Produced by Chris Curnow, Hazel Batey and the Online
Distributed Proofreading Team at https://www.pgdp.net (This
file was produced from images generously made available
by The Internet Archive)






This E text uses UTF-8 (unicode) file encoding. If the apostrophes,
quotation marks and Greek text [ἀπολύτρωσις] in this paragraph
appear as garbage, you may have an incompatible browser or
unavailable fonts. First, make sure that your browser’s “character
set” or “file encoding” is set to Unicode (UTF-8). You may also need
to change the default font.




Illustration: COLOUR-PATCH APPARATUS.


  _THE ROMANCE OF SCIENCE._

  COLOUR MEASUREMENT AND MIXTURE.


  =With Numerous Illustrations.=


  BY CAPTAIN W. de W. ABNEY, C.B., R.E., D.C.L., F.R.S.


  PUBLISHED UNDER THE DIRECTION OF THE COMMITTEE
  OF GENERAL LITERATURE AND EDUCATION APPOINTED BY THE
  SOCIETY FOR PROMOTING CHRISTIAN KNOWLEDGE.


  SOCIETY FOR PROMOTING CHRISTIAN KNOWLEDGE.
  LONDON: NORTHUMBERLAND AVENUE, W.C.;
  43, QUEEN VICTORIA STREET, E.C.
  BRIGHTON: 135, NORTH STREET.
  NEW YORK: E. & J. B. YOUNG & CO.
  1891.




PREFACE.


Some ten years ago there were three measurements of the spectrum which I
set myself to carry out; the last two, at all events, involving new
methods of experimenting. The three measurements were: (1st) The heating
effect; (2nd) the luminosity; and (3rd) the chemical effect on various
salts, of the different rays of the spectrum. The task is now completed,
and it was in carrying out the second part of it that General Festing,
who joined me in the research, and myself were led into a wider study of
colour than at first intended, as the apparatus we devised enabled us to
carry out experiments which, whilst difficult under ordinary
circumstances, became easy to make. On two occasions, at the invitation
of the Society of Arts, I have delivered a short course of lectures on
the subject of Colour, and naturally I chose to treat it from the point
of view of our own methods of experimenting; and these lectures,
expanded and modified, form the basis of the present volume.

As a treatise it must necessarily be incomplete, as it scarcely touches
on the history of the subject--a part which must always be of deep
interest. The solely physiological aspect of colour has also been
scarcely dealt with; that part which the physicist can submit to
measurement being that which alone was practicable under the
circumstances.

        W. De W. Abney.

_South Kensington,
1st May, 1891._




CONTENTS.


CHAPTER I.

Sources of Light--Reflected Light--Reflection from Roughened
Surfaces--Colour Constants p. 11

CHAPTER II.

A Standard of Light--Formation of the Spectrum by Prisms and by the
Diffraction Grating--Wave-lengths of the principal Fraunhofer
Line--Position of Colours in the Spectrum p. 17

CHAPTER III.

The Visible and Invisible Parts of the Spectrum--Methods for showing the
Existence of the Invisible Portions--Phosphorescence--Photography of the
Dark Rays--Thermo-Electric Currents p. 30

CHAPTER IV.

Description of Colour Patch Apparatus--Rotating Sectors--Method of
making a Scale for the Spectrum p. 41

CHAPTER V.

Absorption of the Spectrum--Analysis of Colour--Vibrations of
Rays--Absorption by Pigments--Phosphorescence--Interference p. 51

CHAPTER VI.

Scattered Light--Sunset Colours--Law of the Scattering by Fine
Particles--Sunset Clouds--Luminosities of Sunlight at different
Altitudes of the Sun p. 62

CHAPTER VII.

Luminosity of the Spectrum to Normal-eyed and Colour-blind
Persons--Method of determining the Luminosity of Pigments--Addition of
one Luminosity to another p. 76

CHAPTER VIII.

Methods of Measuring the Intensity of the Different Colours of the
Spectrum, reflected from Pigmented Surfaces--Templates for the Spectrum
p. 88

CHAPTER IX.

Colour Mixtures--Yellow Spot in the Eye--Comparison of Different
Lights--Simple Colours by Mixing Simple Colours--Yellow and Blue from
White p. 112

CHAPTER X.

Extinction of Colour by White Light--Extinction of White Light by Colour
p. 126

CHAPTER XI.

Primary Colours--Molecular Swings--Colour Sensations--Sensations absent
in the Colour-blind p. 133

CHAPTER XII.

Formation of Colour Equations--Kœnig's Curves--Maxwell's Apparatus and
Curves p. 147

CHAPTER XIII.

Match of Compound Colours with Simple Colours--All Colours reduced to
Numbers--Method of Matching a Colour with a Spectrum Colour and White
Light p. 156

CHAPTER XIV.

Complementary Colours--Complementary Pigment Colours--Measurement of
Complementary Colours p. 167

CHAPTER XV.

Persistence of Images on the Retina--The Use of Coloured Discs p. 179

CHAPTER XVI.

Contrast Colours--Measurement of Contrast Colours--Fatigue of the
Eye--After-Images p. 196




LIST OF ILLUSTRATIONS.


    FIG.                                                       PAGE

        Colour-patch apparatus                       _Frontispiece_

    1. Spectrum of sunlight                                      18

    2. Carbon poles of an electric light                         20

    3. Curve for converting prismatic spectrum into wave-lengths 28

    4. The thermopile                                            35

    5. Heating effect of different sources of radiation          38

    6. Colour-patch apparatus                                    42

    7. Rotating sectors                                          45

    8. Spectrum of Carbon Sodium and Lithium                     48

    9. Interference bands                                        60

    10. Absorption of rays by the atmosphere                     68

    11. Luminosity curve of spectrum of the positive pole of the
        electric light                                           79

    12. Rectangles of white and vermilion                        82

    13. Arrangement for measuring the luminosities of pigments   83

    14. Measurement of the intensity of rays reflected from white
        and coloured surfaces                                    88

    15. Intensity of rays reflected from vermilion, emerald green,
        and French ultramarine                                   92

    16. Method of obtaining two patches of identical colour      95

    17. Absorption by red, blue, and green glasses               99

    18. Light reflected from metallic surfaces                  100

    19. Intensities of vermilion, carmine, mercuric iodide, and
        Indian red                                              101

    20. Intensities of gamboge, Indian yellow, cadmium yellow,
        and yellow ochre                                        101

    21. Intensities of emerald green, chromous oxide, and terre
        verte                                                   103

    22. Intensities of indigo, Antwerp blue, cobalt, and French
        ultramarine                                             104

    23. Method of obtaining a colour template                   104

    24. Template of carmine                                     106

    25. Template of luminosity of white light                   108

    26. Absorption of transmitted and reflected light by
        Prussian blue and carmine                               107

    27. Collimator for comparing the intensity of two sources
        of light                                                109

    28. Spectrum intensities of sunlight, gaslight, and blue
        sky                                                     109

    29. Comparison of sun and sky lights                        111

    30. Slide with slits to be used in the spectrum             113

    31. Screen on which to match gamboge                        116

    32. Diaphragm in front of prism                             128

    33. Curve of sensitiveness of silver bromo-iodide           136

    34. Curves of colour sensations                             139

    35. Kœnig's curves of colour sensations                     151

    36. Maxwell's colour-box                                    152

    37. Maxwell's curves of colour sensations                   154

    38. Chromatic circle                                        168

    39. Disc to cause alternate opening and closing of two
        slits                                                   179

    40. Disc painted blue and red                               181

    41. Electro-motor with discs attached                       183

    42. Method of cutting disc to allow an overlap of a second
        disc                                                    184

    43. Arrangement to find value of gamboge in terms of emerald
        green and vermilion                                     188

    44. Disc arranged to give approximately all the spectrum
        colours                                                 192

    45. Method of showing contrast colours                      196




COLOUR MEASUREMENT AND MIXTURE.


CHAPTER I.

  Sources of Light--Reflected Light--Reflection from Roughened
  Surfaces--Colour Constants.

There is nothing, perhaps, in our everyday life which appeals more to
the mind than colour, yet so accustomed are the generality of mankind to
its influence that but few stop to inquire the "why and wherefore" of
its existence, or its cause. To those few, however, there is a source of
endless and boundless enjoyment in its study; for in the realms of
physical and physiological science there is perhaps no other subject in
which experiments give results so fascinating and often so beautiful.
Although its serious study must be undertaken with a clear mind, a good
eye, and a fair supply of patience, yet a general idea of the subject
may be grasped by those who are possessed of but ordinary intelligence.

Colour phenomena are encountered nearly every day of one's life, and the
fact that they are so frequently met with, prevents that attention to
them, or even their remark. Who amongst us, for instance, has noticed
the existence of what are called positive and negative after images,
after looking at some strongly illuminated object, or would have gauged
the fact that a certain portion of the nervous system can be fatigued by
a colour, and give rise to images of its complementary, had not an
enterprising advertiser, who manufactures a household necessary, drawn
attention to it in a manner that could not be misunderstood.

If on an autumn afternoon we pass through a garden whilst it is still
perfectly light, we can notice the gorgeous colouring of the flowers,
and appreciate with the eyes the beauty of each tint. As evening comes
on the tints darken, the darkest-coloured flowers begin to lose their
colour, and only the brightest strike the eye. When night still further
closes in every colour goes, though the outlines of the flowers may
still be distinguished; and it would not be impossible, in some parts,
to see a tiny speck of pale light upon the ground amongst them. This
speck of light we should know from experience to be the light from a
glow-worm. Why is it that we lose the colour of the flowers and
recognize the tiny light from this small worm? The reason for the one is
that in order for objects which are not self-luminous to be seen at all,
light must fall on them and illuminate them, and the light which they
reflect may be coloured if they possess the qualities to reflect
coloured light. The glow-worm's light is seen, not because it does not
emit light in the day-time, but because the eye, being limited in
sensitiveness, is unable to distinguish it when it is flooded with the
light of day. The glow-worm, however, is self-luminous, as is shown by
the fact that it emits light in the dark, the light itself being
slightly coloured if compared with that of day. That a candle-flame or
the sun is self-luminous is an axiom, and need not be philosophised
upon; but what must be impressed on the reader is, that though an object
which requires to be illuminated to be seen, is not self-luminous, yet
when illuminated it does in fact become a source of illumination to the
eye, although the light is only light reflected from its surface. It is
a point worth remembering that the rougher the surface of an object, the
brighter to the eye it will be. That is, a coloured object when polished
will be a bad secondary source of illumination, as the light incident
upon it will be very nearly reflected from the surface, according to
the ordinary laws of reflection; but if it be roughened it will become a
much better source, as the roughnesses, though obeying the laws of
reflection, will reflect light in every direction. A good example of
this is an ordinary sheet of glass. Light from a source falling on its
surface is scarcely reflected in any direction except in that determined
by the ordinary laws of reflection, and it will be scarcely visible to
the eye. Grind its surface, however, and the innumerable facets caused
by the grinding will reflect light back to the eye in whatever position
it be placed, and will thus be distinctly seen.

We may here premise that even the roughest surface will reflect a
greater percentage--varying greatly according to the nature of the
surface--of light in the direction which it would do if it were a smooth
surface than in any other; and in taking measurements of the light
irregularly reflected from a rough surface, this fact must be borne in
mind.

Not only must we know how colour is produced, but we must also be able
to refer it to some standard which shall be readily reproduced, and
which shall be unalterable. There are two variable factors which have to
be taken into account in colour experiments: the first is the quality of
light which illuminates the object, and the second is the sensitiveness
of the eye which perceives it, as light is only a sensation which is
recognized by the brain through the medium of the eye. We shall, as we
go on, see that different qualities of light may cause objects to appear
of different hues, and further that eyes may vary in perceptive power,
to an extent of which the large majority of people are not aware. Hence
it becomes necessary as far as possible to eliminate these variables.

The task which we have set ourselves to perform then, is first to find a
suitable light for experimental work, and next to endeavour to refer
colour to an eye which has no abnormal defects. This being accomplished,
we have then to find means to measure the different constants which are
involved in colour, and to refer the measurements to some standard.
Colour constants are three, viz. hue, luminosity, and purity; and it
will be seen that if these three are determined, the measurement of the
colour is complete.

Perhaps the meaning of these terms may require to be explained. The hue
of a colour is what in common parlance is often called the colour. Thus
we talk of rose, violet, magenta, emerald green, and so on, but for
measuring purposes the hue had best be referred to the spectrum colours
as a standard (the means of doing so will be shortly explained), for
they are simple colours, which can be expressed by numbers. Compound
colours, which it may be said are invariably to be found in nature,
being mixtures of simple colours, can be just as readily referred to the
spectrum. By the luminosity of a colour we mean its brightness, the
standard of reference being the brightness of a white surface when
illuminated by the same white light. By the purity of a colour we mean
its freedom from admixture with white light. An example of different
degrees of purity will be found in washes of water-colours of different
tenuity. Thus if we wash a sheet of paper with a light tint of carmine,
the whiteness of the paper is not obliterated; if we pass another wash
over it the whiteness of the paper is lessened, and so on. The lightest
tint is that which is most lacking in purity.




CHAPTER II.


   A Standard Light--Formation of the Spectrum by Prisms and by the
   Diffraction Grating--Wave-lengths of the principal Fraunhofer
   Line--Position of Colours in the Spectrum.

As we have to turn to the spectrum for pure and simple colours, from
which we may produce any compound colour we may wish to deal with, we
will first consider the light with which we shall form it. A spectrum
may be produced from any source of light, such as sunlight, limelight,
the electric light, gaslight, or incandescence electric light, as also
from incandescent vapours, or gases; but it is only a solid which is, or
is rendered incandescent, that will give us a _continuous_ spectrum, as
it is called, that is, a spectrum which is unbroken by gaps of
non-luminosity, or sudden change of brightness, throughout its length.

Fig. 1.--Spectrum of Sunlight.

The great desideratum for the study of colour is a light which not only
gives a practically continuous spectrum, but one which is produced by
the radiation of matter which is black when cold, and which can be kept
at a constantly high temperature. We have purposely said "black" in the
sentence above, since it is believed that differently coloured bodies,
when heated to equal temperatures, might not give the same relative
intensities to the different parts of the spectrum, the variation being
dependent on the colour of the heated body. A black body must always
give the same visible spectrum when heated to the same temperature. The
spectrum of sunlight (Fig. 1) is not continuous, as we find it crossed
by an innumerable number of fine lines of varying breadth and blackness.
This want of continuity would not be fatal to its adoption were it
possible to use it outside the limits of our atmosphere, as then, unless
the temperature of the sun itself changed, the spectrum produced would
be invariable; but unfortunately the relative brightness or luminosity
of the different parts of the spectrum varies from day to day, and hour
to hour, according to the height of the sun above the horizon (see Chap.
VI.); and its integral brightness varies according to the clearness of
the sky. It is evident then, that, as a reference light, sunlight is
most unsuitable, so we may dismiss it from our possible standards.

Fig. 2.--The Carbon Poles of an Electric Light.

By the process of elimination we may arrive at the light upon which we
can rely, for the purpose we have in view, viz. the production of a
spectrum of moderate size, and sufficiently bright to be well viewed
when projected upon a screen. For some purposes, as for instance in
becoming acquainted with the general character of the spectrum, a
feebler light, such as gaslight, or light from electrical glow lamps,
may be employed, since the spectrum may be viewed directly by the eye
without the intervention of a screen. They have two drawbacks for our
object: one being the want of general intensity, and the other the
feeble luminosity of blue and violet rays in their spectrum (see page
110). The limelight we can also dismiss for want of steadiness. Its
whiteness and luminosity varies according to the oxygen playing on the
lime cylinder, rendering the relative intensities of the different parts
of the spectrum so erratic as to make it unreliable. This leaves the
(electric) arc-light as the only one which is really available. Remember
how the arc-light is produced. A current of electricity passes between
the ends of two thick black carbon rods, or poles as they are called,
through an air space of small interval, and the passage of the current
renders the tips of these rods white-hot (Fig. 2). The centre of the end
of one pole, called the positive pole, where a crater-like depression is
formed, is the part which attains the whitest heat, and its temperature
seems to be constant, and to be that of the volatilization of carbon.
Numerous experiments have been made by the writer, and he has found that
the light emitted by this crater in the positive pole is, within the
limits of the error of observation, always of the same whiteness, and
consequently gives a spectrum which is unvarying in the proportionate
intensities of the different colours. When the experiments made to
determine the luminosity of the spectrum are described, the method of
ascertaining this will be readily understood.

In the spectrum produced by this light there are two places in the
violet where there are bands of violet lines slightly brighter than the
general spectrum. They are principally due to the light emitted from the
incandescent vapour of carbon, which is volatilized and plays between
the two poles (see Fig. 2); but as these bands are of but small visual
intensity, and situated towards the limit of the visible spectrum, they
do not interfere with eye-measures of colours, though they do, to a
certain extent, to the analysis of radiation by photography. If we throw
the positive pole a little behind the negative pole we can, however,
considerably mitigate this evil. We can separate the carbon rods to such
a degree that the white-hot crater faces the observer, and a good deal
of the arc is hidden. This is well seen in the figure.

We have now described the light we have adopted, and the reasons for
adopting it; and having obtained our light, we can now consider by what
plan we shall form our spectrum. There are two ways open to us--one by
glass prisms, and the other by a diffraction grating. Glass prisms
separate white light, or indeed any light, into its components, from the
fact that the refraction of each coloured ray differs from every other.
Thus the red rays are least refracted, and the violet the most, and the
yellow, green and blue are intermediate between them, being placed in
the order of least refrangibility. Between these there is of course
every shade of simple colour, one melting into the other. In order to
form a pure and bright spectrum with prisms, in a room of limited
dimensions, we have to use certain auxiliary apparatus which are not
positively essential, though convenient. The real essentials to form a
spectrum are a narrow slit, a glass prism, with perfectly plane faces,
and a lens. If this be the only apparatus available, the slit must be
placed at a long distance from the prism, the beam of light must pass
through the slit on to the prism, and the lens must be placed at such a
distance from the slit that it forms a sharp image on a screen. When the
light passes through the prism, the screen will have to be rotated in
the arc of a circle, so that its distance from the slit measured along
the line of the ray to the prism, and from the prism to the screen, is
the same as it would be without the intervening prism. An apparatus of
this description is not convenient, however, as it requires much more
space than is often available. If a lens be placed between the slit and
the prism, at exactly its focal length from the former, the light
entering the slit will, after passage through the lens, emerge as
parallel rays, that is, they will emerge as they would do if the slit
were placed at an infinite distance from the observer.

The focal length of this collimating lens need not be greater than
twelve to eighteen inches, so that the great space required by the
cruder apparatus is very much curtailed. The lens and slit are mounted
one at each end of a tube of the necessary length, and are thus handy to
use.

Instead of one prism two or three may be used, giving an angular
dispersion of the spectrum two or three times respectively greater than
that which would be given by only one prism; consequently to obtain a
given length of spectrum with the increased dispersion, the focal length
of the lens used to focus the image on the screen may be diminished.

The drawback to the use of prisms is that the dispersion of the red end
of the spectrum is much less than that of the blue end, and is apt to
give a false impression as to the relative luminosities of, and length
of spectrum occupied by, the different colours. In some text-books it is
told us that the diffraction grating gives us a dispersion which is in
exact relation to the wave-length. This is not true, however, as it can
only give one small portion in such relationship, and that only when it
is specially set for the purpose. The subject of diffraction is one into
which it would be foreign to our purpose to wander. We may say that for
measures such as we shall make, it is handier to employ prisms, as the
prismatic spectrum is more intense than the diffraction spectrum. This
can be readily understood when we consider the subject even
superficially. If we throw a beam of light on a grating which contains
perhaps some 14,000 parallel lines in the space of one inch in width,
the lines being ruled on a plane and bright metallic surface, and
receive the reflected beam on a screen, the appearance that is presented
is a white central spot, together with six or seven spectra of gradually
diminishing brightness on each side of it, all except the first pair
overlapping one another. That these different spectra do exist can be
readily shown by placing in the beam a piece of red glass, when
symmetrical pairs of the red part of the spectrum will be found, one of
each pair being on opposite sides of what will now be the central red
spot. Half the light falling on the grating is concentrated in this
central spot, and the remaining half goes to form the spectra; the pair
nearest the central spot being the brightest. We thus are drawn to the
conclusion that at the outside we can only have less than one-quarter of
the incident light to form the brightest spectrum we can use. With two
good prisms we use at last three-fourths of the incident light, so that
for the same length of spectrum we can get at least three times the
average brightness that we should get were we to employ a diffraction
grating.

We must now refresh the reader's memory with a few simple facts about
light, in order that our meaning may be clear when we speak of rays of
different wave-lengths. Every colour in the spectrum has a different
wave-length, and it is owing to this difference in wave-length that we
are able to separate them by refraction, or diffraction, and to isolate
them. Light, or indeed any radiation, is caused by a rhythmic
oscillation of the impalpable medium which we, for want of a better
term, call ether, and the distance between two of these waves which are
in the same phase is called the wave-length of the particular radiation.
The extent of the oscillation is called the amplitude, which when
squared is in effect a measure of the _intensity_ of the radiation. Thus
at sea the distance between the crests of two waves is the wave-length,
and the height from trough to crest the amplitude; and the intensity, or
power of doing work, of two waves of the same wave-lengths but of
different heights, is as the square of their heights. Thus, if the
height of one were one unit, and of the other two units, the latter
could do four times more work than the former. The waves of radiation
which give the sensation of colour in the spectrum vary in length, not
perhaps to the extent that might be imagined, considering the great
difference that is perceived by the eye, but still they are markedly
different. The fact that the spectrum of sunlight is not continuous, but
is broken up by innumerable fine lines, has already been alluded to.
The position of these lines is always the same, as regards the colour in
which they are situated, and is absolutely fixed directly we know their
wave-length; hence if we know the wave-lengths of these lines, we can
refer the colour in which they lie to them. Now some lines of the
solar-spectrum are blacker and consequently more marked than others, and
instead of referring the colours to the finer lines, we can refer them
to the distance they are from one or more of these darker lines, where
these latter are absolutely fixed; in fact they act as mile-stones on a
road.

In the red we have three lines in the solar spectrum, which for sake of
easy reference are called A, B and C; in the orange we have a line
called D, in the green a line called E, in the blue F, in the violet G,
and in the extreme violet H. These lines are our fiducial lines, and all
colours can be referred to them. The following are the wave-lengths of
these lines, on the scale of =1/10,000,000= of a millimetre as a unit

    A            7594
    B            6867
    C            6562
    D            5892
    E            5269
    F            4861
    G            4307
    H            3968

When the spectrum is produced by prisms the intervals between these
lines are not proportional to the wave-lengths, and consequently if we
measure the distance of a ray in the spectrum from two of these lines,
we have to resort to calculation, or to a graphically drawn curve, to
ascertain its wave-length. For the purpose of experiments in colour the
graphic curve from which the wave-length can immediately be read off is
sufficient. The following diagram (Fig. 3) shows how this can be done.

The names and range of the principal colours which are seen in the
spectrum has been a matter of some controversy. Professor Rood has,
however, made observations which may be accepted as correct with a
moderately bright spectrum. If the spectrum be divided into 1000 parts
between A in the red, and H, the limit of the violet, he makes the
following table of colours.

    +---------------+--------------------------------+
    |    Scale.     |            Colour.             |
    +---------------+--------------------------------+
    |   0 to  149   | Red.                           |
    | 149 to  194   | Orange red.                    |
    | 194 to  210   | Orange.                        |
    | 210 to  230   | Orange yellow.                 |
    | 230 to  240   | Yellow.                        |
    | 240 to  344   | Yellow green and green yellow. |
    | 344 to  447   | Green and blue green.          |
    | 447 to  495   | Azure blue.                    |
    | 495 to  806   | Blue and blue violet.          |
    | 806 to 1000   | Violet.                        |
    +---------------+--------------------------------+

Fig. 3.--Curve for converting the Prismatic Spectrum into Wave-lengths.

In the above scale (Fig. 3) A = 0, B = 74·0, C = 112·7, D = 220·3,
E = 363·1, F = 493·2, G = 753·6, H = 1000.

These are the main subdivisions of colour, but it must be recollected
that one melts into the other. When the spectrum is very bright the
colours tend to alter in hue; thus the orange becomes paler, and the
yellow whiter, and the blue paler. On the other hand, if the spectrum be
diminished in brightness the tendency is for the colours to change in
the opposite direction. Thus the yellow almost disappears and becomes of
a green hue, whilst the orange becomes redder, and the spectrum itself
becomes shorter to the eye than before.

Let us strictly guard ourselves, however, from the criticism that all
eyes see not alike. Suffice it to say that the above table is correct
for the ordinary or normal eye, and does not necessarily apply to those
who have defective vision as regards colour sensation.




CHAPTER III.


  The Visible and Invisible Parts of the Spectrum--Methods for showing
  the Existence of the Invisible Portions--Phosphorescence--Photography
  of the Dark Rays--Thermo-Electric Currents.

We are apt to forget, when looking at the spectrum, that what the eye
sees is not all that is to be found in the prismatic analysis of light.
The spectrum, it must be recollected, is not limited to those rays which
the eye perceives. There are rays both beyond the extreme violet and
below the extreme red, which exist and which exercise a marked effect on
the world's economy. Thus, rays beyond the violet are those which with
the violet and the blue rays principally affect vegetation, enabling
certain chemical changes to take place which are necessary for its
growth and health; whilst the rays below the red are those possessing
the greatest amount of energy, and if they fall upon bodies which absorb
them, as very nearly all bodies do to a certain extent, they heat them.
The warmth we feel from sunlight is principally due to the dark rays
which lie below the red of the spectrum.

The existence of both kinds of these dark rays may be demonstrated in a
very simple manner by the effect that they produce on certain bodies.
For instance, there is a yellow dye with which cheap ribbon is dyed,
which if placed in the spectrum and beyond the violet causes a visible
prolongation of the spectrum. The light in the newly-seen and once
invisible part of the spectrum is yellow, the colour of the ribbon
itself. In fact, the whole of that part of the spectrum, which on the
white screen is seen as blue and violet, becomes yellow, the red and
green remaining unchanged. This change in colour is due to fluorescence,
a phenomenon of light which Sir G. Stokes found was caused by an
alteration in the lengths of the waves of light when reflected from
certain bodies. It is not meant to imply by this that the wave-length of
any ray falling on a body can be altered by reflection, but only that
the body itself on which the rays fall emits rays of light which are not
of the same wave-length as those which fall upon it. Now it is a fact
that the rays that lie beyond the violet, and which are ordinarily
invisible, are shorter than the violet rays, and that these are shorter
than the yellow rays. It follows therefore that when, what we may now
call, the ultra-violet rays fall on the yellow dyed ribbon, the waves
emitted by it are so lengthened that they appear yellow to the eye
instead of dark, violet, or blue.

We can also brush a solution of quinine on the screen, and immediately
the place where the ultra-violet rays fall is illuminated by a violet
light. We do not see the ultra-violet rays themselves, but only the rays
of increased wave-length, which are emitted by their effect on the
sulphate of quinine. Common machine oil as used for engines also emits
greenish rays when excited by the ultra-violet rays, and a very
beautiful colour it is. Fluorescence then is one means of demonstrating
the existence of the ultra-violet rays--or Ritter's rays as they were
formerly called, after their discoverer--in a very simple manner. The
method of rendering the effects of the infra-red rays visible to the eye
is also interesting. All, or at all events most, of our readers have
seen Balmain's luminous paint. A glass or card coated with this
substance, which is essentially a sulphide of calcium, when exposed to
the light of the sun, or of the electric arc, and then taken into
comparative darkness, is seen to shine with a peculiar violet-coloured
light. If when thus excited we place it in a bright spectrum for some
little time, we shall find on shutting off the light that where the
ultra-violet and blue fell on it, the violet light is intenser than the
light of the main part of the screen; where the yellow fell there is
neither increase or diminution in brightness; but that in the red it
becomes darker, and also beyond the limit of the visible spectrum,
indicating the existence of rays beyond, which through their greater
length have not the power of affecting the eye. If the spectrum be shut
off, however, very soon after it falls on the plate, it has been
asserted that the red and infra-red rays have increased the brightness
of that particular part of the plate on which they fell. At first these
two observations seem to contradict one another; they do not in reality.
We may expose a tablet of Balmain's paint to light, and place a heated
iron in contact with the back of the plate; we shall then find that the
iron produces a bright image of its surface on a less bright background.
This bright image will gradually fade away, and the same space will
eventually become dark compared with the rest of the plate. The reason
of this is clear. When light excites the paint a certain amount of
energy is poured into it, which it radiates out slowly as light. When
the hot iron is placed in contact with it, the heat causes the light to
radiate more rapidly, and consequently with greater intensity, at the
part where its surface touches, and the energy of that particular
portion becomes used up. When the energy of radiation of this part
becomes less than that of the rest of the tablet, its light must of
necessity be of less brightness than that of the background, with which
the heated iron has had no contact. For this reason the image of the
iron subsequently appears dark. We shall see presently, and as before
stated, that the principal heating effect of the spectrum lies in the
red and infra-red, and it is owing to the heating of the paint by these
rays that the image might be at first slightly brighter than the
background, and subsequently darker.

There is another way in which the existence of both the ultra-violet and
infra-red rays can be demonstrated, and that is by means of photography.
If we place an ordinary photographic plate in the spectrum and develop
it, we shall find that besides being affected by the blue and violet
rays, it is also affected by the rays beyond the violet, the energy of
these rays being capable of causing a decomposition of the sensitive
silver salt. If quartz prisms and lenses be used, and the electric light
be the source of illumination, the ultra-violet spectrum will extend to
an enormous extent. A more difficult, but perhaps even more interesting
means of illustrating the existence of the infra-red rays, and first due
to the writer, can be made by means of photography. It is possible to
prepare a photographic plate with bromide of silver, which is so
molecularly arranged that it becomes capable of being decomposed not
only by the violet and blue rays, but also by the red rays, and by those
rays which have wave-lengths of nearly three times that of the red rays.
It would be inappropriate to enter into a description of the method of
the preparation of these plates. Those who are curious as to it will
find a description in the Bakerian lecture published in the
Philosophical Transactions of the Royal Society for 1881. With plates so
prepared it has been found possible to obtain impressions in the dark
with the rays coming from a black object, heated to only a black heat.

That these dark rays possess greater energy or capacity for doing work
of some kind than any other rays of the spectrum, can be shown by means
of a linear thermopile (Fig. 4), if it be so arranged as to allow only a
narrow vertical slice of light to reach its face.

Fig. 4.--The Thermopile.

The principle of the thermopile we need not describe in detail. Suffice
it to say that the heating of the soldered junctions of two dissimilar
metals (there are ten pairs of antimony and bismuth in the above
instrument) produces a feeble current of electricity, which, however, is
sufficient to cause a deflection to the suspended needle of a delicate
galvanometer. To the needle is attached a mirror weighing a fraction of
a grain, and the deflections are made visible by the reflection from it
of a beam of light issuing from a fixed point along a scale. The greater
the heating of the junctions of the thermopile, within limits which in
these cases are never exceeded, the greater is the current produced, and
consequently the greater is the deflection of the mirror-bearing
needle, and of the beam of light along the scale. In order to get a
comparative measure of the energies of the different rays, it is
necessary that they should be completely absorbed. Now the junctions
themselves of the pile being metal, and therefore more or less bright,
will not absorb completely, but if they be coated with a fine layer of
lamp-black, the rays falling on the pile will be absorbed by this
substance, and their absorption will cause a rise in temperature in it,
and the heat will be communicated to the thermopile.

If we make a bright spectrum, and one not too long, say three inches in
length, and pass the linear thermopile through its length, we shall find
that when the galvanometer is attached, the galvanometer needle will be
differently deflected in its various parts. The deflection will be
almost insensible in the violet, but sensible in the blue, rather more
in the green, still more in the yellow, and it will further increase in
the red. When, however, the slit of the thermopile is placed beyond the
limit of the visible spectrum, the deflection enormously increases, and
will increase till a position is reached as far below the red as the
yellow is above it. After this maximum is reached, by moving the pile
still further from the red, the galvanometer needle will travel towards
its zero, and finally all deflection will cease. At this point we may
suppose we have reached the limit of the spectrum, but if rock-salt
prisms and lenses be used, the limit will be increased. What the real
limit of the spectrum is, is at present unknown; Mr. Langley with his
bolometer, and rock-salt prisms, an instrument more sensitive than the
thermopile, must have nearly reached it.

Fig. 5.--Heating effect of different Sources of Radiation.

The above figure is a graphic representation of the heating effect of
the spectrum of the electric light, sunlight, and the incandescence
electric light, on the lamp-black coating of the thermopile, as shown by
the galvanometer. The vast difference between the heating effect of the
visible rays of the first two sources compared with the last is clearly
indicated.

Since every ray may be taken as totally absorbed, the heating of the
lamp-black is a measure of the energy or the capacity of performing work
of some description, which they possess. Waves of the sea do work when
they beat against the shore, and they do work when they lift a vessel.
If we notice a ship at anchor we shall find that behind the vessel and
towards the shore the waves are lowered in height or amplitude; the
energy which they have expended in raising the vessel of necessity
causes this lowering. In the same way the waves of light, after falling
on matter whose molecules or atoms are swinging in unison with them, are
destroyed, and the energy is spent in either decomposing the matter into
a simpler form at first--though the subsequent form may be more
complex--or in raising its temperature. As lamp-black or carbon is in
its simplest form, the only work done upon it by the energy of radiation
is the raising of its temperature, and it is for this reason that this
material is so excellent for covering the junctions of the pile. The eye
evidently does not absorb all rays, since only a limited part of the
spectrum is visible, and it would be useless to take a measure of the
heating effect of lamp-black for the visible part of the spectrum as a
measure of its luminosity, since the latter fades off in the red--the
very place in which the heat curve rises rapidly.




CHAPTER IV.


  Description of Colour Patch Apparatus--Rotating Sectors--Method of
  making a Scale for the Spectrum.

Before proceeding further we must describe somewhat in detail two or
three pieces of apparatus to be used in the experiments we shall make.

The first piece was devised by the writer a few years ago, and has got
rid of several objections which existed in older pieces of apparatus. It
is not only useful for lecture purposes, but also for careful laboratory
work. The ordinary lecture apparatus for throwing a spectrum on the
screen is of too crude a form to be effective for the purpose we have in
view; the purity of the colours seen on the screen is more than
doubtful, and this alone unfits it for our experiments. If we want to
form a pure spectrum we must have a narrow slit, prisms with true, flat
surfaces, and lenses of proper curvature. As a rule the ordinary
lecture apparatus for forming the spectrum lacks all of these
requisites.

Fig. 6.--Colour Patch Apparatus.

The accompanying diagram (Fig. 6) will give an idea of the apparatus we
shall employ. On the usual slit S₁ of a collimator C is thrown, by means
of a condensing lens L₁, a beam of light, which emanates from the
intensely white-hot carbon positive pole of the electric light. The
focus is so adjusted that an image of the crater is formed on the slit.
The collimating lens L₂ is filled by this beam, and the rays issue
parallel to one another and fall on the prisms P₁ and P₂, which
disperse them. The dispersed beam falls on a corrected photographic
lens L₃, attached to a camera in the ordinary way. It is of slightly
larger diameter than the height of the prisms, and a spectrum is
formed on the focusing-screen D, which is slewed at a slight angle with
the perpendicular to the axis of the lens L₃. This is necessary, because
the focus of the least refrangible or red rays is longer than that of
the more refrangible or blue rays. By slewing the focusing-screen as
shown, a very good general focus for every ray may be obtained. When
the focusing-screen is removed, the rays form a confused patch of
parti-coloured light on a white screen F, placed some four feet off the
camera. The rays, however, can be collected by a lens L₄, of about two
feet focus, placed near the position of the focusing-screen, and
slightly askew. This forms an image on the screen of the near surface of
the last prism P₂; and if correctly adjusted, the rectangular patch of
light should be pure and without any fringes of colour. The card D
slides into the grooves which ordinarily take the dark slide. In it
will be seen a slit S₂, the utility of which will be explained later on.

We shall usually require a second patch of white light, with which to
compare the first patch. Now, although the light from the positive pole
of the carbons is uniform in quality, it sometimes varies in quantity,
as it is difficult to keep its image always in exactly the centre of the
slit. If we can take one part of the light coming through the slit to
form the spectrum, and another part to form the second patch of white
light, then the brightness of the two will vary together. At first sight
this might appear difficult to attain; but advantage is taken of the
fact that from the first surface of the first prism P₁ a certain amount
of light is reflected. Placing a lens L₅, and a mirror G, in the path of
this reflected beam, another square patch of light can be thrown on the
same screen as that on which the first is thrown, and this second patch
may be made of the same size as the first patch, if the lens L₅ be of
suitable focus, and it can be superposed over the first patch if
required; or, as is useful in some cases, the two patches may be placed
side by side, just touching each other.

We are thus able to secure two square white patches upon the screen F,
one from the re-combination of the spectrum, and one from the reflected
beam. If a rod be placed in the path of these two beams when they are
superposed, each beam will throw a shadow of the rod upon the screen.
The shadow cast by the integrated spectrum will be illuminated by the
reflected beam, and the shadow cast by the latter will be illuminated by
the former. In fact we have an ordinary Rumford photometer, and the two
shadows may be caused to touch one another by moving the rod towards or
from the screen. When the illumination of the two shadows by the white
light is equal, the whole should appear as _one_ unbroken gray patch. To
prevent confusion to the eye a black mask is placed on the screen F with
a square aperture cut out of it, on which the two shadows are caused to
fall. If it be desired to diminish the brightness of either patch, it
can be accomplished by the introduction of rotating sectors M, which can
be opened and closed at pleasure during rotation, in the path of one or
other of the beams.

Fig. 7.--Rotating Sectors.

The annexed figure (Fig. 7) is a bird's-eye view of the instrument. A A
are two sectors, one of which is capable of closing the open aperture by
means of a lever arrangement C, which moves a sleeve in which is fixed a
pin working in a screw groove, which allows the aperture in the sectors
to be opened and closed at pleasure during their revolution; D is an
electro-motor causing the sectors to rotate. To show its efficiency, if
two strips of paper, one coated with lamp-black and the other white, are
placed side by side on the screen, and if one shadow from the rod falls
on the white strip, and the other shadow on the black strip of paper,
and the rotating sectors are interposed in the path of the light
illuminating the shadow cast on the white strip, the aperture of the
sectors can be closed till the white paper appears absolutely blacker
than the black paper. White thus becomes darker than lamp-black, owing
to the want of illumination. This is an interesting experiment, and we
shall see its bearings as we proceed, as it indicates that even
lamp-black reflects a certain amount of white or other light.

Having thus explained the main part of the apparatus with which we shall
work, we can go on and show how monochromatic light of any degree of
purity can be produced on the screen. If the slit in the cardboard slide
D be passed through the spectrum when it has been focused on the
focusing-screen, only one small strip of practically monochromatic light
will reach the screen, and instead of the white patch on the screen we
shall have a succession of coloured patches, the colour varying
according to the position the slit occupies in the spectrum. It should
be noted that the purity of the colour depends on two things--the
narrowness of the slit S₁ of the collimator, and of the slit S₂ in the
card. If two slits be cut in the card D, we shall have two coloured
patches overlapping one another, and if the reflected beam falls on the
same space we shall have a mixture of coloured light with white light,
and either the coloured light or the white light can be reduced in
brightness by the introduction of the rotating sectors. If the rod be
introduced in the path of the rays we shall have two shadows cast, one
illuminated with coloured light, monochromatic or compound, and the
other with white light, and these can be placed side by side, and
surrounded by the black mask as before described.

Fig. 8.--Spectrum of Sodium Lithium and Carbon.

There is one other part of the apparatus which may be mentioned, and
that is the indicator, which tells us what part of the spectrum is
passing through the slit. Just outside the camera, and in a line with
the focusing-screen, is a clip carrying a vertical needle. A small beam
of light passes outside the prism P₁; this is caught by a mirror
attached to the side of the apparatus, and is reflected so as to cast a
shadow of the needle on to the back of the card D, on which a carefully
divided scale of twentieths of an inch is drawn. To fix the position of
the slit the poles of the electric light are brushed over with a
solution of the carbonates of sodium and lithium in hydrochloric acid,
and the image of the arc is thrown on the slit. This gets rid of the
continuous spectrum, and only the bright lines due to the incandescent
vapours appear on the focusing-screen (Fig. 8). Amongst other lines we
have the red and blue lines due to the vapour of lithium; the orange,
yellow (D), and green lines of sodium, together with the violet lines of
calcium (these last due to the impurities of the carbons forming the
poles). These lines are caused successively to fall on the centre of the
slit by moving the card D, which for the nonce is covered with a piece
of ground glass, and the position of the shadow of the needle-point on
the scale is registered for each. A further check can be made by taking
a photograph of these lines, or of the solar spectrum, and having fixed
accurately on the scale any one of these lines already named, the
position of the others on the scale may be ascertained by measurement
from the photograph. Now the wave-lengths of these bright lines have
been most accurately ascertained, in fact as accurately as the dark
lines in the solar spectrum. Thus the scale on the card is a means of
localizing the colour passing through the slit or slits. Should more
than one slit be used in the spectrum the positions of each can be
determined in exactly the same way. The most tedious part of the whole
experimental arrangement with this apparatus is what may be called the
scaling of the spectrum.

A fairly large spectrum may be formed upon the screen without altering
any arrangement of the apparatus, when it has been adjusted to form
colour patches. If a lens L₆ (see Fig. 6) of short focus be placed in
front of L₄ (the big combining lens), an enlarged spectrum will be
thrown upon the screen F, and if slits be placed in the spectrum the
images of their apertures are formed by the respective coloured rays
passing through them, so that the colours which are combined in the
patch can be immediately seen.




CHAPTER V.


  Absorption of the Spectrum--Analysis of Colour--Vibrations of
  Rays--Absorption by Pigments--Phosphorescence--Interference.

We must now briefly consider what is the origin, or at all events the
cause, of the colour which we see in objects. It is not proposed to
enter into this by any means minutely, but only sufficiently to enable
us to understand the subject which is to be brought before you. What for
instance is the cause of the colour of this green solution of
chlorophyll, which is an extract of cabbage leaves? If we place it in
the front of the spectrum apparatus and throw the spectrum on the
screen, we find that while there is a certain amount of blue
transmitted, the green is strong, and there are red bands left, but a
good deal of the spectrum is totally absorbed. Forming a colour patch of
this absorption spectrum on the screen, we see that it is the same
colour as the chlorophyll solution, and of this we can judge more
accurately by using the reflected beam, and placing the rod in position
to cast shadows. (The light of the reflected beam is that of the light
entering the slit.) The colour then of the chlorophyll is due to the
absence of certain colours from the spectrum of white light. When white
light passes through it, the material absorbs, or filters out, some of
the coloured rays, and allows others to pass more or less unaffected,
and it is the re-combination of these last which makes up the colour of
the chlorophyll. We have a green dye which to the eye is very similar in
colour to chlorophyll, but putting a solution of it in front of the
spectrum, we see that it cuts off different rays to the latter. It would
be quite possible to mistake one green for the other, but directly we
analyze the white light which has filtered through each by means of the
spectrum, we at once see that they differ. Hence the spectrum enables
the eye to discriminate by analysis what it would otherwise be unable to
do. Any coloured solution or transparent body may be analyzed in the
same way, and, as we shall see subsequently, the intensity of every ray
after passing through it can be accurately compared with the original
incident light. There are some cases, indeed the majority of cases, in
which the colour transmitted through a small thickness of the material
is different to that transmitted through a greater thickness. For
instance, a weak solution of litmus in water is blue when a thin layer
is examined, and red when it is a thicker or more concentrated layer.
Bichromate of potash is more ruddy as the thickness increases. This can
be readily understood by a reference to the law of absorption. Suppose
we have a thin layer of a liquid which gives a purple colour when two
simple colours, red and blue, pass through it, and that this thin layer
cuts off one-quarter of the red and one-half of the blue incident on it,
another layer of equal thickness will cut off another quarter of the
three-quarters of red passing through the first layer, and half of the
one-half left of the blue; we shall thus have nine-sixteenths of the red
passing and only a quarter of the blue. With a third layer we shall have
twenty-seven sixty-fourths of red and only one-eighth of blue left,
showing that as the thickness of the liquid is increased the blue
rapidly disappears, leaving the red the dominant colour. Now what is
true of two simple colours is equally true of any number of them, where
the rates of absorption differ from one another, and what is true for a
solution is true for a transparent solid. In some opaque bodies, such as
rocks, the reflected colour often differs slightly from that of the same
when they are cut into thin and polished slices, through which the
light can pass. The reason is that when opaque, light penetrates to a
very small distance through the surface, and is reflected back, whilst
in these layers the colour has to struggle through more coloured matter,
and emerges of a different hue.

The question why substances transmit some rays and quench others, brings
us into the domain of molecular physics. Of all branches of physical
science this is perhaps the most fascinating and the most speculative,
yet it is one which is being built up on the solid foundations of
experiment and mathematics, till it has attained an importance which the
questions depending on it fully warrants. We have to picture to
ourselves, in the case in point, molecules, and the atoms composing
them, of a size which no microscope can bring to view, vibrating in
certain definite periods which are similar to the periods of oscillation
of the waves of light. At page 26 we have given the lengths of some of
the waves which give the sensation of coloured light. Now as light, of
whatever colour it may be, is practically transmitted with the same
velocity through air which has the same density throughout, it follows
that the number of vibrations per second of each ray can be obtained by
dividing the velocity of light in any medium by the wave-length. The
following table gives roughly the number of vibrations per second of the
ether giving rise to the colours fixed by the dark solar lines.

    +-----------------------+-----------------+
    |    Name of Line.      |  Millions of    |
    |                       |  Millions of    |
    |                       |   Vibrations    |
    |                       |  per Second.    |
    +-----------------------+-----------------+
    | A in the Red          |  395            |
    | B   "     "           |  437            |
    | C   "     "           |  458            |
    | D   "    Orange       |  510            |
    | E   "    Green        |  570            |
    | F   "    Blue         |  618            |
    | G   "    Violet       |  697            |
    | H   "    Ultra-Violet |  757            |
    +-----------------------+-----------------+

If we endeavour to gauge what this rate of oscillation means we shall
scarcely be able to realize it, even by a comparison with some
physically measurable rate of vibration. A tuning-fork, for instance,
giving the middle C, vibrates 528 times per second. Compare this with
the number of vibrations of the waves of light, and we still are as far
as ever from realizing it, yet the velocity of light, and the lengths of
the different waves have been accurately determined; the latter,
although the much smaller quantity, with even greater accuracy than the
first. These rates of vibration must therefore be--cannot help being--at
all events approximately true. This being so, we know that some of the
atoms of the molecules at least, and perhaps in some cases the
molecules themselves, are vibrating at the same rate as those waves of
light, which they refuse to allow to pass. If we have a child's swing
beginning to oscillate, we know that it is only by well-timed blows that
the extent of the swing is permanently increased, and the energy exerted
by the person who gives the well-timed blow is expended on producing the
increased amplitude. In the same way if the rate of vibration of a wave
of light is in accord with that of a molecule or atom, the amplitude or
swing of the atom or molecule is increased, and the energy of the wave
and therefore its amplitude is totally or partially destroyed; and as
the amplitude is a function of the intensity of the light, the ray fails
to be seen at all, or else is diminished in brightness.

In what way the atoms vibrate where more than one ray is absorbed is
still a matter of speculation, but no doubt as experimental methods are
more fully developed, and mathematicians investigate the results of such
experiments, we shall be able to form a picture of the vibrations
themselves. At page 137 a speculation as to the reason why solids or
liquids can absorb more waves of light than one which are adjacent to
each other is put forward, but it does not deal with the absorptions
which occupy various parts of the spectrum. Again, too, we have the fact
that the energy absorbed by these atoms and molecules from the waves of
light, must show itself as work done on them--it may be as heat or as
chemical action. We shall see by and by that in some cases, no doubt, at
least a part is expended in the latter form of work.

Perhaps this mode of looking at the question of colour in objects may
make the subject more interesting to the reader than it at first appears
to be deserving. The whole subject is one which enlarges the faculty of
making mental pictures, and this is one of the most useful forms of
scientific education.

But how can we distinguish between pigments which to the eye are
apparently the same? If we dye paper with the green dye referred to, we
can place it in the spectrum, and we shall see that the dye reflects
differently to the white paper. In fact we shall find that it refuses to
reflect in those parts of the spectrum which the transparent solution
refused to transmit. So long as the light passes through the dye-stuff,
it is indifferent, as regards the colour produced, whether the colouring
matter be at a distance from the paper or whether the latter be dyed
with it, as we can see at once. If we place the solution of the dye in
the reflected beam of the apparatus and form a patch on the screen, and
alongside throw the patch of white light from the integrated or
recombined spectrum upon the dyed paper, it will be found that the two
colours are alike; that is, the green-coloured light on the white paper,
or the white light on the green paper are the same. Similarly we may
experiment on other dyes, such as magenta, log-wood, &c., and we shall
see that like results are obtained. It should be said, however, that
when the paper is dyed with the colouring matter a _small quantity_ of
white light will be reflected from the surface of the paper itself. We
may now say that the general colour is given to a body by its refusal to
transmit or reflect, more or less completely, certain rays of the
spectrum. Should the solvent form a compound with the dye, perhaps this
would not be absolutely true, but in the large majority of cases the
statement is correct. When we have bodies which are also fluorescent,
this statement would also have to be modified, but we need not consider
these for the present.

Another source of colour in objects, though very rarely met with, and
which for our object we need not stay to explain in detail, is the
interference of light. Such is seen in soap-bubbles. Briefly it may be
said that the colours are due to rays of light reflected from the inner
surface of the film, which quench other rays of light of the same
wave-length reflected from the outer surface. If two series of waves of
the same wave-length are going in the same direction and from the same
source, each of which has the same intensity as the other, that is,
having the same amplitude, and it happens that the one series is exactly
half a wave-length behind the other, then the crest of one wave in the
first series will fill up the trough of the other in the second series,
and no motion would result, and this lack of motion means darkness,
since it is the wave motion which gives the sensation of light. If then
we have white light falling on two reflecting surfaces, such as the
front and back of a soap-film, part of the light will be reflected from
each, and if the film be of such a thickness that the latter reflects
light exactly 1/2 wave-length, 3/2 or 5/2 wave-length, &c., of some
colour behind the former, the colour due to that particular wave-length
will be absent from the reflected white light, and instead of white
light we shall have coloured light, due to the combination of all the
colours less this colour, which is quenched.

A very pretty experiment to make is to throw the image of a soap film on
the screen, and to watch the change in the colours of the film. Their
brilliancy increases as the film becomes thinner, and the bands, which
first appear close to each other, separate, and then we see a large
expanse of changing colour. A soap solution should be made according to
almost any of the published formulæ, and a piece of flat card be dipped
in it, and be drawn across a ring of wire some inch in diameter,
or--what the writer prefers best--the stop of a photographic lens. A
film will form and fill the aperture. The ring or stop may be placed
vertically in a clamp, and a beam of light caused to fall at an angle of
about 45 degrees on to the film. If a lens be placed in the path of the
reflected beam to form an image of the aperture, the colours which the
film shows can be exhibited to an audience, if the diameter of the image
be made four or five feet. Instead of this large image, a small image
may be thrown on the slit of the spectroscope, by using a lens of a
greater focal length, and if the beam be so directed that it falls on
the axis of the collimator, a very fairly bright spectrum may be also
thrown on the screen. The appearance of the spectrum is somewhat like
that shown in the above diagram (Fig. 9).

Fig. 9.--Interference Bands.

If we take a horizontal line across the spectrum, we shall see what
particular colours are missing from the reflected light which falls on
the part of the slit corresponding to that line. The colours of some
objects, such as of the opal, and the lovely colouring of some feathers
are due to interference of light. The partial scattering of different
rays by small particles will also cause light to be coloured, as we
shall see in the experiments we shall make to imitate the colour of
sunlight at various altitudes of the sun. We may, however, take it as a
rule that the colour of objects is produced by the greater or less
absorption of some rays, and the reflection in the case of opaque
bodies, or the transmission, in the case of transparent bodies, of the
remainder.




CHAPTER VI.


  Scattered Light--Sunset Colours--Law of the Scattering by Fine
  Particles--Sunset Clouds--Luminosities of Sunlight at different
  Altitudes of the Sun.

It is probable that we should be able to ascertain approximately the
true colour of sunlight (if we may talk of the colour of white light) if
we could collect all the light from a cloudless sky, and condense it on
a patch of sunlight thrown on a screen. For skylight is, after all, only
a portion of the light of the sun, scattered from small particles in the
atmosphere, part of the light being scattered into space, and part to
our earth. The small particles of water and dust--and when we say small
we mean small when measured on the same scale as we measure the lengths
of waves of light--differentiate between waves of different lengths, and
scatter the blue rays more than the green, and the green than the red;
consequently what the sun lacks in blue and green is to be found in the
light of the sky. The effect that small water particles have upon light
passing through them can be very well seen in the streets of London at
night, when the atmosphere is at all foggy. Gaslights at the far end of
a street appear to become ruby red and dim, and half-way down only
orange, but brighter, whilst close to they are of the ordinary yellow
colour, and of normal brightness. When no fog is present the gas-lights
in the distance and close to are of the same colour and brightness,
showing that their change in appearance is simply due to the misty
atmosphere intervening between them and the observer. We can imitate the
light from the sun, after its passage through various thicknesses of
atmosphere, in a very perfect manner in the lecture-room, using the
electric light as a source. A condensing lens is put in front of the
lamp, and in front of that a circular aperture in a plate. Beyond that
again is a lens which throws an enlarged image of the aperture on the
screen, which we may call our mock sun. If we place a trough of glass,
in which is a dilute solution of hyposulphite of soda, carefully
filtered from motes as far as possible, in front of the aperture, we
have an image of the aperture unaffected by the insertion of the
solution. The white disc on the screen will, as we have said before, be
a close approximation to sunlight on a May-day about noon, when the sky
is clear. By dropping into the trough a little dilute hydrochloric
acid, a change will be found to come over the light of the mock sun; a
pale yellow colour will spread over its surface, and this will give way
to an orange tint, and at the same time its brightness will diminish.
Gradually the orange will give place to red, the luminosity will be very
small, being of the same hue as that seen in the sun when viewed through
a London fog. Finally the last trace of red will so mingle with the
scattered white light that the image will disappear, and then the
experiment is over.

If we track the cause of this change of colour in our artificial sun, we
shall find that it is due to minute particles of sulphur separating out
from the solution of hyposulphite, and the longer the time that elapses
the more turbid the dilute solution will become. This experiment
exemplifies the action of small particles on light. Examining the trough
it will be found that whilst the light which passes _through the
solution_ principally loses blue rays, the light which is scattered from
the sides is almost cerulean in blue, and can well be compared with the
light from the sky. We can analyze the transmitted light very readily by
focusing the beam from the positive pole of the electric light on to the
slit of our colour apparatus, and placing the lens L₆ (Fig. 6) in
position to form the large spectrum on the screen. We can also show the
colour of the light which goes to form the spectrum, by sending the
patch of light reflected from the first surface of the first prism just
above it. We thus have the spectrum and the light forming the spectrum
to compare with one another. Using this apparatus and inserting the
trough of dilute hyposulphite in the beam, the spectrum is of the
character usually seen with the electric light; but on dropping the
dilute hydrochloric acid into the solution the same hues fall on the
slit of the spectroscope which fell upon the screen to form the mock
sun, and the spectrum is seen to change as the light changes from white
to yellow, and from yellow to red. First the violet will disappear, the
blue and the green being dimmed, the former most however; then the blue
will vanish to the eye, the green becoming still less luminous, and the
yellow also fading; the green and yellow will successively disappear,
leaving finally on the screen a red band alone, which will be a near
match to the colour of the unanalyzed light, as may be seen by comparing
it with the adjacent patch formed from the reflected beam.

We have here a proof that the succession of phenomena is caused by a
scattering of the shorter wave-lengths of light, and that the shorter
the waves are the more they are scattered. It has been found
theoretically by Lord Rayleigh that the scattering takes place in
inverse proportion to the fourth power of the wave-length; thus, if two
wave-lengths, which may be waves in the green and violet, are in the
proportion of three to four, the former will be scattered as 1/3⁴ to
1/4⁴, or as 256 to 81, which is approximately as three to one.
Consequently if the green in passing through a certain thickness of a
turbid medium loses one-half the violet in passing through the same
thickness will lose five-sixths of its luminosity. The inverse fourth
powers of the following wave-lengths, which are within the limits of the
whole visible spectrum, are shown below.

    +------+------+------+------+------+
    |  λ   | 7000 | 6000 | 5000 | 4000 |
    +------+------+------+------+------+
    | 1/λ⁴ |    1 | ·504 | ·260 | ·107 |
    +------+------+------+------+------+

Supposing λ7000 by the scattering of small particles loses one-tenth
of its luminosity, then λ6000 would have ·454 of its original
brightness; λ5000, ·234; and λ4000, ·095; that is, whilst λ7000
would lose one-tenth only of its luminosity, λ4000 in the violet
would retain not quite one-hundredth of its brightness.

During the years 1885, 1886, and 1887, the writer measured the
luminosity of the solar spectrum at different times of the year,
and at different hours of the day (see _Phil. Trans._ 1887:
"Transmission of Sunlight through the Earth's Atmosphere"), and from
the results he found that the smallest coefficient of scattering for
one atmosphere at sea-level for each wave-length was ·0013, when λ⁻⁴
was for convenience sake multiplied by 10¹⁷ (thus λ6000⁻⁴ on this
scale was 77·2), and that the mean was ·0017.

The following table shows the loss of light for the rays denoted by the
principal lines given at page 26, using this last coefficient for
different air thicknesses. This is equivalent to giving the intensity of
the rays of sunlight when the sun is at different altitudes.

  +---+------+-----+----------------------------------------------+
  |   |      | 1   | Light after passing through atmospheres of   |
  Line| Wave-| -   | the following thicknesses.                   |
  |   |length| λ⁻⁴ +-+----+----+----+----+----+----+----+----+----+
  |   |      |×10¹⁷|0|  1 |  2 |  3 |  4 |  5 |  6 |  7 |  8 | 32 |
  +---+------+-----+-+----+----+----+----+----+----+----+----+----+
  | A | 7594 |  30 |1|·955|·908|·857|·815|·775|·736|·707|·665|·107|
  | B | 6867 |  45 |1|·926|·858|·795|·735|·684|·632|·583|·542|·086|
  | C | 6562 |  54 |1|·912|·832|·759|·693|·632|·576|·526|·480|·019|
  | D | 5892 |  83 |1|·868|·754|·655|·569|·494|·428|·372|·323|·001|
  | E | 5269 | 129 |1|·803|·644|·518|·427|·334|·268|·216|·173| -- |
  | F | 4861 | 179 |1|·738|·544|·402|·296|·219|·161|·119|·088| -- |
  | G | 4307 | 291 |1|·609|·367|·220|·137|·084|·051|·031|·019| -- |
  | H | 3968 | 403 |1|·506|·254|·128|·071|·033|·016|·008|·004| -- |
  +---+------+------+-+----+----+----+----+----+----+----+----+----+


The sun traverses the following thicknesses of atmosphere when it is at
the angles shown above the horizon.

    1 atmosphere        90°
    2     "             30°
    3     "             19·30
    4     "             14·30
    5     "             11·30
    6     "              9·30
    7     "              8·30
    8     "              7·30

Fig. 10.--Absorption of Rays by the Atmosphere.

It traverses thirty-two atmospheres when it is very nearly setting.
Bougier and Forbes have calculated that the extreme thickness of the
atmosphere, traversed by its light when the sun is on the horizon, is
approximately 35-1/2 atmospheres. The absorption shown by 32 atmospheres
will therefore be very close to that which would be observed at sunset
on an ordinary day, and it will be seen that practically all rays have
been scattered from the light, except the red, and a little bit of the
orange.

As to the luminosity of the sun at these different altitudes, we can
easily find it by reducing the luminosity curve of the sun at some known
altitude by the factors in the table just given, for as many
wave-lengths as we please, and thus construct another curve. The area of
the figure thus obtained would be a measure of the total luminosity on
the same scale as the area of the luminosity curve from which it was
derived.

The following are the approximate luminosities of the sun when the light
shines

    through 0 atmospheres 1
       "    1     "        ·840
       "    2     "        ·705
       "    3     "        ·594
       "    4     "        ·496
       "    5     "        ·417
       "    6     "        ·303
       "    7     "        ·256
       "    8     "        ·215
       "   32     "        ·002

It will thus be seen that the sun is 420 times less bright just at
sunset than it is if it were to shine directly overhead, and about 350
times brighter than it is for a winter sun in a cloudless and mistless
sky at twelve o'clock, for the altitude of the sun in our latitude is
about 30° at that time, and corresponds with a thickness of two
atmospheres, through which the sun has to shine. We all know that to
look at the sun at any time near noon in a cloudless sky dazzles the
eyes, but that near sunset it may be looked at with impunity. The
reduction in luminosity explains this fact.

The distribution of the scattering particles in the atmosphere is very
far from regular. As we ascend, the particles get more sparse, as is
shown by the less scattering that takes place of the blue rays compared
with the red. Thus at an altitude of some 8000 feet the mean coefficient
of scattering is about ·0003, instead of ·0017, which it is at
sea-level. It must be recollected that there is only about three-fourths
of the air above us at 8000 feet, and it is less dense. There will
therefore be a diminution of particles not only because there is less
air, but because the air itself is less capable of keeping them in
suspension. Up to 3000 or 4000 feet there is no very great marked
difference in the scattering of light, as observations carried on during
five years have shown; but above that the scattering rapidly
diminishes, and at 20,000 feet it must be very small indeed, if the
diminution increases as rapidly as has been found it does at the
altitude of 8000 feet.

We must repeat once more that the blue of the sky is principally if not
entirely due to the presence of these particles, the rays scattered by
them, which are principally the blue rays, being reflected back from
them, giving the sensation of blue which we know as sky-blue. The
greater the number of these fine particles that are encountered by
sunlight, the greater the scattering will be, and the bluer the sky. It
is more than probable that the blue sky of Italy, so proverbial for
being beautiful, is due to this cause, since from its geographical
position the small particles of water must be very abundant there.

Carrying this argument further, we should expect that as we mount higher
the blue would become more fully mixed with the darkness of space, and
this Alpine travellers will tell you is the case. At heights of 12,000
feet or more, on a clear day, the sky seems almost black, and it is no
uncommon thing to see this admirably rendered in photographs of Alpine
scenery when taken at a height. Many of the late Mr. Donkin's
photographs show this in great perfection, as also Signor Sella's.

Before quitting this subject we may call attention not only to the
colour of the sun itself at sunset, but also to the colouring of the sky
which accompanies the sun as it sinks. This colouring is often different
to the colour that the sun itself assumes; but we can easily show that
the effects so wonderfully beautiful are entirely dependent on this
scattering of light by these small intervening particles in the air. We
often see a ruddy sun, and perhaps nearly in the zenith, or even further
away from the sun, clouds of a beautiful crimson hue, lying on a sky
which appears almost pea-green, whilst nearer to the sun the sky is a
brilliant orange, which artists imitate with cadmium yellow. Let us fix
our attention first on the crimson cloud. The clouds of which the
colouring is so gorgeous are often not 1000 feet above us, and were we
to be at that altitude we should see the sun not quite so ruddy as we
see it from the earth, and the cloud would consequently be illuminated
by the sun with a more orange tint; but the light reflected from the
cloud to our eyes has to pass through, say 1000 feet of dense
atmosphere, and thus the total atmosphere that the light traverses in
the latter case is always greater than the air thickness through which
the direct light from the sun has to pass; hence more orange is cut off,
and the light reflected from the cloud is redder. This red, however,
will not account for the brilliant crimson and purples which we so
often see. It has to be remembered that not sunlight alone illumines the
cloud, but also the blue light of the sky. The feebler the intensity of
the red, the more will the blue of the sky be felt in the mixture of
light which reaches our eyes, and consequently we may have any tint
ranging from crimson to purple, since red and blue make these hues,
according to the proportions in which they are mixed.

Now let us see how we get the brilliant orange of the sky itself. When
the evening is perfectly clear and free from mist and cloud, the orange
in the sky is very feeble, showing that the intensity depends upon their
presence. Now a look at the table will show that the sun is very close
to the horizon when it becomes ruddy under normal conditions; but that
when the light traverses a thickness of eight atmospheres, the blue and
violet, and most of the green, are absent, leaving a light of yellowish
colour. To traverse eight atmospheres the light has only to come from a
point some eight degrees above the horizon. When the sun is near the
horizon, it sends its rays not only to us and over us, but in every
direction; and an eye placed some few thousand feet above the earth
would see the sun almost of its midday colour, for sunset colours of the
gorgeous character that we see at sea-level are almost absent at high
altitudes. If a cloud or mist were at such an altitude the sunlight
would strike it, and whilst only a small portion would be selectively
scattered, owing to the general grossness of the particles, the major
part would be reflected back to our eyes, and come from an altitude of
over eight to ten degrees, and would therefore, after traversing the
intervening atmosphere, reach us as the orange-coloured light of which
we have just spoken. The clouds which are orange when near the sun, are
usually higher than those which are simultaneously red or purple. The
pea-green colour of the sky is often due to contrast, for the contrast
colour to red is green, and this would make the blue of the sky appear
decidedly greener. Sometimes, however, it is due to an absolute mixture
of the blue of the sky and the orange light which illuminates the same
haze. In the high Alps it is no uncommon occurrence for the snow-clad
mountains to be tipped with the same crimson we have described as
colouring the clouds, and this is usually just after sunset, when the
sun has sunk so low beneath the horizon that the light has to traverse a
greater thickness of dense air, and consequently to pass through a
larger number of small particles than it has when just above the
horizon. In this case the red of the sunlight mixes with blue light of
the sky, and gives us the crimson tints. The deeper and richer tints of
the clouds just after sunset are also due to the same cause, the
thickness of air traversed being greater.

It is worth while to pause a moment and think what extraordinary sensual
pleasure the presence of the small scattering particles floating in the
air causes us; that without them the colouring which impresses itself
upon us so strongly would have been a blank, and that artists would have
to rely upon form principally to convey their feelings of art. Indeed
without these particles there would probably be no sky, and objects
would appear of the same hard definition as do the mountains in the
atmosphereless moon. They would be only directly illuminated by
sunlight, and their shadows by the light reflected from the surrounding
bright surfaces.




CHAPTER VII.


  Luminosity of the Spectrum to Normal-eyed and Colour-blind
  Persons--Method of determining the Luminosity of Pigments--Addition
  of one Luminosity to another.

The determination of the luminosity of a coloured object, as compared
with a colourless surface illuminated by the same light, is the
determination of the second colour constant. We will first take the pure
spectrum colours, and show how their luminosity or relative brightness
can be determined. Viewing a spectrum on the screen, there is not much
doubt that in the yellow there is the greatest brightness, and that the
brightness diminishes both towards the violet and red. Towards the
latter the luminosity gradient is evidently more rapid than towards the
former. This being the case, it is evident that, except at the brightest
part there are always two rays, one on each side of the yellow, which
must be equally luminous. If the spectrum be recombined to form a white
patch upon the screen, and the slide with the slit be passed through
it, patches of equal area of the different colours will successively
appear; but the yellow patch will be the brightest patch. If the patch
formed by the reflected beam be superposed over the colour patch, and
the rod be interposed, we get a coloured stripe alongside a white
stripe, and by placing our rotating sectors in the path of the reflected
beam, the brightness of the latter can be diminished at pleasure.
Suppose the sectors be set at 45°, which will diminish the reflected
beam to one-quarter of its normal intensity, we shall find some place in
the spectrum, between the yellow and the red, where the white stripe is
evidently less bright than the coloured stripe, and by a slight shift
towards the yellow, another place will be found where it is more bright.
Between these two points there must be some place where the brightness
to the eye is the same. This can be very readily found by moving the
slit rapidly backwards and forwards between these two places of "too
dark" and "too light," and by making the path the slit has to travel
less and less, a spot is finally arrived at which gives equal
luminosities. The position that the slit occupies is noted on the scale
behind the slide, as is also the opening of the sectors, in this case
45°. As there is another position in the spectrum between the yellow and
the violet, which is of the same intensity, this must be found in the
same manner, and be similarly noted. In the same way the luminosities of
colours in the spectrum, equivalent to the white light passing through
other apertures of sectors, can be found, and the results may then be
plotted in the form of a curve. This is done by making the scale of the
spectrum the base of the curve, and setting up at each position the
measure of the angular aperture of the sector which was used to give the
equal luminosity or brightness to the white. By joining the ends of
these ordinates by lines a curve is formed, which represents graphically
the luminosity of the spectrum to the observer. In Fig. 11 the maximum
luminosity was taken as 100, and the other ordinates reduced to that
scale. The outside curve of the figure was plotted from observations
made by the writer, who has colour vision which may be considered to be
normal, as it coincides with observations made by the majority of
persons. The inner curve requires a little explanation, though it will
be better understood when the theory of colour vision has been touched
upon.

Fig. 11.--Luminosity Curve of the Spectrum of the Positive Pole of the
Electric Light.

The observer in this case was colour-blind to the red, that is, he had
no perception of red objects as red, but only distinguished them by the
other colours which were mixed with the red. This being premised, we
should naturally expect that his perception of the spectrum would be
shortened, and this the observations fully prove. If it happened that
his perceptions of all other colours were equally acute with a
normal-eyed person, then his illumination value of the part of the
spectrum occupied by the violet and green ought to be the same as that
of the latter. The diagram shows that it is so, and the amount of red
present in each colour to the normal-eyed observer is shown by the
deficiency curve, which was obtained by subtracting the ordinates of
colour-blind curve from those of the normal curve. There are other
persons who are defective in the perception of green, and they again
give a different luminosity curve for the spectrum. These variations in
the perception of the luminosity of the different colours are very
interesting from a physiological point of view, and this mode of
measuring is a very good test as to defective colour vision. We shall
allude to the subject of colour-blindness in a subsequent chapter.

The following are the luminosities for the colours fixed by the
principal lines of the solar spectrum, and for the red and blue lines of
lithium, to which reference has already been made.

  +----------------------------------------------------+
  |               |                |    Luminosity.    |
  |               |                |-------------------+
  |      Line.    |    Colour.     | Normal |  Red     |
  |               |                |  Eye.  | Colour   |
  |               |                |        | Blind.   |
  +---------------+----------------+--------+----------+
  |  A            | Very dark Red  |   --   |   --     |
  |  B            | Red (Crimson)  |   1·0  |   0      |
  |  Red Lithium  | Red (Crimson)  |   8·5  |    ·5    |
  |  C            | Red (Scarlet)  |  20·6  |   2·1    |
  |  D            | Orange         |  98·5  |  53·0    |
  |  E            | Green          |  50·0  |  49·0    |
  |  F            | Blue Green     |   7·0  |   7·0    |
  |  Blue Lithium | Blue           |   1·9  |   1·9    |
  |  G            | Violet         |    ·6  |    ·6    |
  |  H            | Faint Lavender |   --   |   --     |
  +----------------------------------------------------+

The failure of the red colour-blind person to perceive red is very well
shown from this table. It will for instance be noticed that he perceives
about one-tenth of the light at C which the normal-eyed person
perceives.

A modification of this plan can be employed for measuring the luminosity
of the spectrum, and it is _excessively_ useful, because we can adapt it
to the measurement of colours other than these simple ones. In the plan
already explained it was the colour in the patch that was altered, to
get an equal luminosity with a certain luminosity of white light. In the
modified plan the luminosity of the white light is altered, for the
luminosity of the shadow illuminated by the reflected beam can be
altered rapidly at will by opening or closing the apertures of the
sectors whilst it is rotating. The slit in the slide is placed in the
spectrum at any desired point, and the aperture of the sectors altered
till equal luminosities are secured. The readings by this plan are very
accurate, and give the same results as obtained by the previous method
employed.

It must be remembered that we have so far dealt with colours which are
spectrum colours, and which are intense because they are colours
produced by the spectrum of an intensely bright source of light. By an
artifice we can deduce from this curve the luminosity curve of the
spectrum of any other source of light. If by any means we can compare,
_inter se_, the intensity of the same rays in two different sources of
light, one being the electric light, we can evidently from the above
figure deduce the luminosity curve of the spectrum of the other source
of light (see p. 109).

We can now show how we can adapt the last method to the measurement of
the luminosity of the light reflected from pigments.

Fig. 12.--Rectangles of White and Vermilion.

Fig. 13.--Arrangement for measuring the Luminosities of Pigments.

Suppose the luminosity of a vermilion-coloured surface had to be
compared with a white surface when both were illuminated, say by
gaslight, the following procedure is adopted. A rectangular space is cut
out of black paper (Fig. 12) of a size such that its side is rather less
than twice the breadth of the rod used to cast a shadow: a convenient
size is about one inch broad by three-quarters of an inch in height.
One-half of the aperture is filled with a white surface, and the other
half with the vermilion-coloured surface. The light L (Fig. 13)
illuminates the whole, and the rod R, a little over half an inch in
breadth, is placed in such a position that it casts a shadow on the
white surface, the edge of the shadow being placed accurately at the
junction of the vermilion and white surface. A flat silvered mirror M is
placed at such a distance and at such an angle that the light it
reflects casts a second shadow on the vermilion surface. Between R and
L are placed the rotating sectors A. The white strip is caused to be
evidently too dark and then too light by altering the aperture of the
sectors, and an oscillation of diminishing extent is rapidly made till
the two shadows appear equally luminous. A white screen is next
substituted for the vermilion and again a comparison made. The mean of
the two sets of readings of angular apertures gives the relative value
of the two luminosities. It must be stated, however, that any diffused
light which might be in the room would relatively illuminate the white
surface more than the coloured one. To obviate this the receiving screen
is placed in a box, in the front of which a narrow aperture is cut just
wide enough to allow the two beams to reach the screen. An aperture is
also cut at the front angle of the box, through which the observer can
see the screen. When this apparatus is adopted, its efficiency is seen
from the fact that when the apertures of the rotating sectors are closed
the shadow on the white surface appears quite black, which it would not
have done had there been diffused light in any measurable quantity
present within the box. The box, it may be stated, is blackened inside,
and is used in a darkened room. The mirror arrangement is useful, as any
variation in the direct light also shows itself in the reflected light.
Instead of gaslight, reflected skylight or sunlight can be employed by
very obvious artifices, in some cases a gaslight taking the place of the
reflected beam. When we wish to measure luminosities in our standard
light, viz. the light emitted from the crater of the positive pole of
the arc-light, all we have to do is to place the pigment in the white
patch of the recombined spectrum, and illuminate the white surface by
the reflected beam, using of course the rod to cast shadows, as just
described. The rotating sectors must be placed in either one beam or the
other, according to the luminosity of the pigment.

The luminosities of the following colours were taken by the above
method, and subsequently we shall have to use their values.

                            Electric Light.

    White                          100
    Vermilion                       36
    Emerald Green                   30
    Ultramarine                      4·4
    Orange                          39·1
    Black                            3·4
    Black (different surface)        5·1

Suppose we have two or more colours of the spectrum whose luminosities
have been found, the question immediately arises, as to whether, when
these two colours are combined, the luminosity of the compound colour is
the sum of the luminosities of each separately. Thus suppose we have a
slide with two slits placed in the spectrum, and form a colour patch of
the mixture of the two colours and measure its luminosity, and then
measure the luminosity of the patch first when one slit is covered up,
and then the other. Will the sum of the two latter luminosities be equal
to the measure of the luminosity of the compounded colour patch? One
would naturally assume that it would, but the physicist is bound not to
make any assumptions which are not capable of proof; and the truth or
otherwise is perfectly easy to ascertain, by employing the method of
measurement last indicated. Let us get our answer from such an
experiment.

   +-------------+---------------+
   |   Colours   | Observed      |
   |  Measured.  | Luminosity.   |
   +-------------+---------------+
   |  R          |    203·0      |
   |  G          |     38·5      |
   |  V          |      8·5      |
   | (R + G)     |    242        |
   | (G + V)     |     45        |
   | (R + V)     |    214        |
   | (R + G + V) |    250        |
   +-------------+---------------+

Three apertures were employed, one in the red, another in the green, and
the third in the violet, and the luminosity was taken of each
separately, next two together, and then all three combined, with the
results given above.

The accuracy of the measurements will perhaps be best shown by adding
the single colours together, the pairs and the single colours, and
comparing these values with that obtained when the three colours were
combined. When the pairs are shown they will be placed in brackets; thus
(R + G) means that the luminosity of the compound colour made by red and
green are being considered.

     R + G  + V  = 250·0
    (R + G) + V  = 250·5
    (R + V) + G  = 252·5
    (G + V) + R  = 248·0
    (R + G  + V) = 250·0

The mean of the first four is 250·25, which is only 1/10% different from
the value of 250 obtained from the measurement of (R + G + V) combined.
Other measures fully bore out the fact that the luminosity of the mixed
light is equal to the sum of the luminosities of its components. It is
true that we have here only been dealing with spectrum colours, but we
shall see when we come to deal with the mixture of colours reflected
from pigments that the same law is universally true.

It will be proved by and by that a mixture of three colours, and
sometimes of only two colours, be they of the spectrum or of pigments,
can produce the impression of white light. If then we measure all the
components but one, and also the white light produced by all, then the
luminosity of the remaining component can be obtained by deducting the
first measures from the last. For instance, red, green and violet were
mixed to form white light. The luminosity of the white being taken as
100, the red and violet were measured and found to have a luminosity of
44·5 and 3 respectively. This should give the green as having a
luminosity of 52·5. The green was measured and found to be 53, whilst a
measurement of the red and green together gave a luminosity of 96·5
instead of 97.




CHAPTER VIII.


  Methods of Measuring the Intensity of the Different Colours of the
  Spectrum, reflected from Pigmented Surfaces--Templates for the Spectrum.

Fig. 14.--Measurement of the Intensity of Rays reflected from white and
coloured surfaces.

We will now proceed to demonstrate how we can measure the amount of
spectral light reflected by different pigments. Let us take a strip of
card painted with a paste of vermilion, leaving half the breadth white;
and similarly one with emerald green. If we place the first in the
spectrum so that half its breadth falls on the red, and the other half
on the white card, we shall see that apparently the red and orange rays
are undiminished in intensity by reflection from the vermilion, but that
in the green and beyond but very little of the spectrum is reflected.
With the emerald green placed similarly in the spectrum, the red rays
will be found to be absorbed, but in the green rays the full intensity
of colour is found, fading off in the blue. What we now have to do is
to find a method of comparing the intensities of the different rays
reflected from the pigments, with those from the white surface. We will
commence with the second of the two methods which the writer devised
with this object, and then describe the first, which is more complex.
Suppose we have, say a card disc three inches in diameter, painted with
the pigment whose reflective power has to be measured, and place it on a
rotating apparatus with black and white sectors of say five inches
diameter, and capable of overlapping so as to show different proportions
of black to white (see Fig. 42). If we throw a colour patch (shown in
Fig. 14 as the area inside the dotted square) on the combination of
black and white, and at the same time on the pigmented disc, it is
probable that either one or other will be the brighter. By moving the
slit along the spectrum it is evident, however, that a colour can be
found which is equally reflected from them both whilst rotating. Take as
an example the sectors as set at two parts white, to one part black, the
centre disc being vermilion, the slit is moved along the spectrum until
such a point is reached that the colour reflected from the ring and the
disc appears of the same brightness, for it must be recollected that
they cannot differ in hue, as the light is monochromatic. It will be
found that the place where they match in brightness is in the red, the
exact position being fixed by the scale at the back of the slide. Taking
the proportion of black to white as three to one, the match will be
found to take place in the orange. Increasing the proportion of black
more and more, a point will be reached where the reflection takes place
uniformly along the blue end of the spectrum, this will be from the
green to the end of the violet. By sufficiently increasing the number of
matches made, a curve of reflection can be made showing the exact
proportion of each ray of the spectrum that is reflected. The uniform
reflection along the blue end of the spectrum shows that a certain
amount of white light is reflected from the pigment.

Next taking the emerald green disc, if we adopt the same procedure it
will be found that for some shades of the ring there are two places in
the spectrum from which the colours reflected give the same brightness.
By plotting curves in exactly the same way as that shown for the curve
of luminosity at page 78, substituting for the open aperture of the
sector the angular value of the white used, we can show graphically the
correct reflection for each part of the spectrum. Sometimes three places
in the spectrum will be read, as giving equal reflections from the
coloured disc and the grey ring.

The accompanying figures show the results obtained for reflection from
vermilion, emerald green, and French blue, after having made a
correction for the white by adding the amount which the black reflects.

The scale is that of the prismatic spectrum employed. On page 46 we
stated that a white surface could be made to appear darker than a black
surface, by illuminating the latter and cutting off the light from the
former. By placing the black surface in place of one of the coloured
ones, as shown in page 82, the luminosity of the black surface can be
ascertained. In this case it was found that almost exactly 5% of the
white light from the crater of the positive pole was reflected. In the
table the original measures are shown, and also the corrected measures,
and for convenience sake the intensity of every ray throughout the
length of the spectrum reflected from white, has been taken as 100. The
position of the reference lines on the scale (Fig. 15) are as follows--

Fig. 15.--Intensity of Rays reflected from Vermilion, Emerald Green, and
French Ultramarine.

B=101, C=96·25, D=89, E=79·9, F=71·5, G=53·5.


                     VERMILION.

   +-----------------------------------------------+
   |            White Sectors.         |           |
   +-----------------------------------|Reading of |
   | Original     |White Cor-|Corrected| Spectrum  |
   |  Setting.    |rected For| White   | Scale.    |
   |--------------+   Black. |   100.  |           |
   | White.|Black.|          |         |           |
   +-------+------+----------+---------+-----------+
   |    10 |  350 |    27·5  |    7·65 | 71-1/2    |
   |    20 |  340 |    37·0  |   10·15 | 84        |
   |    30 |  330 |    46·5  |   12·95 | 86·2      |
   |    50 |  310 |    65·5  |   18·10 | 88·0      |
   |    70 |  290 |    84·5  |   23·50 | 88·7      |
   |    90 |  270 |   103·5  |   29·7  | 89·5      |
   |   120 |  240 |   132·0  |   37·2  | 90·3      |
   |   150 |  210 |   160·5  |   45·0  | 91        |
   |   180 |  180 |   189·0  |   52·5  | 91·6      |
   |   210 |  150 |   217·5  |   60·2  | 92·5      |
   |   220 |  140 |   227·0  |   63·2  | 93·5      |
   |   230 |  130 |   236·5  |   66·2  | 94·5      |
   |   240 |  120 |   246·0  |   68·5  | 96        |
   |   230 |  130 |   236·5  |   66·2  | 97·7      |
   |   210 |  150 |   217·5  |   60·2  |100·0      |
   +-------+------+----------+---------+-----------+

                     EMERALD GREEN.

    +---------------------------------------+------------+
    |          White Sectors                |            |
    +------------------+--------------------+ Reading of |
    | Original Setting.|White Cor-|Corrected| Spectrum   |
    +--------+---------|rected For| White   | Scale.     |
    | White. |  Black. |  Black.  | 100.    |            |
    +--------+---------+----------+---------+------------+
    |    10  |   350   |   27·5   |   7·65  |     50     |
    |    20  |   340   |   37·0   |   10·15 |     54     |
    |    30  |   330   |   46·5   |   12·95 |     55     |
    |    50  |   310   |   65·5   |   18·10 |     57·5   |
    |    70  |   290   |   84·5   |   23·5  |     60·0   |
    |    90  |   270   |  103·5   |   29·7  |     63·5   |
    |   110  |   250   |  122·5   |   34·7  |     65·5   |
    |   130  |   230   |  141·5   |   39·5  |     67·5   |
    |   150  |   210   |  160·5   |   45·0  |     68·5   |
    |   170  |   190   |  179·5   |   50·0  |     71     |
    |   190  |   170   |  195·5   |   54·7  |     73·5   |
    |   210  |   150   |  217·5   |   60·2  |     75·0   |
    |   220  |   140   |  227     |   63·2  |     76     |
    |   220  |   140   |  227     |   63·2  |     78     |
    |   210  |   150   |  217·5   |   60·2  |     80     |
    |   190  |   170   |  198·5   |   54·7  |     82     |
    |   170  |   190   |  179·5   |   50·0  |     83     |
    |   150  |   210   |  160·5   |   45·0  |     84     |
    |   130  |   230   |  141·5   |   39·5  |     85     |
    |   110  |   250   |  122·5   |   34·7  |     86·5   |
    |    90  |   270   |  103·5   |   29·7  |     87·5   |
    |    70  |   290   |   84·5   |   23·5  |     88·5   |
    |    50  |   310   |   65·5   |   18·10 |     90·0   |
    |    30  |   330   |   46·5   |   12·95 |     92     |
    |    20  |   340   |   37·0   |   10·15 |     94     |
    |    10  |   350   |   27·5   |    7·65 |     98     |
    +--------+---------+----------+---------+------------+

                  FRENCH ULTRAMARINE BLUE.

    +-----------------------------------------+------------+
    | White Sectors.                          |            |
    +-----------------+-----------+-----------+ Reading of |
    |Original Setting.| White     | Corrected | Spectrum   |
    +--------+--------+ corrected |  White    | Scale.     |
    | White. | Black. | for black.|  100.     |            |
    +--------+--------+-----------+-----------+------------+
    |    0   |   360  |    18·0   |     5·0   |     84     |
    |   10   |   350  |    27·5   |     7·65  |     80     |
    |   20   |   340  |    37·0   |    10·15  |     77     |
    |   30   |   330  |    46·5   |    12·95  |     75     |
    |   40   |   320  |    56·0   |    15·6   |     74     |
    |   60   |   300  |    75·0   |    20·7   |     72·5   |
    |   80   |   280  |    94·0   |    25·5   |     70·5   |
    |  100   |   260  |   113·0   |    32·5   |     68     |
    |  120   |   240  |   132·0   |    37·2   |     66·5   |
    |  140   |   220  |   151·0   |    42·3   |     62·5   |
    |  160   |   200  |   170·0   |    47·4   |     59·5   |
    |  170   |   190  |   179·5   |    50·0   |     55     |
    |  160   |   200  |   170·0   |    47·4   |     51     |
    |  140   |   220  |   151·0   |    42·3   |     46     |
    |    0   |   360  |    18·0   |     5·0   |     95     |
    |   10   |   350  |    27·5   |     7·65  |     98     |
    |   20   |   340  |    37·0   |    10·15  |     99     |
    |   30   |   330  |    46·5   |    12·95  |    110     |
    +--------+--------+-----------+-----------+------------+

These three measurements have been given in full, since they will be
useful for reference when other experiments are described.

Fig. 16.--Method of obtaining two Patches of identical Colour.

When we have to measure the colour transmitted through coloured bodies,
we have to adopt a slightly different plan, which is extremely accurate.
The first thing necessary is to make some arrangement whereby two beams
of identical colour--that is, of the same wave-length--reach the screen,
one of which passes through the transparent body to be measured, and the
other unabsorbed. If we in addition have some means of equalizing the
intensity of the two beams, we can then tell the amount cut off by the
body through which one beam passes. The method that would be first
thought of would be to use two spectra, from two sources of light; but
should we adopt that plan there would be no guarantee that the spectra
would not vary in intensity from time to time. The point then that had
to be aimed at was to form two spectra from the same source of light,
and with the same beam that passes through the slit of the collimator.
Here we are helped by the property of Iceland spar, which is able to
split up a ray into two divergent rays. By placing what is called a
double-image prism of Iceland spar at the end of the collimator, we get
two divergent beams of light falling on the prisms, and by turning the
double-image prism we are able to obtain two spectra on the screen of
the camera one above the other, and if the slit of the slide be
sufficiently long two beams would issue through it of identical colour,
and separated from one another by a dark space, the breadth of which
depends on the length of the slit of the collimator. It is to be
observed that by this arrangement we have exactly what we require: a
light from one source passes through the same slit, is decomposed by the
same prisms, and as the beams diverge in a plane passing through the
slit of the collimator, the length of spectrum is the same. The problem
to solve is how to utilize these two spectra now we have got them. We
can make the light from the top spectrum pass through the coloured body
by the following artifice. Let us place a right-angled prism in front of
the top slit, reflecting say the beam to the right, and after it has
travelled a certain distance, catch it by another right-angled prism,
and thus reflect it on to the screen. Already in the path of the ray,
issuing through the slit from the bottom spectrum, the lens L₄ is
placed, forming a square patch on the screen. By placing a similar lens
in the path of the other ray after reflection from the second
right-angled prism, we can superpose a second patch of the same colour
over the first patch, and by putting a rod in the path of the two beams
we can have as before two shadows side by side, but this time each
illuminated by the same colour. One shadow will be more strongly
illuminated than the other, owing to the different intensities of beams
into which the double-image prism splits up the primary ray. The two,
however, can be equalized by placing a rotating apparatus in the path of
one of the beams. When equalized the sector is read off, and tells us
how much brighter one spectrum is than the other. Thus suppose in the
direct beam the sectors had to be closed to an angle of 80°, to effect
this, the bottom spectrum would be 180/80, or 2·25 times brighter than
the bottom spectrum. It should be noted that as the two spectra are
formed by the identical quality of light, this same ratio will hold good
throughout their length. If it does not, it shows that the double-image
prism is not in adjustment, and that the same rays are not coming
through the slit in the slide, and it must be rotated till the readings
throughout are the same. One of the most sensitive tests for adjustment
is to form a patch with orange light, when the slightest deviation from
adjustment will be seen by the two patches differing in hue.

We can now place the coloured transparent object in the path of the beam
which is most convenient, and by again equalizing the shadows, measure
the amount it cuts off; this we can do for any ray we choose. As both
right-angled prisms can be attached to the card or slide which moves
across the spectrum, nothing besides the card need be moved. In the
following diagram we have the proportion of rays transmitted by the
three different glasses, red, green, and blue, in terms of the
unabsorbed spectrum. Take for instance on the scale of the spectrum the
number 11. The curve shows that at that particular part of the spectrum
which lies in the blue, the blue glass only allowed 4/100 or 1/25 of the
ray to pass, whilst the green glass allowed 10/100 or 1/10 to pass. So
at scale No. 4 in the orange, through the blue only 2% was transmitted,
through the green glass 4%, and through the red 20%.

Fig. 17.--Absorption by Red, Blue, and Green Glasses.

Fig. 18.--Light reflected from Metallic Surfaces.

Fig. 19.--1. Vermilion 2. Carmine. 3. Mercuric Iodide. 4. Indian Red.

From such curves as these we can readily derive the luminosity curves of
the spectrum, after the white light has passed through the coloured
object. All we have to do is to alter the ordinates of the luminosity
curve of white light in the proportion to the intensities of the rays
before and after passing through the object. It will be seen that when
the luminosity curve of the spectrum of _any_ source is known, this
method holds good.

Fig. 20.--1. Gamboge. 2. Indian Yellow. 3. Cadmium Yellow. 4. Yellow
Ochre.

The intensity of the different rays of the spectrum reflected from
metallic surfaces can also be measured, if for the first or second
right-angled prism a small piece of the metal is substituted, using it
as a reflecting surface, as can also the rays reflected from any surface
which is bright and polished. In Fig. 18 the dotted curves show the
_luminosity_ of the spectrum reflected from the different metals, curve
V being that of white light. These curves are derived by reducing the
ordinates of curve V proportionately to the intensity curves. Thus at 49
brass reflects 77% of the light, and the luminosity of the white is 80.
The luminosity of the light from the brass is therefore 77/100 of 80,
or 61. This shows the method which is adopted, of deducing luminosities
from intensities.

Fig. 21.--1. Emerald Green. 2. Chromous Oxide. 3. Terre Verte.

The light reflected from pigments can also be measured by the same plan.
The procedure adopted is that carried out when measuring their
luminosities, viz. to cause the ray from one spectrum to fall on a strip
of a white surface, and that from the other on a strip of the coloured
surface (see page 82). This is a more convenient method than that just
described, when the coloured surface is small. The annexed figures
(Figs. 19, 20, 21, 22) show the results obtained from various pigments.

Fig. 22.--1. Indigo. 2. Antwerp Blue. 3. Cobalt. 4. French Ultramarine.

Fig. 23.--Method of obtaining a Colour Template.

From curves such as these we are able to produce the colour of the
pigment on the screen from the spectrum itself. This is a useful proof
of the truth of the measurements made. To do this we must mark off on a
card (Fig. 23) the absolute scale of the spectrum along the radius of a
circle, and draw circles at the various points of the scale from its
centre. From the same centre we must draw lines at angles to the fixed
radius corresponding to the various apertures of the sectors required at
the various points of the scale to measure the light reflected from a
pigment. Where each radial line cuts the circle drawn through the
particular point of the scale to which its angle has reference, gives us
points which joined give a curved figure. Such a figure, when cut out
and rotated in front of the spectrum in the proper position (as for
instance by making the D sodium line correspond with that on the scale),
will cut off exactly the same proportion of each colour that the pigment
absorbs. The spectrum, when recombined, should give a patch of the exact
colour of that measured. The spectrum must be made narrow, as the
template is only theoretically correct for a spectrum of the width of a
line, as can be readily seen.

Templates like these will always enable any colour to be reproduced on
the screen, and if the light be used for the spectrum in which the
colour has to be viewed, be it sunlight, gaslight, starlight--whatever
light it is--the colour obtained will be that which the pigment would
reflect if it were viewed in that light.

The identity of the colour produced on the screen by this plan with that
measured, can be readily seen by placing the latter in the reflected
beam of white light alongside the coloured patch formed on the white
surface.

Fig. 24.--Template of Carmine.

In Fig. 24 we have a mask or template of carmine, which was used for
determining if the measurements were right. The black fingerlike-looking
space on the right was the amount of red reflected light, and the other
that of the blue and violet; scarcely any light at all was reflected
from the green part of the spectrum.

Fig. 26.--Absorption of transmitted and reflected Light by Prussian Blue
and Carmine.

On page 108 we have given the diagram of the luminosity of the spectrum
in reference to a standard white light. It will bring this luminosity
more home if, in a similar manner to that described above, we make a
template of this curve (Fig. 25). We can place a narrow slit
horizontally in front of the condensing lens of the optical lantern, and
throw an image of it on to the screen. If in close contact with this
slit we rotate the template, we shall have on the screen a graduated
strip of white light, giving in black and white the apparent luminosity
of the spectrum as seen by the eye.

Fig. 25.--Template of Luminosity of White Light.

It has been stated in chapter V., that it is generally immaterial
whether a pigment is in contact with the paper or away from it, so long
as the light passes through the pigment. The above figure (Fig. 26)
shows the truth of this assertion. I. and II. are the curves taken of
the light transmitted by Prussian blue and carmine respectively, and
III. and IV., from the light reflected from these colours on paper.

Fig. 27.--Collimator for comparing the intensity of two sources of
Light.

To measure the difference in the intensities of the rays of different
sources of light we can use a spectroscopic arrangement with two slits
(S) (Fig. 27) placed in a line at right angles to the axis of the
collimator. One slit is a little below the other, the rays being
reflected to the collimating lens L, by means of two right-angled prisms
P, and two spectra are formed, one above the other. By placing the
rotating sectors in front of one of the sources, the intensities of the
different parts of the spectrum can be equalized and measured.

Fig. 28.--Spectrum Intensities of Sunlight, Gaslight, and Blue Sky.

The curves for the annexed figure (Fig. 28) were derived from measures
taken in this manner. If the rays of a May-day sun are taken at 100, it
will be seen what a rapid diminution there is in the green and the blue
rays in gaslight. Gaslight only possesses about 20% of the green rays,
whilst of the violet hardly 5%. On the other hand the light which comes
to us from the sky shows a very marked falling off in the yellow and red
rays. A very easy experiment will convince us of the difference in
colour between skylight and gaslight. If we let a beam of daylight fall
on a sheet of paper at the end of a blackened box, and cast a shadow
with a rod by such a beam, and then bring a lighted candle or gas-flame
so that it casts another shadow of the rod alongside, one shadow will be
illuminated by the artificial light, and the other by the daylight. The
difference in colour will be most marked: the blue of the latter light
and the yellow of the former being intensified by the contrast (see page
198).

Fig. 29.--Comparison of Sun and Sky Lights.

By a little trouble the blue light from the sky may be compared with
sunlight. A beam of light B (Fig. 29) is reflected by a silvered glass
mirror from the blue sky into the box HH, at the end of which is a
screen E. Another mirror A, which is preferably of plain glass, reflects
light from the sun on to a second unsilvered mirror G (shown in the
figure as a prism), which again reflects it on to the screen, and each
of these lights casts a shadow from the rod D; K are rotating sectors to
diminish the sunlight, and we can make two equally bright shadows
alongside one another. The bluer colour of the sky will be very
evident.




CHAPTER IX.


  Colour Mixtures--Yellow Spot in the Eye--Comparison of Different
  Lights--Simple Colours by mixing Simple Colours--Yellow and Blue form
  White.

The colour of an object in nature, without exception we might almost
say, is due, not to one simple spectrum colour, or even to a mixture of
two or three of them, but to the whole of white light, from which bands
of colour are more or less abstracted, the absorption taking place over
a considerable portion or portions of the spectrum. Notwithstanding this
we shall now experimentally show that every colour can be formed by the
simple admixture of not more than three simple colours, if they be
rightly chosen, and from this we shall make a deduction regarding vision
itself. We are in a position to obtain three simple colours by means of
a slide containing three slits. Now for our purpose we require that the
three slits can be placed in any part of the spectrum, and that they
can be narrowed or widened at pleasure. Instead of a card the writer
uses a metal slide, as shown in Fig. 30.

Fig. 30.--Slide with slits to be used in the Spectrum.

It will be seen that the three slits can be closed or opened from the
centre by a parallel motion. They also slide in a couple of grooves, so
that they can be moved along the frame into any position. The position
they occupy is indicated by a scale engraved on the front of the slide.
Behind the grooves in which the slits move are another pair of grooves,
into which small pieces of card CCCC can slide, and thus close the
apertures between the slits. By this arrangement all rays except those
coming through the slits themselves are cut off. The metal frame fits on
to an outer wooden frame, which slides in the grooves used with the card
in the apparatus as already described. It is convenient always to keep
the scale on the back of this wooden slide in the same position as
regards the shadow of the needle-point used for registering the
position, and to move the slits along their grooves when a change in
position is required. Using these three slits three different colours
can be thrown on the same square patch on the screen.

A very crucial experiment is to see if we can make white light by the
admixture of three colours, for if this can be done it almost follows
that any colour can be formed. We must use the colour patch apparatus,
and begin with placing one slit in the violet near the line G, another
between E and F, and a third between B and C of the solar spectrum, and
fill up the gaps between them with cards as shown in the figure. For our
present purpose it is better to make the colour patch and the white
patch touch each other, not using the rod, as by this means we avoid
fringes of colour. We shall find that the aperture of the slits can be
so altered that we can produce a perfect match with the white reflected
light. By placing the rotating sectors in front of the reflected beam we
can reduce its intensity, so that the two patches are equally bright. By
a tapering wedge we can measure the width of the slits, and thus get the
proportions of these three different colours which must be used to give
the white. This is a sample of the method that we employ when we match
any other colour. Suppose, for instance, it be wished to measure the
colour of a solution of bichromate of potash; it is placed in the path
of the reflected light, and we have an orange strip of light which we
have to match. In this case it will be found that the slit in the blue
has to be closed entirely, and only the green and red slits opened. The
intensities of the two lights are equalized by the rotating sectors as
before. So again with a solution of permanganate of potash. In this
instance no green light will be required (or if any of it but a trifle),
and the colour of the permanganate will be formed by the rays coming
through the blue and red slits.

This plan is a very useful one for measuring all kinds of transparent
colours in terms of three rays. The method of finding the intensity of
any ray of the spectrum transmitted by any such medium has already been
explained. The latter has one advantage over the former, in that the
measurements by it are exact, whatever source of light be used to form
the spectrum. By the method now described this is not the case. For
instance, the colour of permanganate of potash may be matched in the
electric light with the red and blue slits. If the limelight were
substituted for the electric light, it would be found that the slits
would require other apertures, not proportional to those already formed,
to match the colour of this substance.

Fig. 31.--Screen on which to match Gamboge.

If we wish to register the tint of any pigment, we have to slightly
alter our mode of procedure. Suppose, for instance, we wish to register
the colour of gamboge. In such a case we paint a small bit of card (Fig.
31) with the pigment, and divide the white space on which the colour
patches are thrown into two parts, and cover one-half with the pigmented
card, leaving the other half white. The reflected beam illuminates the
pigment, and the spectrum patch the white. The widths of the three slits
are then altered till the two tints agree, and the brightness matched by
means of the rotating sectors.

There are certain sad and æsthetic colours which it might be considered
cannot be matched by a mixture of three colours. A brown colour, or "eau
de nil," might appear to come out of the range of matching. These
colours, however, can be matched in precisely the same manner as the
brighter colours are matched. Thus a brown pigment will be found to
require red and a little green, and a trifle of blue; and the only
difference between it and a brighter shade of the same colour, is that
more total light has to be cut off from it to give the sombreness. A sad
colour only means a pigment or dye which reflects but little light, and
if that be so it can naturally be matched by using but very small
quantities of the compounding colours.

There is one curious phenomenon to which attention may be called in this
matching, which is worthy of remark. The match will be found to differ
according as the patches are compared from a distance of a couple of
feet, or from a considerable distance. More green will be required in
the latter case than in the former. If matched at a distance of about
six feet, and the eyes be then turned so that the edge of the patch
falls on their centres, it will be noticed that the colour mixture
appears of a green hue. This last experiment indicates that the retina
is not equally sensitive for all colours throughout its area.
Physiologists tell us that what is known as the yellow spot occupies a
central position in the retina, and that it absorbs a part of the
spectrum lying in the green. Now when the eyes are close to the patch,
its image occupies a considerable part of the retina, and the colour is
compounded as it were of the colour as seen on the yellow spot, and of
that beyond it, for the yellow spot will take in an image of from six to
eight degrees in angular measurement. When viewed at a distance we have
the image of the patch falling almost entirely on the yellow spot, and
hence a greater quantity of green is required, as it has to make up the
deficiency caused by the absorption. When the eyes are turned a little
on one side the image falls on the outside of the yellow spot, and the
patch illuminated by the mixed light appears green, compared with the
patch illuminated with the white reflected beam.

It is thus evident that when colour matches have to be made, the
distance of the eye from the screen should always be stated, as also the
dimensions of the patches viewed. It may be fairly asked why, if the
half patch illuminated by the mixed colours appears greener when the eye
is turned, the other should not equally do so. This is a very fair
question to ask. It must be remembered that one strip is illuminated
with white light, in which every coloured ray of light is compounded,
whilst in the other only three rays are blended. The green ray chosen
happens to be taken from that part of the spectrum which is absorbed by
the yellow spot; but all of the green rays of the spectrum are not so
much absorbed, hence in ordinary white light, in which all the green
rays are present, only a small percentage of the total green in the
spectrum is absorbed, compared with that absorbed from the single green
ray with which the match is made. No doubt both patches are really
greener when the eye receives the impression of their images outside the
yellow spot, but one is much greener than the other, and it is thus
_comparatively_ green. It is possible to make a match with some colours
with a blue-green in which the phenomenon described does not appear; but
in cases where a match has to be made with colours in which but little
blue is required, it would be impossible to make it, owing to the blue
existent in such a green-blue ray.

We will now return to our compounding of three colours to make white.
Why have we chosen the positions of the slits which we did in the
spectrum for its formation? Would not other positions answer as well?
Let us give our answer by experiment. Let us move the slit which is now
in the green towards the red; we shall find that as we do so--and
keeping the blue slit of the same width--that we shall have to close the
red slit, and alter the aperture of the green slit itself. If we reason
on this point we shall be forced to the conclusion that the green slit
lets through more red light of some description, as less red from the
red slit is required to make the match. If we move the green slit almost
into the yellowish green, we shall find that the red slit has to be
entirely closed, and that white light is formed of the two colours,
yellowish green and violet. This shows us that the yellowish green
colour here used is formed by a mixture of the red and green rays which
passed through the two slits in their original positions. If we replace
the slits in these positions and close the violet slit, we are at once
able to verify it.

If we again form white light with the slits in their original positions,
and move the green slit towards the blue, we shall find that, keeping
the red slit at a constant aperture, the blue slit will have to be
closed, and the green slit altered in width. The necessity of lessening
the aperture of the blue slit shows that there is a certain amount of
blue light coming through the green slit. At one point, when the slit
has travelled into the blue-green, the blue slit may be entirely closed,
and white light be formed of this and the red, showing that the
blue-green colour is composed of the same proportions of blue and green
which passed through the blue and green slits in their original
position. The positions chosen were arrived at by the writer from
experiments made in this manner, moving first one slit and then the
others, and the position of the green slit was confirmed by a
consideration of the neutral point which exists in a green colour-blind
person's spectrum.

The method of mixing three colours together gives us a means of
imitating all kinds of white light, as it does of coloured light. At
page 110 we have already given a diagram of the relative amounts of
spectrum colours in sunlight, skylight and gaslight. If we by any means
throw a patch of the light which we wish to match on the patch formed by
the colour patch apparatus, and interpose the rod, we can measure the
apertures of the three slits, and thus arrive at the relative
proportions of each colour present. In an experiment carried out,
sunlight, the electric arc-light, and gaslight were compared in this
manner. The following are the results, the red being near the C line,
the green near the E line, and the violet near the G line of the solar
spectrum.

    +--------+-----------+----------+-----------+-----------+
    |        | Sunlight. | Electric | Gaslight. | Skylight. |
    |--------+-----------+----------+-----------+-----------+
    | Red    |   100     |    100   |    100    |    100    |
    | Green  |   193     |    203   |     95    |    256    |
    | Violet |   228     |    250   |     27    |    760    |
    +--------+-----------+----------+-----------+-----------+

Now from the above it might seem that as three simple spectrum colours
will give us the colour of any pigment, that therefore two colours ought
to give us the same colour as any intermediate simple colours in the
spectrum which lie between them; for instance, that the simple
blue-green ought to be obtained by mixing spectral green and spectral
violet together. This can be ascertained with a single colour patch
apparatus, by cutting a slit in the card that fills up the aperture
between the two adjustable slits, and deflecting the beam transmitted
through it by a right-angled prism, and back on to the screen through
another similar prism, as described in chapter VIII. It is more
convenient, however, to use a duplicate apparatus precisely similar to
the first, with the exception that no collimator is required, placing
them side by side, and mirrors making the reflected beam from the first
traverse the second set of prisms. There will be a reflected beam from
the second apparatus, which can be utilized in the same way as was that
from the first apparatus, and the two spectra will vary together in
brightness, as will also the new reflected beam, since they all are
formed by the light coming through one slit. A patch of the colour
intermediate between the two is thrown on the screen from the second
apparatus, and the second patch from the first apparatus overlaps it. A
rod placed in the usual manner throws two shadows, which are illuminated
by the two different beams. If blue-green be a colour it is wished to
match, it will be found that no matter in what part of the violet and
green the slits are placed, no match can be effected. But if some very
small quantity of red light be mixed with simple blue-green, that then a
colour identical in every respect as regards the eye can be obtained
from the violet and green of the first apparatus. It must be remembered
that a mixture of red, green and violet form white, and that they are
mixed in definite proportions. No matter how feeble in intensity the
white may be, the same proportions will still obtain. In the above
experiment, as the blue-green must contain violet and green, the small
quantity of red must combine with the proper proportion of violet and
green, and will form white light, so that the match is obtained by the
residues of the violet and green mixed with the small quantity of white
light, of which the red is the indicator.

We can test the truth of this argument in a very simple way. If we add
to the colour with which the match has to be made a small quantity of
white light from the reflected beam, cutting off more or less by the
rotating sectors, we can get the exact hue of the impure blue-green made
by the mixture of the colours coming through the two slits; and further
we shall find that the amount of white added corresponds with the amount
of red which would be required when the components of the white light in
the terms of the three colours are taken into account. For spectrum
colours between the violet and the green it may therefore safely be said
that no match can be effected by the mixture of violet and green light;
but that it always gives the intermediate colour diluted with white
light. For colours between the green and the red of the spectrum, a very
close, if indeed not an exact match, can be made with the red and green
slits, without the addition of white.

If we take from the second apparatus light from above the position of
the violet slit in the first apparatus, that is, nearer the limit of
visibility, it will be found that a match is made, for at all events a
very considerable way with the violet slit alone, by merely reducing the
aperture, thus showing that the colour is the same, only less intense.
In the same way it will be seen that the rays coming from any point
between the lower limit of the spectrum to a little below the C line are
identical in colour.

As we have arrived at the fact that in colour mixtures of violet and
green, white light is to be found in the colour produced, it follows
that either the violet or the green, or both, must themselves contain
some small proportion of white. It might perhaps be said that violet is
really a mixture of red and blue, and hence the white in the mixture
with the green; but if in the first apparatus we place one slit in the
purest blue we can find, and the other in the red, and throw a violet
patch on the screen from the second apparatus, we shall be unable to
form the same hue of violet by any means; it will always be diluted with
white. Now as the very blue we are using, if matched as above by green
and violet, requires white light to be added to it, and as to match the
violet with the same blue and red, white light has also to be added to
it, it follows that the violet must be freer from white light at all
events than the blue.

There is one other experiment that must be mentioned before leaving for
a time this part of our subject, viz. the formation of white by a
mixture of yellow and blue. If one of the slits be placed in the yellow
of the spectrum, a position will be found in the blue where, if a second
slit be placed, and the apertures are adjusted, an absolute match with
the reflected white of the apparatus can be secured. This experiment
will be referred to later on, when considering the question of primary
colours.

The above experiments have a great bearing on the theory of colour
vision, and should be considered very carefully in connection with the
shortened spectrum which we have shown exists when red colour-blind
people are observing its luminosity.

There is one point to be recollected in relation to the mixtures of the
three or two different colours which make white light. If different
coloured pigments be illuminated by the "made" white light, they will
not appear of the same hues, as a rule, as when viewed by ordinary white
light. They will vary not only in colour, but in brightness. This might
be expected when the spectral light which they reflect is taken into
account.




CHAPTER X.


  Extinction of Colour by White Light--Extinction of White Light by
  Colour.

In the last chapter we have shown the impossibility of matching the hue
of the simple colours between the violet and the green, unless a certain
and appreciable quantity of white light be added to them. We will now
turn to a phase of colour measurement which will materially help us to
see why, in some cases, the addition of white light to the simple
spectrum colours, between the red and green, does not appear necessary
in order to make a match with a mixture of red and green.

We will ask ourselves two questions: one is, whether any colour, and if
so how much, can be added to white without appearing to the eye? and the
other, if any, and if so how much, white light can be added to a colour
without its being perceived?

Perhaps one of the readiest methods of explaining exactly what we mean
is by a rotating disc. Suppose we have a red disc, of nine or ten inches
in diameter, and at every one inch from the centre paste on it a white
wafer about one-eighth of an inch in diameter, and cause it to rapidly
rotate. On examination we shall find that pink rings will be formed by
the combination of the white and red near the centre, but that towards
the margins no rings will be visible, owing of course to more red being
combined with the same amount of white. This shows that the eye is only
sensitive to a certain degree, and cannot distinguish a very small
diminution in colour purity. The intensity of the light has something to
do with the number of these pink rings which are visible, as may readily
be tested in a room. If the rotating disc be placed near a window, and
the number of rings visible be counted, a different number will be
visible when it is placed in a dark corner. A kindred experiment is to
place red circular wafers upon a white disc, and note the rings visible.
This gives the sensitiveness of the eye for the diminution in intensity
at the other end of the scale. It will be found that there is a marked
difference between the two.

Fig. 32.--Diaphragm in front of Prism.

It is more instructive if we experiment with pure colours, and so we
must resort to our colour patch apparatus described in Fig. 6. If a
small circular aperture about quarter of an inch in diameter be cut in a
card, and placed in front of the prism nearest the camera lens (Fig.
32), the colour patch, instead of being an image of the face of the
prism, will be an image of the circular hole, and when the slit is
passed through the spectrum we shall have a coloured spot on the screen,
on which we can superpose a patch of white light from the reflected
beam. There are two ways in which we can reduce the intensity of the
spot, by narrowing the slit through which the spectral ray passes or by
placing the rotating sectors in front of the coloured beam. This last,
perhaps, is the readiest plan, as it only involves the reading of the
sector. We can then diminish the intensity of the coloured spot to such
a degree that by its dilution with white light it will entirely
disappear. It will be found that red disappears at a different aperture
of sector to that required for the green, and the green to that for the
blue.

From our previous experiments in chapter VII. we know the luminosity of
the spectrum to the eye, and it will be of interest to see what relation
the luminosity at which the spots of different colour disappear, when
they are so diluted with white light, bear to the total luminosity of
these rays.

In a set of measurements made it was found that the reduced angular
apertures required for the colours indicated by the following were:

    B required  300°* of aperture.
    C     "      56°      "
    D     "      14°      "
    E     "      22°      "
    F     "     150°      "
    G     "    2100°*     "

The large numbers marked with an asterisk were obtained by placing the
rotating sectors in front of the white reflected beam.

The light of D had to be reduced to 14° before it was extinguished;
therefore to extinguish the original light of this colour in the
spectrum would require 180/14, or 12·9 times the intensity of the white
light of the reflected beam. With the E light it would take 180/22, or
8·2 times the white light to extinguish it, and so on. If we tabulate
the results in this manner, and take the white light necessary to
extinguish the D light empirically as 98·5, which is its percentage
luminosity in the spectrum of the electric light, we can then compare
the extinguishing factor with the luminosity in each case.

    +------------+-------------------------------------------+
    |            |              | White required|            |
    |            |White required| to extinguish | Luminosity |
    |   Colour.  | to Extinguish| the Spectrum, |    of      |
    |            | the Spectrum.|with 50 as That| Spectrum.  |
    |            |              | required at E.|            |
    |------------+--------------+---------------+------------+
    |near line B |     ·6       |     3·9       |    4·9     |
    |    C       |    3·2       |    19·5       |   20·6     |
    |    D       |   12·9       |    78         |   98·5     |
    |    E       |    8·2       |    50         |   50       |
    |    F       |    1·2       |     7·5       |    7·5     |
    |    G       |     ·087     |      ·56      |     ·6     |
    +--------------------------------------------------------+

The very close resemblance between the last two columns indicates that
the same luminosity of white light is necessary to extinguish the same
luminosity of most colours, within the limits of observation that is to
say. Indeed the method of extinction was a plan which Draper and
Vierordt essayed, but the results, tabulated from experiments made by
them with the apparatus they employed, give a curve of intensity very
unlike that given in Chapter VII. In these experiments the luminosity of
the orange light corresponding to the D line coming through the slit was
measured, and it was found to be 37·5/180 of the white light. Now
according to the last table but one 14/180 of this light was
extinguished by the full white light, consequently 37·5/180 × 14/180, or
1/62 of the orange light was extinguished by the white light. In other
words, if white light be sixty-two times brighter than the orange
light, the colour of the latter when the two are mixed will be
invisible. The extinction of all colours requires somewhat more light
than this, and a calculation shows that the extinction of every colour
is effected by white light, which is seventy-five times brighter than
the colour. Artists are well aware that a pale wash of a pigment may be
washed over drawing paper, and when dry is invisible to the eye. The
above experiments fully account for it.

The other experiment which was to be tried was to see how much white
light could be extinguished by a colour. There are several ways by which
this can be effected. For instance we may superpose a white dot on the
colour patch by placing a card, in which a circular hole is cut, in the
reflected beam near the prism, from which the reflection takes place; or
by putting a black circular disc of small dimensions pasted on a glass
in the same position, by which means the white light is superposed over
the whole of the colour patch, with the exception of what, when the
colour is cut off, is a black spot; or again by placing a rod to shade
half the patch from the white light, but leaving the whole of it exposed
to the coloured beam. All these methods have been tried, and it appears
that the size of the piece of the patch over which the white light is
thrown may have some effect on the resulting curve, but of one thing
there is evidence, viz. that a great deal more white light can be mixed
unperceived with orange light, than can be with the green, blue, or
violet. From one experiment it was found that 1/36 part of white light
of the same luminosity as the orange could be mixed with the orange and
not be perceived; but that with the green light at E 1/90 would just be
visible, whilst at F in the blue-green the 1/120 could be distinguished.
Looking at these results, and applying them in elucidating the
experiments in which it was attempted, but without success, to match the
intermediate colours between violet and green (of which the light at F
is a case in point), by mixing them together, unless white light were
added to the simple colour; and the success of the other experiment, in
which orange light could be obtained of the same hue as that at D by a
mixture of the red and green, it will be noticed that 3·3 times more
white light can be added to the orange than to the green light at F,
without its perception. The white light produced by the mixture in the
first case might well show when mixed with the green, but might pass
wholly unperceived when mixed with the orange.




CHAPTER XI.


  Primary Colours--Molecular Swings--Colour Sensations--Sensations
  absent in the Colour-blind.

For some purposes it is advantageous to show experiments before
indicating the deductions from them which may lead to a theory. Those
described in Chapter IX. will enable us to treat the theory of colour
perception from a standpoint of some advantage. How is it that the
combination of three colours suffices to form white, or to match any
colours we wish, be they spectrum colours to which a little white is
added, or the colours of pigments? The most plausible theory that can be
advanced is that it is only necessary for the eye to be furnished with a
three-colour-perceiving apparatus to give the impression of every
colour, and yet this would be somewhat difficult to believe had we not
had the experiments narrated in that chapter before us. We should have
almost expected some machinery in the eye to exist, which would answer
to the rhythmic swing of the rays of every wave-length which together
make up white light. But now we have to stand face to face with the
results of experiment, and we find that at the most only three colours
are necessary to make up white light, and that from these three spectrum
colours we can form any others, with the limitation already mentioned,
when some simple colours are in question.

We must here digress for a moment, and notice the fact that from our
experiments we have derived the three primary colours as they are
called, viz. red, violet, and green; the definition of a primary colour
being that it cannot be formed by the mixture of any other colours. We
have ascertained that yellow and blue make white. It is therefore
evident that blue, yellow, and red cannot be primary colours, since two
of them form white; and we have moreover shown that yellow can be made
from green and red; hence it might be fair to assume that the three
primary colours are red, green, and blue. But blue, when mixed with a
very small percentage of white light, can be made by green and violet.
Hence, in the white light formed by the two colours yellow and blue, we
have the first made by green and red, and the second by green and
violet; hence the three colours which really make the white light are
red, green, and violet. The approximate positions of these three colours
in the spectrum are those already indicated; though, as we shall
presently see, it is highly improbable that any person whose eyes are
what are called normal, has ever experienced the fundamental green
sensation.

The fact that red, yellow, and blue cannot be primary colours has been
mentioned, as even now it is sometimes taught that they are so. As long
as the theory of colour principally lay with artists there was
reasonable ground for their assumption, since they worked with impure
colours, viz. those of pigments; and as we shall see later on the truth
of the assumption agreed with such experiments as they would make. When,
however, the question was taken up by the physicist with more exact
methods of experimenting, and with pure colours, the falsity of the old
triad was soon capable of proof.

To return from our digression: how it is that three mixed colours can
give the sensation of white light is at first sight hard to understand;
but a reference to the action of light on a photographic salt helps us
in some degree. In the case of a sensitive salt, such as the
bromo-iodide of silver, we find that a chemical decomposition is caused
by the violet end of the spectrum, and is only feebly affected by any
other part, though with prolonged exposure even the red will cause it.
The annexed figure (Fig. 33) gives the idea of the relative action of
different parts of this violet portion.

Fig. 33.--Curve of Sensitiveness of Silver Bromo-iodide.

The height of the curve shows the relative effects produced. Now this
curve is not symmetrical, but has a maximum effect nearer to the violet
end of the spectrum than to the red. The atomic composition of the
silver bromo-iodide is probably two atoms of silver and one of bromine
and one of iodine oscillating together, and we can conceive of some one
atom, the period of whose swings in its molecule is isochronous with
some wave-length of light. Further, we can conceive that, like a
pendulum whose vibrations are increased in magnitude by well-timed
blows, the swing of the atom is also increased, and that eventually it
gets beyond the sphere of the attraction of its parent molecule, leaves
it, and is attracted to some neighbouring molecule of different
constitution, and that thus a chemical change is induced. This we can
conceive, but how can other waves, which are not isochronous with the
rhythmic swing of the atoms, alter the composition of the molecule? If
we have an impulse given to a pendulum exactly timed with the period of
oscillation, there is no doubt that the swing is increased. If we have
one nearly in accord, it will be found that though the swings are not
increased in amplitude so greatly as when there is perfect accord, yet
an increased swing is given, and as exact accord is removed further and
further, so the increase in the swing of the pendulum gets smaller and
smaller. In somewhat the same manner it is possible that many series of
waves, differing in wave-length, and therefore in periods of
oscillation, may be capable of increasing the amplitude of a swing, and
with the photographic salt this probably occurs, with the result which
we see in the above figure. Suppose in the eye we have three such
sensitive pendulums which are capable of responding to the beats of
waves of light, it requires no great imagination to see that one such
pendulum will respond not only to that wave of light which is
isochronous with it, but also with waves shorter and longer than that
particular wave. The same pendulum indeed may respond to the whole of
the visible spectrum, but when far off from the maximum the response
would be very small indeed. We may therefore assume that though each
pendulum may have its maximum increase of oscillation at one part of the
spectrum, yet at other parts not only it alone answers to the beating of
the waves, but that the other pendulums are also affected by the same,
and thus the whole spectrum is recognized by the swings more or less
long, of either one, two, or of all three.

To Thomas Young is usually attributed the three-colour theory, though it
seems to have been promulgated in an incomplete state some time before;
Clark-Maxwell and Helmholtz revived it in later years, and it is usually
known as the Young-Helmholtz theory. It should be remarked that the
three fundamental colour sensations are not of necessity the same
sensations as are given by the three primary colours, as we shall see
further on. The following figure (Fig. 34) is taken from Helmholtz's
physiological optics, as diagrammatic of the three sensations.

Fig. 34.--Curves of Colour Sensations.

To this diagram there is an objection, in one respect, viz. that it
gives the same luminosity-value to the blue of the spectrum as it does
to the red and green. It has been seen that if we call the luminosity of
the yellow 100, that of the blue is about 5. The objection does not hold
if it is remembered that the three maxima of impressions are taken as
equal. If the ordinates were increased, so that the maxima were of the
same height as that of the photographic curve, the resemblance between
them and this last would be very marked. It will be noticed that each of
the three colour sensations is not only excited by a limited portion of
the spectrum, but by all of it, the height of the curves being a measure
of their response.

Now assuming that this is the case, since a certain degree of
stimulation given simultaneously to the three sensations causes an
integral sensation of white light, it follows that the colour perceived
in every part of the spectrum is due to the excess of stimulation of
either one or two of the fundamental sensations, together with the
sensation of white light. If this diagram were correct, at no point in
the spectrum is one fundamental sensation excited alone, but we believe
that the diagram obtained by Kœnig (Fig. 35), from colour equations
(which will be explained in our next chapter), is more exact, and that
it is probable that in the extreme violet and extreme red of the
spectrum the only sensations which are stimulated are the violet and red
respectively. Our measures in the red and violet of the spectrum make it
appear that each of the two sensations can be perceived unaccompanied by
any others, and the fact that the red colour blind person perceives a
shortened spectrum in the red end, is a further proof of this deduction,
so far as the red is concerned.

The colour which the fundamental green sensation excites in the normal
eye has probably never been seen, nor can be seen. This is due to the
fact that all three sensations overlap in the green; that is, that the
pendulum which answers to the green colour in the spectrum also affects,
but with much less energy, the other two pendulums, which respond to
the red and violet sensations.

The word pendulum has been used advisedly, for it may equally as well
apply to a molecular aggregation as to one which is visible and
measurable. Without entering into the physiological structure of the
eye, we may say that it has usually been assumed that the pendulums are
the ends of nerves which vibrate with the waves of light; but this seems
rather doubtful. Gross matter, such as these ends are, compared with the
molecules of which they are built up, cannot, as a rule, vibrate with
waves of light, and there seems to be no reason why there should be an
exception in the case of the eye. It seems much more probable that a
chemical decomposition takes place in some substance attached to them,
and where such decomposition takes place electricity of some kind must
be produced. In other sensations of the body the nerves act as telegraph
wires, carrying messages to the brain, and it is not improbable that the
nerves of the eye are employed in somewhat the same manner. Professor
Dewar has shown that when light acts on an extirpated eye, a current of
electricity does traverse the nerves, and of such an amount that it can
be shown to a large audience. This experiment is not, however,
conclusive, as the effect may be mistaken for the cause. This idea,
however, is only hypothetical, as is indeed the hypothesis of the
mechanical action of light on the gross matter of which the rods and
cones attached to the retina are composed.

We have in a previous chapter stated that there are some eyes in which
the sensation of some colour is altogether absent, and in others in
which it is more or less deficient. Thus some eyes appear to be lacking
wholly in the sensation of red, others of green, and some very few of
violet; and there have been cases known in which two sensations, the red
and violet, have been totally absent. In the first case, where the
sensation of red is entirely absent, what is known to the normal-eyed as
white can be matched with a mixture of blue and green, and there is a
place in the spectrum that is recognized as white. Similarly white can
be matched by a green blind person with a mixture of red and blue.

To those who may be curious to see the colour which red and green blind
persons would call white, a very simple means is at hand to demonstrate
it. Using the colour patch apparatus with the three slits inserted in
the slide, and in the positions we have indicated in the violet, green,
and red, and forming white light for ourselves on the screen, if we
cover up the red slit entirely we shall have a patch of sea-green
colour, which a red blind person would call white; and if we cover the
green slit, uncovering of course the red, we shall have a brilliant
purple, which to a green blind person would be white. They both would
call white what the normal-eyed person sees as white, for the simple
reason that either the red or the green mixed with the remaining colours
would be unperceived. The examination of colour-blind people is of prime
importance for testing any theory of colour vision. For instance, if it
were asserted that the fundamental sensations did not overlap as shown
in the diagram above, then it would follow that at some place in the
spectrum there would be a dark point. If they do overlap, it must follow
that both for the red and for the green colour blind person there must
be some place in the spectrum where what is white light to them is
produced.

Colour-blind people were tested with the colour apparatus. The reflected
beam and the colour patch were made to cast shadows as before, and the
rotating sectors placed in the path of the former. A slide with one slit
was passed across the spectrum, and the position noted where it was said
that the two shadows were illuminated with white light; to the
normal-eyed person one shadow of course appeared illuminated with the
sea-green colour, or bluish green, according as the observer was red or
green colour blind. The ray in the spectrum which to the red colour
blind is white, has a wave-length of about 4900, and that for the green
colour blind a wave-length of 5020, which corresponds to the position in
which we usually place the green slit when a normal-eyed person is
making colour matches.

It may be further remarked, that if the maxima of all the three colour
sensations are taken, as in the diagram, as of equal value, that the
place in the spectrum where the white light is perceived by the
colour-blind is where the two sensations are of equal strength, that is,
where the two curves cut one another, and are of equal height. By
obtaining the proportions of the different colours with colour-blind
persons which make up what to them is white light, the curves for the
two sensations can be worked out in the form of simple equations.

The experiments carried out with colour-blind people are of the most
interesting character, and a good deal remains to be done with the data
already obtained from them.

To the popular mind a colour-blind person is usually thought a strange
creature, and it is a matter of wonderment, if not of amusement, that
they cannot distinguish between the red of cherries and the leaves of
the cherry tree. The physicist, studying the theory of colour, views the
matter quite differently, and he looks upon an intelligent observer of
this class as a boon. It may be remarked that both the red-blind and the
green-blind persons would be unable to distinguish between the cherries
and the leaves. The red-blind person would see the cherries as green, as
also the leaves; whilst the green-blind person would see both as red.
Without regarding form it is probable that the red-blind would see the
leaves as a bright green, whilst the green-blind would see them as
darker red than the cherries. Failure to distinguish between the two is
more likely to occur with the green of leaves, and the red of such
fruits as cherries, since the former contains a marked proportion of red
in it, and the latter a small proportion of green.

One highly-educated gentleman was led to know his deficiency in colour
sense, by hearing a companion on a tour going into raptures over a
sunset. He saw but little difference between it and that to be seen at
midday. Testing his vision it appeared that he was totally blind to the
sensation of green, and that white and purple would consequently be
mistaken by him for one another. The crimson on the clouds, illuminated
by the setting sun, would appear to him as only slightly different to
the white clouds which he would see at midday; in fact he would be
always seeing what to us would be a sunset. For this gentleman to mix
spectrum colours to match others would evidently be no guide to
normal-eyed persons.

We believe that amongst us in our daily life we have many persons who
are blind to some colour, but who are not aware of it, or if they are
aware of it, hide their defect as far as possible. That some are
ignorant of it to a late period of their life we know.

We have said that there are cases in which persons are only defective in
colour perceptions, and not wanting in them altogether. The former are
more common than the latter, and to the experimenter are by no means so
interesting. They are only alluded to here to indicate that there are
degrees in the defectiveness of eyes to colour. One point which must be
remembered here is that all colour production for registration by the
mixture of three colours is delusive, unless the eye of the operator is
tested for its colour sense.




CHAPTER XII.


  Formation of Colour Equations--Kœnig's Curves--Maxwell's Apparatus
  and Curves.

The plan of obtaining colour equations will by this time have become
fairly evident. And we may as well illustrate it by equations obtained
with the apparatus we have been using in our previous experiments. Let
us suppose we have an individual who is desirous of having his eye-sight
for colour tested, and that we have the slide with the three slits _in
situ_. It will be found that when we alter their width and form white
light with them, matching in purity the white light of the reflected
beam, that we shall have to reduce the intensity of the latter very
considerably, by means of the rotating sectors. The aperture may
sometimes be as small as 4°, and at other times perhaps somewhere
between 4° and 5°. Now the variation in aperture between 4°, and say
4·7, is very considerable, but it is highly probable that the latter
might be estimated as 4·6, since only degrees are marked on the
sectors. It therefore becomes essential to use a less brilliant
reflected beam for the comparison, and this is secured by using as a
mirror a plain unsilvered glass. What before read 4 will perhaps read
60, and 4·7 will be 70-1/2, whilst 4·6 would be 69, a difference easily
read. We can now commence operations. Let us then place the red slit at
say (35) of the scale, the green at (28), and the violet at (17), and
make white light of the same intensity by altering the apertures of the
slits. Let us do the same with the slits at (34), (28), and (17),
instead of at (35), (28), and (17); and again make white light, and
similarly with the slits at (35), (28), and (18); and let the following
be the results--

    (1) 20(35) + 60(28) + 40(17) = 100 W
    (2) 10(34) + 55(28) + 40(17) = 100 W
    (3) 20(35) + 59(28) + 10(18) = 100 W

Subtracting (1) from (2) we get--

       10(34) = 20(35) + 5(28)
    or   (34) =  2(35) + 1/4(28)

which means that the colour sensation at (34) is made up of two parts of
the sensation of (35), together with 1/4 part of the sensation of (28).

In the same way we find that the colour sensation of (18) is made up of
the sensations of (17) and (28).

    (18) = 4(17) + 1/10(28).

In this way all the different colour sensations can be referred to the
sensations which we may happen to consider as best representing the
fundamental sensations. What these are is a matter still unsettled;
though from the equations formed by colour-blind people, who only
require really two colours to form equations, their places are
approximately known; evidently as before said, the ray in the spectrum
which the green colour-blind person sees as white light, is that where
to the normal eye the green fundamental sensation is purest, being free
from predominance of either of the other two sensations, and might be
taken as a standard colour. Now if our luminosity curve is correct, and
if the sum of the luminosities of each colour separately is equal to the
luminosity of the colours when mixed (which we have shown to be the case
in chapter VII.), it follows that the correctness of the measures can be
checked by using the widths of the slits as multipliers of the
luminosities. These luminosities can then be added together, and they
should equal in luminosity the white light with which the comparison was
made. The results can be compared together by reducing the equations to
the same standard of white light.

The following is a set of observations which bear this out.

The red and violet slits in this case were kept at 35 and 17·8 on the
scale, and the position of the green slit altered.

    +--------------+-----------+-------------+--------------+
    | Position of  |Aperture of| Luminosity  |  Sum of the  |
    |    Slits.    |   Slits.  |  of Colour. |  Luminosity  |
    +---+-----+----+---+---+---+----+----+---+   of each    |
    |   |     |    |   |   |   |    |    |   |    Colour    |
    | R |  G  | V  | R | G | V | R  | G  | V |multiplied by |
    |   |     |    |   |   |   |    |    |   |the Aperture. |
    +---+-----+----+---+---+---+----+----+---+--------------+
    |35 |28·5 |17·8|115| 38|112|18·1|73  |·65|     4930     |
    |35 |28·0 |17·8|119| 45|100|18·1|61·5|·65|     4989     |
    |35 |27·75|17·8|122| 52| 85|18·1|52  |·65|     4960     |
    |35 |27·35|17·8|125| 65| 74|18·1|40  |·65|     4907     |
    |35 |27·0 |17·8|128| 78| 67|18·1|33·2|·65|     4954     |
    |35 |26·3 |17·8|133|125| 40|18·1|20·3|·65|     4987     |
    |35 |26·0 |17·8|134|150| 10|18·1|16·7|·65|     4952     |
    |35 |25·85|17·8|135|170|  0|18·1|15·0|·65|     4993     |
    |   |     |    |   |   |   |    |    |   +--------------+
    |   |     |    |   |   |   |    |    |  Mean   4959     |
    +---+-----+----+---+---+---+----+----+------------------+

The red slit was at a point in the spectrum between C and the red
lithium line, and excited probably the fundamental sensation of red
alone. The violet slit was close to G, and probably in this case the
fundamental sensation of violet was almost excited alone. With the green
slit the reverse was the case, all three fundamental sensations being
excited. At 26·3 the green sensation was probably the fundamental
sensation mixed with white light alone, as at that point the green blind
person saw white light in the spectrum, on the red side of it there
being what he describes as a warm colour, and on the violet side a cold
colour.

An inspection of the table will show how very closely the sum of the
luminosities agree amongst themselves, the white light formed by them
in each case being of equal intensities. It must be recollected that
white light is not necessary to form colour equations; colours may be
mixed to form any other colour, which may be taken as a standard. This
is often useful in the case of the light between the violet and the
blue, where the luminosities are small compared with the luminosity in
the green, yellow, and red.

Fig. 35.--Kœnig's Curves of Colour Sensations.

By taking a large number of colour equations, Kœnig, who works in
Helmholtz's laboratory, has derived what he considers curves of the
three fundamental sensations in a normal-eyed person, and also those of
the colour-blind. It may be said that with the colour-blind only two of
the fundamental sensations are seen, and therefore only two curves are
found, and that these agree in the main with some two of the curves of
the three belonging to the normal-eyed.

Fig. 36. Maxwell's Colour-box.

Maxwell was the first to make a definite piece of apparatus for the
purpose of obtaining colour equations, and we reproduce from his paper
in the _Philosophical Transactions_ of the Royal Society for 18--, a
somewhat modified diagram of it.

This apparatus is often known as Maxwell's colour-box, and is in
fact a spectroscope reversed. With a collimator and prisms we form a
spectrum on the focusing-screen of the camera (Fig. 6), by light
coming through the slit, and we can obtain light on the distant
screen, a patch of any colour, by placing in the spectrum slits as
given at Fig. 30. If we were to illuminate the slits so placed with
white light, and look through the slit of the collimator, we should
see the front surface of the first prism illuminated by the mixture
of the colours which would, when the light illuminated the
collimator slit, have formed one colour patch on the screen. In
Maxwell's apparatus, the slits S₁, S₂, S₃ are illuminated by the
light reflected from a white card C, placed in the sunshine, the
rays passing through them fall on two prisms P₁, P₂, are reflected
back again through these prisms by a concave mirror M₃, are received
on another mirror M, and fall at E on to the eye. At A is an
aperture in the box, letting through white light on to a mirror M₁,
which reflects it through a lens L on to M₂, which again reflects it
on to M, and so to the eye at E. Thus at E an image of the prisms,
and an image of the aperture are seen, and the white light of the
latter can be compared with the mixture of the colours formed by the
prism passing through S₁, S₂, and S₃.

Suppose we have one slit S₁, the white light will be decomposed by the
prisms, and will be seen at E as light of the same colour as would be
seen at S₁, if the light were sent from E to S₁, and so with the other
slits. Thus when two or three of the slits are uncovered, the light
falling on the eye at E will be a mixture of two or three colours.

There are two drawbacks to the mode of illumination used, one being that
the quality of sunlight varies, and therefore colour equations will not
be accurately comparable one with the other; and the second is that the
light reflected from the card is not absolutely the same in all
directions, and it cannot be perpendicularly placed to each of the rays
which strike the prisms, after passing through the different slits. This
latter is a small objection, and is not of much account, but the first
drawback is a more serious one.

Fig. 37.--Maxwell's Curves of Colour Sensations.

With this apparatus, then, Maxwell formed his colour equations, but he
fixed as the colours which may be called his standard colours, portions
of the spectrum which are certainly not pure, and hence he got curves
which are not as perfect as those of Kœnig.

It will be seen, for instance, that his red and violet curves do not
overlap, but touch each other near E. Were this true, the green
colour-blind person should see a dark space in the spectrum, since the
green sensation is missing in such eyes. As a matter of fact the
luminosity of the spectrum is very considerable to such a person at this
point.

It will also be seen that some of his curves are negative curves lying
below the base. This shows that the three standard colours he took are
somewhat wrong. The dotted curve gives the combination of his three
sensations at every point, and should be the luminosity curve; but owing
to his having taken empirically certain standards of luminosity for his
three colours, it does not represent the truth, as may be seen on
comparison with Fig. 11, page 79.

It must be recollected that since Maxwell's observations the subject has
been largely experimented upon, and naturally improved appliances and
greater knowledge have enabled more nearly correct views to be
entertained regarding it.




CHAPTER XIII.


  Match of Compound Colours with Simple Colours--All Colours reduced to
  Numbers--Method of matching a Colour with a Spectrum Colour and White
  Light.

If we place the solution of bichromate of potassium in front of the slit
of the collimator, we shall see that on producing a spectrum on the
screen, all rays from the red to the yellow-green pass; hence bichromate
of potash transmits a colour which is a compound colour.

It has been shown that this orange colour and the spectral yellow can be
matched by mixing the simple colours of red and green together; but it
will be instructive to see if a simple colour in the spectrum itself can
be found which can match such a compound colour as that of the
bichromate.

If we place the bichromate in the reflected beam of the colour patch
apparatus and illuminate one shadow cast by the rod with the light
transmitted by it, and pass a slit along the spectrum, to produce
monochromatic light, with which the other shadow of the rod is
illuminated, a position will be found near the orange sodium line "D,"
where the two colours apparently match in every respect; when the
intensities of the two illuminated shadows are equalized as before by
the rotating sectors. In the same way by filling the part of the square
with the pigment on which the shadow illuminated by the reflected beam
falls, we can see if we can match emerald green, cyanine blue, and other
coloured pigments.

It will often be--more often than not--necessary, however, to dilute the
spectrum colour thrown on the white half of the patch with a trace of
white light. By reference to our previous experiments we arrive at what
may appear an unlooked-for result, that _no matter what the colour_ may
be, we can refer it to one ray of the spectrum, together with a
percentage of added white light. It is worthy of remark, that the place
in the spectrum where the simple and the compound colours match, varies
according to the kind of light with which the pigment is illuminated.
This we can show in a very simple way.

To persons who are totally colour-blind to one sensation, viz. the green
or the red, the matching of a compound colour with a simple one in the
spectrum should possess no difficulties. Taking the trichromic theory
of three sensations for the normal-eyed person, it is evident that only
the following classes of sensations are possible in the normal-eyed, the
green colour-blind and the red colour-blind--

    Normal-eye.      Green colour-blind.      Red colour-blind.

    Red                Red                     --

    Green               --                    Green.

    Violet             Violet                 Violet.

    Mixtures of red     --                     --
    and green

    Mixtures of red    Mixtures of red         --
    and violet         and violet

    Mixtures of green                         Mixtures of green
    and violet                                and violet.

    Mixtures of red,                           --
    green and violet

If we take as a type of colour-blindness the green colour-blind person,
we see that every colour in the spectrum must be either pure red or
violet, or else these colours mixed with more or less white light, since
these two sensations when excited in certain proportions give the
sensation of white. At one place, which is commonly called the neutral
point, the proportions of the two colours are such that the impression
there given is only white; hence it follows that, between this neutral
point and each end of the spectrum, the rays are mixtures of violet and
white, or red and white, the dilution of the colours varying from no
white to all white. As every compound colour must be a mixture of the
same two colours in certain proportions, it follows that the green
colour-blind person can match every compound colour with some one ray of
the spectrum, and that every colour must to him be either red or violet,
diluted with different proportions of white light.

In the same way, a person who is colour-blind to the red can also match
any colour with a single spectrum colour, and he will see it as green or
violet diluted with more or less white light. This can be readily
understood, but it is not quite so plain how any colour sensation felt
by the normal eye can be referred to the spectrum.

If we take three rays in the spectrum--one in the red between C and the
red Lithium line which we will call _R_, another in the green between F
and _b_ which we will call _G_, and a third in the violet near G but on
the _H_ side of it, and which we may call _V_--then by varying their
intensities (which is equivalent to varying the luminosities) and mixing
them, we can give the same impression to the eye that any compound
colour gives; and that any intermediate simple spectrum colour gives, if
very slightly diluted with white light. With these same three colours,
but in different proportions, we can also give the impression of white
light to the eye. The intermediate spectrum colours between the green
and the violet rays selected when slightly diluted are imitated by
mixing these rays together in different proportions, and similarly those
lying between the red and the green by mixing together these rays in
different proportions--and there is some ray present in the spectrum
which, when very slightly diluted with white light, has the same
colorific effect on the eye as the mixtures of the pairs _v_ and _b_,
and _G_ and _R_, in any proportions whatever.

Let the luminosities of the rays _R, G_ and _V_, which give the
impression of white light, be _a_, _b_ and _c_ units respectively, and
_p_, _q_ and _r_ those which give that of the colour which has to be
registered and reproduced. We then get the following equations--where
_W_ is white, _w_ its luminosity, _Z_ the colour, and _z_ its
luminosity--

    _aR_ + _bG_ + _cV_ = _wW_--(i.);
    _pR_ + _qG_ + _rV_ = _zZ_--(ii.);

  Then evidently--

    (_a_ + _b_ + _c_) = _w_; and (_p_ + _q_ + _r_) = _z_.

    Let _p_ = ɑ_a_, _q_ = β_b_, _r_ = ɣ_c_,

  Then we may write (ii.) as--

    ɑ_aR_ + β_bG_ + ɣ_cV_ = _zZ_--(iii.).

  Now either ɑ, β, or ɣ must be smaller than the other two. As an
  example, if ɑ be the smallest, we multiply (i.) by ɑ when we get--

    ɑ_aR_ + ɑ_bG_ + ɑ_cV_= ɑ_wW_--(iv.)

    Subtracting (iv.) from (iii.) and we get--

    (β-ɑ)_bG_ + (ɣ-ɑ)_cV_ = _zZ_ - ɑ_wW_.

Now it has already been stated that between _V_ and _G_ there is some
ray which gives the same sensation of colour, mixed with a very small
quantity of white light, as the above mixture of _V_ and _G_--let us
call it _X_ and its luminosity _x_ [_x_ being evidently equal to
(β-ɑ)_b_ + (ɣ-ɑ)_c_], and μ the luminosity of the small quantity of
white added.

We then get _zZ_ = _xX_ + (μ + ɑ) _W_.

Here we have the colour _Z_ in terms of a single ray, and of white
light.

This same holds good when in (ii.) ɣ is smaller than ɑ and β; but it
does not do so should it happen that β is the smallest, for there is no
part of the spectrum which contains simple colours giving the same
sensation to the eye as mixtures of red and blue. There is, however, a
very simple way in which the registration of such a colour (which it
must be remarked must be of a purple tone) can be effected. It can be
fixed by its complementary. To do this we must add to (ii.) a certain
amount of _R_ and _V_, which will make the whole white. Thus, suppose in
(iii.) ɑ to be larger than ɣ and ɣ than β, then we must add ϕ_bG_ +
θ_cV_ and we have

    ɑ_aR_ + (β + ϕ)_bG_ + (ɣ + θ)_cV_ = _nW_ = _Z_ + ϕ_bG_ + θ_cV_;
    but (β + ϕ), and (ɣ + θ) each equal ɑ ∴ _n_ = ɑ_w_.
                 ∴ _Z_ + ϕ_bG_ + θ_cV_= ɑ_wW_.

Now between _V_ and _G_ in the spectrum there is some single colour
which gives the sensation of the mixture of _G_ and _V_. Let it be _X_´
with luminosity _x_´, together with white whose luminosity is μ´, which
must equal (ϕ_b_ + θ_c_).

    ∴ _Z_ + _x´X_´ + μ´_W_ = ɑ_wW_
       _Z_ = (ɑ_w_ - μ´)_W_ - _x´X´_

which again is the colour expressed in terms of white light less the
complementary colour. We have thus arrived at the very simple deduction
that the hue and luminosity of any colour, however compounded, may be
registered by a reference to white light and a single ray of the
spectrum.

In practice this dominant ray is very easy to find. Suppose we wish to
determine numerically the colour of a signal-green glass in the electric
light, we should proceed as follows--

The colour patch apparatus (described in chapter IV.) is employed, and
the coloured glass is placed between the silvered mirror which reflects
the beam already reflected from the first surface of the first prism of
the spectrum apparatus, and the screen, and a square image of that
surface of the prism showing the tint of the glass is formed on the
screen by means of the lens. Touching this image is a square patch of
white light formed by the re-combination of the spectrum by means of
another lens. An opaque slide containing an adjustable slit is moved
across the spectrum in the manner described in the chapter referred to
until the colour of this last patch is approximately the same hue as
that of the glass.

In the path of the reflected beam, but between the prism and the
silvered mirror, is inserted a piece of plain glass which can be made to
reflect part of the beam into the spectrum patch of light, a square
patch of the white light being formed by means of a third lens. We thus
have monochromatic light mixed with white light. The requisite intensity
of the added white light can be adjusted by means of the rotating
sectors, as described in the same chapter, which open and close at will
during rotation, and the total luminosity of the mixed beams can be
altered by this, together with the adjustable slit in the slide. The
slit may probably have to be moved in the spectrum to make the hue of
these mixed lights the same as that of the glass, but by trial the
position of the ray whose colour when diluted with white makes the match
is readily found. The position of the slit in the spectrum is noted, as
also the aperture of the sectors. The relative luminosities of the beam
reflected from the plain glass mirror and of the coloured ray is next
measured by placing a rod in the path of the two beams, and equalizing
by the sectors the luminosity of the shadows which are illuminated, the
one by the spectral ray, and the other by the white light. When the
sector aperture is noted the registration is complete, as far as hue is
concerned, but the luminosity of the ray transmitted through the glass
should be compared with that of the reflected beam, and then the
luminosity is also recorded.

Should the colour of a pigment be in question, the ray reflected from
the silvered mirror is made to fall on the pigmented surface and the
same procedure adopted.

If a purple glass (say) has to be registered, we proceed in a slightly
different manner. The patch of coloured light passing through the purple
glass is superposed over the spectrum patch, and the slit in the slide
is moved till a ray is found which will make white light when superposed
on the colour of the glass. The luminosities of this white light, of the
reflected beam, and of the spectral colour are compared "inter se," and
there are then sufficient data with which to make numerical
registration.

Coloured glasses to be used at night with oil or gas, or pigments to be
viewed by these lights, must be registered in these lights. As the
spectrum colours are always the same, it is convenient to use the
electric light spectrum, and the only alteration in the apparatus is to
use two gas-lights to illuminate two square apertures, in front of one
of which the glass whose colour has to be measured is placed. The images
of these apertures are thrown on the screen, the coloured image touching
the square image of the spectral colour patch, and the naked image over
the latter. The same determinations are gone through as those just
described.

The following are the determinations of some glasses--
    +-------------+----------+-------------------------+
    |             |          |           |Percentage   |
    |             |          |           |of Luminosity|
    |             |  Wave-   |           |  of Light   |
    |   Glasses   |lengths of|Percentage | Transmitted |
    |  Measured.  | Dominant | of White  |  through    |
    |             |   Ray.   |  Light.   |  the Glass. |
    +-------------+----------+-----------+-------------+
    | Ruby        |   6220   |     2     |    13·1     |
    | Canary      |   5850   |    26     |    82·0     |
    | Bottle Green|   5510   |    31     |    10·6     |
    | No. 1 Signal|          |           |             |
    |   Green     |   4925   |    32     |     6·9     |
    | No. 2 Signal|          |           |             |
    |   Green     |   5100   |    61     |    19·4     |
    | Cobalt      |   4675   |    42     |     3·75    |
    +-------------+----------+-----------+-------------+

The following are determinations of some coloured pigments--

    +--------------+------------+----------+---------------+
    |              |            |          | Percentage    |
    |              |            |Percentage|of Luminosity, |
    |              |Wave-lengths|    of    |    White      |
    |   Coloured   |of Dominant |  White   |    Paper      |
    |    Papers.   |   Ray.     |  Light.  |  being 100.   |
    +--------------+------------+----------+---------------+
    |Vermilion     |   6100     |    2·5   |     14·8      |
    |Emerald Green |   5220     |   59·0   |     22·7      |
    |French Ultra- |            |          |               |
    |  marine Blue |   4720     |   61·0   |      4·4      |
    |Brown Paper   |   5940     |   50·0   |     25·0      |
    |   "    "     |   5870     |   67·0   |     19·5      |
    |Orange        |   5915     |    4·0   |     62·5      |
    |Chrome Yellow |   5835     |   26·0   |     77·7      |
    |Blue Green    |   5005     |   42·5   |     14·8      |
    |Eosin Dye     |   6400     |   72·0   |     44·7      |
    |(Sporting     |            |          |               |
    |    Times)    |            |          |               |
    |Cobalt        |   4820     |   55·5   |     14·5      |
    +--------------+------------+----------+---------------+




CHAPTER XIV.


  Complementary Colours--Complementary Pigment Colours--Measurement of
  Complementary Colours.

We are now in a position to enter into the question of complementary
colours, which is one of supreme interest to artists. A complementary
colour, in its strictest sense, may be described as the colour which,
combined with the colour whose complement is required, makes up white.
In this definition we have three characteristics to take into account,
viz. hue and luminosity, and dilution with white light. As an example of
what we mean we refer to an experiment which was made and described at
page 125. It was said that if the violet slit was placed in a certain
position in the blue of the spectrum, it was possible to move the green
slit into a part of the yellow, so that the two colours when mixed
together would form white. In that case the blue is complementary to the
yellow, and the yellow to the blue, so long as the intensities are
those which make up white light. Again, if it requires the light coming
through the three slits to make up white light, be it the white of the
electric light or that of gaslight, we can obtain the complementary
colour of the light issuing through any one of them by covering that
slit up. Thus suppose the slits to be in the normal position the
complementary colour of the red is a green-blue, formed by the mixture
of the violet and green rays, the complementary colour of the green is a
purple, formed by the mixture of the red and the violet light, whilst
the complementary colour of the violet is greenish yellow, formed by the
mixture of the red and green rays. It will be evident that as the
intensities of the three rays respectively will be different according
as the white light matched is the electric light or gaslight, the
complementary colours in the former will be different in hue and
intensity to those in the latter.

Fig. 38.--Chromatic Circle.

Another couple of striking experiments which the writer devised to show
these colours can be made with the colour patch apparatus, and on the
same principle as that used for obtaining the intensity of the rays
reflected from pigments, and transmitted through coloured transparent
bodies. Instead of the small slit with a right-angled prism in front to
deflect the beam from the top spectrum, where two spectra are produced
(see Fig. 16, p. 95), a single spectrum is used, with a right-angled
prism of such a size that it deflects half of it, which is again
reflected on to the screen by a mirror, and through a lens to form a
second patch of equal size as the undeflected beam. A rod can be so
placed in the path of the beams that two coloured stripes are formed,
together with a white stripe caused by their overlapping. The two
coloured stripes are complementary one to the other. By moving the prism
along the spectrum various coloured stripes can be formed, in some cases
one being much less luminous than the other, and yet they are
complementary. If instead of the large right-angled prism a smaller one
be used, the complementary colour due to a small part of the spectrum
can be shown in the same manner.

It is customary to show the complementary colours diagrammatically by
what is known as the chromatic circle. Roughly it is drawn as in the
above figure (Fig. 38). The three colours, red, green and blue, which
are taken for primary colours, are placed at 120° apart in a circle, and
lines drawn from them through the centre, at which white is supposed to
be situated. Where these lines cut the circumference is placed the
complementary colour. Other colours can be placed round the circle with
their complementary colours opposite, and so a fairly complete diagram
of the spectrum can be made. But it must be remembered that this is
really of no scientific value, as it conveys no idea of the luminosity
of the spectrum colours, nor of the quantities which have to be mixed
together to form the complementaries. Such a circle is, however,
convenient as a sort of _memoria technica_, and can be filled up
according to the fancy of the observer.

The following are pairs of most carefully selected complementary colours
of pigments, as adopted by Professor Church.

    _Complementaries._           _Pigments._

    {Red                   Madder red or crimson vermilion.
    { and
    {Green blue            Viridian, the emerald oxide of
                             chromium with a little cobalt.

    {Orange                Cadmium yellow, of full orange hue.
    { and
    {Greenish blue         Cobalt green.

    {Orange yellow         Cadmium yellow, or deep chrome.
    { and
    {Turquoise             Cœrulium, or cobalt blue, with a
                             little emerald green.

    {Yellow                Lemon yellow, pale chrome, or aureolin.
    { and
    {Blue                  Ultramarine from lapis-lazuli.

    {Greenish yellow       Aureolin with a little viridian.
    { and
    {Violet blue           French ultramarine.

    {Green yellow          Lemon yellow, with some emerald green.
    { and
    {Violet                French ultramarine with madder carmine.

    {Yellowish green       Lemon yellow with much emerald green.
    { and
    {Purplish violet       Madder carmine with French ultramarine.

    {Green                 Emerald green with lemon yellow.
    { and
    {Purple                Madder carmine with French ultramarine.

    {Emerald green         Emerald green alone.
    { and
    {Reddish purple        Madder carmine with a little French ultramarine.

As these pairs of pigments are complementary, it follows that if rotated
together in proper proportions, they should make a grey which will be
indistinguishable from a grey formed by rotating black and white sectors
together. (See chap. XV.)

It will probably happen that a good deal more of one of the pairs of the
colours is required in the disc than of the other, and supposing that
the two are each used of the full brightness which the pigments are
capable of giving, it follows that in a diagram where equal areas are
filled with the pigments as complementary, some means must be adopted to
give the true depth of tone to each. The mixture of white will heighten
the luminosity of either, or the admixture of black will lower it, but
often alters the hue.

One of the most beautiful methods of observing complementary colours is
by means of the polarization of light, which we need not describe in
detail. What is known as Brücke's schistoscope is perhaps one of the
most convenient. Dove's Iceland spar prism is also useful, when two
pigments have to be worked on to paper, so as to be complementary. The
two squares of pigmented paper are placed side by side, and two images
of each are formed. One image of one colour can be caused to overlap the
second of the other, and if the two when superposed appear of a grey
they are complementary one to the other. If too much of one colour
appears, it must be toned down till the grey is formed. This is a very
simple piece of apparatus, and for experiments with pigments will be
found to be very handy. When the right tint of each is secured in this
manner, a further test may be made by making the pigmented surfaces into
sectors, and rotating them together, when if the double-image prism
gives correct results, the angular aperture of the sectors should be
180° each, to match a grey produced by a mixture by rotation of black
and white.

We have already shown how the complementaries of the spectrum colours
can be found; the question is can we find the complementaries of
pigments by the spectrum? There is one very self-evident way. We can
place the three slits in the spectrum as given in chapter IX., and match
in intensity the white light of the reflected beam, and note the
apertures of the slits. We must then in the reflected beam place the
pigment whose complementary colour is required, and match its colour
with the light from the three slits, keeping, for the sake of
convenience, the white light falling on the pigmented surface of
unaltered intensity, and again note the apertures. If we deduct the last
measures from the first, the difference of aperture will give the
complementary colour. Thus it was found that with slits in a certain
position in the spectrum, to make white light the following apertures in
hundredths of a millimetre were required:

         { Red     165
    (1)  { Green    60
         { Violet  100

Emerald green was placed in the patch and was matched by the light from
the three slits, when it was found that it required

         { Red       4
    (2)  { Green    35
         { Violet   25

Deducting one from the other we get as the complementary colour,

         { Red     125
    (3)  { Green    25
         { Violet   75

This is a complementary colour, but like the green itself it is mixed
with white light; but we can easily deduce what is the simplest
complementary colour; for we have only to deduct the possible white
light from the second measure. Now evidently the greatest amount of
white light is when the whole of the green is taken as forming part of
it, with the proper proportions of red and violet, and these we can
obtain by taking the proportions of the colours in (1); therefore
deduct--

         { Red     69
    (4)  { Green   25
         { Violet  41·5

and this would leave as the complementary colour without any admixture
of white--

    (5)  { Red     56
         { Violet  33·5

which is a purple as would be expected.

Now to give the same dilution of white to the complementary that the
emerald green has, we must take away from the emerald green all the
white mixed with it, and add that quantity to the complementary. The
white in the emerald green can be found by treating the whole of the red
as going to form the white; we then have from (1)--

         { Red     40
    (6)  { Green   14·4
         { Violet  24

Deducting these from (2), we find that the colour of emerald green, less
the white light, is 20·6 of green mixed with 1 of violet. To find the
proper dilution of the complementary colour we must add the above
proportions of the three colours, and as our final result we find the
complementary colour, of equal impurity, is a mixture of--

         { Red     96
    (7)  { Green   14·4
         { Violet  57·5

The slits may be set at these apertures and a colour patch thrown on the
screen, and we shall find it of a delicate pink. The truth of this can
be seen by using a double-image prism to view the pigmented surface,
illuminated by the same white light as that in which it was measured,
and the colour patch on the screen by its side. The two colours may be
caused to overlap, when it will be seen that white is produced.

Another example was an orange pigment, and this we will work out in the
form of colour equation. The same mixture gave white, viz.:

      165 R + 60 G + 100 V = W
      165 R + 42 G         = O

    ∴ the complementary colour, which is

      W - O = 18 G + 100 V,

or a dark-blue colour. In this case there was apparently no white light
reflected from the orange. It was slightly glossy, and as polarized
light was used for the reflected beam, it was probably somewhat
quenched; but what is more probable is that the green contains some
violet as well as red, for the reasons given in chapter XI. The reason
we have been particular in showing to what extent complementary colours
must be diluted with white to the same proportion that the colour itself
is diluted, will be apparent if considered for a moment. A deep brown is
in reality orange, much degraded in tone, and can be produced as a
colour patch on the screen if a bright orange pigment be placed in the
reflected beam of the colour patch, and the light nearly shut off by the
rotating sectors. Now the same complementary colour will be found for
both, but if we were to use the bright complementary colour which we
obtained with the orange for the brown, and endeavoured to obtain a
white with it by means of the double-image prism we should fail, as the
complementary colour would predominate. Complementary colours can always
be formed by a mixture of only two rays, and although the overlapping
images may form white, yet when the two are placed side by side, it
often will be found that the complementary, unless diluted with white,
is evidently too dark to be satisfactory, but the luminosity may be
increased by adding white to it, as any amount of white may be added to
the mixture of the two rays which form the complementary, and of course
white will still be formed with the original colour. It is thus quite
feasible to give the complementary the same luminosity as the latter by
adding white light to it. Like the colour itself, the complementary
colour can always be expressed either by a single ray of the spectrum,
or by white light from which a single ray is deducted. (See chapter
XIII.)




CHAPTER XV.


   Persistence of Images on the Retina--The Use of Coloured Discs.

Fig. 39.--Disc to cause alternate opening and closing of two Slits.

By this time we must be thoroughly convinced that by throwing one
coloured patch over another a compound colour can be formed; our next
business is to demonstrate that the same effect can be produced by
successive images of these same colours. Thus we can show that as a
mixture of red and blue produces purple, when the two lights are
superposed, so precisely the same purple can be produced by allowing the
same two colours to strike the eye alternately, and in very rapid
succession. We can make a match of the beautiful purple of permanganate
of potash as before upon the screen, by placing one adjustable slit in
the red and the other in the violet. If we place in front of the slits a
disc cut out with equal angular apertures (Fig. 39), the slit S₁ will be
covered when the slit S₂ is open, and _vice versâ_, and the two will
never be uncovered at the same time when the card is turning round its
centre. When this disc is caused to rotate rapidly, we shall have first
a patch formed by the light coming through one slit, and then another
formed by that coming through the other slit, thrown on the screen on
the same place in rapid succession, and the effect on the eye should be
precisely the same as if the disc was not there, save in the matter of
intensity. Applying this artifice experimentally to the two slits which
were used to give the colour of permanganate, the experiment tells us
that such is the case. It would be going away from the intention of
this work were the physiological aspect of this experiment dwelt upon;
it need only be stated that an impression on the retina lasts an
appreciable time, though short, and that the impression made by the blue
patch has not had time to disappear before there is an impression made
by the red patch, and so on. As the retina retains these two impressions
together, they produce the impression of purple.

Fig. 40.--Disc painted Blue and Red.

For experiments in colour this duration of impressions is of great
value, for we can take advantage of it to compound the colours of
pigments together in a very simple manner. For instance, we can take a
circular disc painted in sectors with blue and red (Fig. 40), and
produce a purple by causing it to rotate round its centre. Small discs
of two inches in diameter may be painted with different coloured
sectors, and if a pin be passed through the centre, a smart movement of
a finger at the periphery will cause it to rotate sufficiently quickly
to make the colours blend. A more convenient plan for exact work is,
however, to have an electro-motor similar to that which moves the
rotating movable sectors (Fig. 41), and at the end of the spindle to fix
a cap with a screw and nut attached. The disc, perforated at the centre
with a clean-cut hole, can be slipt over the screw, and fastened by the
circular nut. When the armature rotates, the disc also rotates at the
same speed, and the colours thus blend without any exertion on the part
of the observer. Ordinary tops can also be used, but it is somewhat
fatiguing to have to wind them up and start them afresh for each
experiment. The motor shown in the figure rotates sufficiently rapidly,
with discs of eight inches in diameter, to blend colours. It may here be
remarked that the stronger the light in which such sectors rotate, the
quicker the rotation should be. Too slow a rotation allows a
scintillation which is destructive of accuracy of reading. To blend some
colours together also requires more rapid rotation than with others. The
brighter the colour the more rapid it should be. We learn from this that
the diminution of the more intense impressions on the retina is more
rapid at first than of the feebler.

Fig. 41.--Electro-motor with Discs attached.

Fig. 42.--Method of cutting Disc to allow an overlap of a second Disc.

Very convenient discs for producing colours by rotation of sectors may
be made by the following: vermilion (V), emerald green (E), French
ultramarine blue (U), chrome yellow (Y), lamp-black (X), and (zinc)
white (W). With these nearly every colour can be produced, or its value
derived. The chrome yellow disc is somewhat superfluous, but is
sometimes useful. The alteration in the proportions of the colours can
be readily made by Clark-Maxwell's plan. From the circumference to the
centre he cut the discs open, as at _ab_ (Fig. 42). Any moderate number
of discs, similarly cut, may be slipt over one another, and only a
sector of each is left visible. It should be remarked that this
necessitates the rotating apparatus being viewed with a direct light, as
in the case of two or three overlapping discs it is impossible to keep
them entirely flat, and shades are apt to be introduced. If we wish to
produce a white, or rather a grey, from three colours, we can take three
small discs of V, E and U, of equal diameter, and behind them place
discs of black and white, of larger diameter, rotating the whole five on
a common centre. We shall find that by altering the proportions of the
three first we can get a grey which can be exactly matched by a mixture
of black and white, X and W. It has already been shown that even
lamp-black reflects a certain amount of white light, so this amount of
reflected white light has to be added to the white in the outside
sectors. In the sectors used in the following experiments it was found
that the following proportions of the three colours were required--

    V = 124°
    E = 143°
    U = 93°
        ----
        360°

and to make the same grey it required

    X = 278°
    W =  82°
        ----
        360°

Now the black reflected 3·4% of white light, so that really the
proportions of black and white were

    X = 268·6
    W =  91·4
        -----
        360·0

These matches were made in the light emitted by the crater of the
positive pole of the electric light, and are correct only for this
light. The greys here are dark greys, and such greys can be matched
exactly by throwing the white light in which the comparisons were made
on a white card, and reducing the intensity by means of the rotating
sectors. We can prove whether our matches are fairly correct from our
previous measures of the luminosity of these three colours, in
comparison with that of white. The luminosities of V, E, and U, as
found from the measures (pp. 93-95), are 36, 30, and 4·4, white being
100; 124 of V would have a luminosity of (124×36)/360, or 12·4; 143 of E
would have 11·92; and 93 of U would have 1·14; which, added to either,
give a luminosity of 25·46. The luminosity of 91·4/360 of white, which
is that of the mixture of black and white, comes to 25·39, so that we
may assume our observations have been fairly correct.

The influence of the kind of light in which the match was made is well
exemplified by taking the matched discs whilst rotating into a room
illuminated by the light from the sky, when it is seen that the grey of
the outer discs is bluish; or again, if the matched discs be examined in
gaslight, the inner grey will be found too blue.

The match of grey in this last light was found to be

    V = 119°
    E = 148°
    U = 93°
        ----
        360°

which matched with

    X = 244°
    W = 116°

(In this case the black and white are the corrected black and white.)

The importance of making matches in a uniform light is fairly
demonstrated by this experiment, and we cannot be wrong in asserting
that as skylight and sunlight and cloudlight (the last being often a
mixture of the two first), are so variable no measures made on one day
can be fairly compared with those made on another, more especially if
the observers are different. With an emerald green, a vermilion, an
ultramarine, a white, and a black disc any colour may be reproduced in
the rotation apparatus, the three first nearly matching what we have
already stated to be the three primary colours.

It may seem curious that both black and white may have to be mixed with
the colours, to produce a pigment colour; but a little reflection will
show how it is. For instance, suppose we want to know the colour
composition of gamboge (Y) in terms of vermilion (V), emerald green (E),
and ultramarine blue (U). We must make a disc painted with gamboge, and
also a black and a white disc of the same diameter, but rather larger
than the other three discs, and place them on the spindle of the
electro-motor (Fig. 43). We shall soon see on rotating them that no blue
is required in the inner disc, and that all that remains to do is to use
the red and the green. Mix these two, however, in whatever proportions
we may, the mixture will never attain the same luminosity, consequently
we must darken the yellow with black. Even then we shall find that, add
what black we may, the rotating red and green sectors will always be a
little less saturated with colour; which means that on rotation they
produce a certain quantity of white light mixed with the yellow. This we
might expect, for as emerald green, besides green and red, also contains
a fair proportion of blue, and as red, green and blue when mixed give
white, it follows that when V and E are rotated together, a grey or
subdued white light must be mixed with the colour produced. Turning back
to Chapter XIII. we also see that as the emerald green is expressible by
a single ray of the spectrum, mixed with white light this result might
have been foretold.

Fig. 43.--Arrangement to find value of Gamboge in terms of Emerald Green
and Vermilion.

This necessitates adding some white to the rotating sectors of the
yellow and black, as the yellow reflects but little white light, and
finally we shall get an absolute match, of which the final results are

    172 V + 188 E = 75 Y + 45 W + 240 X.

This equation is full of meaning. It tells us in the first place what we
have already known, that V and E are one or both impure colours, and
that when rotated together in the proportions indicated, they produce at
least a luminosity of white equal to 53/360 of a white disc (as the
black used reflected just 3·4% of white light). Further, it tells us
that we can obtain the luminosity of Y, when we know the luminosities of
V and E. At page 186, the luminosities of these colours are given as 36
and 30 respectively, white being 100. This makes the luminosity of the
colours on the left hand of the equation 17·2 + 15·67, or 32·87, and on
the right =75/360= Y + 14·76, and consequently the luminosity of Y =
86·9. In the same way we can obtain any other colour in terms of these
standards.

We may here show how we can obtain the luminosity of any colour by means
of the three inner discs, and the black and white outer discs. We have
already shown that any colour may be matched by the combination of not
more than two simple colours, after deducting white from it; and from
this we deduce that any coloured pigment will form a grey with some two
of the three coloured discs, V, E, and U; and this being done we can
then calculate the luminosity. For instance, with an orange-coloured
pigment we should proceed to make a disc of the same diameter as that of
the three above; an inspection would show us that in this colour red
predominates, and therefore we could do without the red disc. We should
then alter the proportions of V, U, and O, till they gave a match which
was the same as that of a grey given by the rotating black and white
sectors.

In an experiment with an orange of this kind, the following results were
obtained--

    E  115° }
    U  150° } = { W   85°
    O   95° }   { X  275°

We can now from these deduce the luminosity of the orange employed in
this case.

The luminosities of E and U, as already found, were 30 and 4·4, whilst
the black (X) reflected 3·4% of white light; we thus get the following
equations--

    115 × 30 + 150 × 4·4 + 95 O = (85 + 3·4 × 275) 100.
        This gives 95 O = 9435 - (3450 + 660).
          O = 56.

That is, the luminosity of the orange is ·56 that of white; by direct
measurement it was ·57.

In a similar way the luminosity of chrome yellow (Y) is found. In this
case--

    E  35 }
    U 204 } = { W 101
    Y 121 }   { X 259

Similar equations were formed as the above.

    35 × 30 + 204 × 4·4 + 121 Y = (101 + 3·4 × 259) 100
        whence Y = 77·6.

That is, the luminosity of the chrome yellow is ·78; the same as was
obtained by direct measurement.

In the same manner the luminosity of any colour can be found. Thus that
of a purple, or of green, can be ascertained; of the former by using the
green disc with either the red or the blue disc, and the latter by the
red and blue disc. From this it is apparent that we can check the
luminosities derived from other means by this plan.

A taking experiment can be made with colour discs to imitate all the
colours of the spectrum in their proper order, though diluted more or
less by white light. This can be done by rotating V, E, and U together;
but in order to get additional luminosity in the yellow, we can use
chrome yellow as well. If a disc be made as in the figure (Fig. 44), it
will on rotating give a fair imitation of the spectrum, if it be viewed
through a slit held in front of the disc.

Fig. 44.--Disc arranged to give approximately all the Spectrum Colours.

The mixture of colours by means of rotating sectors is one which the
artist cannot use for artistic purposes, and it might seem that for him
any deductions made from this method are useless; but it is not so.
Suppose we take black lines ruled closely together on paper, and examine
the surface from such a distance that the lines are no longer
distinguishable it will appear of a grey; and if we take the amount of
black on the paper and amount of white, and prepare two sectors of black
and white, whose angles are in these proportions, and rotate them
alongside the ruled surface, it will be found that the grey of one
matches the grey of the other. If instead of lines of black and white we
have them of light yellow and cobalt blue, a grey is also produced when
the surface covered by the blue is to that covered by the yellow in
correct proportions, and may be matched by rotating sectors containing
merely black and white. Now some artists employ stippling, filling up
cross-hatching of one colour with dots of a totally different colour, or
they place dots side by side. When seen from the distance at which the
picture should be viewed, these various colours blend one into another,
and form a tint which is the same as that which would be obtained by
rotating these colours together in the proportion in which they cover
the ground. Artists, however, generally mix their pigments together on
the palette, and the resulting mixtures are often totally unlike those
which are obtained by rotating the same colours together, a noteworthy
example is that of yellow and blue. By rotation, and when in proper
proportion, these two give a white, but when mixed on the palette a
green results. What causes this difference? Experimental proof is always
the most satisfactory proof, so let us have recourse to the spectrum
apparatus to obtain an answer. Let a spectrum be thrown on the screen,
and in it place a strip of paper painted with the yellow, and then
another with the blue. With the first it will be seen that the blue rays
are not reflected, but only the green and yellow and red, taking the
spectrum as roughly made up of these four colours. With the latter the
yellow is not reflected, and but very little red, but the blue and the
green are reflected strongly. Now we have already said that the
reflection of colour from a surface is indicative of the colours the
particles of pigments when taken thin enough to be transparent would
transmit; hence we may take it that the yellow pigment transmits the
red, yellow, and green, and the blue pigment scarcely anything but blue
and green. When we have a mixture of these fine particles of pigment on
paper, some will underlie the others. But let us pay attention to what
would happen if a yellow particle were at the top, and a blue one
beneath it. White light would impinge on the yellow particle, but only
red, yellow, and green would pass out or be reflected from it. This
sifted light would next fall on the blue particle and--as we have
seen--only blue and green can pass through or be reflected from it; but
as the yellow particle has already deprived the white light of its blue
component, the green light alone would pass to the paper, and be
reflected either direct from the surface of the paper, or through the
particles themselves to the eye. If the blue particle were on the top,
precisely the same effect would be produced; it would only allow blue
and green to pass to the yellow particle, and as the yellow is opaque to
the blue, only green light again would pass. Similarly if side by side
the same phenomena would occur, since the light reflected from one on to
the other would be deprived of all colour except the green. A very
pretty experimental proof of this is to place a yellow solution of dye
in front of the slit of the colour apparatus, and having formed the
yellow colour patch to place in it a piece of paper covered with a blue
pigment: the latter becomes green. By placing a blue solution in front
of the slit, and using a piece of yellow pigmented paper, the same
result is obtained. The artist therefore in mixing his pigments calls
into play the law of absorption, and from his mixtures very naturally
assumes that blue and yellow make green. He makes a neutral tint of
blue, red, and yellow, and as the red cuts off the green, this naturally
follows from the above. Such experiments as these led him to the
conclusion that red, yellow, and blue are the three primary colours, an
assumption which had he used simple spectrum colours instead of compound
colours, such as pigments, he would not have ventured to make.




CHAPTER XVI.


  Contrast Colours--Measurement of Contrast Colours--Fatigue of the
  Eye--After-Images.

Fig. 45.--Method of showing Contrast Colours.

There is a phenomenon in colour which must be alluded to, and which
possesses more than a passing interest to the art world, and that is
colour contrast. Perhaps one of the best methods of showing this is by
our colour patch apparatus. If we throw the reflected beam and the
colour patch on a square as before, and place a rather thinner rod in
front, so that the two shadows lie on a background of the combined white
light and spectral colours, on passing a slit through the spectrum, the
shadow which is illuminated by white light will appear anything but
white. Thus if we allow yellow spectral light to illuminate one shadow,
the other will appear decidedly of a blue hue; if a green ray it will
be of a ruddy hue; if a blue ray of a yellow hue; that is, all the
contrast hues will appear to the eye to tend towards a complementary
tone to the spectral light. The kind of white light illuminating the
shadow has a marked effect on the tone, as might be expected. The
following table shows the contrast colour of the white illuminated
shadow when the white light used was that of a candle.

  +---------------+-------------------+---------------+------------------+
  |               |     Contrast      |               |   Contrast       |
  |   Spectrum    |     Colours in    |   Spectrum    |  Colours in      |
  |    Colour.    |  Electric light.  |    Colour.    |   Gaslight.      |
  +---------------+-------------------+---------------+------------------+
  | Cherry red    | Green gray        | Cherry red    | Green gray       |
  | Scarlet       | Bluish green gray | Scarlet       | Sap green        |
  | Terra-cotta   | Blue gray         | Light red     | Green gray       |
  | Raw sienna    | Light blue gray   | Olive green   | Pink gray        |
  | Olive green   | Umber             | Apple green   | Mauve & black    |
  | Emerald green | Pinkish lavender  | Emerald green | Pink terra-cotta |
  | Grass green   | Light pink        | Emerald green | Pink terra-cotta |
  | Bluish green  | Dark pink         | Bluish green  |Pinker terra-cotta|
  | Signal green  | Salmon            | Peacock blue  | Salmon           |
  | Cyanine blue  | Yellow ochre      | Prussian blue | Reddish yellow   |
  | Ultramarine   | Raw sienna        | Ultramarine   | Raw sienna       |
  | Violet blue   | Brownish yellow   | Violet blue   | Brownish Orange  |
  | Blue violet   | Green yellow brown| Blue violet   | Brownish yellow  |
  | Violet        | Burnt sienna      | Violet        | Yellow ochre     |
  +---------------+-------------------+---------------+------------------+

The contrasts here shown are not so visible when the two shadows of the
rod occupy the whole of the white square, but are decidedly increased
by the shadows occupying only a part of the field, the margins being
illuminated with a mixture of the two lights. Not only are there
contrasts with coloured light and white, but the relative position of
one colour to another may alter the hue of each to the eye. The
following experiments indicate what change can be expected in contrasted
colours. The double colour apparatus was used as described at page 122,
and a slit was placed in four different positions in the spectrum, viz.
in the red, orange, green, and violet, to form patches, and another slit
was placed in the same four positions in the other spectrum, and the
contrasts noted.

    +-----------------+----------------------------------------------+
    |Original Colours.|       Change due to Contrast.                |
    +--------+--------+----------------------+-----------------------+
    | Red    | Orange | Red became yellower  | Orange became green   |
    |        |        |                      |   grey                |
    |  "     | Green  |  "  unaltered, but   | Green unaltered, but  |
    |        |        |       brighter       |   brighter            |
    |  "     | Blue   |  "  became more      | Blue became greener   |
    |        |        |       orange         |                       |
    |  "     | Violet |  "  became orange    | Violet, no marked     |
    |        |        |                      |   change              |
    | Green  | Orange | Green became bluer   | Orange became yellower|
    |   "    | Blue   |   "   became olive   | Blue became more      |
    |        |        |                      |   violet              |
    |   "    | Violet |   "   became yellower| Violet became bluer   |
    | Orange | Blue   | Orange became redder | Blue became bluer     |
    |   "    | Violet |   "   became greener | Violet became bluer   |
    | Violet | Blue   | Hardly altered       | Hardly altered        |
    +--------+--------+----------------------+-----------------------+

These contrasts were in most cases very marked, as would be seen by
causing the same colours to fall on a different part of the screen,
outside that on which the comparisons were made.

This phenomenon of contrast is one which is most valuable for artistic
purposes, for it gives a power of increasing the value of the colour of
pigments which is used by the artist almost intuitively. Thus he can
heighten the tone of his orange pigment, with which he makes a sunset
sky, by placing in juxtaposition with it some bit of blue coloured
space. The blue becomes bluer, and the orange more orange, by this
artifice. All these artifices--or rather we should say intuitive
applications of science--are most necessary when the small range of
luminosity of colours with which he has to deal is taken into account.
For instance, in a picture of a sun-lighted snow mountain and deep pine
forests, the utmost luminosity he can give to the former is that of
white paper when seen in the shade, which, in comparison with what he
sees, is really a mixture of 90% of black with the light from the snow,
so that his range of luminosity is only nine-tenths of that which occurs
in nature. It is in adapting this low scale to his picture that true
genius of the artist is seen.

It might seem that these contrast colours being only a physiological
effect, could not be accurately measured, but such is not the case, if
a little artifice be employed. If we use the second colour patch
apparatus side by side with the first, we can very readily and with very
close approximation determine the contrast colours we see. Suppose by
the second apparatus we form a colour patch of say red, and place a thin
rod in the beam of this ray and of the reflected beam, and about six
inches from it form another patch with the first apparatus, using the
three slits to make colour mixtures; by first noting the contrast
colour, and then approximating in the second patch to what the eye
perceives, we can little by little get a fairly exact match to the
contrast colour, and can definitely note it. We now give the results of
three measures made for the contrast colours which presented themselves
to the eye when they were caused by a red ray near the lithium line,
another near the E line in the green, and the third near the G line in
the violet.

To make white light and the contrast colours, the slits had to be of the
following apertures--

    +-----------------+-------+--------+---------+
    |    Colour.      |  Red. | Green. | Violet. |
    +-----------------+-------+--------+---------+
    | White light     | 15·7  |   6·5  |    9·8  |
    | Contrast to Red | 13·5  |  11·8  |   22·5  |
    | " Green         | 15·8  |   5·1  |    4·8  |
    | " Violet        | 15·9  |   7·2  |    4·2  |
    +-----------------+-------+--------+---------+

Thus to form the contrast to red took 13·5 of red, 11·8 of green, and
22·5 of violet. Now from each of these there can be deducted the amount
of white light, which will leave only two colours mixed. Calculating
this out we find that the contrasts are--

    +-----------------+-------+--------+---------+
    | Contrast Colour |  Red. | Green. | Violet. |
    | to              |       |        |         |
    +-----------------+-------+--------+---------|
    |Red              |  --   |   3·5  |   16·7  |
    |Green            | 15·7  |   3·2  |    --   |
    |Violet           | 19·4  |   9·5  |    --   |
    +-----------------+-------+--------+---------+

If the contrasts were exactly complementary colours, the proportions of
the two colours left should be the same as those of the same colours as
given, which with the original colour make white light. It will be seen
that such is not the case. A very simple way of testing this is to form
a patch of white light with the three slits in the first apparatus, and
then to obtain the contrasts by the other apparatus, with the same
colours one after the other that pass through the three slits. If now we
cover up the slit in the first apparatus through which the colour whose
contrast in the second apparatus is sought passes, we may dilute it with
white light as we will, but in no case has the writer found that an
exact match to the contrast colour can be obtained in this way. Thus,
supposing we wanted to try the experiment with the same red light as
that which comes through the red slit, we should use that same light in
the second apparatus, and form the contrast colour with the white beam,
and then in the first apparatus cover up the red slit, leaving the
violet and green to form a patch on the screen. We should then dilute
the colour of this patch with white light, and note if it appeared the
same as the contrast colour.

Another phenomenon which presents itself is the fatigue of the
colour-sensation apparatus of the eye, induced by looking at a bright
object. For instance, if we look at a crimson wafer or spot for some
time, and then turn the eye so that it rests on a grey surface, an image
of the spot will still be seen, but as of a greenish-blue colour. This
is due to the fact that the red-seeing apparatus is fatigued and
exhausted, whilst the green and violet-seeing machinery has not been
largely exercised. Consequently when looking at grey paper the grey of
the paper is seen in the retina at all parts as grey, except in the
small part of the retina which has got diminished power of perceiving a
red sensation; hence a sea-green image will be seen until the fatigue
has passed away. This colour can be reproduced with very fair accuracy
by allowing only one eye to be fatigued, and then using the other to
obtain a colour mixture corresponding to it. It will then be found that
the colour is the same as the complementary colour, much diluted with
white light.

To the same cause may be traced positive and negative after-images, as
they are called. If we look at a strongly-illuminated coloured form,
such as a church window, and close the eyes, the window will still be
seen, at first of its original colour (a positive after-image), and it
will then fade and be seen in its complementary colours (a negative
after-image). The positive image is due to the persistence of what we
may call nerve irritation, whilst the negative image is due to the
physiological excitation of all the nerve fibrils, which ordinarily
speaking give the sensation of a very dull white light. The previous
fatigue of one set of fibrils, however, prevents them being excited to
the same degree as the others, hence we get a complementary image. It
would be out of place to pursue this subject further, as we have only
dealt with the physical measurement of colour-sensations, and these are
beyond it.




INDEX.


  Absorption by red, blue, and green glasses,               53

  Absorption of light in the earth's atmosphere,            67

  Absorption, reference to law of,                          53

  After-glow,                                               74

  Arc light,                                                20

  Artists and colours,                                     195


  Balmain's paint,                                          33

  Black body,                                               18

  Blindness to green,                                      142

  Blindness to red,                                     79-142

  Bromo-iodide of silver,                                  136


  Carbon poles,                                             20

  Carmine, light reflected from,                           107

     "     template,                                       106

  Chlorophyll, green solution of,                           51

  Collimating lens, focal length of,                        22

  Colour, analysis of,                                      52

  Colour-blind, red and green,                          79, 80

  Colour-blindness,                          142-146, 157, 159

  Colour constants,                                         15

  Colour equations, formation of,                     147, 148

  Colour, extinction of, by white light,                   126

  Colour mixtures,                                         113

  Colour patch apparatus,                                41-52

  Colour sensation of the eye,                             202

  Coloured discs, use of,                                  189

  Coloured glasses, measurement of,                        162

  Colours, complementary of pigments,                  170-172

  Colours, complementary of spectrum,                      167

  Colours, how matched,                               156, 157

  Complementary colours, measurement of,               173-178

  Compound colours, definition of,                          16

  Continuous spectrum,                                      17

  Contrast colours,                                    196-200


  Diffraction gratings,                                     23

       "      spectra,                                      24

  Dimness and brightness of spectrum,                       29

  Discs, spinning,                                         182

  Dust, particles of,                                       62


  Electric light, contrast colours in,                     197

  Electric light, crater of positive pole of,               20

  Emerald green, light reflected from,                      94

  Equations, colour,                                       147

  Essentials of spectrum,                                   22

  Extraction of colour by white light,                     126

  Extraction of white light by colour,                     131

  Eye, sensitiveness of,                                    15


  Fatigue of the retina,                                   202

  Fluorescence,                                             31

  Fundamental sensations,                                  140


  Gamboge, matching,                                       189

  Glass, light from sheet of,                               14

  Glass prisms,                                         21, 22

  Glow-worm,                                                13

  Green colour-blindness,                                  142


  Heating effect of radiation,                              38

  Hue,                                                      15


  Images, after,                                           202

  Images, persistence of, on retina,                       179

  Impurity of simple colours,                              124

  Indicator of sectors,                                     48

  Infra-red rays,                                           32

      "     photography with,                               34

  Insensitiveness of the yellow spot to green,             118

  Intensities of limelight, gaslight, and blue sky
    compared,                                         110, 121

  Interference,                                         58, 59

  Interference bands on soap film,                          60

  Invisible spectrum, methods for showing existence of, 32, 33


  Kœnig's curves,                                          151

  Kœnig's experiments,                                     140


  Law of the scattering by fine particles,                  66

  Light from sun, imitation of,                             63

  Light, quality of, illumining object,                     14

  Light scattered,                                          62

  Limelight,                                                19

  Lines in solar spectrum,                                  26

  Luminosity,                                               13

  Luminosity, addition of one to another,                85-87

  Luminosity of colour,                                     16

  Luminosity of pigments, methods of determining,       81, 82

  Luminosity of spectrum to normal-eyed and colour-blind
    persons,                                             76-78

  Luminosity of sun at different altitudes,              69-71


  Maxwell's colour-box,                               152, 153

  Maxwell's discs,                                     184-186

  Measurement of amount of light reflected by different
    pigments,                                            88-92

  Metals, light reflected from,                            100

  Mock suns, cause of change of colour in,                  64

  Molecular physics,                                        54

  Molecular swings,                                   136, 137

  Monochromatic light,                                      47


  Negative images,                                         203

  Normal vision,                                            77


  Orange, finding luminosity of,                           190


  Percentages of skylight, sunlight, and gaslight,    110, 111

  Phosphorescence,                                      32, 56

  Pigments, absorption by,                              57, 58

  Plan of forming spectrum,                                 21

  Polished and uneven surfaces,                             13

  Primary colours, definition of,                      133-135

  Prism, Iceland spar,                                      96

  Prismatic spectrum into wave-lengths, conversion of,      28

  Prisms, drawback to use of,                               23

  Prussian blue template,                                  107

      "            "      light reflected from,            107

  Purity of colour,                                         16


  Rays, infra-red,                                          34

  Rays, photography of dark,                                34

  Rays, ultra-violet,                                       34

  Registering tint of pigments,                            116

      "            "  colours,                             156

  Retina, persistence of images on,                        179

  Ritter's rays,                                            32

  Rood's colour scale,                                      26

  Rotating sectors,                                         46


  Scaling of spectrum,                                      49

  Sectors, rotating,                                        46

  Simple colours, how obtained,                       112, 113

  Slits placed in spectrum,                                113

  Soap-bubbles,                                         58, 59

  Soap-films,                                               59

  Spectrum, absorption of,                              51, 52

  Spectrum of sunlight,                                     18

  Sun, mock,                                                64

  Sunset clouds,                                68, 69, 72, 73

  Sunset sky,                                           72, 73


  Thermopile, heating effects of,                           36

  Thermopile, principle of,                                 35


  Ultramarine, light reflected from,                        95

  Ultra-violet rays,                                        31


  Vermilion, light reflected from,                          93

  Vibrations of rays per second,                            55

  Violet bands, brightness of,                              21

  Visible and invisible parts of spectrum,                  30


  Water, particles of,                                      62

  Wave-length of lines in solar spectrum,                   26

  White light and contrast colours,                    200-202

  White light, extinction of by colour,                    131

  White light, formation of by mixture of yellow and blue, 125

  White light, how made,                     114, 115, 119-123

  White light, impression of,                               81


  Yellow and blue make white,                              125

  Yellow, chrome, luminosity of,                           191

  Yellow spot,                                             117

  Young-Helmholtz theory,                                  138



THE END.




Richard Clay & Sons, Limited, London & Bungay.




PUBLICATIONS OF THE

=Society for Promoting Christian Knowledge.=


THE ROMANCE OF SCIENCE.

A series of books which shows that science has for the masses as great
interest as, and more edification than, the romances of the day.

_Small Post 8vo, Cloth boards._

=Coal, and what we get from it.= Expanded from the Notes of a
Lecture delivered at the London Institution. By Professor Raphael
Meldola, F.R.S., F.I.C. With several Illustrations. 2_s._ 6_d._

=Colour Measurement and Mixture.= By Captain W. de W. Abney, L.B.,
R.E., F.R.S. With Numerous Illustrations. 2_s._ 6_d._

=The Making of Flowers.= By the Rev. Professor George Henslow,
M.A., F.L.S., F.G.S. With Several Illustrations. 2_s._ 6_d._

=The Birth and Growth of Worlds.= A Lecture by Professor A. H.
Green, M.A., F.R.S. 1_s._

=Soap-Bubbles, and the Forces which Mould Them.= A course of
Lectures by C. V. Boys, A.R.S.M., F.R.S. With numerous diagrams.
2_s._ 6_d._

=Spinning Tops.= By Professor J. Perry, M.E., D.Sc., F.R.S. With
numerous diagrams. 2_s._ 6_d._

=Diseases of Plants.= By Professor Marshall Ward. With Numerous
Illustrations. 2_s._ 6_d._

=The Story of a Tinder-Box.= A course of Lectures by Charles
Meymott Tidy, M.B., M.S., F.C.S. With Numerous Illustrations. 2_s._

=Time and Tide.= A Romance of the Moon. By Sir Robert S. Ball,
LL.D., Royal Astronomer of Ireland. With Illustrations. 2_s._ 6_d._




MANUALS OF HEALTH.

_Fcap. 8vo, 128 pp., limp cloth, price 1s. each._


=Health and Occupation.= By B. W. Richardson, Esq., F.R.S., M.D.

=Habitation in Relation to Health (The).= By F. S. B. Chaumont, M.D.,
F.R.S.

=On Personal Care of Health.= By the late E. A. Parkes, M.D., F.R.S.

=Water, Air, and Disinfectant.= By W. Noel Hartley, Esq., King's
College.




MANUALS OF ELEMENTARY SCIENCE.

_Fcap. 8vo, 128 pp., with Illustrations, limp cloth, 1s. each._


=Physiology.= By F. le Gros Clarke, F.R.S., St. Thomas's Hospital.

=Geology.= By the Rev. T. G. Bonney, M.A., F.G.S., Fellow and late
Tutor of St. John's College, Cambridge.

=Chemistry.= By Albert J. Bernays.

=Astronomy.= By W. H. M. Christie, M.A., the Royal Observatory,
Greenwich.

=Botany.= By Robert Bentley, Professor of Botany in King's College,
London.

=Zoology.= By Alfred Newton, M.A., F.R.S., Professor of Zoology and
Comparative Anatomy in the University of Cambridge.

=Matter and Motion.= By the late J. Clerk Maxwell, M.A., Trinity
College, Cambridge.

=Spectroscope and its Work (The).= By the late Richard A. Proctor.

=Crystallography.= By Henry Palin Gurney, M.A., Clare College,
Cambridge.

=Electricity.= By the late Professor Fleeming Jenkin.




=The Fathers for English Readers.=

_A series of Monograms on the Chief Fathers of the Church, the Fathers
selected being centres of influence at important periods of Church
History and in important spheres of action._

Fcap. 8vo, cloth, boards, 2s. each.


_Leo the Great._ By the Rev. Charles Gore, M.A.

_Gregory the Great._ By the Rev. J. Barmby, B.D.

_Saint Ambrose_: his Life, Times, and Teaching. By the Rev. Robinson
Thornton, D.D.

_Saint Athanasius_: his Life and Times. By the Rev. R. Wheler Bush.
(2_s._ 6_d._)

_Saint Augustine._ By the Rev. E. L. Cutts, B.A.

_Saint Basil the Great._ By the Rev. _Richard T. Smith_, B.D.

_Saint Bernard_: Abbot of Clairvaux, A.D. 1091-1153. By the Rev. S.
J. Eales, M.A., D.C.L. (2_s._ 6_d._)

_Saint Hilary of Poitiers, and Saint Martin of Tours._ By the Rev.
J. Gibson Cazenove, D.D.

_Saint Jerome._ By the Rev. Edward L. Cutts, B.A.

_Saint John of Damascus._ By the Rev. J. H. Lupton, M.A.

_Saint Patrick_: his Life and Teaching. By the Rev. E. J. Newell,
M.A. (2_s._ 6_d._)

_Synesius of Cyrene_, Philosopher and Bishop. By Alice Gardner.

_The Apostolic Fathers._ By the Rev. H. S. Holland.

_The Defenders of the Faith_; or, The Christian Apologists of the
Second and Third Centuries. By the Rev. F. Watson, M.A.

_The Venerable Bede._ By the Rev. G. F. Browne.




MISCELLANEOUS PUBLICATIONS.

                                                           s. d.

  _Animal Creation (The)._ A popular Introduction
  to Zoology. By the late Thomas Rymer Jones, F.R.S.
  With 488 Woodcuts. Post 8vo.             _Cloth boards_  7  6

  _Beauty in Common Things._ Illustrated by 12
  Drawings from Nature, by Mrs. J. W. Whymper, and
  printed in Colours, with descriptions by the Author of
  "Life Underground," &c. 4to.            _Cloth boards_  10  6

  _Birds' Nests and Eggs._ With 22 coloured plates
  of Eggs. Square 16mo.                    _Cloth boards_  3  0

  _British Birds in their Haunts._ By the late Rev.
  C. A. Johns, B.A., F.L.S. With 190 engravings by
  Wolf and Whymper. Post 8vo.              _Cloth boards_  6  0

  _Evenings at the Microscope_; or, Researches among
  the Minuter Organs and Forms of Animal Life. By
  Philip H. Gosse, F.R.S. With 112 woodcuts. Post
  8vo.                                     _Cloth boards_  4  0

  _Fern Portfolio (The)._  By Francis G. Heath,
  Author of "Where to find Ferns," &c. With 15 plates,
  elaborately drawn life-size, exquisitely coloured from
  Nature, and accompanied with descriptive text.
                                           _Cloth boards_  8  0

  _Fishes, Natural History of British_: their Structure,
  Economic Uses, and Capture by Net and Rod. By the
  late Frank Buckland. With numerous illustrations.
  Crown 8vo.                               _Cloth boards_  5  0

  _Flowers of the Field._ By the late Rev. C. A.
  Johns, B.A., F.L.S. With numerous woodcuts. Post
  8vo.                                     _Cloth boards_  5  0

  _Forest Trees (The) of Great Britain._ By the late
  Rev. C. A. Johns, B.A., F.L.S. With 150 woodcuts.
  Post 8vo.                                _Cloth boards_  5  0

  _Freaks and Marvels of Plant Life_; or, Curiosities
  of Vegetation. By M. C. Cooke, M.A., LL.D. With
  numerous illustrations. Post 8vo.        _Cloth boards_  6  0

  _Man and his Handiwork._ By the late Rev. J. G.
  Wood, Author of "Lane and Field," &c. With about
  500 illustrations. Large Post 8vo.      _Cloth boards_  10  6

  _Natural History of the Bible (The)._ By the Rev.
  Canon Tristram, Author of "The Land of Israel," &c.
  With numerous illustrations. Crown 8vo.  _Cloth boards_  5  0

  _Nature and her Servants_; or, Sketches of the
  Animal Kingdom. By the Rev. Theodore Wood.
  With numerous woodcuts. Large Post 8vo.  _Cloth boards_  5  0

  _Ocean (The)._ By Philip Henry Gosse, F.R.S.,
  Author of "Evenings at the Microscope." With 51
  illustrations and woodcuts. Post 8vo.    _Cloth boards_  3  0

  _Our Bird Allies._ By the Rev. Theodore Wood.
  With numerous illustrations. Fcap. 8vo.  _Cloth boards_  2  6

  _Our Insect Allies._ By the Rev. Theodore Wood.
  With numerous illustrations. Fcap. 8vo.  _Cloth boards_  2  6

  _Our Insect Enemies._ By the Rev. Theodore Wood.
  With numerous illustrations. Fcap. 8vo.  _Cloth boards_  2  6

  _Our Island Continent._  A Naturalist's Holiday in
  Australia. By J. E. Taylor, F.L.S., F.G.S. With
  Map. Fcap. 8vo.                          _Cloth boards_  2  6

  _Our Native Songsters._ By Anne Pratt, Author of
  "Wild Flowers." With 72 coloured plates. 16mo.
                                           _Cloth boards_  6  0

  _Selborne (The Natural History of)._ By the Rev.
  Gilbert White.  With Frontispiece, Map, and 50
  woodcuts. Post 8vo.                      _Cloth boards_  2  6

  _Toilers in the Sea._ By M. C. Cooke, M.A., LL.D.
  Post 8vo. With numerous illustrations.   _Cloth boards_  5  0

  _Wayside Sketches._ By F. Edward Hulme, F.L.S.,
  F.S.A. With numerous illustrations. Crown 8vo.
                                           _Cloth boards_  5  0

  _Where to find Ferns._ By Francis G. Heath,
  Author of "The Fern Portfolio," &c. With numerous
  illustrations. Fcap. 8vo.                _Cloth boards_  1  6

  _Wild Flowers._ By Anne Pratt, Author of "Our
  Native Songsters," &c. With 192 coloured plates. In
  two volumes. 16mo.                       _Cloth boards_ 12  0




LONDON:

Northumberland Avenue, Charing Cross, W.C.;
43, Queen Victoria Street, E.C.
BRIGHTON: 135, North Street.




Transcribers Note:
Page 162 The following equation:
    ∴ _Z_ + _x´X_´ + μ´_W_ = ɑ_wW_
       _Z_ = (ɑ_w_ - μ´)_W_ - _x´X´_
Is printed as
    ∴ _Z_ + _x₁X_´ + μ´_W_ = ɑ_wW_
       _Z_ = (ɑ_w_ - μ´)_W_ - _x´X´_
in the original.





End of Project Gutenberg's Colour Measurement and Mixture, by W. de W. Abney