CHAPTER IV.
An independent investigator of this subject was Clerk Maxwell, who experimented with a “colour-box” of his own design, by which he mixed the simple colours of the spectrum, and the results he got are really the first which are founded on measurement. He measured something, but hardly arrived at the colour sensation. His colour-box took two forms, both on the same principles, so only one will be here described, the diagram and description being taken from his classic paper in the Philosophical Transactions of the Royal Society for 1860.
“The experimental method which I have used consists in forming a combination of three colours belonging to different portions of the spectrum, the quantity of each being so adjusted that the mixture shall be white, and equal in intensity to a given white. [Fig. 14] represents the instrument for making the observations. It consists of two tubes, or long boxes of deal, of rectangular section, joined together at an angle of about 100°.
Fig. 14.
Maxwell’s colour-box.
“The part A K is about five feet long, seven inches broad, and four deep; K N is about two feet long, five inches broad, and four deep; B D is a partition parallel to the side of the long box. The whole of the inside of the instrument is painted black, and the only openings are at the end A C, and at E. At the angle there is a lid, which is opened when the optical parts have to be adjusted or cleaned.
“At E is a fine vertical slit, L is a lens; at P there are two equilateral prisms. The slit E, the lens L, and the prisms P are so adjusted, that when light is admitted at E, a pure spectrum is formed at A B, the extremity of the long box. A mirror at M is also adjusted so as to reflect the light from E, along the narrow compartment of the box to B C.
“At A B is a rectangular frame of brass, having a rectangular aperture of six inches by one. On this frame are placed six brass sliders, X Y Z. Each of these carries a knife-edge of brass in the plane of the surface of the frame.
“These six movable knife-edges form three slits, X Y Z, which may be so adjusted as to coincide with any three portions of the pure spectrum formed by light from E. The intervals behind the sliders are closed by hinged shutters, which allow the sliders to move without letting light pass between them.
“The inner edge of the brass frame is graduated to twentieths of an inch, so that the position of any slit can be read off. The breadth of the slit is ascertained by means of a wedge-shaped piece of metal, six inches long, and tapering to a point from a width of half an inch. This is gently inserted into each slit, and the breadth is determined by the distance to which it enters, the divisions on the wedge corresponding to the 200th of an inch difference in breadth, so that the unit of breadth is ·005 inch.
“Now suppose light to enter at E, to pass through the lens, and to be refracted by the two prisms at P, a pure spectrum, showing Fraunhofer’s lines, is formed at A B, but only that part is allowed to pass which falls on the three slits, X Y Z. The rest is stopped by the shutters. Suppose that the portion falling on X belongs to the red part of the spectrum; then, of the white light entering at E, only the red will come through the slit X. If we were to admit red light at X, it would be refracted to E, by the principle in optics that the course of the ray may be reversed.
“If, instead of red light, we were to admit white light at X, still only red light would come to E; for all other light would be either more or less refracted, and would not reach the slit at E. Applying the eye at the slit E, we should see the prism P uniformly illuminated with red light, of the kind corresponding to the part of the spectrum which falls on the slit X, when white light is admitted at E.
“Let the slit Y correspond to another portion of the spectrum, say the green; then if white light is admitted at Y, the prism, as seen by an eye at E, will be uniformly illuminated with green light; and if white light be admitted at X and Y simultaneously, the colour seen at E will be a compound of red and green, the proportions depending on the breadth of the slits and the intensity of the light which enters them. The third slit Z, enables us to combine any three kinds of light in any given proportions, so that an eye at E shall see the face of the prism at P, uniformly illuminated with the colour resulting from the combination of the three. The position of these three rays in the spectrum is found by admitting the light at E, and comparing the position of the slits with the position of the principal fixed lines; and the breadth of the slits is determined by means of the wedges.
“At the same time, white light is admitted through B C to the mirror of black glass at M, whence it is reflected to E, past the edge of the prism at P, so that the eye at E sees through the lens a field consisting of two portions, separated by the edge of the prism; that on the left hand being compounded of three colours of the spectrum refracted by the prism, while that on the right hand is white light reflected from the mirror. By adjusting the slits properly, these two portions of the field may be made equal, both in colour and brightness, so that the edge of the prism becomes almost invisible.
“In making experiments, the instrument was placed on a table in a room moderately lighted, with the end A B turned towards a large board covered with white paper, and placed in the open air, so as to be uniformly illuminated by the sun. In this way the three slits and the mirror M were all illuminated with white light of the same intensity, and all were affected in the same ratio by any change of illumination; so that if the two halves of the field were rendered equal when the sun was under a cloud, they were found nearly correct when the sun again appeared. No experiments, however, were considered good unless the sun remained uniformly bright during the whole series of experiments.
“After each set of experiments light was admitted at E, and the position of the fixed lines D and F of the spectrum was read off on the scale at A B. It was found that after the instrument had been in use some time these positions were invariable, showing that the eye-hole, the prisms, and the scale might be considered as rigidly connected.”
Fig. 15.
With this instrument he made mixtures of three colours, to match with white. By shifting the slits into various positions and taking as his three standard colours a red near the C line, a green near E, and a blue between F and G (see frontispiece), he obtained a variety of matches, from which he formed equations. After eliminating, or rather reducing the errors to the most probable value by the method of least squares, he got from his matches with white a table of colour values in terms of the three standard colours, from which the diagram of the spectrum ([Fig. 15]) was made. (The heights of the dotted curves are derived from the widths of the slits, and the continuous curve is the sum of these heights.) Now what appears to be a properly chosen colour does not necessarily stimulate only one sensation. Indeed the probabilities are against it, except in the extreme red and extreme violet. If colours intermediate to the standard colours be matched by a mixture of the latter, we do not arrive at any solution of the amount of stimulation of each sensation, since the chosen standard colours themselves may be due to a stimulation of all three sensations. As a matter of fact, Clerk Maxwell chose colours which do not best represent the colour sensations. The red is too near the yellow, as is also the green. The blue should also be nearer the violet end of the spectrum than the position which he chose for it. We may take it, then, that except as a first approximation, Clerk Maxwell’s diagrams need not be seriously taken into account. The diagram itself shows that the colour sensations are not represented by the colours he chose. Supposing any one in whom the sensation of green is absent were examining the spectrum, there would, according to the diagram, be no light visible at the green at E. Anticipating for a moment what we shall deal with in detail shortly, it may be stated that in cases where it is proved that a green sensation is absent, there is no position in any part of the spectrum where there is an absence of light. Had he chosen any other green, the same criticism would have been valid. The diagram as it stands is really a diagram of colour mixtures in terms of three arbitrarily chosen colours, and not of colour sensations. It merely indicates what proportions were needed of the three colours, which he took as standards, to match the intermediate spectrum colours. The negative sign in some of the equations—given in the appendix, [page 201]—may be somewhat puzzling to those who have not made colour matches, but not to those who have actually made experiments. It means that where it is present no match of colour by a mixture of the standard colours is possible; and that it would be only possible if a certain quantity of the colour to which is attached a negative sign were to be abstracted—an impossible condition to fulfil, but one which may often occur in colour-matching experiments. Later you will find that when colours are chosen as standards so that the resulting equations give no negative sign for any colour, we have a criterion as to the colours which give the nearest approach to the true sensations. The next diagram ([Fig. 16]) of colour sensations is due to Kœnig, who investigated the subject with Von Helmholtz. By a modified method, which perhaps need not be explained in detail here, he produced them, and they must be apparently not far from the actual state of things, supposing this theory be proved to be true. For my own part, I am under the impression that the positions of the colours which most nearly approach the colour sensations might be slightly altered in regard to the green and the blue, for reasons that will subsequently be given when the later experiments of General Festing and myself come to be described. For the immediate purpose of the lecture, the curves are sufficiently accurate, and I will ask you to notice what they tell us. It is presupposed in these diagrams that, if the three colour-perceiving apparatus are equally stimulated, a sensation of white will be produced; and the reverse, of course, is true, in that white will give rise to equal stimulation of the three apparatus. It follows, then, that in the parts of the spectrum where all three curves of sensation are seen to take a part in the production of a colour, such as at the E line, the colour is really due to the extra stimulation of one or two of the apparatus above that required to produce a certain amount of white. The colour in every part of the spectrum may be represented by not more than two sensations, with a proportion of white. In the orange and scarlet there are only two sensations excited, without any sensible amount of white, as the amount of violet sensation is extremely small. At the extreme ends of the spectrum only one sensation—the red or the violet—is excited; but in the region of the green the colour must be largely diluted with the sensation of white. As an example, we may take the part of the spectrum where the red and the violet sensation curves cut each other. At this point the green sensation curve rises higher than the intersection of the other curves. The red and the violet sensations have only to be mixed with an equal amount of the green sensation to make white, so that the height of the green sensation curve above the point of intersection represents the amount of pure green sensation which is stimulated. The colour is therefore caused by the green sensation, largely diluted with white. A scrutiny of the curves will show that at no point is the green sensation so free from any other as at this point, if we regard white by itself as a neutral colour. Looking at these figures, we can readily see what effect the removal of any one or two of the three sensations would have upon the colour vision of the individual. The probabilities, however, against two of the three sensations being absent must evidently be very much smaller than that there should be an absence of only one of the sensations, either red, green, or violet.
Fig. 16.
It will be well that we should also have before us the theory which is the only serious rival to that of Young, viz., that of Hering. In the report of the Colour Vision Committee there is an excellent description of this theory. As it was furnished by Dr. Michael Foster, we may be sure that the ideas of its originator are correctly given, and therefore I will quote it in his words:—
“Another theory, that of Hering, starts from the observation that when we examine our own sensations of light we find that certain of these seem to be quite distinct in nature from each other, so that each is something sui generis, whereas we easily recognise all other colour sensations as various mixtures of these. Thus, the sensation of red and the sensation of yellow are to us quite distinct; we do not recognise anything common to the two, but orange is obviously a mixture of red and yellow. Green and blue are equally distinct from each other and from red and yellow, but in violet and purple we recognise a mixture of red and blue. White again is quite distinct from all the colours in the narrower sense of that word, and black, which we must accept as a sensation, as an affection of consciousness, even if we regard it as the absence of sensation from the field of vision, is again distinct from everything else. Hence the sensations caused by different kinds of light or by the absence of light, which thus appear to us quite distinct, and which we may speak of as ‘native’ or ‘fundamental’ sensations, are white, black, red, yellow, green, blue. Each of these seems to us to have nothing in common with any of the others, whereas in all other colours we can recognise a mixture of two or more of these. This result of common experience suggests the idea that these fundamental sensations are the primary sensations, concerning which we are enquiring. And Hering’s theory attempts to reconcile, in some such way as follows, the various facts of colour vision with the supposition that we possess these six fundamental sensations. The six sensations readily fall into three pairs, the members of each pair having analogous relations to each other. In each pair the one colour is complementary to the other—white to black, red to green, and yellow to blue. Now, in the chemical changes undergone by living subjects, we may recognise two main phases, an upward constructive phase, in which matter previously not living becomes living, and a downward destructive phase, in which living matter breaks down into dead or less living matter. Adopting this view, we may, on the one hand, suppose that rays of light, differing in their wave-length, may affect the chemical changes of the visual substance in different ways, some promoting constructive changes (changes of assimilation), others promoting destructive changes (changes of dissimilation); and on the other hand, that the different changes in the visual substance may give rise to different sensations.
“We may, for instance, suppose that there exists in the retina a visual substance of such a kind that when rays of light of certain wave-lengths—the longer ones, for instance, of the red side of the spectrum—fall upon it, dissimilative changes are induced or encouraged, while assimilative changes are similarly promoted by the incidence of rays of other wave-lengths, the shorter ones of the blue side. But it must be remembered that in dealing with sensations it is difficult to determine what part of the apparatus causes them; we may accordingly extend the above view to the whole visual apparatus, central as well as peripheral, and suppose that when rays of a certain wave-length fall upon the retina, they in some way or other, in some part or other of the visual apparatus, induce or promote dissimilative changes, and so give rise to sensations of a certain kind, while rays of another wave-length similarly induce or promote assimilative changes, and so give rise to a sensation of a different kind.
“The hypothesis of Hering applies this view to the six fundamental sensations spoken of above, and supposes that each of the three pairs is the outcome of a particular set of dissimilative and assimilative changes. It supposes the existence of what we may call a red-green visual substance of such a nature that so long as dissimilative and assimilative changes are in equilibrium, we experience no sensation; but when dissimilative changes are increased, we experience a sensation of (fundamental) red, and when assimilative changes are increased, we experience a sensation of (fundamental) green.
“A similar yellow-blue visual substance is supposed to furnish, through dissimilative changes a yellow, through assimilative changes a blue sensation; and a white-black visual substance similarly provides for a dissimilative sensation of white and an assimilative sensation of black. The two members of each pair are therefore not only complementary but also antagonistic. Further, these substances are supposed to be of such a kind that while the white-black substance is influenced in the same way, though in different degrees, by rays along the whole range of the spectrum, the two other substances are differently influenced by rays of different wave-length. Thus, in the part of the spectrum which we call red, rays promote great dissimilative changes of the red-green substance with comparatively slight effect on the yellow-blue substance; hence our sensation of red.
Fig. 17.
“In that part of the spectrum which we call yellow, the rays effect great dissimilative changes of the yellow-blue substance; but their action on the red-green substance does not lead to an excess of either dissimilation or assimilation, this substance being neutral to them; hence our sensation of yellow. The green rays, again, promote assimilation of the red-green substance, leaving the assimilation of the yellow-blue substance equal to its dissimilation; and similarly blue rays cause assimilation of the yellow-blue substance, and leave the red-green substance neutral. Finally, at the extreme blue end of the spectrum, the rays once more provoke dissimilation of the red-green substance, and by adding red to blue give violet. When orange rays fall on the retina, there is an excess of dissimilation of both the red-green and the yellow-blue substance; when greenish-blue rays are perceived, there is an excess of assimilation of both these substances; and other intermediate hues correspond to various degrees of dissimilation or assimilation of the several visual substances. When all the rays together fall upon the retina, the red-green and yellow-blue substances remain in equilibrium, but the white-black substance undergoes great changes of dissimilation, and we say the light is white.”
It has been said by the same writer that this theory is tri-chromic. For my own part I do not see that it is so in the sense in which that word is used in the theory of Young. It may be a tetra-chromic, for as far as colour is concerned the black-white sensation must be excluded; but it appears to me that it cannot be strictly brought under the head of tri-chromic.