation given of the cause of ordinary
spectroscopic binaries, and of irregular proper motions of Sirius and
Procyon, leads to the inference that if ever the plane of such a
binary orbit were edge-on to us there ought to be an eclipse of the
luminous partner whenever the non-luminous one is interposed between
us. This should give rise either to intermittence in the star's light
or else to variability.  It was by supposing the existence of a dark
companion to Algol that its discoverer, Goodricke of York,[16] in
1783, explained variable stars of this type. Algol (beta Persei)
completes the period of variable brightness in 68.8 hours. It loses
three-fifths of its light, and regains it in twelve hours. In 1889
Vogel,[17] with the Potsdam spectrograph, actually found that the
luminous star is receding before each eclipse, and approaching us
after each eclipse; thus entirely supporting Goodricke's opinion.
There are many variables of the Algol type, and information is
steadily accumulating. But all variable stars do not suffer the sudden
variations of Algol. There are many types, and the explanations of
others have not proved so easy.

The Harvard College photographs have disclosed the very great
prevalence of variability, and this is certainly one of the lines in
which modern discovery must progress.

Roberts, in South Africa, has done splendid work on the periods of
variables of the Algol type.

_New Stars_.--Extreme instances of variable stars are the new stars
such as those detected by Hipparchus, Tycho Brahe, and Kepler, of
which many have been found in the last half-century. One of the latest
great "Novæ" was discovered in Auriga by a Scotsman, Dr. Anderson, on
February 1st, 1892, and, with the modesty of his race, he communicated
the fact to His Majesty's Astronomer for Scotland on an unsigned
post-card.[18] Its spectrum was observed and photographed by Huggins
and many others. It was full of bright lines of hydrogen, calcium,
helium, and others not identified. The astounding fact was that lines
were shown in pairs, bright and dark, on a faint continuous spectrum,
indicating apparently that a dark body approaching us at the rate of
550 miles a second[19] was traversing a cold nebulous atmosphere, and
was heated to incandescence by friction, like a meteor in our
atmosphere, leaving a luminous train behind it. It almost disappeared,
and on April 26th it was of the sixteenth magnitude; but on August
17th it brightened to the tenth, showing the principal nebular band in
its spectrum, and no sign of approach or recession.  It was as if it
emerged from one part of the nebula, cooled down, and rushed through
another part of the nebula, rendering the nebular gas more luminous
than itself.[20]

Since 1892 one Nova after another has shown a spectrum as described
above, like a meteor rushing towards us and leaving a train behind,
for this seems to be the obvious meaning of the spectra.

The same may be said of the brilliant Nova Persei, brighter at its
best than Capella, and discovered also by Dr. Anderson on February
22nd, 1901. It increased in brightness as it reached the densest part
of the nebula, then it varied for some weeks by a couple of
magnitudes, up and down, as if passing through separate nebular
condensations. In February, 1902, it could still be seen with an
opera-glass. As with the other Novæ, when it first dashed into the
nebula it was vaporised and gave a continuous spectrum with dark lines
of hydrogen and helium. It showed no bright lines paired with the dark
ones to indicate a train left behind; but in the end its own
luminosity died out, and the nebular spectrum predominated.

The nebular illumination as seen in photographs, taken from August to
November, seemed to spread out slowly in a gradually increasing circle
at the rate of 90" in forty-eight days. Kapteyn put this down to the
velocity of light, the original outburst sending its illumination to
the nebulous gas and illuminating a spherical shell whose radius
increased at the velocity of light. This supposition seems correct, in
which case it can easily be shown from the above figures that the
distance of this Nova was 300 light years.

_Star Catalogues._--Since the days of very accurate observations
numerous star-catalogues have been produced by individuals or by
observatories. Bradley's monumental work may be said to head the list.
Lacaille's, in the Southern hemisphere, was complementary.  Then
Piazzi, Lalande, Groombridge, and Bessel were followed by Argelander
with his 324,000 stars, Rumker's Paramatta catalogue of the southern
hemisphere, and the frequent catalogues of national observatories.
Later the Astronomische Gesellschaft started their great catalogue,
the combined work of many observatories. Other southern ones were
Gould's at Cordova and Stone's at the Cape.

After this we have a new departure. Gill at the Cape, having the comet
1882.ii. all to himself in those latitudes, wished his friends in
Europe to see it, and employed a local photographer to strap his
camera to the observatory equatoreal, driven by clockwork, and
adjusted on the comet by the eye. The result with half-an-hour's
exposure was good, so he tried three hours. The result was such a
display of sharp star images that he resolved on the Cape Photographic
Durchmusterung, which after fourteen years, with Kapteyn's aid in
reducing, was completed. Meanwhile the brothers Henry, of Paris, were
engaged in going over Chacornac's zodiacal stars, and were about to
catalogue the Milky Way portion, a serious labour, when they saw
Gill's Comet photograph and conceived the idea of doing the rest of
their work by photography.  Gill had previously written to Admiral
Mouchez, of the Paris Observatory, and explained to him his project
for charting the heavens photographically, by combining the work of
many observatories. This led Admiral Mouchez to support the brothers
Henry in their scheme.[21] Gill, having got his own photographic work
underway, suggested an international astrographic chart, the materials
for different zones to be supplied by observatories of all nations,
each equipped with similar photographic telescopes. At a conference in
Paris, 1887, this was decided on, the stars on the charts going down
to the fourteenth magnitude, and the catalogues to the eleventh.

[Illustration: GREAT COMET, Nov. 14TH, 1882. (Exposure 2hrs. 20m.)  By
kind permission of Sir David Gill. From this photograph originated all
stellar chart-photography.]

This monumental work is nearing completion. The labour involved was
immense, and the highest skill was required for devising instruments
and methods to read off the star positions from the plates.

Then we have the Harvard College collection of photographic plates,
always being automatically added to; and their annex at Arequipa in
Peru.

Such catalogues vary in their degree of accuracy; and fundamental
catalogues of standard stars have been compiled. These require
extension, because the differential methods of the heliometer and the
camera cannot otherwise be made absolute.

The number of stars down to the fourteenth magnitude may be taken at
about 30,000,000; and that of all the stars visible in the greatest
modern telescopes is probably about 100,000,000.

_Nebulæ and Star-clusters._--Our knowledge of nebulæ really dates from
the time of W. Herschel. In his great sweeps of the heavens with his
giant telescopes he opened in this direction a new branch of
astronomy.  At one time he held that all nebulæ might be clusters of
innumerable minute stars at a great distance. Then he recognised the
different classes of nebulæ, and became convinced that there is a
widely-diffused "shining fluid" in space, though many so-called nebulæ
could be resolved by large telescopes into stars.  He considered that
the Milky Way is a great star cluster, whose form may be conjectured
from numerous star-gaugings. He supposed that the compact "planetary
nebulæ" might show a stage of evolution from the diffuse nebulæ, and
that his classifications actually indicate various stages of
development. Such speculations, like those of the ancients about the
solar system, are apt to be harmful to true progress of knowledge
unless in the hands of the ablest mathematical physicists; and
Herschel violated their principles in other directions. But here his
speculations have attracted a great deal of attention, and, with
modifications, are accepted, at least as a working hypothesis, by a
fair number of people.

When Sir John Herschel had extended his father's researches into the
Southern Hemisphere he was also led to the belief that some nebulae
were a phosphorescent material spread through space like fog or mist.

Then his views were changed by the revelations due to the great
discoveries of Lord Rosse with his gigantic refractor,[22] when one
nebula after another was resolved into a cluster of minute stars. At
that time the opinion gained ground that with increase of telescopic
power this would prove to be the case with all nebulæ.

In 1864 all doubt was dispelled by Huggins[23] in his first examination
of the spectrum of a nebula, and the subsequent extension of this
observation to other nebulæ; thus providing a certain test which
increase in the size of telescopes could never have given. In 1864
Huggins found that all true nebulae give a spectrum of bright
lines. Three are due to hydrogen; two (discovered by Copeland) are
helium lines; others are unknown. Fifty-five lines have been
photographed in the spectrum of the Orion nebula. It seems to be
pretty certain that all true nebulae are gaseous, and show almost
exactly the same spectrum.

Other nebulæ, and especially the white ones like that in Andromeda,
which have not yet been resolved into stars, show a continuous
spectrum; others are greenish and give no lines.

A great deal has to be done by the chemist before the astronomer can
be on sure ground in drawing conclusions from certain portions of his
spectroscopic evidence.

The light of the nebulas is remarkably actinic, so that photography
has a specially fine field in revealing details imperceptible in the
telescope. In 1885 the brothers Henry photographed, round the star
Maia in the Pleiades, a spiral nebula 3' long, as bright on the plate
as that star itself, but quite invisible in the telescope; and an
exposure of four hours revealed other new nebula in the same
district. That painstaking and most careful observer, Barnard, with
101/4 hours' exposure, extended this nebulosity for several degrees,
and discovered to the north of the Pleiades a huge diffuse nebulosity,
in a region almost destitute of stars. By establishing a 10-inch
instrument at an altitude of 6,000 feet, Barnard has revealed the wide
distribution of nebular matter in the constellation Scorpio over a
space of 4° or 5° square.  Barnard asserts that the "nebular
hypothesis" would have been killed at its birth by a knowledge of
these photographs. Later he has used still more powerful instruments,
and extended his discoveries.

The association of stars with planetary nebulæ, and the distribution
of nebulæ in the heavens, especially in relation to the Milky Way, are
striking facts, which will certainly bear fruit when the time arrives
for discarding vague speculations, and learning to read the true
physical structure and history of the starry universe.

_Stellar Spectra._--When the spectroscope was first available for
stellar research, the leaders in this branch of astronomy were Huggins
and Father Secchi,[24] of Rome. The former began by devoting years of
work principally to the most accurate study of a few stars.  The
latter devoted the years from 1863 to 1867 to a general survey of the
whole heavens, including 4,000 stars. He divided these into four
principal classes, which have been of the greatest service. Half of
his stars belonged to the first class, including Sirius, Vega,
Regulus, Altair. The characteristic feature of their spectra is the
strength and breadth of the hydrogen lines and the extreme faintness
of the metallic lines. This class of star is white to the eye, and
rich in ultra violet light.

The second class includes about three-eighths of his stars, including
Capella, Pollux, and Arcturus. These stars give a spectrum like that
of our sun, and appear yellowish to the eye.

The third class includes alpha Herculis, alpha Orionis (Betelgeux), Mira
Ceti, and about 500 red and variable stars.  The spectrum has fluted
bands shaded from blue to red, and sharply defined at the more
refrangible edge.

The fourth class is a small one, containing no stars over fifth
magnitude, of which 152 Schjellerup, in Canes Venatici, is a good
example. This spectrum also has bands, but these are shaded on the
violet side and sharp on the red side. They are due to carbon in some
form.  These stars are ruby red in the telescope.

It would appear, then, that all stars are suns with continuous
spectra, and the classes are differentiated by the character of the
absorbent vapours of their atmospheres.

It is very likely that, after the chemists have taught us how to
interpret all the varieties of spectrum, it will be possible to
ascribe the different spectrum-classes to different stages in the
life-history of every star.  Already there are plenty of people ready
to lay down arbitrary assumptions about the lessons to be drawn from
stellar spectra. Some say that they know with certainty that each star
begins by being a nebula, and is condensed and heated by condensation
until it begins to shine as a star; that it attains a climax of
temperature, then cools down, and eventually becomes extinct.  They go
so far as to declare that they know what class of spectrum belongs to
each stage of a star's life, and how to distinguish between one that
is increasing and another that is decreasing in temperature.

The more cautious astronomers believe that chemistry is not
sufficiently advanced to justify all of these deductions; that, until
chemists have settled the lately raised question of the transmutation
of elements, no theory can be sure. It is also held that until they
have explained, without room for doubt, the reasons for the presence
of some lines, and the absence of others, of any element in a stellar
spectrum; why the arc-spectrum of each element differs from its spark
spectrum; what are all the various changes produced in the spectrum of
a gas by all possible concomitant variations of pressure and
temperature; also the meanings of all the flutings in the spectra of
metalloids and compounds; and other equally pertinent matters--until
that time arrives the part to be played by the astronomer is one of
observation. By all means, they say, make use of "working hypotheses"
to add an interest to years of laborious research, and to serve as a
guide to the direction of further labours; but be sure not to fall
into the error of calling any mere hypothesis a theory.

_Nebular Hypothesis._--The Nebular Hypothesis, which was first, as it
were, tentatively put forward by Laplace as a note in his _Système du
Monde_, supposes the solar system to have been a flat, disk-shaped
nebula at a high temperature in rapid rotation. In cooling it
condensed, leaving revolving rings at different distances from the
centre. These themselves were supposed to condense into the nucleus
for a rotating planet, which might, in contracting, again throw off
rings to form satellites.  The speculation can be put in a really
attractive form, but is in direct opposition to many of the actual
facts; and so long as it is not favoured by those who wish to maintain
the position of astronomy as the most exact of the sciences--exact in
its facts, exact in its logic--this speculation must be recorded by
the historian, only as he records the guesses of the ancient Greeks--as
an interesting phase in the history of human thought.

Other hypotheses, having the same end in view, are the meteoritic
hypothesis of Lockyer and the planetesimal hypothesis that has been
largely developed in the United States. These can best be read in the
original papers to various journals, references to which may be found
in the footnotes of Miss Clerke's _History of Astronomy during the
Nineteenth Century_. The same can be said of Bredichin's hypothesis of
comets' tails, Arrhenius's book on the applications of the theory of
light repulsion, the speculations on radium, the origin of the sun's
heat and the age of the earth, the electron hypothesis of terrestrial
magnetism, and a host of similar speculations, all combining to throw
an interesting light on the evolution of a modern train of thought
that seems to delight in conjecture, while rebelling against that
strict mathematical logic which has crowned astronomy as the queen of
the sciences.


FOOTNOTES:

[1] _R. S. Phil Trans_., 1810 and 1817-24.

[2] One of the most valuable contributions to our knowledge of stellar
parallaxes is the result of Gill's work (_Cape Results_, vol. iii.,
part ii., 1900).

[3] Taking the velocity of light at 186,000 miles a second, and the
earth's mean distance at 93,000,000 miles, 1 light year=5,865,696,000,000
miles or 63,072 astronomical units; 1 astronomical unit a year=2.94
miles a second; and the earth's orbital velocity=18.5 miles a second.

[4] Ast. Nacht., 1889.

[5] R. S. Phil. Trans., 1718.

[6] Mem. Acad. des Sciences, 1738, p. 337.

[7] R. S Phil. Trans., 1868.

[8] _R.S. Phil Trans._, 1783.

[9] See Kapteyn's address to the Royal Institution, 1908. Also Gill's
presidential address to the British Association, 1907.

[10] _Brit. Assoc. Rep._, 1905.

[11] R. S. Phil. Trans., 1803, 1804.

[12] Ibid, 1824.

[13] Connaisance des Temps, 1830.

[14] _R. A. S. Mem._, vol. xlvii., p. 178; _Ast. Nach._, No. 3,142;
Catalogue published by Lick Observatory, 1901.

[15] _R. A. S., M. N._, vol. vi.

[16] _R. S. Phil. Trans._, vol. lxxiii., p. 484.

[17] _Astr. Nach._, No. 2,947.

[18] _R. S. E. Trans_., vol. xxvii. In 1901 Dr. Anderson discovered
Nova Persei.

[19] _Astr. Nach_., No. 3,079.

[20] For a different explanation see Sir W. Huggins's lecture, Royal
Institution, May 13th, 1892.

[21] For the early history of the proposals for photographic
cataloguing of stars, see the _Cape Photographic Durchmusterung_, 3
vols. (_Ann. of the Cape Observatory_, vols. in., iv., and v.,
Introduction.)

[22] _R. S. Phil. Trans._, 1850, p. 499 _et seq._

[23] _Ibid_, vol. cliv., p. 437.

[24] _Brit. Assoc. Rep._, 1868, p. 165.



INDEX


Abul Wefa, 24
Acceleration of moon's mean motion, 60
Achromatic lens invented, 88
Adams, J. C., 61, 65, 68, 69, 70, 87, 118, 124
Airy, G. B., 13, 30, 37, 65, 69, 70, 80, 81, 114, 119
Albetegnius, 24
Alphonso, 24
Altazimuth, 81
Anaxagoras, 14, 16
Anaximander, 14
Anaximenes, 14
Anderson, T. D., 137, 138
Ångstrom, A. J., 102
Antoniadi, 113
Apian, P., 63
Apollonius, 22, 23
Arago, 111
Argelander, F. W. A., 139
Aristarchus, 18, 29
Aristillus, 17, 19
Aristotle, 16, 30, 47
Arrhenius, 146
Arzachel, 24
Asshurbanapal, 12
Asteroids, discovery of, 67, 119
Astrology, ancient and modern, 1-7, 38

Backlund, 122
Bacon, R., 86
Bailly, 8, 65
Barnard, E. E., 115, 143
Beer and Mädler, 107, 110, 111
Behaim, 74
Bessel, F.W., 65, 79, 128, 134, 139
Biela, 123
Binet, 65
Biot, 10
Bird, 79, 80
Bliss, 80
Bode, 66, 69
Bond, G. P., 99, 117, 122
Bouvard, A., 65, 68
Bradley, J., 79, 80, 81, 87, 127, 128, 139
Bredechin, 146
Bremiker, 71
Brewster, D., 52, 91, 112
Brinkley, 128
Bruno, G., 49
Burchardt, 65, 123
Burnham, S. W., 134

Callippus, 15, 16, 31
Carrington, R. C., 97, 99, 114
Cassini, G. D., 107, 114, 115, 116, 117, 118
Cassini, J., 109, 129
Chacornac, 139
Chaldæan astronomy, 11-13
Challis, J., 69, 70, 71, 72
Chance, 88
Charles, II., 50, 81
Chinese astronomy, 8-11
Christie, W. M. H. (Ast. Roy.), 64, 82, 125
Chueni, 9
Clairaut, A. C., 56, 63, 65
Clark, A. G., 89, 135
Clerke, Miss, 106, 146
Comets, 120
Common, A. A., 88
Cooke, 89
Copeland, R., 142
Copernicus, N., 14, 24-31, 37, 38, 41, 42, 49, 128
Cornu, 85
Cowell, P. H., 3, 5, 64, 83
Crawford, Earl of, 84
Cromellin, A. C., 5, 64

D'Alembert, 65
Damoiseau, 65
D'Arrest, H. L., 34
Dawes, W. R., 100, 111
Delambre, J. B. J., 8, 27, 51, 65, 68
De la Rue, W., 2, 94, 99, 100, 131
Delaunay, 65
Democritus, 16
Descartes, 51
De Sejour, 117
Deslandres, II., 101
Desvignolles, 9
De Zach, 67
Digges, L., 86
Dollond, J., 87, 90
Dominis, A. di., 86
Donati, 120
Doppler, 92, 129
Draper, 99
Dreyer, J. L. E., 29,77
Dunthorne, 60
Dyson, 131

Eclipses, total solar, 103
Ecphantes, 16
Eddington, 131
Ellipse, 41
Empedocles, 16
Encke, J. F., 119, 122, 123, 133
Epicycles, 22
Eratosthenes, 18
Euclid, 17
Eudoxus, 15, 31
Euler, L., 60, 61, 62, 65, 88, 119

Fabricius, D.,95, 120, 121
Feil and Mantois, 88
Fizeau, H. L., 85, 92, 99
Flamsteed, J., 50, 58, 68, 78, 79, 93
Fohi, 8
Forbes, J. D., 52, 91
Foucault, L., 85, 99
Frauenhofer, J., 88, 90, 91

Galilei, G., 38, 46-49, 77, 93, 94, 95, 96, 107, 113, 115, 116, 133
Galle, 71, 72
Gascoigne, W., 45, 77
Gauss, C. F., 65, 67
Gauthier, 98
Gautier, 89
Gilbert, 44
Gill, D., 84, 85, 128, 135, 139, 140
Goodricke, J., 136
Gould, B. A., 139
Grant, R., 27, 47, 51, 86, 134
Graham, 79
Greek astronomy, 8-11
Gregory, J. and D., 87
Grimaldi, 113
Groombridge, S., 139
Grubb, 88, 89
Guillemin, 122
Guinand, 88

Hale, G. E., 101
Hall, A., 112
Hall, C. M., 88
Halley, E., 19, 51, 58, 60, 61, 62, 63, 64, 79, 120, 122, 125, 129
Halley's comet, 62-64
Halm, 85
Hansen, P. A., 3, 65
Hansky, A. P., 100
Harding, C. L., 67
Heliometer, 83
Heller, 120
Helmholtz, H. L. F., 35
Henderson, T., 128
Henry, P. and P., 139, 140, 143
Heraclides, 16
Heraclitus, 14
Herodotus, 13
Herschel, W., 65, 68, 97, 107, 110, 114, 115, 116, 117, 118, 126, 127,
  130, 131, 132, 141, 142
Herschel, J., 97, 111, 133, 134, 142
Herschel, A. S., 125
Hevelius, J., 178
Hind, J. R., 5, 64, 120, 121, 122
Hipparchus, 3, 18, 19, 20, 22, 23, 24, 26, 36, 55, 60, 74, 93, 137
Hooke, R., 51, 111, 114
Horrocks, J., 50, 56
Howlett, 100
Huggins, W., 92, 93, 99, 106, 120, 129, 137, 138, 142, 144
Humboldt and Bonpland, 124
Huyghens, C., 47, 77, 87, 110, 116, 117

Ivory, 65

Jansen, P. J. C., 105, 106
Jansen, Z., 86

Kaiser, F., 111
Kapteyn, J. C., 131, 138, 139
Keeler, 117
Kepler, J., 17, 23, 26, 29, 30, 36, 37, 38-46, 48, 49, 50, 52, 53, 63,
  66, 77, 87, 93, 127, 137
Kepler's laws, 42
Kirchoff, G.R., 91
Kirsch, 9
Knobel, E.B., 12, 13
Ko-Show-King, 76

Lacaile, N.L., 139
Lagrange, J.L., 61, 62, 65, 119
La Hire, 114
Lalande, J.J.L., 60, 63, 65, 66, 72, 139
Lamont, J., 98
Langrenus, 107
Laplace, P.S. de, 50, 58, 61, 62, 65,66, 123, 146
Lassel, 72, 88, 117, 118
Law of universal gravitation, 53
Legendre, 65
Leonardo da Vinci, 46
Lewis, G.C., 17
Le Verrier, U.J.J., 65, 68, 70, 71,72, 110, 118, 125
Lexell, 66, 123
Light year, 128
Lipperhey, H., 86
Littrow, 121
Lockyer, J.N., 103, 105, 146
Logarithms invented, 50
Loewy, 2, 100
Long inequality of Jupiter and Saturn, 50, 62
Lowell, P., 111, 112, 118
Lubienietz, S. de, 122
Luther, M., 38
Lunar theory, 37, 50, 56, 64

Maclaurin, 65
Maclear, T., 128
Malvasia, 77
Martin, 9
Maxwell, J. Clerk, 117
Maskelyne, N., 80, 130
McLean, F., 89
Medici, Cosmo di, 48
Melancthon, 38
Melotte, 83, 116
Meteors, 123
Meton, 15
Meyer, 57, 65
Michaelson, 85
Miraldi, 110, 114
Molyneux, 87
Moon, physical observations, 107
Mouchez, 139
Moyriac de Mailla, 8

Napier, Lord, 50
Nasmyth and Carpenter, 108
Nebulae, 141, 146
Neison, E., 108
Neptune, discovery of, 68-72
Newall, 89
Newcomb, 85
Newton, H.A., 124
Newton, I., 5, 19, 43, 49, 51-60, 62, 64, 68, 77, 79, 87, 90, 93, 94,
  114, 127, 133
Nicetas, 16, 25
Niesten, 115
Nunez, P., 35

Olbers, H.W.M., 67
Omar, 11, 24
Oppolzer, 13, 125
Oudemans, 129

Palitsch, G., 64
Parallax, solar, 85, 86
Parmenides, 14
Paul III., 30
Paul V., 48
Pemberton, 51
Peters, C.A.F., 125, 128, 135
Photography, 99
Piazzi, G., 67, 128, 129, 139
Picard, 54, 77, 114
Pickering, E.C., 118, 135
Pingré, 13, 122
Plana, 65
Planets and satellites, physical observations, 109-119
Plato, 17, 23, 26, 40
Poisson, 65
Pond, J., 80
Pons, 122
Porta, B., 86
Pound, 87, 114
Pontecoulant, 64
Precession of the equinoxes, 19-21, 55, 57
Proctor, R.A., 111
Pritchett, 115
Ptolemy, 11, 13, 21, 22, 23, 24, 93
Puiseux and Loewy, 108
Pulfrich, 131
Purbach, G., 24
Pythagoras, 14, 17, 25, 29

Ramsay, W., 106
Ransome and May, 81
Reflecting telescopes invented, 87
Regiomontanus (Müller), 24
Respighi, 82
Retrograde motion of planets, 22
Riccioli, 107
Roberts, 137
Römer, O.,78, 114
Rosse, Earl of, 88, 142
Rowland, H. A., 92, 102
Rudolph H.,37, 39
Rumker, C., 139

Sabine, E., 98
Savary, 133
Schaeberle, J. M., 135
Schiaparelli, G. V., 110, 111, 124, 125
Scheiner, C., 87, 95, 96
Schmidt, 108
Schott, 88
Schröter, J. H., 107, 110, 111, 124, 125
Schuster, 98
Schwabe, G. H., 97
Secchi, A., 93, 144
Short, 87
Simms, J., 81
Slipher, V. M., 119
Socrates, 17
Solon, 15
Souciet, 8
South, J., 133
Spectroscope, 89-92
Spectroheliograph, 101
Spoerer, G. F. W., 98
Spots on the sun, 84;
  periodicity of, 97
Stars, Parallax, 127;
  proper motion, 129;
  double, 132;
  binaries, 132, 135;
  new, 19, 36, 137;
  catalogues of, 19, 36, 139;
  spectra of, 143
Stewart, B., 2, 100
Stokes, G. G., 91
Stone, E. J., 139
Struve, C. L., 130
Struve, F. G. W,, 88, 115, 128, 133

Telescopes invented, 47, 86;
  large, 88
Temple, 115, 125
Thales, 13, 16
Theon, 60
Transit circle of Römer, 78
Timocharis, 17, 19
Titius, 66
Torricelli, 113
Troughton, E., 80
Tupman, G. L., 120
Tuttle, 125
Tycho Brahe, 23, 25, 30, 33-38, 39, 40, 44, 50, 75, 77, 93, 94, 129, 137

Ulugh Begh, 24
Uranus, discovery of, 65

Velocity of light, 86, 128;
  of earth in orbit, 128
Verbiest, 75
Vogel, H. C., 92, 129, 135, 136
Von Asten, 122

Walmsley, 65
Walterus, B., 24, 74
Weiss, E., 125
Wells, 122
Wesley, 104
Whewell, 112
Williams, 10
Wilson, A., 96, 100
Winnecke, 120
Witte, 86
Wollaston, 90
Wolf, M., 119, 125, 132
Wolf, R., 98
Wren, C., 51
Wyllie, A., 77

Yao, 9
Young, C. A., 103
Yu-Chi, 8

Zenith telescopes, 79, 82
Zöllner, 92
Zucchi, 113