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diff --git a/38984-8.txt b/38984-8.txt new file mode 100644 index 0000000..a22785d --- /dev/null +++ b/38984-8.txt @@ -0,0 +1,5202 @@ +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 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/(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 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 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 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 + + 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 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 (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. + + + + +Richard Clay & Sons, Limited, London & Bungay. + + + + +PUBLICATIONS OF THE + +=Society for Promoting Christian Knowledge.= + + +THE ROMANCE OF SCIENCE. + +A series of books which shows that science has for the masses as great +interest as, and more edification than, the romances of the day. + +_Small Post 8vo, Cloth boards._ + +=Coal, and what we get from it.= Expanded from the Notes of a +Lecture delivered at the London Institution. 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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. 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