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+Project Gutenberg's Colour Measurement and Mixture, by W. de W. Abney
+
+This eBook is for the use of anyone anywhere at no cost and with
+almost no restrictions whatsoever.  You may copy it, give it away or
+re-use it under the terms of the Project Gutenberg License included
+with this eBook or online at www.gutenberg.org
+
+
+Title: Colour Measurement and Mixture
+
+Author: W. de W. Abney
+
+Release Date: February 26, 2012 [EBook #38984]
+
+Language: English
+
+Character set encoding: UTF-8
+
+*** START OF THIS PROJECT GUTENBERG EBOOK COLOUR MEASUREMENT AND MIXTURE ***
+
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+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.
+
+
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+
+
+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
+
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diff --git a/38984-0.zip b/38984-0.zip
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+Project Gutenberg's Colour Measurement and Mixture, by W. de W. Abney
+
+This eBook is for the use of anyone anywhere at no cost and with
+almost no restrictions whatsoever.  You may copy it, give it away or
+re-use it under the terms of the Project Gutenberg License included
+with this eBook or online at www.gutenberg.org
+
+
+Title: Colour Measurement and Mixture
+
+Author: W. de W. Abney
+
+Release Date: February 26, 2012 [EBook #38984]
+
+Language: English
+
+Character set encoding: ISO-8859-1
+
+*** START OF THIS PROJECT GUTENBERG EBOOK COLOUR MEASUREMENT AND MIXTURE ***
+
+
+
+
+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)
+
+
+
+
+
+
+
+
+
+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--K[oe]nig'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. K[oe]nig'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 formul�, 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/(3^4) to
+1/(4^4), 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.
+
+    +-----------+------+------+------+------+
+    | [Lamda]   | 7000 | 6000 | 5000 | 4000 |
+    +-----------+------+------+------+------+
+    |1/[Lamda]^4|    1 | �504 | �260 | �107 |
+    +-----------+------+------+------+------+
+
+Supposing [Lamda]7000 by the scattering of small particles loses one-tenth
+of its luminosity, then [Lamda]6000 would have �454 of its original
+brightness; [Lamda]5000, �234; and [Lamda]4000, �095; that is, whilst [Lamda]7000
+would lose one-tenth only of its luminosity, [Lamda]4000 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 [Lamda]^-4 was for
+convenience sake multiplied by 10^17 (thus [Lamda]6000^-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|[Lamda]^-4+-+----+----+----+----+----+----+----+----+----+
+  |   |      |  x10^17  |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 �sthetic 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 x 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 K[oe]nig (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--K[oe]nig'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.--K[oe]nig's Curves of Colour Sensations.
+
+By taking a large number of colour equations, K[oe]nig, 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 K[oe]nig.
+
+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_ = [Alpha]_a_, _q_ = [Beta]_b_, _r_ = [Gamma]_c_,
+
+  Then we may write (ii.) as--
+
+    [Alpha]_aR_ + [Beta]_bG_ + [Gamma]_cV_ = _zZ_--(iii.).
+
+  Now either [Alpha], [Beta], or [Gamma] must be smaller than the other two. As an
+  example, if [Alpha] be the smallest, we multiply (i.) by [Alpha] when we get--
+
+    [Alpha]_aR_ + [Alpha]_bG_ + [Alpha]_cV_= [Alpha]_wW_--(iv.)
+
+    Subtracting (iv.) from (iii.) and we get--
+
+    ([Beta]-[Alpha])_bG_ + ([Gamma]-[Alpha])_cV_ = _zZ_ - [Alpha]_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
+([Beta]-[Alpha])_b_ + ([Gamma]-[Alpha])_c_], and [Mu] the luminosity of the small quantity of
+white added.
+
+We then get _zZ_ = _xX_ + ([Mu] + [Alpha]) _W_.
+
+Here we have the colour _Z_ in terms of a single ray, and of white
+light.
+
+This same holds good when in (ii.) [Gamma] is smaller than [Alpha] and [Beta]; but it
+does not do so should it happen that [Beta] 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.) [Alpha] to be larger than [Gamma] and [Gamma] than [Beta], then we must add PhphPhi Pi mu [Phi]_bG_ +
+[Theta]_cV_ and we have
+
+    [Alpha]_aR_ + ([Beta] + [Phi])_bG_ + ([Gamma] + [Theta])_cV_ = _nW_ = _Z_ + [Phi]_bG_ + [Theta]_cV_;
+    but ([Beta] + [Phi]), and ([Gamma] + [Theta]) each equal [Alpha] Therefore _n_ = [Alpha]_w_.
+                 Therefore _Z_ + [Phi]_bG_ + [Theta]_cV_= [Alpha]_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 [Mu]�, which
+must equal ([Phi]_b_ + [Theta]_c_).
+
+    Therefore _Z_ + _x�X_� + [Mu]�_W_ = [Alpha]_wW_
+       _Z_ = ([Alpha]_w_ - [Mu]�)_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             C[oe]rulium, 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 Br�cke'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
+
+    Therefore 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 vers�_, 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 (124x36)/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 x 30 + 150 x 4�4 + 95 O = (85 + 3�4 x 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 x 30 + 204 x 4�4 + 121 Y = (101 + 3�4 x 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
+
+
+  K[oe]nig's curves,                                          151
+
+  K[oe]nig'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.
+
+
+
+
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+
+  _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
+
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+  Wood, Author of "Lane and Field," &c. With about
+  500 illustrations. Large Post 8vo.      _Cloth boards_  10  6
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+  _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
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+  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
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+  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.;
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+
+
+
+Transcribers Note:
+Page 162 The following equation:
+    Therefore _Z_ + _x�X_� + [Mu]�_W_ = [Alpha]_wW_
+       _Z_ = ([Alpha]_w_ - [Mu]�)_W_ - _x�X�_
+Is printed as
+    Therefore _Z_ + _x1X_� + [Mu]�_W_ = [Alpha]_wW_
+       _Z_ = ([Alpha]_w_ - [Mu]�)_W_ - _x�X�_
+in the original.
+
+
+
+
+
+End of Project Gutenberg's Colour Measurement and Mixture, by W. de W. Abney
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+<pre>
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+Project Gutenberg's Colour Measurement and Mixture, by W. de W. Abney
+
+This eBook is for the use of anyone anywhere at no cost and with
+almost no restrictions whatsoever.  You may copy it, give it away or
+re-use it under the terms of the Project Gutenberg License included
+with this eBook or online at www.gutenberg.org
+
+
+Title: Colour Measurement and Mixture
+
+Author: W. de W. Abney
+
+Release Date: February 26, 2012 [EBook #38984]
+
+Language: English
+
+Character set encoding: UTF-8
+
+*** START OF THIS PROJECT GUTENBERG EBOOK COLOUR MEASUREMENT AND MIXTURE ***
+
+
+
+
+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)
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+</pre>
+
+
+
+<p>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.</p>
+<a name="frontispiece" id="frontispiece"></a>
+<div class="figcenter" style="width: 402px;">
+<img src="images/i_002.jpg" width="402" height="253" alt="" title="">
+<span class="caption">COLOUR-PATCH APPARATUS.</span>
+</div><br>
+
+
+<h2><i>THE ROMANCE OF SCIENCE.</i></h2>
+<hr style="width: 95%;">
+<h1>  COLOUR MEASUREMENT</h1>
+<p class='center larger'>  AND</p>
+<h1>MIXTURE.</h1>
+
+
+<p class='padtop center smaller'>  <b>With Numerous Illustrations.</b></p>
+
+
+<p class='padtop center smaller'>  BY</p>
+<p class='center larger'>  CAPTAIN W. <span class="smcap">de W. ABNEY, c.b., r.e., d.c.l., f.r.s.</span></p>
+
+
+<p class='padtop center smaller'>  PUBLISHED UNDER THE DIRECTION OF THE COMMITTEE<br>
+  OF GENERAL LITERATURE AND EDUCATION APPOINTED BY THE<br>
+  SOCIETY FOR PROMOTING CHRISTIAN KNOWLEDGE.</p>
+
+
+<p class='padtop center smaller'>  SOCIETY FOR PROMOTING CHRISTIAN KNOWLEDGE.<br>
+  LONDON: NORTHUMBERLAND AVENUE, W.C.;<br>
+  43, QUEEN VICTORIA STREET, E.C.<br>
+  BRIGHTON: 135, NORTH STREET.<br>
+  NEW YORK: E. &amp; J. B. YOUNG &amp; CO.<br>
+  1891.</p><br>
+
+
+<hr style="width: 65%;">
+<h2>PREFACE.</h2>
+
+
+<p>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.</p>
+
+<p>As a treatise it must necessarily be incomplete,
+as it scarcely touches on the history of the subject&mdash;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.</p>
+
+<p class="rtnote"><span class="smcap">W. de W. Abney.</span></p>
+<br>
+<p><span style="margin-left: 2em;"><i>South Kensington,</i></span><br>
+<span style="margin-left: 2em;"><i>1st May, 1891.</i></span><br>
+</p>
+
+
+<hr style="width: 65%;">
+<h2>CONTENTS.</h2>
+
+
+
+<h3><a href="#CHAPTER_I">CHAPTER I.</a></h3>
+
+<p>    Sources of Light&mdash;Reflected Light&mdash;Reflection from Roughened
+    Surfaces&mdash;Colour Constants <span class="sidenote"><i>p.</i> 11</span></p>
+
+
+<h3><a href="#CHAPTER_II">CHAPTER II.</a></h3>
+
+<p>    A Standard of Light&mdash;Formation of the Spectrum by Prisms and by
+    the Diffraction Grating&mdash;Wave-lengths of the principal Fraunhofer
+    Line&mdash;Position of Colours in the Spectrum <span class="sidenote"><i>p.</i> 17</span></p>
+
+
+<h3><a href="#CHAPTER_III">CHAPTER III.</a></h3>
+
+<p>    The Visible and Invisible Parts of the Spectrum&mdash;Methods
+    for showing the Existence of the Invisible
+    Portions&mdash;Phosphorescence&mdash;Photography of the Dark
+    Rays&mdash;Thermo-Electric Currents <span class="sidenote"><i> p.</i> 30</span></p>
+
+
+<h3><a href="#CHAPTER_IV">CHAPTER IV.</a></h3>
+
+<p>    Description of Colour Patch Apparatus&mdash;Rotating Sectors&mdash;Method of
+    making a Scale for the Spectrum <span class="sidenote"><i>p.</i> 41</span></p>
+
+
+<h3><a href="#CHAPTER_V">CHAPTER V.</a></h3>
+
+<p>    Absorption of the Spectrum&mdash;Analysis of Colour&mdash;Vibrations of
+    Rays&mdash;Absorption by Pigments&mdash;Phosphorescence&mdash;Interference <span class="sidenote"><i>p.</i> 51</span></p>
+<p><span class="pagenum">[Pg viii]</span></p>
+
+<h3><a href="#CHAPTER_VI">CHAPTER VI.</a></h3>
+
+<p>    Scattered Light&mdash;Sunset Colours&mdash;Law of the Scattering by Fine
+    Particles&mdash;Sunset Clouds&mdash;Luminosities of Sunlight at different
+    Altitudes of the Sun <span class="sidenote"><i>p.</i> 62</span></p>
+
+
+<h3><a href="#CHAPTER_VII">CHAPTER VII.</a></h3>
+
+<p>    Luminosity of the Spectrum to Normal-eyed and Colour-blind
+    Persons&mdash;Method of determining the Luminosity of Pigments&mdash;Addition
+    of one Luminosity to another <span class="sidenote"><i>p.</i> 76</span></p>
+
+
+<h3><a href="#CHAPTER_VIII">CHAPTER VIII.</a></h3>
+
+<p>    Methods of Measuring the Intensity of the Different Colours of the
+    Spectrum, reflected from Pigmented Surfaces&mdash;Templates for
+    the Spectrum <span class="sidenote"><i>p.</i> 88</span></p>
+
+
+<h3><a href="#CHAPTER_IX">CHAPTER IX.</a></h3>
+
+<p>    Colour Mixtures&mdash;Yellow Spot in the Eye&mdash;Comparison of Different
+    Lights&mdash;Simple Colours by Mixing Simple Colours&mdash;Yellow and
+    Blue from White <span class="sidenote"><i>p.</i> 112</span></p>
+
+
+<h3><a href="#CHAPTER_X">CHAPTER X.</a></h3>
+
+<p>    Extinction of Colour by White Light&mdash;Extinction of White Light
+    by Colour <span class="sidenote"><i>p.</i> 126</span></p>
+
+
+<h3><a href="#CHAPTER_XI">CHAPTER XI.</a></h3>
+
+<p>    Primary Colours&mdash;Molecular Swings&mdash;Colour Sensations&mdash;Sensations
+    absent in the Colour-blind <span class="sidenote"><i>p.</i> 133</span></p>
+
+
+<h3><a href="#CHAPTER_XII">CHAPTER XII.</a></h3>
+
+<p>    Formation of Colour Equations&mdash;Kœnig's Curves&mdash;Maxwell's Apparatus
+    and Curves <span class="sidenote"><i>p.</i> 147</span></p>
+
+
+<h3><a href="#CHAPTER_XIII">CHAPTER XIII.</a></h3>
+
+<p>    Match of Compound Colours with Simple Colours&mdash;All Colours
+    reduced to Numbers&mdash;Method of Matching a Colour with a
+    Spectrum Colour and White Light <span class="sidenote"><i>p.</i> 156</span></p>
+<p><span class="pagenum">[Pg ix]</span></p>
+
+
+<h3><a href="#CHAPTER_XIV">CHAPTER XIV.</a></h3>
+
+    <p>Complementary Colours&mdash;Complementary Pigment Colours&mdash;Measurement
+    of Complementary Colours <span class="sidenote"><i>p.</i> 167</span></p>
+
+
+<h3><a href="#CHAPTER_XV">CHAPTER XV.</a></h3>
+
+    <p>Persistence of Images on the Retina&mdash;The Use of Coloured Discs <span class="sidenote"><i>p.</i> 179</span></p>
+
+
+<h3><a href="#CHAPTER_XVI">CHAPTER XVI.</a></h3>
+
+    <p>Contrast Colours&mdash;Measurement of Contrast Colours&mdash;Fatigue of
+    the Eye&mdash;After-Images <span class="sidenote"><i>p.</i> 196</span></p>
+
+
+<hr style="width: 65%;">
+<h2>LIST OF ILLUSTRATIONS.</h2>
+
+<div class="center">
+<table border="0" cellpadding="4" cellspacing="0" summary="">
+<tr><td align="right"> FIG.</td><td align="left"></td><td align="right">PAGE</td></tr>
+<tr><td align="right"></td><td align="left">Colour-patch apparatus</td><td align="right"><i><a href="#frontispiece">Frontispiece</a></i></td></tr>
+<tr><td align="right"> 1.</td><td align="left">Spectrum of sunlight</td><td align="right"><a href="#Page_18">18</a> </td></tr>
+<tr><td align="right"> 2.</td><td align="left">Carbon poles of an electric light</td><td align="right"><a href="#Fig_2">20</a> </td></tr>
+<tr><td align="right"> 3.</td><td align="left">Curve for converting prismatic spectrum into wave-lengths</td><td align="right"><a href="#Page_28">28</a> </td></tr>
+<tr><td align="right"> 4.</td><td align="left">The thermopile</td><td align="right"><a href="#Fig_4">35</a> </td></tr>
+<tr><td align="right"> 5.</td><td align="left">Heating effect of different sources of radiation</td><td align="right"><a href="#Page_38">38</a> </td></tr>
+<tr><td align="right"> 6.</td><td align="left">Colour-patch apparatus</td><td align="right"><a href="#Page_42">42</a> </td></tr>
+<tr><td align="right"> 7.</td><td align="left">Rotating sectors</td><td align="right"><a href="#Page_45">45</a> </td></tr>
+<tr><td align="right"> 8.</td><td align="left">Spectrum of Carbon Sodium and Lithium</td><td align="right"><a href="#Page_48">48</a> </td></tr>
+<tr><td align="right"> 9.</td><td align="left">Interference bands</td><td align="right"><a href="#Page_60">60</a> </td></tr>
+<tr><td align="right"> 10.</td><td align="left">Absorption of rays by the atmosphere</td><td align="right"><a href="#Page_68">68</a> </td></tr>
+<tr><td align="right"> 11.</td><td align="left">Luminosity curve of spectrum of the positive pole of the electric light</td><td align="right"><a href="#Page_79">79</a> </td></tr>
+<tr><td align="right"> 12.</td><td align="left">Rectangles of white and vermilion</td><td align="right"><a href="#Page_82">82</a> </td></tr>
+<tr><td align="right"> 13.</td><td align="left">Arrangement for measuring the luminosities of pigments</td><td align="right"><a href="#Fig_13">83</a> </td></tr>
+<tr><td align="right"> 14.</td><td align="left">Measurement of the intensity of rays reflected from white and coloured surfaces</td><td align="right"><a href="#Page_88">88</a> </td></tr>
+<tr><td align="right"> 15.</td><td align="left">Intensity of rays reflected from vermilion, emerald green, and French ultramarine</td><td align="right"><a href="#Page_92">92</a> <span class="pagenum">[Pg 10]</span></td></tr>
+<tr><td align="right"> 16.</td><td align="left">Method of obtaining two patches of identical colour</td><td align="right"><a href="#Fig_16">95</a> </td></tr>
+<tr><td align="right"> 17.</td><td align="left">Absorption by red, blue, and green glasses</td><td align="right"><a href="#Page_99">99</a> </td></tr>
+<tr><td align="right"> 18.</td><td align="left">Light reflected from metallic surfaces</td><td align="right"><a href="#Page_100">100</a> </td></tr>
+<tr><td align="right"> 19.</td><td align="left">Intensities of vermilion, carmine, mercuric iodide, and Indian red</td><td align="right"><a href="#Page_101">101</a> </td></tr>
+<tr><td align="right"> 20.</td><td align="left">Intensities of gamboge, Indian yellow, cadmium yellow, and yellow ochre</td><td align="right"><a href="#Fig_20">101</a> </td></tr>
+<tr><td align="right"> 21.</td><td align="left">Intensities of emerald green, chromous oxide, and terre verte</td><td align="right"><a href="#Page_103">103</a> </td></tr>
+<tr><td align="right"> 22.</td><td align="left">Intensities of indigo, Antwerp blue, cobalt, and French ultramarine</td><td align="right"><a href="#Page_104">104</a> </td></tr>
+<tr><td align="right"> 23.</td><td align="left">Method of obtaining a colour template</td><td align="right"><a href="#Fig_23">104</a> </td></tr>
+<tr><td align="right"> 24.</td><td align="left">Template of carmine</td><td align="right"><a href="#Page_106">106</a> </td></tr>
+<tr><td align="right"> 25.</td><td align="left">Template of luminosity of white light</td><td align="right"><a href="#Page_108">108</a> </td></tr>
+<tr><td align="right"> 26.</td><td align="left">Absorption of transmitted and reflected light by Prussian blue and carmine</td><td align="right"><a href="#Page_107">107</a> </td></tr>
+<tr><td align="right"> 27.</td><td align="left">Collimator for comparing the intensity of two sources of light</td><td align="right"><a href="#Page_109">109</a> </td></tr>
+<tr><td align="right"> 28.</td><td align="left">Spectrum intensities of sunlight, gaslight, and blue sky</td><td align="right"><a href="#Fig_28">109</a> </td></tr>
+<tr><td align="right"> 29.</td><td align="left">Comparison of sun and sky lights</td><td align="right"><a href="#Page_111">111</a> </td></tr>
+<tr><td align="right"> 30.</td><td align="left">Slide with slits to be used in the spectrum</td><td align="right"><a href="#Page_113">113</a> </td></tr>
+<tr><td align="right"> 31.</td><td align="left">Screen on which to match gamboge</td><td align="right"><a href="#Page_116">116</a> </td></tr>
+<tr><td align="right"> 32.</td><td align="left">Diaphragm in front of prism</td><td align="right"><a href="#Page_128">128</a> </td></tr>
+<tr><td align="right"> 33.</td><td align="left">Curve of sensitiveness of silver bromo-iodide</td><td align="right"><a href="#Page_136">136</a> </td></tr>
+<tr><td align="right"> 34.</td><td align="left">Curves of colour sensations</td><td align="right"><a href="#Page_139">139</a> </td></tr>
+<tr><td align="right"> 35.</td><td align="left">Kœnig's curves of colour sensations</td><td align="right"><a href="#Page_151">151</a> </td></tr>
+<tr><td align="right"> 36.</td><td align="left">Maxwell's colour-box</td><td align="right"><a href="#Page_152">152</a> </td></tr>
+<tr><td align="right"> 37.</td><td align="left">Maxwell's curves of colour sensations</td><td align="right"><a href="#Page_154">154</a> </td></tr>
+<tr><td align="right"> 38.</td><td align="left">Chromatic circle</td><td align="right"><a href="#Page_168">168</a> </td></tr>
+<tr><td align="right"> 39.</td><td align="left">Disc to cause alternate opening and closing of two slits</td><td align="right"><a href="#Page_179">179</a> </td></tr>
+<tr><td align="right"> 40.</td><td align="left">Disc painted blue and red</td><td align="right"><a href="#Page_181">181</a> </td></tr>
+<tr><td align="right"> 41.</td><td align="left">Electro-motor with discs attached</td><td align="right"><a href="#Page_183">183</a> </td></tr>
+<tr><td align="right"> 42.</td><td align="left">Method of cutting disc to allow an overlap of a second disc</td><td align="right"><a href="#Fig_42">184</a> </td></tr>
+<tr><td align="right"> 43.</td><td align="left">Arrangement to find value of gamboge in terms of emerald green and vermilion</td><td align="right"><a href="#Page_188">188</a> </td></tr>
+<tr><td align="right"> 44.</td><td align="left">Disc arranged to give approximately all the spectrum colours</td><td align="right"><a href="#Page_192">192</a> </td></tr>
+<tr><td align="right"> 45.</td><td align="left">Method of showing contrast colours</td><td align="right"><a href="#Page_196">196</a> </td></tr>
+</table></div>
+<p><span class="pagenum">[Pg 11]</span></p>
+
+<br>
+
+<hr style="width: 65%;">
+<h2>COLOUR MEASUREMENT</h2>
+<p class='center smaller'>AND</p><h1>MIXTURE.</h1>
+
+<hr style="width: 25%;">
+<h3><a name="CHAPTER_I" id="CHAPTER_I"></a>CHAPTER I.</h3>
+
+<blockquote>Sources of Light&mdash;Reflected Light&mdash;Reflection from Roughened
+Surfaces&mdash;Colour Constants.
+</blockquote>
+
+
+<p>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
+<span class="pagenum">[Pg 12]</span>
+of patience, yet a general idea of the subject may
+be grasped by those who are possessed of but
+ordinary intelligence.</p>
+
+<p>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.</p>
+
+<p>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
+<span class="pagenum"><a name="Page_13" id="Page_13">[Pg 13]</a></span>
+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
+<span class="pagenum"><a name="Page_14" id="Page_14">[Pg 14]</a></span>
+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.</p>
+
+<p>We may here premise that even the roughest
+surface will reflect a greater percentage&mdash;varying
+greatly according to the nature of the surface&mdash;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.</p>
+
+<p>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
+<span class="pagenum"><a name="Page_15" id="Page_15">[Pg 15]</a></span>
+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.</p>
+
+<p>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.</p>
+
+<p>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
+<span class="pagenum"><a name="Page_16" id="Page_16">[Pg 16]</a></span>
+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.</p><br>
+<span class="pagenum"><a name="Page_17" id="Page_17">[Pg 17]</a></span>
+
+
+
+
+<hr style="width: 65%;">
+<h2><a name="CHAPTER_II" id="CHAPTER_II"></a>CHAPTER II.</h2>
+
+<blockquote><p>A Standard Light&mdash;Formation of the Spectrum by Prisms and by the
+Diffraction Grating&mdash;Wave-lengths of the principal Fraunhofer
+Line&mdash;Position of Colours in the Spectrum.</p></blockquote>
+
+
+<p>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 <i>continuous</i> 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.</p>
+
+<div class="figright" style="width: 78px;">
+<img src="images/i_018.jpg" width="78" height="392" alt="" title="">
+<span class="caption">Fig. 1.&mdash;Spectrum of Sunlight.</span>
+</div>
+
+<p>The great desideratum for the study of colour
+is a light which not only gives a practically
+<span class="pagenum"><a name="Page_18" id="Page_18">[Pg 18]</a></span>
+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 (<a href="#Page_18">Fig.
+1</a>) 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
+<span class="pagenum"><a name="Page_19" id="Page_19">[Pg 19]</a></span>
+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
+<a href="#CHAPTER_VI">Chap. VI</a>.); 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.</p>
+<a name="Fig_2" id="Fig_2"></a>
+<div class="figright" style="width: 150px;">
+<img src="images/i_020.png" width="150" height="269" alt="" title="">
+<span class="caption">Fig. 2.&mdash;The Carbon Poles
+of an Electric Light.</span>
+</div>
+
+<p>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 <a href="#Page_110">page 110</a>). 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
+<span class="pagenum"><a name="Page_20" id="Page_20">[Pg 20]</a></span>
+(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 (<a href="#Fig_2">Fig. 2</a>). 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.</p>
+
+<p>In the spectrum produced by this light there are
+<span class="pagenum"><a name="Page_21" id="Page_21">[Pg 21]</a></span>
+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
+<a href="#Fig_2">Fig. 2</a>); 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.</p>
+
+<p>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&mdash;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
+<span class="pagenum"><a name="Page_22" id="Page_22">[Pg 22]</a></span>
+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.</p>
+
+<p>The focal length of this collimating lens need
+<span class="pagenum"><a name="Page_23" id="Page_23">[Pg 23]</a></span>
+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.</p>
+
+<p>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.</p>
+
+<p>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
+<span class="pagenum"><a name="Page_24" id="Page_24">[Pg 24]</a></span>
+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.</p>
+
+<p>We must now refresh the reader's memory with
+<span class="pagenum">[Pg 25]</span>
+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 <i>intensity</i> 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,
+<span class="pagenum"><a name="Page_26" id="Page_26">[Pg 26]</a></span>
+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.</p>
+
+<p>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 <b>1/10,000,000</b> of a millimetre as a unit</p>
+
+<div class="center">
+<table border="0" cellpadding="4" cellspacing="0" summary="">
+<tr><td align="left"></td><td align="left">A</td><td align="left"> &nbsp; &nbsp;  &nbsp; &nbsp;  &nbsp; &nbsp;  &nbsp; &nbsp; </td><td align="left">7594</td></tr>
+<tr><td align="left"></td><td align="left">B</td><td align="left"></td><td align="left">6867</td></tr>
+<tr><td align="left"></td><td align="left">C</td><td align="left"></td><td align="left">6562</td></tr>
+<tr><td align="left"></td><td align="left">D</td><td align="left"></td><td align="left">5892</td></tr>
+<tr><td align="left"></td><td align="left">E</td><td align="left"></td><td align="left">5269</td></tr>
+<tr><td align="left"></td><td align="left">F</td><td align="left"></td><td align="left">4861</td></tr>
+<tr><td align="left"></td><td align="left">G</td><td align="left"></td><td align="left">4307</td></tr>
+<tr><td align="left"></td><td align="left">H</td><td align="left"></td><td align="left">3968</td></tr>
+</table></div>
+
+<p>When the spectrum is produced by prisms the
+intervals between these lines are not proportional
+<span class="pagenum">[Pg 27]</span>
+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 (<a href="#Page_28">Fig. 3</a>) shows how this can be done.</p>
+
+<p>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.</p>
+
+
+<div class="center">
+<table border="1" cellpadding="4" cellspacing="0" summary="">
+<tr><td align="center">Scale.</td><td align="center">Colour.</td></tr>
+<tr><td align="left"> &nbsp; &nbsp; 0 to 149</td><td align="left"> Red.</td></tr>
+<tr><td align="left"> 149 to 194</td><td align="left">Orange red.</td></tr>
+<tr><td align="left"> 194 to 210</td><td align="left">Orange.</td></tr>
+<tr><td align="left"> 210 to 230</td><td align="left">Orange yellow.</td></tr>
+<tr><td align="left"> 230 to 240</td><td align="left">Yellow.</td></tr>
+<tr><td align="left"> 240 to 344</td><td align="left">Yellow green and green yellow.</td></tr>
+<tr><td align="left"> 344 to 447</td><td align="left">Green and blue green.</td></tr>
+<tr><td align="left"> 447 to 495</td><td align="left">Azure blue.</td></tr>
+<tr><td align="left"> 495 to 806</td><td align="left">Blue and blue violet.</td></tr>
+<tr><td align="left"> 806 to 1000</td><td align="left">Violet.&nbsp; </td></tr>
+</table></div>
+<br>
+<p><span class="pagenum"><a name="Page_28" id="Page_28">[Pg 28]</a></span></p>
+
+<div class="figcenter" style="width: 350px;">
+<img src="images/hb028.png" width="401" height="182" alt="" title="">
+<span class="caption">Fig. 3.&mdash;Curve for converting the Prismatic Spectrum into Wave-lengths.
+</span>
+</div><p><br><span class="pagenum"><a name="Page_29" id="Page_29">[Pg 29]</a></span></p>
+
+<p>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.</p>
+
+<p>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.</p>
+
+<p>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.</p><br>
+<span class="pagenum"><a name="Page_30" id="Page_30">[Pg 30]</a></span>
+
+<hr style="width: 65%;">
+<h2><a name="CHAPTER_III" id="CHAPTER_III"></a>CHAPTER III.</h2>
+
+<blockquote><p>The Visible and Invisible Parts of the Spectrum&mdash;Methods for showing
+the Existence of the Invisible
+Portions&mdash;Phosphorescence&mdash;Photography of the Dark
+Rays&mdash;Thermo-Electric Currents.</p></blockquote>
+
+
+<p>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
+<span class="pagenum"><a name="Page_31" id="Page_31">[Pg 31]</a></span>
+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.</p>
+
+<p>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
+<span class="pagenum"><a name="Page_32" id="Page_32">[Pg 32]</a></span>
+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.</p>
+
+<p>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&mdash;or Ritter's rays as they were formerly called,
+after their discoverer&mdash;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
+<span class="pagenum"><a name="Page_33" id="Page_33">[Pg 33]</a></span>
+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
+<span class="pagenum"><a name="Page_34" id="Page_34">[Pg 34]</a></span>
+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.</p>
+
+<p>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
+<span class="pagenum"><a name="Page_35" id="Page_35">[Pg 35]</a></span>
+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.</p>
+
+<p>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 (<a name="Fig_4" id="Fig_4"></a>Fig. 4), if it be so arranged
+as to allow only a narrow vertical slice of light to
+reach its face.</p>
+
+<div class="figcenter" style="width: 350px;">
+<img src="images/i_044.png" width="350" height="463" alt="" title="">
+<span class="caption">Fig. 4.&mdash;The Thermopile.
+</span>
+</div>
+
+<p>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
+<span class="pagenum"><a name="Page_36" id="Page_36">[Pg 36]</a></span>
+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
+<span class="pagenum">[Pg 37]</span>
+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.</p>
+
+<p>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
+<span class="pagenum"><a name="Page_38" id="Page_38">[Pg 38]</a></span>
+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.</p>
+
+<div class="figcenter" style="width: 401px;">
+<img src="images/i_038.png" width="401" height="404" alt="" title="">
+<span class="caption">Fig. 5.&mdash;Heating effect of different Sources of Radiation.
+</span>
+</div>
+<p>The above figure is a graphic representation
+of the heating effect of the spectrum of the electric
+<span class="pagenum">[Pg 39]</span>
+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.</p>
+
+<p>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&mdash;though the subsequent form may be more
+complex&mdash;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
+<span class="pagenum">[Pg 40]</span>
+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&mdash;the very place in which the heat curve rises
+rapidly.</p><br>
+<span class="pagenum"><a name="Page_41" id="Page_41">[Pg 41]</a></span>
+
+
+
+<hr style="width: 65%;">
+<h2><a name="CHAPTER_IV" id="CHAPTER_IV"></a>CHAPTER IV.</h2>
+
+<blockquote><p>Description of Colour Patch Apparatus&mdash;Rotating Sectors&mdash;Method of
+making a Scale for the Spectrum.</p></blockquote>
+
+
+<p>Before proceeding further we must describe somewhat
+in detail two or three pieces of apparatus to
+be used in the experiments we shall make.</p>
+
+<p>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
+<span class="pagenum"><a name="Page_42" id="Page_42">[Pg 42]</a></span>
+apparatus for forming the spectrum lacks all of
+these requisites.</p>
+
+<div class="figcenter" style="width: 401px;">
+<img src="images/i_042.png" width="401" height="474" alt="" title="">
+<span class="caption">Fig. 6.&mdash;Colour Patch Apparatus.
+</span>
+</div>
+<p>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
+<span class="pagenum">[Pg 43]</span>
+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
+<span class="pagenum">[Pg 44]</span>
+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.</p>
+
+<p>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.</p>
+
+<p>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
+<span class="pagenum"><a name="Page_45" id="Page_45">[Pg 45]</a></span>
+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 <i>one</i> 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.</p>
+
+<div class="figcenter" style="width: 350px;">
+<img src="images/i_046.png" width="350" height="286" alt="" title="">
+<span class="caption">Fig. 7.&mdash;Rotating Sectors.
+</span>
+</div>
+<p>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
+<span class="pagenum"><a name="Page_46" id="Page_46">[Pg 46]</a></span>
+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
+<span class="pagenum"><a name="Page_47" id="Page_47">[Pg 47]</a></span>
+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.</p>
+
+<p>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&mdash;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
+<span class="pagenum"><a name="Page_48" id="Page_48">[Pg 48]</a></span>
+compound, and the other with white light, and
+these can be placed side by side, and surrounded
+by the black mask as before described.</p>
+
+<div class="figright" style="width: 78px;">
+<img src="images/i_048.png" width="75" height="303" alt="" title="">
+<span class="caption">Fig. 8.&mdash;Spectrum of Sodium Lithium and Carbon.
+</span>
+</div>
+<p>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
+<span class="pagenum"><a name="Page_49" id="Page_49">[Pg 49]</a></span>
+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.</p>
+<span class="pagenum">[Pg 50]</span>
+
+<p>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 <a href="#Page_42">Fig. 6</a>) 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.</p><br>
+<span class="pagenum"><a name="Page_51" id="Page_51">[Pg 51]</a></span>
+
+
+
+<hr style="width: 65%;">
+<h2><a name="CHAPTER_V" id="CHAPTER_V"></a>CHAPTER V.</h2>
+
+<blockquote><p>Absorption of the Spectrum&mdash;Analysis of Colour&mdash;Vibrations of
+Rays&mdash;Absorption by Pigments&mdash;Phosphorescence&mdash;Interference.</p></blockquote>
+
+
+<p>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
+<span class="pagenum"><a name="Page_52" id="Page_52">[Pg 52]</a></span>
+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
+<span class="pagenum"><a name="Page_53" id="Page_53">[Pg 53]</a></span>
+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
+<span class="pagenum"><a name="Page_54" id="Page_54">[Pg 54]</a></span>
+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.</p>
+
+<p>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
+<span class="pagenum"><a name="Page_55" id="Page_55">[Pg 55]</a></span>
+giving rise to the colours fixed by the dark solar
+lines.</p>
+
+
+<div class="center">
+<table border="1" cellpadding="4" cellspacing="0" summary="">
+<tr><td align="left"><span class="smcap">Name of Line.</span></td><td align="left"><span class="smcap">Millions of  Millions of; Vibrations per Second.</span></td></tr>
+<tr><td align="left"> A in the Red&nbsp;</td><td align="left">&nbsp; 395&nbsp; &nbsp;</td></tr>
+<tr><td align="left"> B&nbsp; "&nbsp; &nbsp; "&nbsp;</td><td align="left">&nbsp; 437&nbsp; &nbsp;</td></tr>
+<tr><td align="left"> C&nbsp; "&nbsp; &nbsp; "&nbsp;</td><td align="left">&nbsp; 458&nbsp; &nbsp;</td></tr>
+<tr><td align="left"> D&nbsp; "&nbsp; &nbsp; Orange</td><td align="left">&nbsp; 510&nbsp; &nbsp;</td></tr>
+<tr><td align="left"> E&nbsp; "&nbsp; &nbsp; Green</td><td align="left">&nbsp; 570&nbsp; &nbsp;</td></tr>
+<tr><td align="left"> F&nbsp; "&nbsp; &nbsp; Blue</td><td align="left">&nbsp; 618&nbsp; &nbsp;</td></tr>
+<tr><td align="left"> G&nbsp; "&nbsp; &nbsp; Violet</td><td align="left">&nbsp; 697&nbsp; &nbsp;</td></tr>
+<tr><td align="left"> H&nbsp; "&nbsp; &nbsp; Ultra-Violet</td><td align="left">&nbsp; 757&nbsp; &nbsp;</td></tr>
+</table></div>
+
+<p>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&mdash;cannot
+help being&mdash;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
+<span class="pagenum"><a name="Page_56" id="Page_56">[Pg 56]</a></span>
+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.</p>
+
+<p>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
+<span class="pagenum"><a name="Page_57" id="Page_57">[Pg 57]</a></span>
+these atoms and molecules from the waves of light,
+must show itself as work done on them&mdash;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.</p>
+
+<p>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.</p>
+
+<p>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
+<span class="pagenum"><a name="Page_58" id="Page_58">[Pg 58]</a></span>
+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,
+&amp;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
+<i>small quantity</i> 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.</p>
+
+<p>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
+<span class="pagenum"><a name="Page_59" id="Page_59">[Pg 59]</a></span>
+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 &frac12;
+wave-length, 3/2 or 5/2 wave-length, &amp;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.</p>
+
+<p>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,
+<span class="pagenum"><a name="Page_60" id="Page_60">[Pg 60]</a></span>
+and be drawn across a ring of wire some inch in
+diameter, or&mdash;what the writer prefers best&mdash;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).</p>
+
+<div class="figcenter" style="width: 300px;">
+<img src="images/i_060.png" width="300" height="133" alt="" title="">
+<span class="caption">Fig. 9.&mdash;Interference Bands.
+</span>
+</div>
+<p>If we take a horizontal line across the spectrum,
+<span class="pagenum">[Pg 61]</span>
+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.</p><br>
+<span class="pagenum"><a name="Page_62" id="Page_62">[Pg 62]</a></span>
+
+
+
+<hr style="width: 65%;">
+<h2><a name="CHAPTER_VI" id="CHAPTER_VI"></a>CHAPTER VI.</h2>
+
+<blockquote><p>Scattered Light&mdash;Sunset Colours&mdash;Law of the Scattering by Fine
+Particles&mdash;Sunset Clouds&mdash;Luminosities of Sunlight at different
+Altitudes of the Sun.</p></blockquote>
+
+
+<p>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&mdash;and when we say small we
+mean small when measured on the same scale as we
+measure the lengths of waves of light&mdash;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.
+<span class="pagenum"><a name="Page_63" id="Page_63">[Pg 63]</a></span>
+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
+<span class="pagenum"><a name="Page_64" id="Page_64">[Pg 64]</a></span>
+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.</p>
+
+<p>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 <i>through the solution</i> 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 (<a href="#Page_42">Fig. 6</a>) in position
+<span class="pagenum">[Pg 65]</span>
+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.</p>
+
+<p>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
+<span class="pagenum"><a name="Page_66" id="Page_66">[Pg 66]</a></span>
+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.</p>
+
+
+<div class="center">
+<table border="1" cellpadding="4" cellspacing="0" summary="">
+<tr><td align="left"> λ</td><td align="left"> 7000</td><td align="left"> 6000</td><td align="left"> 5000</td><td align="left"> 4000</td></tr>
+<tr><td align="left"> 1/λ⁴</td><td align="right"> 1</td><td align="left"> ·504</td><td align="left"> ·260</td><td align="left"> ·107</td></tr>
+</table></div>
+
+<p>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.</p>
+
+<p>During the years 1885, 1886, and 1887, the writer measured the
+luminosity of the solar spectrum at <span class="pagenum"><a name="Page_67" id="Page_67">[Pg 67]</a></span> different times of the
+year, and at different hours of the day (see <i>Phil. Trans.</i> 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.</p>
+
+
+<div class="center">
+<table border="1" cellpadding="4" cellspacing="0" summary="">
+<tr><td align="left" rowspan="2">Line.</td><td align="left" rowspan="2"> Wave-length.</td><td align="left" rowspan="2"><u> &nbsp;1 &nbsp;</u><br>λ⁻⁴<br>× 10¹⁷</td><td align="left" colspan="10"> Light after passing through atmospheres of the following thicknesses.</td></tr>
+<tr><td align="right">0</td><td align="right"> 1</td><td align="right"> 2</td><td align="right"> 3</td><td align="right"> 4</td><td align="right"> 5</td><td align="right"> 6</td><td align="right"> 7</td><td align="right"> 8</td><td align="right"> 32</td></tr>
+<tr><td align="left">A</td><td align="right"> 7594</td><td align="right">    30</td><td align="right">1</td><td align="right"> ·955</td><td align="left"> ·908</td><td align="right"> ·857</td><td align="left"> ·815</td><td align="right"> ·775</td><td align="right"> ·736</td><td align="right"> ·707</td><td align="right"> ·665</td><td align="right"> ·107</td></tr>
+<tr><td align="left">B</td><td align="right"> 6867</td><td align="right">    45</td><td align="right">1</td><td align="right"> ·926</td><td align="left"> ·858</td><td align="right"> ·795</td><td align="left"> ·735</td><td align="right"> ·684</td><td align="right"> ·632</td><td align="right"> ·583</td><td align="right"> ·542</td><td align="right"> ·086</td></tr>
+<tr><td align="left">C</td><td align="right"> 6562</td><td align="right">    54</td><td align="right">1</td><td align="right"> ·912</td><td align="left"> ·832</td><td align="right"> ·759</td><td align="left"> ·693</td><td align="right"> ·632</td><td align="right"> ·576</td><td align="right"> ·526</td><td align="right"> ·480</td><td align="right"> ·019</td></tr>
+<tr><td align="left">D</td><td align="right"> 5892</td><td align="right">    83</td><td align="right">1</td><td align="right"> ·868</td><td align="left"> ·754</td><td align="right"> ·655</td><td align="left"> ·569</td><td align="right"> ·494</td><td align="right"> ·428</td><td align="right"> ·372</td><td align="right"> ·323</td><td align="right"> ·001</td></tr>
+<tr><td align="left">E</td><td align="right"> 5269</td><td align="right">   129</td><td align="right">1</td><td align="right"> ·803</td><td align="left"> ·644</td><td align="right"> ·518</td><td align="left"> ·427</td><td align="right"> ·334</td><td align="right"> ·268</td><td align="right"> ·216</td><td align="right"> ·173</td><td align="right"> &mdash;</td></tr>
+<tr><td align="left">F</td><td align="right"> 4861</td><td align="right">   179</td><td align="right">1</td><td align="right"> ·738</td><td align="left"> ·544</td><td align="right"> ·402</td><td align="left"> ·296</td><td align="right"> ·219</td><td align="right"> ·161</td><td align="right"> ·119</td><td align="right"> ·088</td><td align="right"> &mdash;</td></tr>
+<tr><td align="left">G</td><td align="right"> 4307</td><td align="right">   291</td><td align="right">1</td><td align="right"> ·609</td><td align="left"> ·367</td><td align="right"> ·220</td><td align="left"> ·137</td><td align="right"> ·084</td><td align="right"> ·051</td><td align="right"> ·031</td><td align="right"> ·019</td><td align="right"> &mdash;</td></tr>
+<tr><td align="left">H</td><td align="right"> 3968</td><td align="right">   403</td><td align="right">1</td><td align="right"> ·506</td><td align="left"> ·254</td><td align="right"> ·128</td><td align="left"> ·071</td><td align="right"> ·033</td><td align="right"> ·016</td><td align="right"> ·008</td><td align="right"> ·004</td><td align="right"> &mdash;</td></tr>
+</table></div>
+<p>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.</p>
+<span class="pagenum"><a name="Page_68" id="Page_68">[Pg 68]</a></span>
+
+<p>The sun traverses the following thicknesses of
+atmosphere when it is at the angles shown above
+the horizon.</p>
+
+
+<div class="center">
+<table border="0" cellpadding="4" cellspacing="0" summary="">
+<tr><td align="left">1</td><td align="left"> atmosphere&nbsp;</td><td align="left">90°</td></tr>
+<tr><td align="left">2</td><td align="center"> "</td><td align="left">30°</td></tr>
+<tr><td align="left">3</td><td align="center"> "</td><td align="left">19·30</td></tr>
+<tr><td align="left">4</td><td align="center"> "</td><td align="left">14·30</td></tr>
+<tr><td align="left">5</td><td align="center"> "</td><td align="left">11·30</td></tr>
+<tr><td align="left">6</td><td align="center"> "</td><td align="left">&nbsp; 9·30</td></tr>
+<tr><td align="left">7</td><td align="center"> "</td><td align="left">&nbsp; 8·30</td></tr>
+<tr><td align="left">8</td><td align="center"> "</td><td align="left">&nbsp; 7·30</td></tr>
+</table></div>
+
+<div class="figcenter" style="width: 401px;">
+<img src="images/i_069.png" width="401" height="269" alt="" title="">
+<span class="caption">Fig. 10.&mdash;Absorption of Rays by the Atmosphere.
+</span>
+</div>
+<p>It traverses thirty-two atmospheres when it is
+very nearly setting. Bougier and Forbes have
+calculated that the extreme thickness of the</p>
+
+<p><span class="pagenum"><a name="Page_69" id="Page_69">[Pg 69]</a></span>
+atmosphere, traversed by its light when the sun is
+on the horizon, is approximately 35&frac12; 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.</p>
+
+<p>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.</p>
+
+<p>The following are the approximate luminosities
+of the sun when the light shines</p>
+
+
+<div class="center">
+<table border="0" cellpadding="4" cellspacing="0" summary="">
+<tr><td align="center">through</td><td align="center"> 0</td><td align="center"> atmospheres&nbsp;</td><td align="center"> 1</td></tr>
+<tr><td align="center">"</td><td align="center"> 1</td><td align="center"> "</td><td align="center">·840</td></tr>
+<tr><td align="center">"</td><td align="center"> 2</td><td align="center"> "</td><td align="center">·705</td></tr>
+<tr><td align="center">"</td><td align="center">3</td><td align="center"> "</td><td align="center"> ·594</td></tr>
+<tr><td align="center">"</td><td align="center"> 4</td><td align="center"> "</td><td align="center"> ·496</td></tr>
+<tr><td align="center">"</td><td align="center"> 5</td><td align="center"> "</td><td align="center"> ·417</td></tr>
+<tr><td align="center">"</td><td align="center"> 6</td><td align="center"> "</td><td align="center"> ·303</td></tr>
+<tr><td align="center">"</td><td align="center">7</td><td align="center"> "</td><td align="center"> ·256</td></tr>
+<tr><td align="center">"</td><td align="center"> 8</td><td align="center"> "</td><td align="center"> ·215</td></tr>
+<tr><td align="center">"</td><td align="center"> 32</td><td align="center"> "</td><td align="center"> ·002</td></tr>
+</table></div>
+<p><span class="pagenum">[Pg 70]</span></p>
+
+<p>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.</p>
+
+<p>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
+<span class="pagenum">[Pg 71]</span>
+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.</p>
+
+<p>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.</p>
+
+<p>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.</p>
+
+<p>Before quitting this subject we may call attention
+<span class="pagenum"><a name="Page_72" id="Page_72">[Pg 72]</a></span>
+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
+<span class="pagenum"><a name="Page_73" id="Page_73">[Pg 73]</a></span>
+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.</p>
+
+<p>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
+<span class="pagenum"><a name="Page_74" id="Page_74">[Pg 74]</a></span>
+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
+<span class="pagenum">[Pg 75]</span>
+and richer tints of the clouds just after sunset
+are also due to the same cause, the thickness of
+air traversed being greater.</p>
+
+<p>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.</p><br>
+<span class="pagenum"><a name="Page_76" id="Page_76">[Pg 76]</a></span>
+
+
+
+<hr style="width: 65%;">
+<h2><a name="CHAPTER_VII" id="CHAPTER_VII"></a>CHAPTER VII.</h2>
+
+<blockquote><p>Luminosity of the Spectrum to Normal-eyed and Colour-blind
+Persons&mdash;Method of determining the Luminosity of Pigments&mdash;Addition
+of one Luminosity to another.</p></blockquote>
+
+
+<p>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
+<span class="pagenum"><a name="Page_77" id="Page_77">[Pg 77]</a></span>
+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
+<span class="pagenum">[Pg 78]</span>
+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
+<span class="pagenum"><a name="Page_79" id="Page_79">[Pg 79]</a></span>
+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.</p>
+
+<div class="figcenter" style="width: 401px;">
+<img src="images/i_079.png" width="401" height="271" alt="" title="">
+<span class="caption">Fig. 11.&mdash;Luminosity Curve of the Spectrum of the Positive Pole
+of the Electric Light.
+</span>
+</div>
+
+<p>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
+<span class="pagenum"><a name="Page_80" id="Page_80">[Pg 80]</a></span>
+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.</p>
+
+<p>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.</p>
+
+<div class="center">
+<table border="1" cellpadding="4" cellspacing="0" summary="">
+<tr><td align="left" rowspan="2">Line.</td><td align="left" rowspan="2">Colour.</td><td align="center" colspan="2">Luminosity.</td></tr>
+<tr><td align="left"> Normal Eye.</td><td align="left">&nbsp; Red Colour Blind.</td></tr>
+<tr><td align="left">A</td><td align="left"> Very dark Red&nbsp;</td><td align="right">&mdash;</td><td align="right">&mdash;</td></tr>
+<tr><td align="left">B</td><td align="left"> Red (Crimson)&nbsp;</td><td align="right">1·0</td><td align="right">&nbsp; 0</td></tr>
+<tr><td align="left">Red Lithium&nbsp;</td><td align="left"> Red (Crimson)&nbsp;</td><td align="right">&nbsp; 8·5&nbsp;</td><td align="right">&nbsp; &nbsp; ·5</td></tr>
+<tr><td align="left">C</td><td align="left"> Red (Scarlet)&nbsp;</td><td align="right">&nbsp; 20·6&nbsp;</td><td align="right">&nbsp; 2·1</td></tr>
+<tr><td align="left">D</td><td align="left"> Orange</td><td align="right">&nbsp; 98·5&nbsp;</td><td align="right">&nbsp; 53·0</td></tr>
+<tr><td align="left">E</td><td align="left"> Green&nbsp;</td><td align="right">&nbsp; 50·0&nbsp;</td><td align="right">&nbsp; 49·0</td></tr>
+<tr><td align="left">F</td><td align="left"> Blue Green&nbsp; &nbsp;</td><td align="right">&nbsp; 7·0&nbsp;</td><td align="right">&nbsp; 7·0</td></tr>
+<tr><td align="left">Blue Lithium</td><td align="left"> Blue&nbsp;</td><td align="right">&nbsp; 1·9&nbsp;</td><td align="right">&nbsp; 1·9</td></tr>
+<tr><td align="left">G</td><td align="left"> Violet</td><td align="right">&nbsp; &nbsp; ·6&nbsp;</td><td align="right">&nbsp; &nbsp; ·6</td></tr>
+<tr><td align="left">H</td><td align="left"> Faint Lavender</td><td align="right">&nbsp; &mdash;&nbsp;</td><td align="right">&nbsp; &mdash;</td></tr>
+</table></div>
+
+<p>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.</p>
+<p><span class="pagenum"><a name="Page_81" id="Page_81">[Pg 81]</a></span>
+</p>
+<p>A modification of this plan can be employed for
+measuring the luminosity of the spectrum, and it is
+<i>excessively</i> 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.</p>
+
+<p>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, <i>inter se</i>, the intensity of the
+same rays in two different sources of light, one
+being the electric light, we can evidently from the
+<span class="pagenum"><a name="Page_82" id="Page_82">[Pg 82]</a></span>
+above figure deduce the luminosity curve of the
+spectrum of the other source of light (see <a href="#Page_109">p. 109</a>).</p>
+
+<p>We can now show how we can adapt the last
+method to the measurement of the luminosity of
+the light reflected from pigments.</p>
+
+<div class="figright" style="width: 200px;">
+<img src="images/i_083.jpg" width="200" height="201" alt="" title="" >
+<span class="caption">Fig. 12.&mdash;Rectangles of White and Vermilion.</span>
+</div>
+<a name="Fig_13" id="Fig_13"></a>
+<div class="figright" style="width: 251px;">
+<img src="images/i_084.jpg" width="251" height="101" alt="" title="">
+<span class="caption">Fig. 13.&mdash;Arrangement for measuring the Luminosities of Pigments.</span>
+</div>
+
+<p>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
+<span class="pagenum">[Pg 83]</span>
+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
+<span class="pagenum">[Pg 84]</span>
+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.</p>
+
+<p>The luminosities of the following colours were taken by the above
+method, and subsequently we shall have to use their values.</p>
+
+<div class="center">
+<table border="0" cellpadding="4" cellspacing="0" summary="">
+<tr><td align="right" colspan="2"> <span class="smcap">Electric Light.</span></td></tr>
+<tr><td align="left"> White</td><td align="left">100</td></tr>
+<tr><td align="left"> Vermilion</td><td align="left">&nbsp; 36</td></tr>
+<tr><td align="left"> Emerald Green</td><td align="left">&nbsp; 30</td></tr>
+<tr><td align="left"> Ultramarine</td><td align="left">&nbsp; &nbsp; 4·4</td></tr>
+<tr><td align="left"> Orange</td><td align="left">&nbsp; 39·1</td></tr>
+<tr><td align="left"> Black</td><td align="left">&nbsp; &nbsp; 4</td></tr>
+<tr><td align="left"> " (different surface)</td><td align="left">&nbsp; &nbsp; 5·1</td></tr>
+</table></div>
+<p><span class="pagenum"><a name="Page_85" id="Page_85">[Pg 85]</a></span></p>
+
+<p>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.</p>
+
+
+<div class="center">
+<table border="1" cellpadding="4" cellspacing="0" summary="">
+<tr><td align="left"> <span class="smcap">Colours Measured.</span></td><td align="left"> Observed Luminosity.</td></tr>
+<tr><td align="left"> R</td><td align="left"> 203·0</td></tr>
+<tr><td align="left"> G</td><td align="left"> &nbsp; 38·5</td></tr>
+<tr><td align="left"> V</td><td align="left"> &nbsp; &nbsp; 8·5</td></tr>
+<tr><td align="left"> (R + G)</td><td align="left"> 242</td></tr>
+<tr><td align="left"> (G + V)</td><td align="left"> &nbsp; 45</td></tr>
+<tr><td align="left"> (R + V)</td><td align="left"> 214</td></tr>
+<tr><td align="left"> (R + G + V)</td><td align="left"> 250</td></tr>
+</table></div>
+<p><span class="pagenum">[Pg 86]</span></p>
+
+<p>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.</p>
+
+<p>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.</p>
+
+
+<div class="center">
+<table border="0" cellpadding="4" cellspacing="0" summary="">
+<tr><td align="left"> R + G + V</td><td align="left"> =</td><td align="left">250·0</td></tr>
+<tr><td align="left"> (R + G) + V</td><td align="left"> =</td><td align="left">250·5</td></tr>
+<tr><td align="left"> (R + V) + G</td><td align="left"> =</td><td align="left">252·5</td></tr>
+<tr><td align="left"> (G + V) + R</td><td align="left"> =</td><td align="left">248·0</td></tr>
+<tr><td align="left"> (R + G + V)</td><td align="left"> =</td><td align="left">250·0</td></tr>
+</table></div>
+<p>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.</p>
+<p><span class="pagenum">[Pg 87]</span></p>
+
+<p>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.</p><br>
+<span class="pagenum"><a name="Page_88" id="Page_88">[Pg 88]</a></span>
+
+
+
+<hr style="width: 65%;">
+<h2><a name="CHAPTER_VIII" id="CHAPTER_VIII"></a>CHAPTER VIII.</h2>
+
+<blockquote><p>Methods of Measuring the Intensity of the Different Colours of the
+Spectrum, reflected from Pigmented Surfaces&mdash;Templates for the
+Spectrum.</p></blockquote>
+
+<div class="figcenter" style="width: 300px;">
+<img src="images/i_090.png" width="300" height="275" alt="" title="">
+<span class="caption">Fig. 14.&mdash;Measurement of the Intensity of Rays reflected from white
+and coloured surfaces.
+</span>
+</div>
+<p>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.
+<span class="pagenum">[Pg 89]</span>
+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 <a href="#Fig_42">Fig. 42</a>). If we
+throw a colour patch (shown in <a href="#Page_88">Fig. 14</a> as the area
+inside the dotted square) on the combination of black
+<span class="pagenum">[Pg 90]</span>
+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.</p>
+<span class="pagenum">[Pg 91]</span>
+
+<p>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.</p>
+
+<p>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.</p>
+
+<p>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&mdash;
+</p>
+
+<span class="pagenum"><a name="Page_92" id="Page_92">[Pg 92]</a></span>
+
+<div class="figcenter" style="width: 401px;">
+<img src="images/i_093.png" width="401" height="193" alt="" title="">
+<span class="caption">Fig. 15.&mdash;Intensity of Rays reflected from Vermilion, Emerald Green, and French Ultramarine.
+</span>
+</div><p><span class="pagenum"><a name="Page_93" id="Page_93">[Pg 93]</a></span></p>
+
+<p>
+<span style="margin-left: 2em;">B=101, C=96·25, D=89, E=79·9, F=71·5, G=53·5.</span><br>
+</p>
+
+<h3>VERMILION.</h3>
+
+<div class="center">
+<table border="1" cellpadding="4" cellspacing="0" summary="">
+<tr><td align="left" colspan="4"> <span class="smcap">White Sectors.</span></td><td align="left" rowspan="3"> <span class="smcap">Reading of Spectrum Scale.</span></td></tr>
+<tr><td align="left"  colspan="2"> <span class="smcap">Original Setting.</span></td><td align="left" rowspan="2"><span class="smcap">White Corrected For Black.</span></td><td align="left" rowspan="2"><span class="smcap">Corrected White 100.</span></td></tr>
+<tr><td align="left"> <span class="smcap">White.</span></td><td align="left"> <span class="smcap">Black.</span></td></tr>
+<tr><td align="right"> 10</td><td align="right"> 350</td><td align="right"> 27·5</td><td align="right"> 7·65</td><td align="right"> 71&frac12; &nbsp;</td></tr>
+<tr><td align="right"> 20</td><td align="right"> 340</td><td align="right"> 37·0</td><td align="right"> 10·15</td><td align="right"> 84 &nbsp; &nbsp;</td></tr>
+<tr><td align="right"> 30</td><td align="right"> 330</td><td align="right"> 46·5</td><td align="right"> 12·95</td><td align="right"> 86·2</td></tr>
+<tr><td align="right"> 50</td><td align="right"> 310</td><td align="right"> 65·5</td><td align="right"> 18·10</td><td align="right"> 88·0</td></tr>
+<tr><td align="right"> 70</td><td align="right"> 290</td><td align="right"> 84·5</td><td align="right"> 23·50</td><td align="right"> 88·7</td></tr>
+<tr><td align="right"> 90</td><td align="right"> 270</td><td align="right"> 103·5</td><td align="right"> 29·7 &nbsp;</td><td align="right"> 89·5</td></tr>
+<tr><td align="right"> 120</td><td align="right"> 240</td><td align="right"> 132·0</td><td align="right"> 37·2 &nbsp;</td><td align="right"> 90·3</td></tr>
+<tr><td align="right"> 150</td><td align="right"> 210</td><td align="right"> 160·5</td><td align="right"> 45·0 &nbsp;</td><td align="right"> 91 &nbsp; &nbsp;</td></tr>
+<tr><td align="right"> 180</td><td align="right"> 180</td><td align="right"> 189·0</td><td align="right"> 52·5 &nbsp;</td><td align="right"> 91·6</td></tr>
+<tr><td align="right"> 210</td><td align="right"> 150</td><td align="right"> 217·5</td><td align="right"> 60·2 &nbsp;</td><td align="right"> 92·5</td></tr>
+<tr><td align="right"> 220</td><td align="right"> 140</td><td align="right"> 227·0</td><td align="right"> 63·2 &nbsp;</td><td align="right"> 93·5</td></tr>
+<tr><td align="right"> 230</td><td align="right"> 130</td><td align="right"> 236·5</td><td align="right"> 66·2 &nbsp;</td><td align="right"> 94·5</td></tr>
+<tr><td align="right"> 240</td><td align="right"> 120</td><td align="right"> 246·0</td><td align="right"> 68·5 &nbsp;</td><td align="right"> 96 &nbsp; &nbsp;</td></tr>
+<tr><td align="right"> 230</td><td align="right"> 130</td><td align="right"> 236·5</td><td align="right"> 66·2 &nbsp;</td><td align="right"> 97·7</td></tr>
+<tr><td align="right"> 210</td><td align="right"> 150</td><td align="right"> 217·5</td><td align="right"> 60·2 &nbsp;</td><td align="right"> 100·0</td></tr>
+</table></div>
+<p><span class="pagenum"><a name="Page_94" id="Page_94">[Pg 94]</a></span></p>
+
+<h3>EMERALD GREEN.</h3>
+<div class="center">
+<table border="1" cellpadding="4" cellspacing="0" summary="">
+<tr><td align="left" colspan="4"> <span class="smcap">White Sectors.</span></td><td align="left" rowspan="3"> <span class="smcap">Reading of Spectrum Scale.</span></td></tr>
+<tr><td align="left"  colspan="2"> <span class="smcap">Original Setting.</span></td><td align="left" rowspan="2"><span class="smcap">White Corrected For Black.</span></td><td align="left" rowspan="2"><span class="smcap">Corrected White 100.</span></td></tr>
+<tr><td align="left"> <span class="smcap">White.</span></td><td align="left"> <span class="smcap">Black.</span></td></tr>
+<tr><td align="right"> 10</td><td align="right"> 350</td><td align="right"> 27·5</td><td align="right"> 7·65</td><td align="right"> 50 &nbsp; &nbsp;</td></tr>
+<tr><td align="right"> 20</td><td align="right"> 340</td><td align="right"> 37·0</td><td align="right"> 10·15</td><td align="right"> 54 &nbsp; &nbsp;</td></tr>
+<tr><td align="right"> 30</td><td align="right"> 330</td><td align="right"> 46·5</td><td align="right"> 12·95</td><td align="right"> 55 &nbsp; &nbsp;</td></tr>
+<tr><td align="right"> 50</td><td align="right"> 310</td><td align="right"> 65·5</td><td align="right"> 18·10</td><td align="right"> 57·5</td></tr>
+<tr><td align="right"> 70</td><td align="right"> 290</td><td align="right"> 84·5</td><td align="right"> 23·5 &nbsp;</td><td align="right"> 60·0</td></tr>
+<tr><td align="right"> 90</td><td align="right"> 270</td><td align="right"> 103·5</td><td align="right"> 29·7 &nbsp;</td><td align="right"> 63·5</td></tr>
+<tr><td align="right"> 110</td><td align="right"> 250</td><td align="right"> 122·5</td><td align="right"> 34·7 &nbsp;</td><td align="right"> 65·5</td></tr>
+<tr><td align="right"> 130</td><td align="right"> 230</td><td align="right"> 141·5</td><td align="right"> 39·5 &nbsp;</td><td align="right"> 67·5</td></tr>
+<tr><td align="right"> 150</td><td align="right"> 210</td><td align="right"> 160·5</td><td align="right"> 45·0 &nbsp;</td><td align="right"> 68·5</td></tr>
+<tr><td align="right"> 170</td><td align="right"> 190</td><td align="right"> 179·5</td><td align="right"> 50·0 &nbsp;</td><td align="right"> 71 &nbsp; &nbsp;</td></tr>
+<tr><td align="right"> 190</td><td align="right"> 170</td><td align="right"> 195·5</td><td align="right"> 54·7 &nbsp;</td><td align="right"> 73·5</td></tr>
+<tr><td align="right"> 210</td><td align="right"> 150</td><td align="right"> 217·5</td><td align="right"> 60·2 &nbsp;</td><td align="right"> 75·0</td></tr>
+<tr><td align="right"> 220</td><td align="right"> 140</td><td align="right"> 227 &nbsp; &nbsp;</td><td align="right"> 63·2 &nbsp;</td><td align="right"> 76 &nbsp; &nbsp;</td></tr>
+<tr><td align="right"> 220</td><td align="right"> 140</td><td align="right"> 227 &nbsp; &nbsp;</td><td align="right"> 63·2 &nbsp;</td><td align="right"> 78 &nbsp; &nbsp;</td></tr>
+<tr><td align="right"> 210</td><td align="right"> 150</td><td align="right"> 217·5</td><td align="right"> 60·2 &nbsp;</td><td align="right"> 80 &nbsp; &nbsp;</td></tr>
+<tr><td align="right"> 190</td><td align="right"> 170</td><td align="right"> 198·5</td><td align="right"> 54·7 &nbsp;</td><td align="right"> 82 &nbsp; &nbsp;</td></tr>
+<tr><td align="right"> 170</td><td align="right"> 190</td><td align="right"> 179·5</td><td align="right"> 50·0 &nbsp;</td><td align="right"> 83 &nbsp; &nbsp;</td></tr>
+<tr><td align="right"> 150</td><td align="right"> 210</td><td align="right"> 160·5</td><td align="right"> 45·0 &nbsp;</td><td align="right"> 84 &nbsp; &nbsp;</td></tr>
+<tr><td align="right"> 130</td><td align="right"> 230</td><td align="right"> 141·5</td><td align="right"> 39·5 &nbsp;</td><td align="right"> 85 &nbsp; &nbsp;</td></tr>
+<tr><td align="right"> 110</td><td align="right"> 250</td><td align="right"> 122·5</td><td align="right"> 34·7 &nbsp;</td><td align="right"> 86·5</td></tr>
+<tr><td align="right"> 90</td><td align="right"> 270</td><td align="right"> 103·5</td><td align="right"> 29·7 &nbsp;</td><td align="right"> 87·5</td></tr>
+<tr><td align="right"> 70</td><td align="right"> 290</td><td align="right"> 84·5</td><td align="right"> 23·5 &nbsp;</td><td align="right"> 88·5</td></tr>
+<tr><td align="right"> 50</td><td align="right"> 310</td><td align="right"> 65·5</td><td align="right"> 18·10</td><td align="right"> 90·0</td></tr>
+<tr><td align="right"> 30</td><td align="right"> 330</td><td align="right"> 46·5</td><td align="right"> 12·95</td><td align="right"> 92 &nbsp; &nbsp;</td></tr>
+<tr><td align="right"> 20</td><td align="right"> 340</td><td align="right"> 37·0</td><td align="right"> 10·15</td><td align="right"> 94 &nbsp; &nbsp;</td></tr>
+<tr><td align="right"> 10</td><td align="right"> 350</td><td align="right"> 27·5</td><td align="right"> 7·65</td><td align="right"> 98 &nbsp; &nbsp;</td></tr>
+</table></div>
+<p><span class="pagenum"><a name="Page_95" id="Page_95">[Pg 95]</a></span></p>
+
+<h3>FRENCH ULTRAMARINE BLUE.</h3>
+<div class="center">
+<table border="1" cellpadding="4" cellspacing="0" summary="">
+<tr><td align="left" colspan="4"> <span class="smcap">White Sectors.</span></td><td align="left" rowspan="3"> <span class="smcap">Reading of Spectrum Scale.</span></td></tr>
+<tr><td align="left"  colspan="2"> <span class="smcap">Original Setting.</span></td><td align="left" rowspan="2"><span class="smcap">White Corrected For Black.</span></td><td align="left" rowspan="2"><span class="smcap">Corrected White 100.</span></td></tr>
+<tr><td align="left"> <span class="smcap">White.</span></td><td align="left"> <span class="smcap">Black.</span></td></tr>
+<tr><td align="right"> 0</td><td align="right"> 360</td><td align="right"> 18·0</td><td align="right"> 5·0</td><td align="right"> 84 &nbsp; &nbsp;</td></tr>
+<tr><td align="right"> 10</td><td align="right"> 350</td><td align="right"> 27·5</td><td align="right"> 7·65</td><td align="right"> 80 &nbsp; &nbsp;</td></tr>
+<tr><td align="right"> 20</td><td align="right"> 340</td><td align="right"> 37·0</td><td align="right"> 10·15</td><td align="right"> 77 &nbsp; &nbsp;</td></tr>
+<tr><td align="right"> 30</td><td align="right"> 330</td><td align="right"> 46·5</td><td align="right"> 12·95</td><td align="right"> 75 &nbsp; &nbsp;</td></tr>
+<tr><td align="right"> 40</td><td align="right"> 320</td><td align="right"> 56·0</td><td align="right"> 15·6 &nbsp;</td><td align="right"> 74 &nbsp; &nbsp;</td></tr>
+<tr><td align="right"> 60</td><td align="right"> 300</td><td align="right"> 75·0</td><td align="right"> 20·7 &nbsp;</td><td align="right"> 72·5</td></tr>
+<tr><td align="right"> 80</td><td align="right"> 280</td><td align="right"> 94·0</td><td align="right"> 25·5 &nbsp;</td><td align="right"> 70·5</td></tr>
+<tr><td align="right"> 100</td><td align="right"> 260</td><td align="right"> 113·0</td><td align="right"> 32·5 &nbsp;</td><td align="right"> 68 &nbsp; &nbsp;</td></tr>
+<tr><td align="right"> 120</td><td align="right"> 240</td><td align="right"> 132·0</td><td align="right"> 37·2 &nbsp;</td><td align="right"> 66·5</td></tr>
+<tr><td align="right"> 140</td><td align="right"> 220</td><td align="right"> 151·0</td><td align="right"> 42·3 &nbsp;</td><td align="right"> 62·5</td></tr>
+<tr><td align="right"> 160</td><td align="right"> 200</td><td align="right"> 170·0</td><td align="right"> 47·4 &nbsp;</td><td align="right"> 59·5</td></tr>
+<tr><td align="right"> 170</td><td align="right"> 190</td><td align="right"> 179·5</td><td align="right"> 50·0 &nbsp;</td><td align="right"> 55 &nbsp; &nbsp;</td></tr>
+<tr><td align="right"> 160</td><td align="right"> 200</td><td align="right"> 170·0</td><td align="right"> 47·4 &nbsp;</td><td align="right"> 51 &nbsp; &nbsp;</td></tr>
+<tr><td align="right"> 140</td><td align="right"> 220</td><td align="right"> 151·0</td><td align="right"> 42·3 &nbsp;</td><td align="right"> 46 &nbsp; &nbsp;</td></tr>
+<tr><td align="right"> 0</td><td align="right"> 360</td><td align="right"> 18·0</td><td align="right"> 5·0 &nbsp;</td><td align="right"> 95 &nbsp; &nbsp;</td></tr>
+<tr><td align="right"> 10</td><td align="right"> 350</td><td align="right"> 27·5</td><td align="right"> 7·65</td><td align="right"> 98 &nbsp; &nbsp;</td></tr>
+<tr><td align="right"> 20</td><td align="right"> 340</td><td align="right"> 37·0</td><td align="right"> 10·15</td><td align="right"> 99 &nbsp; &nbsp;</td></tr>
+<tr><td align="right"> 30</td><td align="right"> 330</td><td align="right"> 46·5</td><td align="right"> 12·95</td><td align="right"> 110 &nbsp; &nbsp;</td></tr>
+</table></div><br>
+
+<p>These three measurements have been given in
+full, since they will be useful for reference when
+other experiments are described.</p>
+<a name="Fig_16" id="Fig_16"></a>
+<div class="figcenter" style="width: 350px;">
+<img src="images/i_098.jpg" width="350" height="150" alt="" title="">
+<span class="caption">Fig. 16.&mdash;Method of obtaining two Patches of identical Colour.
+</span>
+</div>
+<p>When we have to measure the colour transmitted
+through coloured bodies, we have to adopt a slightly
+different plan, which is extremely accurate. The
+<span class="pagenum"><a name="Page_96" id="Page_96">[Pg 96]</a></span>
+first thing necessary is to make some arrangement
+whereby two beams of identical colour&mdash;that is, of
+the same wave-length&mdash;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
+<span class="pagenum">[Pg 97]</span>
+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
+<span class="pagenum">[Pg 98]</span>
+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.</p>
+
+<p>We can now place the coloured transparent
+object in the path of the beam which is most
+<span class="pagenum"><a name="Page_99" id="Page_99">[Pg 99]</a></span>
+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%.</p>
+
+<div class="figcenter" style="width: 401px;">
+<img src="images/i_100.png" width="401" height="262" alt="" title="">
+<span class="caption">Fig. 17.&mdash;Absorption by Red, Blue, and Green Glasses.
+</span>
+</div><p><span class="pagenum"><a name="Page_100" id="Page_100">[Pg 100]</a></span>
+</p>
+
+<div class="figcenter" style="width: 401px;">
+<img src="images/i_101.png" width="401" height="250" alt="" title="">
+<span class="caption">Fig. 18.&mdash;Light reflected from Metallic Surfaces.
+</span>
+</div>
+<span class="pagenum"><a name="Page_101" id="Page_101">[Pg 101]</a></span>
+<div class="figcenter" style="width: 401px;">
+<img src="images/i_102.png" width="401" height="335" alt="" title="">
+<span class="caption">1. Vermilion 2. Carmine. 3. Mercuric Iodide.
+4. Indian Red.<br> Fig. 19.
+</span>
+</div>
+<p>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 <i>any</i> source is
+known, this method holds good.</p>
+<a name="Fig_20" id="Fig_20"></a>
+<div class="figcenter" style="width: 401px;">
+<img src="images/i_103.png" width="401" height="347" alt="" title="">
+<span class="caption">1. Gamboge. 2. Indian Yellow. 3. Cadmium Yellow.
+4. Yellow Ochre.<br> Fig. 20.
+</span>
+</div>
+<p>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
+<span class="pagenum">[Pg 102]</span>
+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 <a href="#Page_100">Fig. 18</a> the dotted curves show the
+<i>luminosity</i> 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
+<span class="pagenum"><a name="Page_103" id="Page_103">[Pg 103]</a></span>
+61. This shows the method which is adopted, of
+deducing luminosities from intensities.</p>
+
+<div class="figcenter" style="width: 401px;">
+<img src="images/i_104.png" width="401" height="324" alt="" title="">
+<span class="caption">1. Emerald Green. 2. Chromous Oxide. 3. Terre Verte.
+Fig. 21.</span></div>
+
+<p>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 <a href="#Page_82">page 82</a>). 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.</p>
+<p><span class="pagenum"><a name="Page_104" id="Page_104">[Pg 104]</a></span>
+</p>
+<div class="figcenter" style="width: 401px;">
+<img src="images/i_105.png" width="401" height="338" alt="" title="">
+<span class="caption">1. Indigo. 2. Antwerp Blue. 3. Cobalt.
+4. French Ultramarine. Fig. 22.</span></div>
+<a name="Fig_23" id="Fig_23"></a>
+<div class="figright" style="width: 200px;">
+<img src="images/i_106.png" width="200" height="198" alt="" title="">
+<span class="caption">Fig. 23.&mdash;Method of obtaining a Colour
+Template.</span></div>
+
+<p>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
+<span class="pagenum">[Pg 105]</span>
+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.</p>
+
+<p>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&mdash;whatever
+light it is&mdash;the colour obtained will be
+<span class="pagenum"><a name="Page_106" id="Page_106">[Pg 106]</a></span>
+that which the pigment would reflect if it were
+viewed in that light.</p>
+
+<p>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.</p>
+
+<div class="figcenter" style="width: 300px;">
+<img src="images/i_107.jpg" width="300" height="297" alt="" title="">
+<span class="caption">Fig. 24.&mdash;Template of Carmine.
+</span>
+</div>
+<p>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
+<span class="pagenum"><a name="Page_107" id="Page_107">[Pg 107]</a></span>
+and violet; scarcely any light at all was reflected
+from the green part of the spectrum.</p>
+
+<div class="figcenter" style="width: 401px;">
+<img src="images/i_108.png" width="401" height="263" alt="" title="">
+<span class="caption">Fig. 26.&mdash;Absorption of transmitted and reflected Light by Prussian
+Blue and Carmine.
+</span>
+</div>
+<p>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 (<a href="#Page_108">Fig. 25</a>).
+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.</p><p>
+<span class="pagenum"><a name="Page_108" id="Page_108">[Pg 108]</a></span>
+</p>
+<div class="figcenter" style="width: 401px;">
+<img src="images/i_109.png" width="401" height="225" alt="" title="">
+<span class="caption">Fig. 25.&mdash;Template of Luminosity of White Light.
+</span>
+</div><p>
+<span class="pagenum"><a name="Page_109" id="Page_109">[Pg 109]</a></span>
+</p>
+<p>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 (<a href="#Page_107">Fig. 26</a>) 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.</p>
+
+<div class="figright" style="width: 200px;">
+<img src="images/i_110.png" width="200" height="187" alt="" title="">
+<span class="caption">Fig. 27.&mdash;Collimator for comparing
+the intensity of two sources of Light.
+</span>
+</div>
+<p>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.</p>
+<a name="Fig_28" id="Fig_28"></a>
+<div class="figcenter" style="width: 401px;">
+<img src="images/i_111.png" width="401" height="287" alt="" title="">
+<span class="caption">Fig. 28.&mdash;Spectrum Intensities of Sunlight, Gaslight, and Blue Sky.
+</span>
+</div>
+<p>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
+<span class="pagenum"><a name="Page_110" id="Page_110">[Pg 110]</a></span>
+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
+<span class="pagenum"><a name="Page_111" id="Page_111">[Pg 111]</a></span>
+and the yellow of the former being intensified
+by the contrast (see <a href="#Page_198">page 198</a>).</p>
+
+<div class="figright" style="width: 200px;">
+<img src="images/i_112.png" width="200" height="227" alt="" title="">
+<span class="caption">Fig. 29.&mdash;Comparison of Sun and
+Sky Lights.
+</span>
+</div>
+<p>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.</p><br>
+<span class="pagenum"><a name="Page_112" id="Page_112">[Pg 112]</a></span>
+
+
+
+<hr style="width: 65%;">
+<h2><a name="CHAPTER_IX" id="CHAPTER_IX"></a>CHAPTER IX.</h2>
+
+<blockquote><p>Colour Mixtures&mdash;Yellow Spot in the Eye&mdash;Comparison of Different
+Lights&mdash;Simple Colours by mixing Simple Colours&mdash;Yellow and Blue
+form White.
+</p></blockquote>
+
+
+<p>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,
+<span class="pagenum"><a name="Page_113" id="Page_113">[Pg 113]</a></span>
+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.</p>
+
+<div class="figcenter" style="width: 300px;">
+<img src="images/i_114.png" width="300" height="177" alt="" title="">
+<span class="caption">Fig. 30.&mdash;Slide with slits to be used in the Spectrum.
+</span>
+</div>
+<p>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
+<span class="pagenum"><a name="Page_114" id="Page_114">[Pg 114]</a></span>
+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.</p>
+
+<p>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
+<span class="pagenum"><a name="Page_115" id="Page_115">[Pg 115]</a></span>
+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.</p>
+
+<p>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.</p><p>
+<span class="pagenum"><a name="Page_116" id="Page_116">[Pg 116]</a></span>
+</p>
+<div class="figright" style="width: 60px;">
+<img src="images/i_117.jpg" width="60" height="62" alt="" title="">
+<span class="caption">Fig. 31.&mdash;Screen on which to match Gamboge.
+</span>
+</div>
+<p>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.</p>
+
+<p>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
+<span class="pagenum"><a name="Page_117" id="Page_117">[Pg 117]</a></span>
+can naturally be matched by using but very small
+quantities of the compounding colours.</p>
+
+<p>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
+<span class="pagenum"><a name="Page_118" id="Page_118">[Pg 118]</a></span>
+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.</p>
+
+<p>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
+<span class="pagenum"><a name="Page_119" id="Page_119">[Pg 119]</a></span>
+it is thus <i>comparatively</i> 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.</p>
+
+<p>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&mdash;and keeping the blue slit of the same
+width&mdash;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
+<span class="pagenum">[Pg 120]</span>
+positions. If we replace the slits in these positions
+and close the violet slit, we are at once able to
+verify it.</p>
+
+<p>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.</p>
+
+<p>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
+<span class="pagenum"><a name="Page_121" id="Page_121">[Pg 121]</a></span>
+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.</p>
+
+
+<div class="center">
+<table border="1" cellpadding="4" cellspacing="0" summary="">
+<tr><td align="right"></td><td align="center"> <span class="smcap">Sunlight.</span></td><td align="center"> <span class="smcap">Electric<br> Light.</span></td><td align="center"> <span class="smcap">Gaslight.</span></td><td align="center"> <span class="smcap">Skylight.</span></td></tr>
+<tr><td align="right"> Red</td><td align="right"> 100</td><td align="right"> 100</td><td align="right"> 100</td><td align="right"> 100</td></tr>
+<tr><td align="right"> Green</td><td align="right"> 193</td><td align="right"> 203</td><td align="right"> 95</td><td align="right"> 256</td></tr>
+<tr><td align="right"> Violet</td><td align="right"> 228</td><td align="right"> 250</td><td align="right"> 27</td><td align="right"> 760</td></tr>
+</table></div>
+<p>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
+<span class="pagenum">[Pg 122]</span>
+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
+<span class="pagenum">[Pg 123]</span>
+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.</p>
+
+<p>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
+<span class="pagenum"><a name="Page_124" id="Page_124">[Pg 124]</a></span>
+an exact match, can be made with the red and
+green slits, without the addition of white.</p>
+
+<p>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.</p>
+
+<p>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
+<span class="pagenum"><a name="Page_125" id="Page_125">[Pg 125]</a></span>
+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.</p>
+
+<p>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.</p>
+
+<p>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.</p>
+
+<p>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.</p><br>
+<span class="pagenum"><a name="Page_126" id="Page_126">[Pg 126]</a></span>
+
+
+<hr style="width: 65%;">
+<h2><a name="CHAPTER_X" id="CHAPTER_X"></a>CHAPTER X.</h2>
+
+<blockquote><p>Extinction of Colour by White Light&mdash;Extinction of White Light by
+Colour.</p></blockquote>
+
+
+<p>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.</p>
+
+<p>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?</p>
+<span class="pagenum">[Pg 127]</span>
+
+<p>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.</p>
+
+<div class="figright" style="width: 60px;">
+<img src="images/i_129.jpg" width="60" height="57" alt="" title="">
+<span class="caption">Fig. 32.&mdash;Diaphragm in front of Prism.
+</span>
+</div>
+<p>It is more instructive if we experiment with pure
+colours, and so we must resort to our colour patch
+<span class="pagenum"><a name="Page_128" id="Page_128">[Pg 128]</a></span>
+apparatus described in <a href="#Page_42">Fig. 6</a>. 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.</p>
+
+<p>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
+<span class="pagenum">[Pg 129]</span>
+colour disappear, when they are so diluted with
+white light, bear to the total luminosity of these
+rays.</p>
+
+<p>In a set of measurements made it was found that
+the reduced angular apertures required for the
+colours indicated by the following were:</p>
+
+
+<div class="center">
+<table border="0" cellpadding="4" cellspacing="0" summary="">
+<tr><td align="right"> B</td><td align="center">required</td><td align="right">300°*</td><td align="center"> of aperture.</td></tr>
+<tr><td align="right"> C</td><td align="center">"</td><td align="right">56° &nbsp;</td><td align="center">"</td></tr>
+<tr><td align="right"> D</td><td align="center">"</td><td align="right">14° &nbsp;</td><td align="center">"</td></tr>
+<tr><td align="right"> E</td><td align="center">"</td><td align="right">22° &nbsp;</td><td align="center">"</td></tr>
+<tr><td align="right"> F</td><td align="center">"</td><td align="right">150° &nbsp;</td><td align="center">"</td></tr>
+<tr><td align="right"> G</td><td align="center">"</td><td align="right">2100°*</td><td align="center">"</td></tr>
+</table></div>
+<p>The large numbers marked with an asterisk were
+obtained by placing the rotating sectors in front of
+the white reflected beam.</p>
+
+<p>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.</p>
+<span class="pagenum">[Pg 130]</span>
+
+
+<div class="center">
+<table border="1" cellpadding="4" cellspacing="0" summary="">
+<tr><td align="center"> <span class="smcap">Colour. &nbsp; &nbsp; &nbsp; &nbsp;</span></td>
+<td align="center"><span class="smcap">White required<br> to extinguish<br> the Spectrum.</span></td>
+<td align="center"> <span class="smcap">White required<br> to extinguish<br> the Spectrum,<br> with 50 as That<br> required at E.</span></td>
+<td align="center"><span class="smcap">Luminosity<br> of<br> Spectrum.</span></td></tr>
+<tr><td align="right"> near line B</td><td align="right"> ·6 &nbsp; &nbsp;</td><td align="right"> 3·9 &nbsp;</td><td align="right"> 4·9</td></tr>
+<tr><td align="right"> C</td><td align="right"> 3·2 &nbsp; &nbsp;</td><td align="right"> 19·5 &nbsp;</td><td align="right"> 20·6</td></tr>
+<tr><td align="right"> D</td><td align="right"> 12·9 &nbsp; &nbsp;</td><td align="right"> 78 &nbsp; &nbsp; &nbsp;</td><td align="right"> 98·5</td></tr>
+<tr><td align="right"> E</td><td align="right"> 8·2 &nbsp; &nbsp;</td><td align="right"> 50 &nbsp; &nbsp; &nbsp;</td><td align="right"> 50 &nbsp; &nbsp;</td></tr>
+<tr><td align="right"> F</td><td align="right"> 1·2 &nbsp; &nbsp;</td><td align="right"> 7·5 &nbsp;</td><td align="right"> 7·5</td></tr>
+<tr><td align="right"> G</td><td align="right"> ·087</td><td align="right"> ·56</td><td align="right"> ·6</td></tr>
+</table></div>
+<p>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
+<span class="pagenum"><a name="Page_131" id="Page_131">[Pg 131]</a></span>
+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.</p>
+
+<p>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
+<span class="pagenum">[Pg 132]</span>
+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.</p><br>
+<span class="pagenum"><a name="Page_133" id="Page_133">[Pg 133]</a></span>
+
+
+
+<hr style="width: 65%;">
+<h2><a name="CHAPTER_XI" id="CHAPTER_XI"></a>CHAPTER XI.</h2>
+
+<blockquote><p>Primary Colours&mdash;Molecular Swings&mdash;Colour Sensations&mdash;Sensations
+absent in the Colour-blind.</p></blockquote>
+
+
+<p>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
+<span class="pagenum">[Pg 134]</span>
+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.</p>
+
+<p>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
+<span class="pagenum"><a name="Page_135" id="Page_135">[Pg 135]</a></span>
+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.</p>
+
+<p>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.</p>
+
+<p>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
+<span class="pagenum"><a name="Page_136" id="Page_136">[Pg 136]</a></span>
+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.</p>
+
+<div class="figcenter" style="width: 401px;">
+<img src="images/i_137.png" width="401" height="330" alt="" title="">
+<span class="caption">Fig. 33.&mdash;Curve of Sensitiveness of Silver Bromo-iodide.
+</span>
+</div>
+<p>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
+<span class="pagenum"><a name="Page_137" id="Page_137">[Pg 137]</a></span>
+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
+<span class="pagenum"><a name="Page_138" id="Page_138">[Pg 138]</a></span>
+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.</p>
+
+<p>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
+<span class="pagenum"><a name="Page_139" id="Page_139">[Pg 139]</a></span>
+Helmholtz's physiological optics, as diagrammatic
+of the three sensations.</p>
+
+<div class="figright" style="width: 102px;">
+<img src="images/i_140.png" width="102" height="393" alt="" title="">
+<span class="caption">Fig. 34.&mdash;Curves of Colour Sensations.
+</span>
+</div>
+<p>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.</p>
+
+<p>Now assuming that this is the case, since a
+<span class="pagenum"><a name="Page_140" id="Page_140">[Pg 140]</a></span>
+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 (<a href="#Page_151">Fig. 35</a>), 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.</p>
+
+<p>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
+<span class="pagenum">[Pg 141]</span>
+less energy, the other two pendulums, which
+respond to the red and violet sensations.</p>
+
+<p>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,
+<span class="pagenum"><a name="Page_142" id="Page_142">[Pg 142]</a></span>
+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.</p>
+
+<p>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.</p>
+
+<p>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
+<span class="pagenum">[Pg 143]</span>
+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.</p>
+
+<p>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
+<span class="pagenum">[Pg 144]</span>
+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.</p>
+
+<p>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.</p>
+
+<p>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.</p>
+
+<p>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
+<span class="pagenum">[Pg 145]</span>
+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.</p>
+
+<p>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
+<span class="pagenum">[Pg 146]</span>
+to mix spectrum colours to match others would
+evidently be no guide to normal-eyed persons.</p>
+
+<p>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.</p>
+
+<p>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.</p><br>
+<span class="pagenum"><a name="Page_147" id="Page_147">[Pg 147]</a></span>
+
+
+
+<hr style="width: 65%;">
+<h2><a name="CHAPTER_XII" id="CHAPTER_XII"></a>CHAPTER XII.</h2>
+
+<blockquote><p>Formation of Colour Equations&mdash;Kœnig's Curves&mdash;Maxwell's
+Apparatus and Curves.</p></blockquote>
+
+
+<p>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 <i>in situ</i>. 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
+<span class="pagenum"><a name="Page_148" id="Page_148">[Pg 148]</a></span>
+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&frac12;, 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&mdash;</p>
+
+<p class="center">(1) 20(35) + 60(28) + 40(17) = 100 W<br>
+(2) 10(34) + 55(28) + 40(17) = 100 W<br>
+(3) 20(35) + 59(28) + 10(18) = 100 W</p>
+
+<p>Subtracting (1) from (2) we get&mdash;</p>
+
+<p class="center">
+       10(34) = 20(35) + 5(28)<br>
+    or (34) = 2(35) + &frac14;(28)
+</p>
+
+<p>which means that the colour sensation at (34) is
+made up of two parts of the sensation of (35),
+together with &frac14; part of the sensation of (28).</p>
+
+<p>In the same way we find that the colour sensation
+of (18) is made up of the sensations of (17) and (28).</p>
+
+<p class="center">(18) = 4(17) + 1/10(28).</p>
+<p><span class="pagenum">[Pg 149]</span></p>
+
+<p>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.</p>
+
+<p>The following is a set of observations which bear
+this out.</p>
+
+<p>The red and violet slits in this case were kept at
+<span class="pagenum">[Pg 150]</span>
+35 and 17·8 on the scale, and the position of the
+green slit altered.</p>
+
+
+<div class="center">
+<table border="1" cellpadding="4" cellspacing="0" summary="">
+<tr>
+<td align="center" colspan="3"> <span class="smcap">Position of Slits.</span></td>
+<td align="center" colspan="3"> <span class="smcap">Aperture of Slits.</span></td>
+<td align="center" colspan="3"> <span class="smcap">Luminosity of <br>Colour.</span></td>
+<td align="center" rowspan="2"> <span class="smcap">Sum of the<br> Luminosity of<br> Each Colour<br> Multiplied by<br> the Aperture.</span></td></tr>
+<tr><td align="center"> R</td><td align="center"> G</td><td align="center"> V</td><td align="center"> R</td><td align="center"> G</td><td align="center"> V</td><td align="center"> R</td><td align="center"> G</td><td align="center"> V</td></tr>
+<tr><td align="right"> 35</td><td align="right"> 28·5 &nbsp;</td><td align="right"> 17·8</td><td align="right"> 115</td><td align="right"> 38</td><td align="right"> 112</td><td align="right"> 18·1</td><td align="right"> 73</td><td align="right"> ·65</td><td align="right"> 4930</td></tr>
+<tr><td align="right"> 35</td><td align="right"> 28·0 &nbsp;</td><td align="right"> 17·8</td><td align="right"> 119</td><td align="right"> 45</td><td align="right"> 100</td><td align="right"> 18·1</td><td align="right"> 61·5</td><td align="right"> ·65</td><td align="right"> 4989</td></tr>
+<tr><td align="right"> 35</td><td align="right"> 27·75</td><td align="right"> 17·8</td><td align="right"> 122</td><td align="right"> 52</td><td align="right"> 85</td><td align="right"> 18·1</td><td align="right"> 52</td><td align="right"> ·65</td><td align="right"> 4960</td></tr>
+<tr><td align="right"> 35</td><td align="right"> 27·35</td><td align="right"> 17·8</td><td align="right"> 125</td><td align="right"> 65</td><td align="right"> 74</td><td align="right"> 18·1</td><td align="right"> 40</td><td align="right"> ·65</td><td align="right"> 4907</td></tr>
+<tr><td align="right"> 35</td><td align="right"> 27·0 &nbsp;</td><td align="right"> 17·8</td><td align="right"> 128</td><td align="right"> 78</td><td align="right"> 67</td><td align="right"> 18·1</td><td align="right"> 33·2</td><td align="right"> ·65</td><td align="right"> 4954</td></tr>
+<tr><td align="right"> 35</td><td align="right"> 26·3 &nbsp;</td><td align="right"> 17·8</td><td align="right"> 133</td><td align="right"> 125</td><td align="right"> 40</td><td align="right"> 18·1</td><td align="right"> 20·3</td><td align="right"> ·65</td><td align="right"> 4987</td></tr>
+<tr><td align="right"> 35</td><td align="right"> 26·0 &nbsp;</td><td align="right"> 17·8</td><td align="right"> 134</td><td align="right"> 150</td><td align="right"> 10</td><td align="right"> 18·1</td><td align="right"> 16·7</td><td align="right"> ·65</td><td align="right"> 4952</td></tr>
+<tr><td align="right"> 35</td><td align="right"> 25·85</td><td align="right"> 17·8</td><td align="right"> 135</td><td align="right"> 170</td><td align="right"> 0</td><td align="right"> 18·1</td><td align="right"> 15·0</td><td align="right">·65</td><td align="right"> 4993</td></tr>
+<tr><td align="right"></td><td align="right"></td><td align="right"></td><td align="right"></td><td align="right"></td><td align="right"></td><td align="right"></td><td align="right"><td align="right"></td><td align="right"> Mean 4959</td></tr>
+</table></div>
+<p>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.</p>
+
+<p>An inspection of the table will show how very
+closely the sum of the luminosities agree amongst
+<span class="pagenum"><a name="Page_151" id="Page_151">[Pg 151]</a></span>
+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.</p>
+
+<div class="figcenter" style="width: 401px;">
+<img src="images/i_152.png" width="401" height="249" alt="" title="">
+<span class="caption">Fig. 35.&mdash;Kœnig&#39;s Curves of Colour Sensations.
+</span>
+</div>
+<p>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
+<span class="pagenum"><a name="Page_152" id="Page_152">[Pg 152]</a></span>
+curves are found, and that these agree in the main
+with some two of the curves of the three belonging
+to the normal-eyed.</p>
+
+<div class="figleft" style="width: 150px;">
+<img src="images/i_153.jpg" width="150" height="448" alt="" title="">
+<span class="caption">Fig. 36. Maxwell&#39;s Colour-box.
+</span>
+</div>
+
+<p>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 <i>Philosophical Transactions</i>
+of the Royal Society for 18&mdash;,
+a somewhat modified diagram
+of it.</p>
+
+<p>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
+(<a href="#Page_42">Fig. 6</a>), 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 <a href="#Page_113">Fig.
+30.</a> 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
+<span class="pagenum"><a name="Page_153" id="Page_153">[Pg 153]</a></span>
+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.</p>
+
+<p>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.</p>
+
+<p>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
+<span class="pagenum"><a name="Page_154" id="Page_154">[Pg 154]</a></span>
+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.</p>
+
+<div class="figcenter" style="width: 401px;">
+<img src="images/i_155.png" width="401" height="290" alt="" title="">
+<span class="caption">Fig. 37.&mdash;Maxwell&#39;s Curves of Colour Sensations.
+</span>
+</div>
+
+<p>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.</p><p>
+<span class="pagenum">[Pg 155]</span>
+</p>
+<p>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.</p>
+
+<p>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 <a href="#Page_79">Fig. 11</a>,
+page 79.</p>
+
+<p>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.</p><br>
+<span class="pagenum"><a name="Page_156" id="Page_156">[Pg 156]</a></span>
+
+
+
+<hr style="width: 65%;">
+<h2><a name="CHAPTER_XIII" id="CHAPTER_XIII"></a>CHAPTER XIII.</h2>
+
+<blockquote><p>Match of Compound Colours with Simple Colours&mdash;All Colours reduced
+to Numbers&mdash;Method of matching a Colour with a Spectrum Colour and
+White Light.</p></blockquote>
+
+
+<p>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.</p>
+
+<p>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.</p>
+
+<p>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
+<span class="pagenum"><a name="Page_157" id="Page_157">[Pg 157]</a></span>
+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.</p>
+
+<p>It will often be&mdash;more often than not&mdash;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 <i>no matter what the colour</i> 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.</p>
+
+<p>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
+<span class="pagenum">[Pg 158]</span>
+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&mdash;</p>
+
+
+<div class="center">
+<table border="0" cellpadding="4" cellspacing="0" summary="">
+<tr><td align="left"> Normal-eye.</td><td align="left">Green colour-blind.</td><td align="left">Red colour-blind.</td></tr>
+<tr><td align="left"> Red</td><td align="left"> Red</td><td align="left">&mdash;</td></tr>
+<tr><td align="left"> Green</td><td align="left"> &mdash;</td><td align="left">Green.</td></tr>
+<tr><td align="left"> Violet</td><td align="left"> Violet</td><td align="left">Violet.</td></tr>
+<tr><td align="left"> Mixtures of red and green</td><td align="left"> &mdash;</td><td align="left"> &mdash;</td></tr>
+<tr><td align="left"> Mixtures of red and violet</td><td align="left"> Mixtures of red and violet</td><td align="left"> &mdash;</td></tr>
+<tr><td align="left"> Mixtures of green and violet</td><td align="left"></td><td align="left"> Mixtures of green and violet.</td></tr>
+<tr><td align="left"> Mixtures of red, green and violet</td><td align="left"></td><td align="left">&mdash;</td></tr>
+</table></div>
+<p>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
+<span class="pagenum"><a name="Page_159" id="Page_159">[Pg 159]</a></span>
+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.</p>
+
+<p>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.</p>
+
+<p>If we take three rays in the spectrum&mdash;one in
+the red between C and the red Lithium line which
+we will call <i>R</i>, another in the green between F and
+<i>b</i> which we will call <i>G</i>, and a third in the violet
+near G but on the <i>H</i> side of it, and which we may
+call <i>V</i>&mdash;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
+<span class="pagenum">[Pg 160]</span>
+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&mdash;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 <i>v</i> and <i>b</i>, and <i>G</i> and <i>R</i>, in any proportions
+whatever.</p>
+
+<p>Let the luminosities of the rays <i>R, G</i> and <i>V</i>,
+which give the impression of white light, be <i>a</i>, <i>b</i>
+and <i>c</i> units respectively, and <i>p</i>, <i>q</i> and <i>r</i> those which
+give that of the colour which has to be registered
+and reproduced. We then get the following equations&mdash;where
+<i>W</i> is white, <i>w</i> its luminosity, <i>Z</i> the
+colour, and <i>z</i> its luminosity&mdash;</p>
+
+<p class="center"><i>aR</i> + <i>bG</i> + <i>cV</i> = <i>wW</i>&mdash;(i.);<br>
+<i>pR</i> + <i>qG</i> + <i>rV</i> = <i>zZ</i>&mdash;(ii.);
+</p>
+
+<p>Then evidently&mdash;</p>
+
+<p class="center">(<i>a</i> + <i>b</i> + <i>c</i>) = <i>w</i>; and (<i>p</i> + <i>q</i> + <i>r</i>) = <i>z</i>.</p>
+
+<p class="center">Let <i>p</i> = ɑ<i>a</i>, <i>q</i> = β<i>b</i>, <i>r</i> = ɣ<i>c</i>,</p>
+
+<p>Then we may write (ii.) as&mdash;</p>
+
+<p class="center">α<i>aR</i> + β<i>bG</i> + ɣ<i>cV</i> = <i>zZ</i>&mdash;(iii.).</p>
+<p><span class="pagenum">[Pg 161]</span>
+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&mdash;</p>
+
+<p class="center">ɑ<i>aR</i> + ɑ<i>bG</i> + ɑ<i>cV</i>= ɑ<i>wW</i>&mdash;(iv.)
+<br>
+Subtracting (iv.) from (iii.) and we get&mdash;
+<br>
+(β-ɑ)<i>bG</i> + (ɣ-ɑ)<i>cV</i> = <i>zZ</i> - ɑ<i>wW</i>.
+</p>
+
+<p>Now it has already been stated that between <i>V</i>
+and <i>G</i> 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 <i>V</i> and
+<i>G</i>&mdash;let us call it <i>X</i> and its luminosity <i>x</i> [<i>x</i> being
+evidently equal to (β-ɑ)<i>b</i> + (ɣ-ɑ)<i>c</i>], and μ the
+luminosity of the small quantity of white added.</p>
+
+<p>We then get <i>zZ</i> = <i>xX</i> + (μ + ɑ) <i>W</i>.</p>
+
+<p>Here we have the colour <i>Z</i> in terms of a single
+ray, and of white light.</p>
+
+<p>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 <i>R</i> and <i>V</i>, which will make the whole white.
+Thus, suppose in (iii.) ɑ to be larger than ɣ and ɣ
+<span class="pagenum"><a name="Page_162" id="Page_162">[Pg 162]</a></span>
+than β, then we must add ϕ<i>bG</i> + θ<i>cV</i> and we
+have</p>
+
+<p class="center">ɑ<i>aR</i> + (β + ϕ)<i>bG</i> + (ɣ + θ)<i>cV</i> = <i>nW</i> = <i>Z</i> + ϕ<i>bG</i> + θ<i>cV</i>;<br>
+but (β + ϕ), and (ɣ + θ) each equal ɑ ∴ <i>n</i> = ɑ<i>w</i>.<br>
+∴ <i>Z</i> + ϕ<i>bG</i> + θ<i>cV</i>= ɑ<i>wW</i>.
+</p>
+
+<p>Now between <i>V</i> and <i>G</i> in the spectrum there is
+some single colour which gives the sensation of the
+mixture of <i>G</i> and <i>V</i>. Let it be <i>X</i>´ with luminosity
+<i>x</i>´, together with white whose luminosity is μ´,
+which must equal (ϕ<i>b</i> + θ<i>c</i>).</p>
+
+<p class="center">∴ <i>Z</i> + <i>x´X´</i> + μ´<i>W</i> = ɑ<i>wW</i><br>
+<i>Z</i> = (ɑ<i>w</i> - μ´)<i>W</i> - <i>x´X´</i>
+</p>
+
+<p>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.</p>
+
+<p>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&mdash;</p>
+
+<p>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
+<span class="pagenum">[Pg 163]</span>
+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.</p>
+
+<p>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
+<span class="pagenum">[Pg 164]</span>
+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.</p>
+
+<p>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.</p>
+
+<p>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.</p>
+
+<p>Coloured glasses to be used at night with oil or
+<span class="pagenum">[Pg 165]</span>
+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.</p>
+
+<p>The following are the determinations of some
+glasses&mdash;</p>
+
+
+<div class="center">
+<table border="1" cellpadding="4" cellspacing="0" summary="">
+<tr><td align="center"> <span class="smcap">Glasses Measured.</span></td>
+<td align="center"><span class="smcap">Wave-lengths of Dominant Ray.</span></td>
+<td align="center"><span class="smcap">Percentage of White Light.</span></td>
+<td align="center"> <span class="smcap">Percentage of Luminosity of Light Transmitted through the Glass.</span></td></tr>
+<tr><td align="left"> Ruby</td><td align="right"> 6220</td><td align="right"> 2</td><td align="right"> 13·1 &nbsp;</td></tr>
+<tr><td align="left"> Canary</td><td align="right"> 5850</td><td align="right"> 26</td><td align="right"> 82·0 &nbsp;</td></tr>
+<tr><td align="left"> Bottle Green</td><td align="right"> 5510</td><td align="right"> 31</td><td align="right"> 10·6 &nbsp;</td></tr>
+<tr><td align="left"> No. 1 Signal Green</td><td align="right"> 4925</td><td align="right"> 32</td><td align="right"> 6·9 &nbsp;</td></tr>
+<tr><td align="left"> No. 2 Signal Green</td><td align="right"> 5100</td><td align="right"> 61</td><td align="right"> 19·4 &nbsp;</td></tr>
+<tr><td align="left"> Cobalt</td><td align="right"> 4675</td><td align="right"> 42</td><td align="right"> 3·75</td></tr>
+</table></div>
+<p><span class="pagenum">[Pg 166]</span></p>
+
+<p>The following are determinations of some
+coloured pigments&mdash;</p>
+
+
+<div class="center">
+<table border="1" cellpadding="4" cellspacing="0" summary="">
+<tr><td align="right"> <span class="smcap">Coloured Papers.</span></td><td align="right"><span class="smcap">Wave-lengths of Dominant Ray.</span></td><td align="right"><span class="smcap"> Percentage of White Light.</span></td><td align="right"> <span class="smcap">Percentage of Luminosity, White Paper being 100.</span></td></tr>
+<tr><td align="right"> Vermilion</td><td align="right"> 6100</td><td align="right"> 2·5</td><td align="right"> 14·8</td></tr>
+<tr><td align="right"> Emerald Green</td><td align="right"> 5220</td><td align="right"> 59·0</td><td align="right"> 22·7</td></tr>
+<tr><td align="right"> French Ultramarine Blue</td><td align="right"> 4720</td><td align="right"> 61·0</td><td align="right"> 4·4</td></tr>
+<tr><td align="right"> Brown Paper</td><td align="right"> 5940</td><td align="right"> 50·0</td><td align="right"> 25·0</td></tr>
+<tr><td align="right"> Brown Paper</td><td align="right"> 5870</td><td align="right"> 67·0</td><td align="right"> 19·5</td></tr>
+<tr><td align="right"> Orange</td><td align="right"> 5915</td><td align="right"> 4·0</td><td align="right"> 62·5</td></tr>
+<tr><td align="right"> Chrome Yellow</td><td align="right"> 5835</td><td align="right"> 26·0</td><td align="right"> 77·7</td></tr>
+<tr><td align="right"> Blue Green</td><td align="right"> 5005</td><td align="right"> 42·5</td><td align="right"> 14·8</td></tr>
+<tr><td align="right"> Eosin Dye  (<i>Sporting Times</i>)</td><td align="right"> 6400</td><td align="right"> 72·0</td><td align="right"> 44·7</td></tr>
+<tr><td align="right"> Cobalt</td><td align="right"> 4820</td><td align="right"> 55·5</td><td align="right"> 14·5</td></tr>
+</table></div><br>
+<p><span class="pagenum"><a name="Page_167" id="Page_167">[Pg 167]</a></span></p>
+
+
+
+<hr style="width: 65%;">
+<h2><a name="CHAPTER_XIV" id="CHAPTER_XIV"></a>CHAPTER XIV.</h2>
+
+<blockquote><p>Complementary Colours&mdash;Complementary Pigment Colours&mdash;Measurement
+of Complementary Colours.</p></blockquote>
+
+<p>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
+<span class="pagenum"><a name="Page_168" id="Page_168">[Pg 168]</a></span>
+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.</p>
+
+<div class="figcenter" style="width: 300px;">
+<img src="images/i_170.jpg" width="300" height="297" alt="" title="">
+<span class="caption">Fig. 38.&mdash;Chromatic Circle.
+</span>
+</div>
+
+<p>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 <a href="#Fig_16">Fig. 16</a>, p. 95), a single spectrum
+<span class="pagenum">[Pg 169]</span>
+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
+<span class="pagenum"><a name="Page_170" id="Page_170">[Pg 170]</a></span>
+small part of the spectrum can be shown in the
+same manner.</p>
+
+<p>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 (<a href="#Page_168">Fig. 38</a>). 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 <i>memoria technica</i>, and can
+be filled up according to the fancy of the observer.</p>
+
+<p>The following are pairs of most carefully selected
+complementary colours of pigments, as adopted by
+Professor Church.</p>
+
+
+<div class="center">
+<table border="0" cellpadding="4" cellspacing="0" summary="">
+<tr><td align="right" rowspan="4"><span class="moustache">{</span></td><td align="center"><i>Complementaries.</i></td><td align="center"><i>Pigments.</i></td></tr>
+<tr><td align="left" >Red</td><td align="left">Madder red or crimson vermilion.</td></tr>
+<tr><td align="left">&nbsp;  and</td><td align="left"></td></tr>
+<tr><td align="left">Green blue </td><td align="left">Viridian, the emerald oxide of chromium with a little cobalt.</td></tr>
+<tr><td align="right" rowspan="4"><span class="moustache">{</span></td><td align="center"></td><td align="center"></td></tr>
+<tr><td align="left" >Orange</td><td align="left">Cadmium yellow, of full orange hue.<span class="pagenum">[Pg 171]</span></td></tr>
+<tr><td align="left">&nbsp;  and</td><td align="left"></td></tr>
+<tr><td align="left">Greenish blue </td><td align="left">Cobalt green.</td></tr>
+<tr><td align="right" rowspan="4"><span class="moustache">{</span></td><td align="center"></td><td align="center"></td></tr>
+<tr><td align="left" >Orange yellow</td><td align="left">Cadmium yellow, or deep chrome.</td></tr>
+<tr><td align="left">&nbsp;  and</td><td align="left"></td></tr>
+<tr><td align="left">Turquoise </td><td align="left">Cœrulium, or cobalt blue, with a little emerald green.</td></tr>
+<tr><td align="right" rowspan="4"><span class="moustache">{</span></td><td align="center"></td><td align="center"></td></tr>
+<tr><td align="left" >Yellow</td><td align="left">Lemon yellow, pale chrome, or aureolin.<br></td></tr>
+<tr><td align="left">&nbsp;  and</td><td align="left"></td></tr>
+<tr><td align="left">Blue </td><td align="left">Ultramarine from lapis-lazuli.</td></tr>
+<tr><td align="right" rowspan="4"><span class="moustache">{</span></td><td align="center"></td><td align="center"></td></tr>
+<tr><td align="left" >Greenish yellow</td><td align="left"> Aureolin with a little viridian.<br></td></tr>
+<tr><td align="left">&nbsp;  and</td><td align="left"></td></tr>
+<tr><td align="left">Violet blue</td><td align="left">French ultramarine.</td></tr>
+<tr><td align="right" rowspan="4"><span class="moustache">{</span></td><td align="center"></td><td align="center"></td></tr>
+<tr><td align="left" >Green yellow</td><td align="left">Lemon yellow, with some emerald green.<br></td></tr>
+<tr><td align="left">&nbsp;  and</td><td align="left"></td></tr>
+<tr><td align="left">Violet</td><td align="left">French ultramarine with madder carmine.</td></tr>
+<tr><td align="right" rowspan="4"><span class="moustache">{</span></td><td align="center"></td><td align="center"></td></tr>
+<tr><td align="left" >Yellowish green</td><td align="left">Lemon yellow with much emerald green.</td></tr>
+<tr><td align="left">&nbsp;  and</td><td align="left"></td></tr>
+<tr><td align="left">Purplish violet</td><td align="left"> Madder carmine with French ultramarine.</td></tr>
+<tr><td align="right" rowspan="4"><span class="moustache">{</span></td><td align="center"></td><td align="center"></td></tr>
+<tr><td align="left" >Green</td><td align="left">Emerald green with lemon yellow.</td></tr>
+<tr><td align="left">&nbsp;  and</td><td align="left"></td></tr>
+<tr><td align="left">Purple</td><td align="left"> Madder carmine with French ultramarine.</td></tr>
+<tr><td align="right" rowspan="4"><span class="moustache">{</span></td><td align="center"></td><td align="center"></td></tr>
+<tr><td align="left" >Emerald green</td><td align="left">Emerald green alone.</td></tr>
+<tr><td align="left">&nbsp;  and</td><td align="left"></td></tr>
+<tr><td align="left">Reddish purple</td><td align="left">Madder carmine with a little French ultramarine.</td></tr>
+</table></div><br>
+<p><span class="pagenum">[Pg 172]</span></p>
+
+<p>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 <a href="#CHAPTER_XV">chap. XV.</a>)</p>
+
+<p>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.</p>
+
+<p>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
+<span class="pagenum"><a name="Page_173" id="Page_173">[Pg 173]</a></span>
+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.</p>
+
+<p>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
+<span class="pagenum">[Pg 174]</span>
+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:</p>
+
+
+
+<div class="center">
+<table border="0" cellpadding="4" cellspacing="0" summary="">
+<tr><td align="left" rowspan="4">(1)</td>
+<td align="left" rowspan="4"><span class="moustache">{</span></td><td align="left"></td><td align="right"></td></tr>
+<tr><td align="left">Red&nbsp; &nbsp;</td><td align="right">165</td></tr>
+<tr><td align="left">Green&nbsp; &nbsp;</td><td align="right">60</td></tr>
+<tr><td align="left">Violet&nbsp; </td><td align="right">100</td></tr>
+</table></div>
+
+<p>Emerald green was placed in the patch and was
+matched by the light from the three slits, when it
+was found that it required</p>
+
+<div class="center">
+<table border="0" cellpadding="4" cellspacing="0" summary="">
+<tr><td align="left" rowspan="4">(2)</td>
+<td align="left" rowspan="4"><span class="moustache">{</span></td><td align="left"></td><td align="right"></td></tr>
+<tr><td align="left">Red&nbsp; &nbsp;</td><td align="right">4</td></tr>
+<tr><td align="left">Green&nbsp; &nbsp;</td><td align="right">35</td></tr>
+<tr><td align="left">Violet&nbsp; </td><td align="right">25</td></tr>
+</table></div>
+
+<p>Deducting one from the other we get as the
+complementary colour,</p>
+
+
+<div class="center">
+<table border="0" cellpadding="4" cellspacing="0" summary="">
+<tr><td align="left" rowspan="4">(3)</td>
+<td align="left" rowspan="4"><span class="moustache">{</span></td><td align="left"></td><td align="right"></td></tr>
+<tr><td align="left">Red&nbsp; &nbsp;</td><td align="right">125</td></tr>
+<tr><td align="left">Green&nbsp; &nbsp;</td><td align="right">25</td></tr>
+<tr><td align="left">Violet&nbsp; </td><td align="right">75</td></tr>
+</table></div>
+
+<p>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,
+<span class="pagenum">[Pg 175]</span>
+and these we can obtain by taking the proportions
+of the colours in (1); therefore deduct&mdash;</p>
+
+<div class="center">
+<table border="0" cellpadding="4" cellspacing="0" summary="">
+<tr><td align="left" rowspan="4">(4)</td>
+<td align="left" rowspan="4"><span class="moustache">{</span></td><td align="left"></td><td align="right"></td></tr>
+<tr><td align="left">Red&nbsp; &nbsp;</td><td align="right">69 &nbsp; &nbsp;</td></tr>
+<tr><td align="left">Green&nbsp; &nbsp;</td><td align="right">25 &nbsp; &nbsp;</td></tr>
+<tr><td align="left">Violet&nbsp; </td><td align="right">41.5</td></tr>
+</table></div>
+
+<p>and this would leave as the complementary colour
+without any admixture of white&mdash;</p>
+<div class="center">
+<table border="0" cellpadding="4" cellspacing="0" summary="">
+<tr><td align="left" rowspan="3">(5)</td>
+<td align="left" rowspan="3"><span class="moustache">{</span></td><td align="left"></td><td align="right"></td></tr>
+<tr><td align="left">Red&nbsp; &nbsp;</td><td align="right">56 &nbsp; &nbsp;</td></tr>
+<tr><td align="left">Violet&nbsp; </td><td align="right">33.5</td></tr>
+</table></div>
+
+<p>which is a purple as would be expected.</p>
+
+<p>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)&mdash;</p>
+
+<div class="center">
+<table border="0" cellpadding="4" cellspacing="0" summary="">
+<tr><td align="left" rowspan="4">(6)</td>
+<td align="left" rowspan="4"><span class="moustache">{</span></td><td align="left"></td><td align="right"></td></tr>
+<tr><td align="left">Red&nbsp; &nbsp;</td><td align="right">40 &nbsp; &nbsp;</td></tr>
+<tr><td align="left">Green&nbsp; &nbsp;</td><td align="right">14.4</td></tr>
+<tr><td align="left">Violet&nbsp; </td><td align="right">24 &nbsp; &nbsp;</td></tr>
+</table></div>
+
+<p>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
+<span class="pagenum">[Pg 176]</span>
+our final result we find the complementary colour,
+of equal impurity, is a mixture of&mdash;</p>
+
+<div class="center">
+<table border="0" cellpadding="4" cellspacing="0" summary="">
+<tr><td align="left" rowspan="4">(7)</td>
+<td align="left" rowspan="4"><span class="moustache">{</span></td><td align="left"></td><td align="right"></td></tr>
+<tr><td align="left">Red&nbsp; &nbsp;</td><td align="right">96 &nbsp; &nbsp;</td></tr>
+<tr><td align="left">Green&nbsp; &nbsp;</td><td align="right">14.4</td></tr>
+<tr><td align="left">Violet&nbsp; </td><td align="right">57.5</td></tr>
+</table></div>
+
+<p>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.</p>
+
+<p>Another example was an orange pigment, and
+this we will work out in the form of colour equation.
+The same mixture gave white, viz.:</p>
+
+<p class="center">165 R + 60 G + 100 V = W<br>
+165 R + 42 G = O<br>
+∴ the complementary colour, which is<br>
+W - O = 18 G + 100 V,</p>
+
+<p>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
+<span class="pagenum">[Pg 177]</span>
+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
+<span class="pagenum">[Pg 178]</span>
+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.)</p><br>
+<span class="pagenum"><a name="Page_179" id="Page_179">[Pg 179]</a></span>
+
+
+
+<hr style="width: 65%;">
+<h2><a name="CHAPTER_XV" id="CHAPTER_XV"></a>CHAPTER XV.</h2>
+
+<blockquote><p>Persistence of Images on the Retina&mdash;The Use of Coloured Discs.</p></blockquote>
+
+<div class="figcenter" style="width: 300px;">
+<img src="images/i_181.jpg" width="300" height="296" alt="" title="">
+<span class="caption">Fig. 39.&mdash;Disc to cause alternate opening and closing of two Slits.
+</span>
+</div>
+
+<p>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 (<a href="#Page_179">Fig. 39</a>), the
+slit S₁ will be covered when the slit S₂ is open,
+<span class="pagenum">[Pg 180]</span>
+and <i>vice versâ</i>, 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
+<span class="pagenum"><a name="Page_181" id="Page_181">[Pg 181]</a></span>
+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.</p>
+
+<div class="figright" style="width: 251px;">
+<img src="images/i_182.jpg" width="251" height="252" alt="" title="">
+<span class="caption">Fig. 40.&mdash;Disc painted Blue and Red.
+</span>
+</div>
+<p>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
+<span class="pagenum"><a name="Page_182" id="Page_182">[Pg 182]</a></span>
+is, however, to have an electro-motor similar to
+that which moves the rotating movable sectors
+(<a href="#Page_183">Fig. 41</a>), and at the end of the spindle to fix a cap
+with a screw and nut attached. The disc, perforated
+<span class="pagenum"><a name="Page_183" id="Page_183">[Pg 183]</a></span>
+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.</p>
+
+<div class="figcenter" style="width: 450px;">
+<img src="images/i_183.jpg" width="450" height="276" alt="" title="">
+<span class="caption">Fig. 41.&mdash;Electro-motor with Discs attached.
+</span>
+</div><br>
+<a name="Fig_42" id="Fig_42"></a>
+<div class="figright" style="width: 150px;">
+<img src="images/i184.jpg" width="150" height="150" alt="" title="">
+<span class="caption">Fig. 42.&mdash;Method of cutting
+Disc to allow an overlap of a second Disc.</span>
+</div>
+
+<p>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
+<span class="pagenum"><a name="Page_184" id="Page_184">[Pg 184]</a></span>
+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 <i>ab</i> (<a href="#Fig_42">Fig. 42</a>). 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
+<span class="pagenum">[Pg 185]</span>
+following proportions of the three colours were
+required&mdash;</p>
+
+
+<div class="center">
+<table border="0" cellpadding="4" cellspacing="0" summary="">
+<tr><td align="right">V</td><td align="right">=</td><td align="right"> 124°</td></tr>
+<tr><td align="right">E</td><td align="right">=</td><td align="right"> 143°</td></tr>
+<tr><td align="right">U</td><td align="right">=</td><td align="right"> <u> &nbsp; 93°</u></td></tr>
+<tr><td align="right"></td><td align="right"></td><td align="right">360°</td></tr>
+</table></div>
+
+<p>and to make the same grey it required</p>
+
+
+<div class="center">
+<table border="0" cellpadding="4" cellspacing="0" summary="">
+<tr><td align="right">X</td><td align="right">=</td><td align="right"> 278°</td></tr>
+<tr><td align="right">W</td><td align="right">=</td><td align="right"><u>&nbsp; 82°</u></td></tr>
+<tr><td align="right"></td><td align="right"></td><td align="right">360°</td></tr>
+</table></div>
+
+<p>Now the black reflected 3·4% of white light, so
+that really the proportions of black and white were</p>
+
+
+<div class="center">
+<table border="0" cellpadding="4" cellspacing="0" summary="">
+<tr><td align="right">X</td><td align="right">=</td><td align="right"> 268·6</td></tr>
+<tr><td align="right">W</td><td align="right">=</td><td align="right"><u>&nbsp; 91·4</u></td></tr>
+<tr><td align="right"></td><td align="right"></td><td align="right">360·0</td></tr>
+</table></div>
+
+<p>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
+<span class="pagenum">[Pg 186]</span>
+from the measures (<a href="#Page_93">pp. 93-95</a>), 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.</p>
+
+<p>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.</p>
+
+<p>The match of grey in this last light was found
+to be</p>
+
+
+<div class="center">
+<table border="0" cellpadding="4" cellspacing="0" summary="">
+<tr><td align="right">V</td><td align="right">=</td><td align="right"> 119°</td></tr>
+<tr><td align="right">E</td><td align="right">=</td><td align="right"> 148°</td></tr>
+<tr><td align="right">U</td><td align="right">=</td><td align="right"> <u>&nbsp; 93°</u></td></tr>
+<tr><td align="right"></td><td align="right"></td><td align="right">360°</td></tr>
+<tr><td align="right">which matched with</td></tr>
+<tr><td align="right">X</td><td align="right">=</td><td align="right"> 244°</td></tr>
+<tr><td align="right">W</td><td align="right">=</td><td align="right"> 116°</td></tr>
+</table></div>
+
+<p>(In this case the black and white are the corrected
+black and white.)</p>
+
+<p>The importance of making matches in a uniform
+<span class="pagenum">[Pg 187]</span>
+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.</p>
+
+<p>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 (<a href="#Page_188">Fig. 43</a>). 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
+<span class="pagenum"><a name="Page_188" id="Page_188">[Pg 188]</a></span>
+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.</p>
+
+<div class="figcenter" style="width: 300px;">
+<img src="images/i_189.jpg" width="300" height="290" alt="" title="">
+<span class="caption">Fig. 43.&mdash;Arrangement to find value of Gamboge in terms of
+Emerald Green and Vermilion.</span>
+</div><p>
+
+<span class="pagenum"><a name="Page_189" id="Page_189">[Pg 189]</a></span>
+</p>
+<p>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</p>
+
+<p class="center">172 V + 188 E = 75 Y + 45 W + 240 X.</p>
+
+<p>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 <b>75/360</b> 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.</p>
+
+<p>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
+<span class="pagenum"><a name="Page_190" id="Page_190">[Pg 190]</a></span>
+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.</p>
+
+<p>In an experiment with an orange of this kind,
+the following results were obtained&mdash;</p>
+<div class="center">
+<table border="0" cellpadding="4" cellspacing="0" summary="">
+<tr><td align="right">E<br>U<br>O</td><td align="right"> 115°<br>150°<br>95°</td>
+<td align="right"></td>
+<td align="right" rowspan="4"><span class="moustachetp">}</span></td>
+<td align="center" rowspan="4">=</td>
+<td align="center" rowspan="4"><span class="moustachesm">{</span></td>
+<td align="right"> W<br>X</td><td align="right"> 85°<br>275°</td></tr>
+</table></div>
+
+<p>We can now from these deduce the luminosity
+of the orange employed in this case.</p>
+
+<p>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&mdash;</p>
+
+<p class="center">115 × 30 + 150 × 4·4 + 95 O = (85 + 3·4 × 275) 100.<br>
+This gives 95 O = 9435 - (3450 + 660).<br>
+O = 56.
+</p>
+<p><span class="pagenum"><a name="Page_191" id="Page_191">[Pg 191]</a></span>
+</p>
+<p>That is, the luminosity of the orange is ·56 that
+of white; by direct measurement it was ·57.</p>
+
+<p>In a similar way the luminosity of chrome yellow
+(Y) is found. In this case&mdash;</p>
+
+<div class="center">
+<table border="0" cellpadding="4" cellspacing="0" summary="">
+<tr><td align="right">E<br>U<br>O</td><td align="right"> 35<br>204<br>121</td><td align="right"></td><td align="right" rowspan="4"><span class="moustachetp">}</span></td><td align="center" rowspan="4">=</td><td align="center" rowspan="4"><span class="moustachesm">{</span></td>
+<td align="right"> W<br>X</td><td align="right"> 101<br>259</td></tr>
+</table></div>
+
+
+<p>Similar equations were formed as the above.</p>
+
+<p class="center">35 × 30 + 204 × 4·4 + 121 Y = (101 + 3·4 × 259) 100<br>
+whence Y = 77·6.
+</p>
+
+<p>That is, the luminosity of the chrome yellow is
+·78; the same as was obtained by direct measurement.</p>
+
+<p>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.</p>
+
+<p>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.</p><p>
+<span class="pagenum"><a name="Page_192" id="Page_192">[Pg 192]</a></span>
+</p>
+<div class="figcenter" style="width: 300px;">
+<img src="images/i_193.jpg" width="300" height="300" alt="" title="">
+<span class="caption">Fig. 44.&mdash;Disc arranged to give approximately all the Spectrum
+Colours.</span></div>
+
+<p>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
+<span class="pagenum">[Pg 193]</span>
+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,
+<span class="pagenum">[Pg 194]</span>
+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&mdash;as we have
+seen&mdash;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,
+<span class="pagenum"><a name="Page_195" id="Page_195">[Pg 195]</a></span>
+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.</p><br>
+<span class="pagenum"><a name="Page_196" id="Page_196">[Pg 196]</a></span>
+
+
+
+<hr style="width: 65%;">
+<h2><a name="CHAPTER_XVI" id="CHAPTER_XVI"></a>CHAPTER XVI.</h2>
+
+<blockquote><p>Contrast Colours&mdash;Measurement of Contrast Colours&mdash;Fatigue of the
+Eye&mdash;After-Images.</p></blockquote>
+
+<div class="figright" style="width: 200px;">
+<img src="images/i197.jpg" width="200" height="178" alt="" title="">
+<span class="caption">Fig. 45.&mdash;Method of showing
+Contrast Colours.</span>
+</div>
+
+<p>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
+<span class="pagenum"><a name="Page_197" id="Page_197">[Pg 197]</a></span>
+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.</p>
+
+
+<div class="center">
+<table border="1" cellpadding="4" cellspacing="0" summary="">
+<tr><td align="left"><span class="smcap">Spectrum Colour.</span></td><td align="left"><span class="smcap">Contrast Colours in Electric light.</span></td><td align="left"><span class="smcap">Spectrum Colour.</span></td><td align="left"> <span class="smcap">Contrast Colours in Gaslight.</span></td></tr>
+<tr><td align="left">Cherry red&nbsp; &nbsp;</td><td align="left"> Green gray</td><td align="left"> Cherry red&nbsp; &nbsp;</td><td align="left"> Green gray</td></tr>
+<tr><td align="left">Scarlet</td><td align="left"> Bluish green gray</td><td align="left"> Scarlet</td><td align="left"> Sap green</td></tr>
+<tr><td align="left">Terra-cotta</td><td align="left"> Blue gray&nbsp;</td><td align="left"> Light red&nbsp; &nbsp;</td><td align="left"> Green gray</td></tr>
+<tr><td align="left">Raw sienna</td><td align="left"> Light blue gray&nbsp; &nbsp;</td><td align="left"> Olive green&nbsp;</td><td align="left"> Pink gray</td></tr>
+<tr><td align="left">Olive green</td><td align="left"> Umber</td><td align="left"> Apple green&nbsp;</td><td align="left"> Mauve &amp; black</td></tr>
+<tr><td align="left">Emerald green</td><td align="left"> Pinkish lavender&nbsp;</td><td align="left"> Emerald green</td><td align="left"> Pink terra-cotta</td></tr>
+<tr><td align="left">Grass green</td><td align="left"> Light pink</td><td align="left"> Emerald green</td><td align="left"> Pink terra-cotta</td></tr>
+<tr><td align="left">Bluish green</td><td align="left"> Dark pink&nbsp;</td><td align="left"> Bluish green&nbsp;</td><td align="left"> Pinker terra-cotta</td></tr>
+<tr><td align="left">Signal green</td><td align="left"> Salmon&nbsp; &nbsp;</td><td align="left"> Peacock blue&nbsp;</td><td align="left"> Salmon</td></tr>
+<tr><td align="left">Cyanine blue</td><td align="left"> Yellow ochre</td><td align="left"> Prussian blue</td><td align="left"> Reddish yellow</td></tr>
+<tr><td align="left">Ultramarine</td><td align="left"> Raw sienna</td><td align="left"> Ultramarine&nbsp;</td><td align="left"> Raw sienna</td></tr>
+<tr><td align="left">Violet blue</td><td align="left"> Brownish yellow</td><td align="left"> Violet blue&nbsp;</td><td align="left"> Brownish orange</td></tr>
+<tr><td align="left">Blue violet&nbsp;</td><td align="left"> Green yellow brown</td><td align="left"> Blue violet&nbsp;</td><td align="left"> Brownish yellow</td></tr>
+<tr><td align="left">Violet</td><td align="left"> Burnt sienna</td><td align="left"> Violet</td><td align="left"> Yellow ochre</td></tr>
+</table></div>
+
+<p>The contrasts here shown are not so visible when
+the two shadows of the rod occupy the whole of
+<span class="pagenum"><a name="Page_198" id="Page_198">[Pg 198]</a></span>
+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.</p>
+
+<div class="center">
+<table border="1" cellpadding="4" cellspacing="0" summary="">
+<tr><td align="center" colspan = "2"><span class="smcap">Original Colours.</span></td><td align="center" colspan="2"><span class="smcap">Change due to Contrast.</span></td></tr>
+<tr><td align="left"> Red</td><td align="left"> Orange</td><td align="left"> Red became yellower</td><td align="left"> Orange became green grey</td></tr>
+<tr><td align="left"> Red</td><td align="left"> Green</td><td align="left"> Red unaltered, but brighter</td><td align="left"> Green unaltered, but brighter</td></tr>
+<tr><td align="left"> Red</td><td align="left"> Blue</td><td align="left"> Red became more orange</td><td align="left"> Blue became greener</td></tr>
+<tr><td align="left"> Red</td><td align="left"> Violet</td><td align="left"> Red became orange</td><td align="left"> Violet, no marked change</td></tr>
+<tr><td align="left"> Green</td><td align="left"> Orange</td><td align="left"> Green became bluer</td><td align="left"> Orange became yellower</td></tr>
+<tr><td align="left"> Green</td><td align="left"> Blue</td><td align="left"> Green became olive</td><td align="left"> Blue became more violet</td></tr>
+<tr><td align="left"> Green</td><td align="left"> Violet</td><td align="left"> Green became yellower</td><td align="left"> Violet became bluer</td></tr>
+<tr><td align="left"> Orange</td><td align="left"> Blue</td><td align="left"> Orange became redder</td><td align="left"> Blue became bluer</td></tr>
+<tr><td align="left"> Orange</td><td align="left"> Violet</td><td align="left"> Orange became greener</td><td align="left"> Violet became bluer</td></tr>
+<tr><td align="left"> Violet</td><td align="left"> Blue</td><td align="left"> Hardly altered</td><td align="left"> Hardly altered</td></tr>
+</table></div>
+<p><span class="pagenum">[Pg 199]</span></p>
+
+<p>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.</p>
+
+<p>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&mdash;or
+rather we should say intuitive applications of science&mdash;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.</p>
+
+<p>It might seem that these contrast colours being
+only a physiological effect, could not be accurately
+<span class="pagenum"><a name="Page_200" id="Page_200">[Pg 200]</a></span>
+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.</p>
+
+<p>To make white light and the contrast colours, the
+slits had to be of the following apertures&mdash;</p>
+
+<div class="center">
+<table border="1" cellpadding="4" cellspacing="0" summary="">
+<tr><td align="left"><span class="smcap">Colour.</span></td><td align="right"><span class="smcap">Red.</span></td><td align="right"><span class="smcap">Green.</span></td><td align="right"><span class="smcap">Violet.</span></td></tr>
+<tr><td align="left"> White light</td><td align="right">15·7</td><td align="right"> 6·5</td><td align="right"> 9·8</td></tr>
+<tr><td align="left"> Contrast to Red</td><td align="right">13·5</td><td align="right">11·8</td><td align="right">22·5</td></tr>
+<tr><td align="left"> Contrast to Green</td><td align="right">15·8</td><td align="right"> 5·1</td><td align="right"> 4·8</td></tr>
+<tr><td align="left"> Contrast to Violet</td><td align="right">15·9</td><td align="right"> 7·2</td><td align="right"> 4·2</td></tr>
+</table></div>
+
+<p>Thus to form the contrast to red took 13·5 of red,
+<span class="pagenum">[Pg 201]</span>
+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&mdash;</p>
+
+
+<div class="center">
+<table border="1" cellpadding="4" cellspacing="0" summary="">
+<tr><td align="right"> <span class="smcap">Contrast Colour to</span></td><td align="right"><span class="smcap">Red.</span></td><td align="right"> <span class="smcap">Green.</span></td><td align="right"> <span class="smcap">Violet.</span></td></tr>
+<tr><td align="left">Red</td><td align="center">&mdash;</td><td align="center"> 3·5</td><td align="center"> 16·7</td></tr>
+<tr><td align="left">Green</td><td align="center"> 15·7</td><td align="center"> 3·2</td><td align="center"> &mdash;</td></tr>
+<tr><td align="left">Violet</td><td align="center"> 19·4</td><td align="center"> 9·5</td><td align="center"> &mdash;</td></tr>
+</table></div>
+
+<p>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
+<span class="pagenum"><a name="Page_202" id="Page_202">[Pg 202]</a></span>
+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.</p>
+
+<p>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
+<span class="pagenum"><a name="Page_203" id="Page_203">[Pg 203]</a></span>
+the complementary colour, much diluted with white
+light.</p>
+
+<p>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.</p><br>
+<span class="pagenum">[Pg 205]</span>
+
+
+
+<hr style="width: 65%;">
+<h2>INDEX.</h2>
+
+
+<div class="center">
+<table border="0" cellpadding="4" cellspacing="0" summary="">
+<tr><td align="left">Absorption by red, blue, and green glasses,</td><td align="right"><a href="#Page_53">53</a> </td></tr>
+<tr><td align="left">Absorption of light in the earth's atmosphere,</td><td align="right"> <a href="#Page_67">67</a> </td></tr>
+<tr><td align="left">Absorption, reference to law of,</td><td align="right"><a href="#Page_53">53</a> </td></tr>
+<tr><td align="left">After-glow,</td><td align="right"><a href="#Page_74">74</a> </td></tr>
+<tr><td align="left">Arc light,</td><td align="right"><a href="#Page_20">20</a> </td></tr>
+<tr><td align="left">Artists and colours,</td><td align="right"> <a href="#Page_195">195</a> </td></tr>
+<tr><td align="left">Balmain's paint,</td><td align="right"><a href="#Page_33">33</a> </td></tr>
+<tr><td align="left">Black body,</td><td align="right"><a href="#Page_18">18</a> </td></tr>
+<tr><td align="left">Blindness to green,</td><td align="right"> <a href="#Page_142">142</a> </td></tr>
+<tr><td align="left">Blindness to red,</td><td align="right"><a href="#Page_79">79-142</a></td></tr>
+<tr><td align="left">Bromo-iodide of silver,</td><td align="right"><a href="#Page_136">136</a> </td></tr>
+<tr><td align="left">Carbon poles,</td><td align="right"><a href="#Page_20">20</a> </td></tr>
+<tr><td align="left">Carmine, light reflected from,</td><td align="right"> <a href="#Page_107">107</a> </td></tr>
+<tr><td align="left">" template,</td><td align="right"><a href="#Page_106">106</a> </td></tr>
+<tr><td align="left">Chlorophyll, green solution of,</td><td align="right"><a href="#Page_51">51</a> </td></tr>
+<tr><td align="left">Collimating lens, focal length of,</td><td align="right"><a href="#Page_22">22</a> </td></tr>
+<tr><td align="left">Colour, analysis of,</td><td align="right"><a href="#Page_52">52</a> </td></tr>
+<tr><td align="left">Colour-blind, red and green,</td><td align="right"><a href="#Page_79">79</a> , <a href="#Page_80">80</a> </td></tr>
+<tr><td align="left">Colour-blindness,</td><td align="right"><a href="#Page_142">142-146</a>, <a href="#Page_157">157</a> , <a href="#Page_159">159</a> </td></tr>
+<tr><td align="left">Colour constants,</td><td align="right"><a href="#Page_15">15</a> </td></tr>
+<tr><td align="left">Colour equations, formation of,</td><td align="right"><a href="#Page_147">147</a> , <a href="#Page_148">148</a> </td></tr>
+<tr><td align="left">Colour, extinction of, by white light,</td><td align="right"><a href="#Page_126">126</a> </td></tr>
+<tr><td align="left">Colour mixtures,</td><td align="right"><a href="#Page_113">113</a> </td></tr>
+<tr><td align="left">Colour patch apparatus,</td><td align="right"><a href="#Page_41">41-52</a> </td></tr>
+<tr><td align="left">Colour sensation of the eye,</td><td align="right"><a href="#Page_202">202</a> </td></tr>
+<tr><td align="left">Coloured discs, use of,</td><td align="right"><a href="#Page_189">189</a> </td></tr>
+<tr><td align="left">Coloured glasses, measurement of,</td><td align="right"><a href="#Page_162">162</a> </td></tr>
+<tr><td align="left">Colours, complementary of pigments,</td><td align="right"><a href="#Page_170">170-172</a> </td></tr>
+<tr><td align="left">Colours, complementary of spectrum,</td><td align="right"><a href="#Page_167">167</a> </td></tr>
+<tr><td align="left">Colours, how matched,</td><td align="right"><a href="#Page_156">156</a> , <a href="#Page_157">157</a> </td></tr>
+<tr><td align="left">Complementary colours, measurement of,</td><td align="right"><a href="#Page_173">173-178</a> </td></tr>
+<tr><td align="left">Compound colours, definition of,</td><td align="right"><a href="#Page_16">16</a> </td></tr>
+<tr><td align="left">Continuous spectrum,</td><td align="right"><a href="#Page_17">17</a> </td></tr>
+<tr><td align="left">Contrast colours,</td><td align="right"><a href="#Page_196">196-200</a> </td></tr>
+<tr><td align="left">Diffraction gratings,</td><td align="right"><a href="#Page_23">23</a> </td></tr>
+<tr><td align="left">" spectra,</td><td align="right"><a href="#Page_24">24</a> </td></tr>
+<tr><td align="left">Dimness and brightness of spectrum,</td><td align="right"><a href="#Page_29">29</a> </td></tr>
+<tr><td align="left">Discs, spinning,</td><td align="right"><a href="#Page_182">182</a> </td></tr>
+<tr><td align="left">Dust, particles of,</td><td align="right"><a href="#Page_62">62</a> </td></tr>
+<tr><td align="left">Electric light, contrast colours in,</td><td align="right"><a href="#Page_197">197</a> </td></tr>
+<tr><td align="left">Electric light, crater of positive pole of,</td><td align="right"><a href="#Page_20">20</a> </td></tr>
+<tr><td align="left">Emerald green, light reflected from,</td><td align="right"><a href="#Page_94">94</a> <span class="pagenum">[Pg 206]</span></td></tr>
+<tr><td align="left">Equations, colour,</td><td align="right"><a href="#Page_147">147</a> </td></tr>
+<tr><td align="left">Essentials of spectrum,</td><td align="right"><a href="#Page_22">22</a> </td></tr>
+<tr><td align="left">Extraction of colour by white light,</td><td align="right"><a href="#Page_126">126</a> </td></tr>
+<tr><td align="left">Extraction of white light by colour,</td><td align="right"><a href="#Page_131">131</a> </td></tr>
+<tr><td align="left">Eye, sensitiveness of,</td><td align="right"><a href="#Page_15">15</a> </td></tr>
+<tr><td align="left">Fatigue of the retina,</td><td align="right"><a href="#Page_202">202</a> </td></tr>
+<tr><td align="left">Fluorescence,</td><td align="right"><a href="#Page_31">31</a> </td></tr>
+<tr><td align="left">Fundamental sensations,</td><td align="right"><a href="#Page_140">140</a> </td></tr>
+<tr><td align="left">Gamboge, matching,</td><td align="right"><a href="#Page_189">189</a> </td></tr>
+<tr><td align="left">Glass, light from sheet of,</td><td align="right"><a href="#Page_14">14</a> </td></tr>
+<tr><td align="left">Glass prisms,</td><td align="right"><a href="#Page_21">21</a> , <a href="#Page_22">22</a> </td></tr>
+<tr><td align="left">Glow-worm,</td><td align="right"><a href="#Page_13">13</a> </td></tr>
+<tr><td align="left">Green colour-blindness,</td><td align="right"><a href="#Page_142">142</a> </td></tr>
+<tr><td align="left">Heating effect of radiation,</td><td align="right"><a href="#Page_38">38</a> </td></tr>
+<tr><td align="left">Hue,</td><td align="right"><a href="#Page_15">15</a> </td></tr>
+<tr><td align="left">Images, after,</td><td align="right"><a href="#Page_202">202</a> </td></tr>
+<tr><td align="left">Images, persistence of, on retina,</td><td align="right"><a href="#Page_179">179</a> </td></tr>
+<tr><td align="left">Impurity of simple colours,</td><td align="right"><a href="#Page_124">124</a> </td></tr>
+<tr><td align="left">Indicator of sectors,</td><td align="right"><a href="#Page_48">48</a> </td></tr>
+<tr><td align="left">Infra-red rays,</td><td align="right"><a href="#Page_32">32</a> </td></tr>
+<tr><td align="left">"&nbsp; photography with,</td><td align="right"><a href="#Page_34">34</a> </td></tr>
+<tr><td align="left">Insensitiveness of the yellow spot to green,</td><td align="right"><a href="#Page_118">118</a> </td></tr>
+<tr><td align="left">Intensities of limelight, gaslight, and blue sky compared,</td><td align="right"><a href="#Page_110">110</a> , <a href="#Page_121">121</a> </td></tr>
+<tr><td align="left">Interference,</td><td align="right"><a href="#Page_58">58</a> , <a href="#Page_59">59</a> </td></tr>
+<tr><td align="left">Interference bands on soap film,</td><td align="right"><a href="#Page_60">60</a> </td></tr>
+<tr><td align="left">Invisible spectrum, methods for showing existence of,</td><td align="right"><a href="#Page_32">32</a> , <a href="#Page_33">33</a> </td></tr>
+<tr><td align="left">Kœnig's curves,</td><td align="right"><a href="#Page_151">151</a> </td></tr>
+<tr><td align="left">Kœnig's experiments,</td><td align="right"><a href="#Page_140">140</a> </td></tr>
+<tr><td align="left">Law of the scattering by fine particles,</td><td align="right"><a href="#Page_66">66</a> </td></tr>
+<tr><td align="left">Light from sun, imitation of,</td><td align="right"><a href="#Page_63">63</a> </td></tr>
+<tr><td align="left">Light, quality of, illumining object,</td><td align="right"><a href="#Page_14">14</a> </td></tr>
+<tr><td align="left">Light scattered,</td><td align="right"><a href="#Page_62">62</a> </td></tr>
+<tr><td align="left">Limelight,</td><td align="right"><a href="#Page_19">19</a> </td></tr>
+<tr><td align="left">Lines in solar spectrum,</td><td align="right"><a href="#Page_26">26</a> </td></tr>
+<tr><td align="left">Luminosity,</td><td align="right"><a href="#Page_13">13</a> </td></tr>
+<tr><td align="left">Luminosity, addition of one to another,</td><td align="right"><a href="#Page_85">85-87</a> </td></tr>
+<tr><td align="left">Luminosity of colour,</td><td align="right"><a href="#Page_16">16</a> </td></tr>
+<tr><td align="left">Luminosity of pigments, methods of determining,</td><td align="right"><a href="#Page_81">81</a> , <a href="#Page_82">82</a> </td></tr>
+<tr><td align="left">Luminosity of spectrum to normal-eyed and colour-blind persons,</td><td align="right"><a href="#Page_76">76-78</a> </td></tr>
+<tr><td align="left">Luminosity of sun at different altitudes,</td><td align="right"><a href="#Page_69">69-71</a> </td></tr>
+<tr><td align="left">Maxwell's colour-box,</td><td align="right"><a href="#Page_152">152</a> , <a href="#Page_153">153</a> </td></tr>
+<tr><td align="left">Maxwell's discs,</td><td align="right"><a href="#Page_184">184-186</a> </td></tr>
+<tr><td align="left">Measurement of amount of light reflected by different pigments,</td><td align="right"><a href="#Page_88">88-92</a> </td></tr>
+<tr><td align="left">Metals, light reflected from,</td><td align="right"><a href="#Page_100">100</a> </td></tr>
+<tr><td align="left">Mock suns, cause of change of colour in,</td><td align="right"><a href="#Page_64">64</a> </td></tr>
+<tr><td align="left">Molecular physics,</td><td align="right"><a href="#Page_54">54</a> </td></tr>
+<tr><td align="left">Molecular swings,</td><td align="right"><a href="#Page_136">136</a> , <a href="#Page_137">137</a> </td></tr>
+<tr><td align="left">Monochromatic light,</td><td align="right"><a href="#Page_47">47</a> </td></tr>
+<tr><td align="left">Negative images,</td><td align="right"><a href="#Page_203">203</a> </td></tr>
+<tr><td align="left">Normal vision,</td><td align="right"><a href="#Page_77">77</a> </td></tr>
+<tr><td align="left">Orange, finding luminosity of,</td><td align="right"><a href="#Page_190">190</a> </td></tr>
+<tr><td align="left">Percentages of skylight, sunlight, and gaslight,</td><td align="right"><a href="#Page_110">110</a> , <a href="#Page_111">111</a> </td></tr>
+<tr><td align="left">Phosphorescence,</td><td align="right"><a href="#Page_32">32</a> , <a href="#Page_56">56</a> </td></tr>
+<tr><td align="left">Pigments, absorption by,</td><td align="right"><a href="#Page_57">57</a> , <a href="#Page_58">58</a> </td></tr>
+<tr><td align="left">Plan of forming spectrum,</td><td align="right"><a href="#Page_21">21</a> </td></tr>
+<tr><td align="left">Polished and uneven surfaces,</td><td align="right"><a href="#Page_13">13</a> </td></tr>
+<tr><td align="left">Primary colours, definition of,</td><td align="right"><a href="#Page_133">133-</a> <a href="#Page_135">135</a> </td></tr>
+<tr><td align="left">Prism, Iceland spar,</td><td align="right"><a href="#Page_96">96</a> <span class="pagenum">[Pg 207]</span></td></tr>
+<tr><td align="left">Prismatic spectrum into wave-lengths, conversion of,</td><td align="right"><a href="#Page_28">28</a> </td></tr>
+<tr><td align="left">Prisms, drawback to use of,</td><td align="right"><a href="#Page_23">23</a> </td></tr>
+<tr><td align="left">Prussian blue template,</td><td align="right"><a href="#Page_107">107</a> </td></tr>
+<tr><td align="left">"&nbsp; &nbsp; " light reflected from,</td><td align="right"><a href="#Page_107">107</a> </td></tr>
+<tr><td align="left">Purity of colour,</td><td align="right"><a href="#Page_16">16</a> </td></tr>
+<tr><td align="left">Rays, infra-red,</td><td align="right"><a href="#Page_34">34</a> </td></tr>
+<tr><td align="left">Rays, photography of dark,</td><td align="right"><a href="#Page_34">34</a> </td></tr>
+<tr><td align="left">Rays, ultra-violet,</td><td align="right"><a href="#Page_34">34</a> </td></tr>
+<tr><td align="left">Registering tint of pigments,</td><td align="right"><a href="#Page_116">116</a> </td></tr>
+<tr><td align="left">"&nbsp; &nbsp; "&nbsp; colours,</td><td align="right"><a href="#Page_156">156</a> </td></tr>
+<tr><td align="left">Retina, persistence of images on,</td><td align="right"><a href="#Page_179">179</a> </td></tr>
+<tr><td align="left">Ritter's rays,</td><td align="right"><a href="#Page_32">32</a> </td></tr>
+<tr><td align="left">Rood's colour scale,</td><td align="right"><a href="#Page_26">26</a> </td></tr>
+<tr><td align="left">Rotating sectors,</td><td align="right"><a href="#Page_46">46</a> </td></tr>
+<tr><td align="left">Scaling of spectrum,</td><td align="right"><a href="#Page_49">49</a> </td></tr>
+<tr><td align="left">Sectors, rotating,</td><td align="right"><a href="#Page_46">46</a> </td></tr>
+<tr><td align="left">Simple colours, how obtained,</td><td align="right"><a href="#Page_112">112</a> , <a href="#Page_113">113</a> </td></tr>
+<tr><td align="left">Slits placed in spectrum,</td><td align="right"><a href="#Page_113">113</a> </td></tr>
+<tr><td align="left">Soap-bubbles,</td><td align="right"><a href="#Page_58">58</a> , <a href="#Page_59">59</a> </td></tr>
+<tr><td align="left">Soap-films,</td><td align="right"><a href="#Page_59">59</a> </td></tr>
+<tr><td align="left">Spectrum, absorption of,</td><td align="right"><a href="#Page_51">51</a> , <a href="#Page_52">52</a> </td></tr>
+<tr><td align="left">Spectrum of sunlight,</td><td align="right"><a href="#Page_18">18</a> </td></tr>
+<tr><td align="left">Sun, mock,</td><td align="right"><a href="#Page_64">64</a> </td></tr>
+<tr><td align="left">Sunset clouds,</td><td align="right"><a href="#Page_68">68</a> , <a href="#Page_69">69</a> , <a href="#Page_72">72</a> , <a href="#Page_73">73</a> </td></tr>
+<tr><td align="left">Sunset sky,</td><td align="right"><a href="#Page_72">72</a> , <a href="#Page_73">73</a> </td></tr>
+<tr><td align="left">Thermopile, heating effects of,</td><td align="right"><a href="#Page_36">36</a> </td></tr>
+<tr><td align="left">Thermopile, principle of,</td><td align="right"><a href="#Page_35">35</a> </td></tr>
+<tr><td align="left">Ultramarine, light reflected from,</td><td align="right"><a href="#Page_95">95</a> </td></tr>
+<tr><td align="left">Ultra-violet rays,</td><td align="right"><a href="#Page_31">31</a> </td></tr>
+<tr><td align="left">Vermilion, light reflected from,</td><td align="right"><a href="#Page_93">93</a> </td></tr>
+<tr><td align="left">Vibrations of rays per second,</td><td align="right"><a href="#Page_55">55</a> </td></tr>
+<tr><td align="left">Violet bands, brightness of,</td><td align="right"><a href="#Page_21">21</a> </td></tr>
+<tr><td align="left">Visible and invisible parts of spectrum,</td><td align="right"><a href="#Page_30">30</a> </td></tr>
+<tr><td align="left">Water, particles of,</td><td align="right"><a href="#Page_62">62</a> </td></tr>
+<tr><td align="left">Wave-length of lines in solar spectrum,</td><td align="right"><a href="#Page_26">26</a> </td></tr>
+<tr><td align="left">White light and contrast colours,</td><td align="right"><a href="#Page_200">200-202</a> </td></tr>
+<tr><td align="left">White light, extinction of by colour,</td><td align="right"><a href="#Page_131">131</a> </td></tr>
+<tr><td align="left">White light, formation of by mixture of yellow and blue,</td><td align="right"><a href="#Page_125">125</a> </td></tr>
+<tr><td align="left">White light, how made,</td><td align="right"><a href="#Page_114">114</a> , <a href="#Page_115">115</a> , <a href="#Page_119">119-123</a> </td></tr>
+<tr><td align="left">White light, impression of,</td><td align="right"><a href="#Page_81">81</a> </td></tr>
+<tr><td align="left">Yellow and blue make white,</td><td align="right"><a href="#Page_125">125</a> </td></tr>
+<tr><td align="left">Yellow, chrome, luminosity of,</td><td align="right"><a href="#Page_191">191</a> </td></tr>
+<tr><td align="left">Yellow spot,</td><td align="right"><a href="#Page_117">117</a> </td></tr>
+<tr><td align="left">Young-Helmholtz theory,</td><td align="right"><a href="#Page_138">138</a> </td></tr>
+</table></div>
+
+
+
+<p>THE END.</p><p>
+<span class="pagenum">[Pg 208]</span>
+</p>
+
+
+
+<p>
+<span class="smcap">Richard Clay &amp; Sons, Limited,<br>
+London &amp; Bungay.</span><br>
+</p>
+<p><span class="pagenum">[Pg 209]</span></p>
+
+
+
+<hr style="width: 65%;">
+<h2>PUBLICATIONS
+
+<br>OF THE
+
+<br>Society for Promoting Christian Knowledge.</h2>
+
+
+<h3>THE ROMANCE OF SCIENCE.</h3>
+
+<p class='center'>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.</p>
+
+<p class='center'><i>Small Post 8vo, Cloth boards.</i></p>
+
+<blockquote><p><b>Coal, and what we get from it.</b> Expanded from the Notes of a Lecture
+delivered at the London Institution. By Professor <span class="smcap">Raphael Meldola</span>,
+F.R.S., F.I.C. With several Illustrations. 2<i>s.</i> 6<i>d.</i></p>
+
+<p><b>Colour Measurement and Mixture.</b> By Captain <span class="smcap">W. de W. Abney</span>, L.B.,
+R.E., F.R.S. With Numerous Illustrations. 2<i>s.</i> 6<i>d.</i></p>
+
+<p><b>The Making of Flowers.</b> By the Rev. Professor <span class="smcap">George Henslow</span>, M.A.,
+F.L.S., F.G.S. With Several Illustrations. 2<i>s.</i> 6<i>d.</i></p>
+
+<p><b>The Birth and Growth of Worlds.</b> A Lecture by Professor <span class="smcap">A. H. Green</span>,
+M.A., F.R.S. 1<i>s.</i></p>
+
+<p><b>Soap-Bubbles, and the Forces which Mould Them.</b> A course of Lectures
+by <span class="smcap">C. V. Boys</span>, A.R.S.M., F.R.S. With numerous diagrams. 2<i>s.</i> 6<i>d.</i></p>
+
+<p><b>Spinning Tops.</b> By Professor <span class="smcap">J. Perry</span>, M.E., D.Sc., F.R.S. With
+numerous diagrams. 2<i>s.</i> 6<i>d.</i></p>
+
+<p><b>Diseases of Plants.</b> By Professor <span class="smcap">Marshall Ward</span>. With Numerous
+Illustrations. 2<i>s.</i> 6<i>d.</i></p>
+
+<p><b>The Story of a Tinder-Box.</b> A course of Lectures by <span class="smcap">Charles Meymott
+Tidy</span>, M.B., M.S., F.C.S. With Numerous Illustrations. 2<i>s.</i></p>
+
+<p><b>Time and Tide.</b> A Romance of the Moon. By Sir <span class="smcap">Robert S. Ball</span>, LL.D.,
+Royal Astronomer of Ireland. With Illustrations. 2<i>s.</i> 6<i>d.</i>
+</p></blockquote>
+<p><span class="pagenum">[Pg 210]</span></p>
+
+<br>
+<h3>MANUALS OF HEALTH.</h3>
+
+<p class='center'><i>Fcap. 8vo, 128 pp., limp cloth, price 1s. each.</i></p>
+
+<blockquote><p><b>Health and Occupation.</b> By <span class="smcap">B. W. Richardson</span>, Esq., F.R.S., M.D.</p>
+
+<p><b>Habitation in Relation to Health (The).</b> By F. S. B. <span class="smcap">Chaumont</span>, M.D.,
+F.R.S.</p>
+
+<p><b>On Personal Care of Health.</b> By the late <span class="smcap">E. A. Parkes</span>, M.D., F.R.S.</p>
+
+<p><b>Water, Air, and Disinfectant.</b> By <span class="smcap">W. Noel Hartley</span>, Esq., King's
+College.
+</p></blockquote>
+
+<br>
+<h3>MANUALS OF ELEMENTARY SCIENCE.</h3>
+
+<p class='center'><i>Fcap. 8vo, 128 pp., with Illustrations, limp cloth, 1s. each.</i></p>
+
+<blockquote><p><b>Physiology.</b> By <span class="smcap">F. le Gros Clarke</span>, F.R.S., St. Thomas's Hospital.</p>
+
+<p><b>Geology.</b> By the Rev. <span class="smcap">T. G. Bonney</span>, M.A., F.G.S., Fellow and late
+Tutor of St. John's College, Cambridge.</p>
+
+<p><b>Chemistry.</b> By <span class="smcap">Albert J. Bernays</span>.</p>
+
+<p><b>Astronomy.</b> By <span class="smcap">W. H. M. Christie</span>, M.A., the Royal Observatory,
+Greenwich.</p>
+
+<p><b>Botany.</b> By <span class="smcap">Robert Bentley</span>, Professor of Botany in King's College,
+London.</p>
+
+<p><b>Zoology.</b> By <span class="smcap">Alfred Newton</span>, M.A., F.R.S., Professor of Zoology and
+Comparative Anatomy in the University of Cambridge.</p>
+
+<p><b>Matter and Motion.</b> By the late <span class="smcap">J. Clerk Maxwell</span>, M.A., Trinity
+College, Cambridge.</p>
+
+<p><b>Spectroscope and its Work (The).</b> By the late <span class="smcap">Richard A. Proctor</span>.</p>
+
+<p><b>Crystallography.</b> By <span class="smcap">Henry Palin Gurney</span>, M.A., Clare College,
+Cambridge.</p>
+
+<p><b>Electricity.</b> By the late Professor <span class="smcap">Fleeming Jenkin</span>.</p></blockquote>
+<p><span class="pagenum">[Pg 211]</span></p>
+
+<br>
+<h3>The Fathers for English Readers.</h3>
+
+<p class='center'><i>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.</i></p>
+
+<p class='center'>Fcap. 8vo, cloth, boards, 2s. each.</p>
+
+<p>
+<span style="margin-left: 2em;"><i>Leo the Great.</i></span><br>
+<span style="margin-left: 4em;">By the Rev. <span class="smcap">Charles Gore</span>, M.A.</span><br>
+<br>
+<span style="margin-left: 2em;"><i>Gregory the Great.</i> </span><br>
+<span style="margin-left: 4em;">By the Rev. <span class="smcap">J. Barmby</span>, B.D.</span><br>
+<br>
+<span style="margin-left: 2em;"><i>Saint Ambrose</i>: his Life, Times, and Teaching. </span><br>
+<span style="margin-left: 4em;">By the Rev. <span class="smcap">Robinson Thornton</span>, D.D.</span><br>
+<br>
+<span style="margin-left: 2em;"><i>Saint Athanasius</i>: his Life and Times.</span><br>
+<span style="margin-left: 4em;">By the Rev. <span class="smcap">R. Wheler Bush</span>. (2<i>s.</i> 6<i>d.</i>)</span><br>
+<br>
+<span style="margin-left: 2em;"><i>Saint Augustine.</i> </span><br>
+<span style="margin-left: 4em;">By the Rev. <span class="smcap">E. L. Cutts</span>, B.A.</span><br>
+<br>
+<span style="margin-left: 2em;"><i>Saint Basil the Great.</i> </span><br>
+<span style="margin-left: 4em;">By the Rev. <i>Richard T. Smith</i>, B.D.</span><br>
+<br>
+<span style="margin-left: 2em;"><i>Saint Bernard</i>: Abbot of Clairvaux, <span class="smcap">A.D.</span> 1091-1153.</span><br>
+<span style="margin-left: 4em;"> By the Rev. <span class="smcap">S. J. Eales</span>, M.A., D.C.L. (2<i>s.</i> 6<i>d.</i>)</span><br>
+<br>
+<span style="margin-left: 2em;"><i>Saint Hilary of Poitiers, and Saint Martin of Tours.</i> </span><br>
+<span style="margin-left: 4em;">By the Rev. <span class="smcap">J. Gibson Cazenove</span>, D.D.</span><br>
+<br>
+<span style="margin-left: 2em;"><i>Saint Jerome.</i> </span><br>
+<span style="margin-left: 4em;">By the Rev. <span class="smcap">Edward L. Cutts</span>, B.A.</span><br>
+<br>
+<span style="margin-left: 2em;"><i>Saint John of Damascus.</i> </span><br>
+<span style="margin-left: 4em;">By the Rev. <span class="smcap">J. H. Lupton</span>, M.A.</span><br>
+<br>
+<span style="margin-left: 2em;"><i>Saint Patrick</i>: his Life and Teaching. </span><br>
+<span style="margin-left: 4em;">By the Rev. <span class="smcap">E. J. Newell</span>, M.A. (2<i>s.</i> 6<i>d.</i>)</span><br>
+<br>
+<span style="margin-left: 2em;"><i>Synesius of Cyrene</i>, Philosopher and Bishop. </span><br>
+<span style="margin-left: 4em;">By <span class="smcap">Alice Gardner</span>.</span><br>
+<br>
+<span style="margin-left: 2em;"><i>The Apostolic Fathers.</i> </span><br>
+<span style="margin-left: 4em;">By the Rev. <span class="smcap">H. S. Holland</span>.</span><br>
+<br>
+<span style="margin-left: 2em;"><i>The Defenders of the Faith</i>; </span><br>
+<span style="margin-left: 2em;">or, The Christian Apologists of the Second and Third Centuries. </span><br>
+<span style="margin-left: 4em;">By the Rev. <span class="smcap">F. Watson</span>, M.A.</span><br>
+<br>
+<span style="margin-left: 2em;"><i>The Venerable Bede.</i> </span><br>
+<span style="margin-left: 4em;">By the Rev. <span class="smcap">G. F. Browne</span>.</span><br>
+</p>
+<p><span class="pagenum">[Pg 212]</span></p>
+
+<br>
+<h3>MISCELLANEOUS PUBLICATIONS.</h3>
+<div class="center">
+<table border="0" cellpadding="4" cellspacing="0" summary="">
+<tr><td align="left"></td><td align="left"></td><td align="left">&nbsp; &nbsp; &nbsp; &nbsp;<i>s.</i> <i>d.&nbsp; &nbsp;</i></td></tr>
+<tr><td align="left"><i>Animal Creation (The).</i> A popular Introduction to Zoology. By the late <span class="smcap">Thomas Rymer Jones</span>, F.R.S. With 488 Woodcuts. Post 8vo.</td><td align="left"><i>Cloth boards</i>&nbsp;</td><td align="right">7&nbsp; 6</td></tr>
+<tr><td align="left"><i>Beauty in Common Things.</i> Illustrated by 12 Drawings from Nature, by Mrs. J. W. Whymper, and printed in Colours, with descriptions by the Author of "Life Underground," &amp;c. 4to.</td><td align="left"><i>Cloth boards</i>&nbsp;</td><td align="right">10&nbsp; 6</td></tr>
+<tr><td align="left"><i>Birds' Nests and Eggs.</i> With 22 coloured plates of Eggs. Square 16mo.</td><td align="left"><i>Cloth boards</i>&nbsp;</td><td align="right">3&nbsp; 0</td></tr>
+<tr><td align="left"><i>British Birds in their Haunts.</i> By the late Rev. <span class="smcap">C. A. Johns</span>, B.A., F.L.S. With 190 engravings by Wolf and Whymper. Post 8vo.</td><td align="left"><i>Cloth boards</i>&nbsp;</td><td align="right">6&nbsp; 0</td></tr>
+<tr><td align="left"><i>Evenings at the Microscope</i>; or, Researches among the Minuter Organs and Forms of Animal Life. By <span class="smcap">Philip H. Gosse</span>, F.R.S. With 112 woodcuts. Post 8vo.</td><td align="left"><i>Cloth boards</i>&nbsp;</td><td align="right">4&nbsp; 0</td></tr>
+<tr><td align="left"><i>Fern Portfolio (The).</i>&nbsp; By <span class="smcap">Francis G. Heath</span>, Author of "Where to find Ferns," &amp;c. With 15 plates, elaborately drawn life-size, exquisitely coloured from Nature, and accompanied with descriptive text.</td><td align="left"><i>Cloth boards</i>&nbsp;</td><td align="right">8&nbsp; 0</td></tr>
+<tr><td align="left"><i>Fishes, Natural History of British</i>: their Structure, Economic Uses, and Capture by Net and Rod. By the late <span class="smcap">Frank Buckland</span>. With numerous illustrations. Crown 8vo.</td><td align="left"><i>Cloth boards</i>&nbsp;</td><td align="right">5&nbsp; 0</td></tr>
+<tr><td align="left"><i>Flowers of the Field.</i> By the late Rev. C. A. <span class="smcap">Johns</span>, B.A., F.L.S. With numerous woodcuts. Post 8vo.</td><td align="left"><i>Cloth boards</i>&nbsp;</td><td align="right">5&nbsp; 0<span class="pagenum">[Pg 213]</span></td></tr>
+<tr><td align="left"><i>Forest Trees (The) of Great Britain.</i> By the late Rev. <span class="smcap">C. A. Johns</span>, B.A., F.L.S. With 150 woodcuts. Post 8vo. &nbsp;</td><td align="left"><i>Cloth boards</i>&nbsp;</td><td align="right">5&nbsp; 0</td></tr>
+<tr><td align="left"><i>Freaks and Marvels of Plant Life</i>; or, Curiosities of Vegetation. By <span class="smcap">M. C. Cooke</span>, M.A., LL.D. With numerous illustrations. Post 8vo.</td><td align="left"><i>Cloth boards</i>&nbsp;</td><td align="right">6&nbsp; 0</td></tr>
+<tr><td align="left"><i>Man and his Handiwork.</i> By the late Rev. J. G. <span class="smcap">Wood</span>, Author of "Lane and Field," &amp;c. With about 500 illustrations. Large Post 8vo.</td><td align="left"><i>Cloth boards</i>&nbsp;</td><td align="right">10&nbsp; 6</td></tr>
+<tr><td align="left"><i>Natural History of the Bible (The).</i> By the Rev. <span class="smcap">Canon Tristram</span>, Author of "The Land of Israel," &amp;c. With numerous illustrations. Crown 8vo.</td><td align="left"><i>Cloth boards</i>&nbsp;</td><td align="right">5&nbsp; 0</td></tr>
+<tr><td align="left"><i>Nature and her Servants</i>; or, Sketches of the Animal Kingdom. By the Rev. <span class="smcap">Theodore Wood</span>. With numerous woodcuts. Large Post 8vo.</td><td align="left"><i>Cloth boards</i>&nbsp;</td><td align="right">5&nbsp; 0</td></tr>
+<tr><td align="left"><i>Ocean (The).</i> By <span class="smcap">Philip Henry Gosse</span>, F.R.S., Author of "Evenings at the Microscope." With 51 illustrations and woodcuts. Post 8vo.</td><td align="left"><i>Cloth boards</i>&nbsp;</td><td align="right">3&nbsp; 0</td></tr>
+<tr><td align="left"><i>Our Bird Allies.</i> By the Rev. <span class="smcap">Theodore Wood</span>. With numerous illustrations. Fcap. 8vo.</td><td align="left"><i>Cloth boards</i>&nbsp;</td><td align="right">2&nbsp; 6</td></tr>
+<tr><td align="left"><i>Our Insect Allies.</i> By the Rev. <span class="smcap">Theodore Wood</span>. With numerous illustrations. Fcap. 8vo.</td><td align="left"><i>Cloth boards</i>&nbsp;</td><td align="right">2&nbsp; 6</td></tr>
+<tr><td align="left"><i>Our Insect Enemies.</i> By the Rev. <span class="smcap">Theodore Wood</span>. With numerous illustrations. Fcap. 8vo.</td><td align="left"><i>Cloth boards</i>&nbsp;</td><td align="right">2&nbsp; 6</td></tr>
+<tr><td align="left"><i>Our Island Continent.</i>&nbsp; A Naturalist's Holiday in Australia. By <span class="smcap">J. E. Taylor</span>, F.L.S., F.G.S. With Map. Fcap. 8vo. &nbsp; &nbsp;</td><td align="left"><i>Cloth boards</i>&nbsp;</td><td align="right">2&nbsp; 6 <span class="pagenum">[Pg 214]</span></td></tr>
+<tr><td align="left"><i>Our Native Songsters.</i> By <span class="smcap">Anne Pratt</span>, Author of "Wild Flowers." With 72 coloured plates. 16mo.</td><td align="left"><i>Cloth boards</i>&nbsp;</td><td align="right">6&nbsp; 0</td></tr>
+<tr><td align="left"><i>Selborne (The Natural History of).</i> By the Rev. <span class="smcap">Gilbert White</span>.&nbsp; With Frontispiece, Map, and 50 woodcuts. Post 8vo.</td><td align="left"><i>Cloth boards</i>&nbsp;</td><td align="right">2&nbsp; 6</td></tr>
+<tr><td align="left"><i>Toilers in the Sea.</i> By <span class="smcap">M. C. Cooke</span>, M.A., LL.D. Post 8vo. With numerous illustrations.&nbsp; &nbsp;</td><td align="left"><i>Cloth boards</i>&nbsp;</td><td align="right">5&nbsp; 0</td></tr>
+<tr><td align="left"><i>Wayside Sketches.</i> By <span class="smcap">F. Edward Hulme</span>, F.L.S., F.S.A. With numerous illustrations. Crown 8vo.</td><td align="left"><i>Cloth boards</i>&nbsp;</td><td align="right">5&nbsp; 0</td></tr>
+<tr><td align="left"><i>Where to find Ferns.</i> By <span class="smcap">Francis G. Heath</span>, Author of "The Fern Portfolio," &amp;c. With numerous illustrations. Fcap. 8vo. &nbsp;</td><td align="left"><i>Cloth boards</i>&nbsp;</td><td align="right">1&nbsp; 6</td></tr>
+<tr><td align="left"><i>Wild Flowers.</i> By <span class="smcap">Anne Pratt</span>, Author of "Our Native Songsters," &amp;c. With 192 coloured plates. In two volumes. 16mo. &nbsp;</td><td align="left"><i>Cloth boards</i></td><td align="right">12&nbsp; 0</td></tr>
+</table></div><br>
+<hr style="width: 45%;">
+<p class='center'>LONDON:</p>
+
+<p class='center'>
+<span class="smcap">Northumberland Avenue, Charing Cross</span>, W.C.;<br>
+43, <span class="smcap">Queen Victoria Street</span>, E.C.<br>
+BRIGHTON: 135, <span class="smcap">North Street.</span><br>
+</p>
+<p><span class="pagenum">[Pg 215]</span>
+
+<h2>Transcribers Note</h2>
+<p>On Page 162 the equation :</p>
+<p class="center">∴ <i>Z</i> + <i>x´X´</i> + μ´<i>W</i> = ɑ<i>wW</i><br>
+<i>Z</i> = (ɑ<i>w</i> - μ´)<i>W</i> - <i>x´X´</i>
+</p>
+<p>is printed as:</p>
+<p class="center">∴ <i>Z</i> + <i>x₁X´</i> + μ´<i>W</i> = ɑ<i>wW</i><br>
+<i>Z</i> = (ɑ<i>w</i> - μ´)<i>W</i> - <i>x´X´</i>
+</p>
+
+
+
+
+
+
+
+
+<pre>
+
+
+
+
+
+End of Project Gutenberg's Colour Measurement and Mixture, by W. de W. Abney
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+</pre>
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+</body>
+</html>
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+Project Gutenberg's Colour Measurement and Mixture, by W. de W. Abney
+
+This eBook is for the use of anyone anywhere at no cost and with
+almost no restrictions whatsoever.  You may copy it, give it away or
+re-use it under the terms of the Project Gutenberg License included
+with this eBook or online at www.gutenberg.org
+
+
+Title: Colour Measurement and Mixture
+
+Author: W. de W. Abney
+
+Release Date: February 26, 2012 [EBook #38984]
+
+Language: English
+
+Character set encoding: ASCII
+
+*** START OF THIS PROJECT GUTENBERG EBOOK COLOUR MEASUREMENT AND MIXTURE ***
+
+
+
+
+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)
+
+
+
+
+
+
+
+
+
+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--K[oe]nig'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. K[oe]nig'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 formulae, 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/(3^4) to
+1/(4^4), 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.
+
+    +-----------+------+------+------+------+
+    | [Lamda]   | 7000 | 6000 | 5000 | 4000 |
+    +-----------+------+------+------+------+
+    |1/[Lamda]^4|    1 | .504 | .260 | .107 |
+    +-----------+------+------+------+------+
+
+Supposing [Lamda]7000 by the scattering of small particles loses one-tenth
+of its luminosity, then [Lamda]6000 would have .454 of its original
+brightness; [Lamda]5000, .234; and [Lamda]4000, .095; that is, whilst [Lamda]7000
+would lose one-tenth only of its luminosity, [Lamda]4000 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 [Lamda]^-4 was for
+convenience sake multiplied by 10^17 (thus [Lamda]6000^-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|[Lamda]^-4+-+----+----+----+----+----+----+----+----+----+
+  |   |      |  x10^17  |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 deg.
+    2     "             30 deg.
+    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 deg. 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 deg., 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 deg. 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 deg., 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 aesthetic 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 deg.* of aperture.
+    C     "      56 deg.      "
+    D     "      14 deg.      "
+    E     "      22 deg.      "
+    F     "     150 deg.      "
+    G     "    2100 deg.*     "
+
+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 deg. 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 x 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 K[oe]nig (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--K[oe]nig'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 deg., and at other times perhaps somewhere
+between 4 deg. and 5 deg. Now the variation in aperture between 4 deg., 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.--K[oe]nig's Curves of Colour Sensations.
+
+By taking a large number of colour equations, K[oe]nig, 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 K[oe]nig.
+
+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_ = [Alpha]_a_, _q_ = [Beta]_b_, _r_ = [Gamma]_c_,
+
+  Then we may write (ii.) as--
+
+    [Alpha]_aR_ + [Beta]_bG_ + [Gamma]_cV_ = _zZ_--(iii.).
+
+  Now either [Alpha], [Beta], or [Gamma] must be smaller than the other two. As an
+  example, if [Alpha] be the smallest, we multiply (i.) by [Alpha] when we get--
+
+    [Alpha]_aR_ + [Alpha]_bG_ + [Alpha]_cV_= [Alpha]_wW_--(iv.)
+
+    Subtracting (iv.) from (iii.) and we get--
+
+    ([Beta]-[Alpha])_bG_ + ([Gamma]-[Alpha])_cV_ = _zZ_ - [Alpha]_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
+([Beta]-[Alpha])_b_ + ([Gamma]-[Alpha])_c_], and [Mu] the luminosity of the small quantity of
+white added.
+
+We then get _zZ_ = _xX_ + ([Mu] + [Alpha]) _W_.
+
+Here we have the colour _Z_ in terms of a single ray, and of white
+light.
+
+This same holds good when in (ii.) [Gamma] is smaller than [Alpha] and [Beta]; but it
+does not do so should it happen that [Beta] 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.) [Alpha] to be larger than [Gamma] and [Gamma] than [Beta], then we must add PhphPhi Pi mu [Phi]_bG_ +
+[Theta]_cV_ and we have
+
+    [Alpha]_aR_ + ([Beta] + [Phi])_bG_ + ([Gamma] + [Theta])_cV_ = _nW_ = _Z_ + [Phi]_bG_ + [Theta]_cV_;
+    but ([Beta] + [Phi]), and ([Gamma] + [Theta]) each equal [Alpha] Therefore _n_ = [Alpha]_w_.
+                 Therefore _Z_ + [Phi]_bG_ + [Theta]_cV_= [Alpha]_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 [Mu]', which
+must equal ([Phi]_b_ + [Theta]_c_).
+
+    Therefore _Z_ + _x'X_' + [Mu]'_W_ = [Alpha]_wW_
+       _Z_ = ([Alpha]_w_ - [Mu]')_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 deg. 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             C[oe]rulium, 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 Bruecke'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 deg. 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
+
+    Therefore 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 versa_, 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 deg.
+    E = 143 deg.
+    U = 93 deg.
+        ----
+        360 deg.
+
+and to make the same grey it required
+
+    X = 278 deg.
+    W =  82 deg.
+        ----
+        360 deg.
+
+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 (124x36)/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 deg.
+    E = 148 deg.
+    U = 93 deg.
+        ----
+        360 deg.
+
+which matched with
+
+    X = 244 deg.
+    W = 116 deg.
+
+(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 deg. }
+    U  150 deg. } = { W   85 deg.
+    O   95 deg. }   { X  275 deg.
+
+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 x 30 + 150 x 4.4 + 95 O = (85 + 3.4 x 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 x 30 + 204 x 4.4 + 121 Y = (101 + 3.4 x 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
+
+
+  K[oe]nig's curves,                                          151
+
+  K[oe]nig'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.
+
+
+
+
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+
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+  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:
+    Therefore _Z_ + _x'X_' + [Mu]'_W_ = [Alpha]_wW_
+       _Z_ = ([Alpha]_w_ - [Mu]')_W_ - _x'X'_
+Is printed as
+    Therefore _Z_ + _x1X_' + [Mu]'_W_ = [Alpha]_wW_
+       _Z_ = ([Alpha]_w_ - [Mu]')_W_ - _x'X'_
+in the original.
+
+
+
+
+
+End of Project Gutenberg's Colour Measurement and Mixture, by W. de W. Abney
+
+*** END OF THIS PROJECT GUTENBERG EBOOK COLOUR MEASUREMENT AND MIXTURE ***
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