# Popular Science Monthly/Volume 9/October 1876/The Constants of Color

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THE
POPULAR SCIENCE
MONTHLY.
OCTOBER, 1876.
* THE CONSTANTS OF COLOR.
By Prof. O. N. ROOD,
OF COLUMBIA COLLEGE.
THE tints produced by Nature and art are so manifold, often so vague and indefinite, so affected by their environment, or by the illumination under which they are seen, that at first it might well appear as though nothing about them were constant; as though they had no fixed properties which could be used in reducing them to order, and in arranging in a simple but vast series the immense multitude of which they consist.
Let us examine the matter more closely. We have seen that when a single set of waves acts on the eye a color-sensation is produced, which is perfectly well defined, and which can be indicated with precision by referring it to some portion of the spectrum. We have also found that, when waves of light having all possible lengths act on the eye simultaneously, the sensation of white is produced. Let us suppose that by the first method a definite color-sensation is generated, and afterward by the second method the sensation of white is added to it: white light is added to or mixed with colored light. This mixture may be accomplished with an ordinary spectroscope, by removing the scale from the scale-telescope, and replacing it by a vertical slit, as indicated in Fig. 1, which is a view from above. Then, if white light be allowed to enter this slit, it will be reflected from the surface of the prism into the observing-telescope, and we shall find that the spectrum is crossed by a vertical band of white light. By moving with the hand the scale-telescope, this white band may be made to travel slowly over the whole spectrum, and furnish us with a series of mixtures of white light with the various prismatic tints. (See Fig. 2.) The general effect of this proceeding will be to diminish the action of the colored light; the resultant light will indeed ​sent to the eye more light, but it will appear paler; the color-element will begin to be pushed into the background. Conversely, if we now should subject our mixture of white and colored light to analysis by a second spectroscope, we should infallibly detect the presence of the white as well as of the colored light; or, if no white light were present, that would also be equally apparent.
Fig. 1.—O the observing-telescope; S the scale-telescope; L the source of light which furnishes the spectrum; W the white light which is projected on the spectrum.
Taking all this into consideration, it is evident that when a particular color is presented to us we can affirm that it is perfectly pure, viz., entirely free from white light; or that it contains mingled with it a larger or smaller proportion of this foreign element. This furnishes us with our first clew toward a classification of colors: our pure standard colors are to be those found in the spectrum; the colored light coming from the surfaces of natural objects, or from painted surfaces, we must compare with the tints of the spectrum. If this is done, in almost every case the presence of more or less white light will be detected; in the great majority of instances its preponderance over the colored light will be found quite marked. To illustrate by an example: If white paper be painted with vermilion, and compared with a solar spectrum, it will be found that it corresponds in general tone with a certain portion of the red space; but the two colors never match perfectly, that from the paper always appearing too pale. If, now, white light be added to the pure spectral tint, by reflecting a small amount of it into the observing-telescope, it will become possible to match the two colors, and, if we know what proportion of white light has been added, we can afterward say that the light reflected ​from the vermilion consists, for example, of eighty per cent, of red light from such a region of the spectrum, plus twenty per cent, of white light. If we set the amount of light reflected by white paper as 100, then a surface painted with "emerald-green" reflects about eight parts of white light; artificial ultramarine, two or three parts; red lead, seven or eight, etc. Some white light is always present; its general effect is to soften the color and reduce its action on the eye; when the proportion of white is very large, only a faint reminiscence of the original hue remains; we say the tint is greenish-gray,
Fig. 2.—Spectrum crossed by Band of Superimposed White Light.
bluish-gray, or reddish-gray. The specific effects produced by the mixture of white with colored light will be considered in a future chapter; it is enough for us at present to have obtained an idea of one of the constants of color, viz., its purity. The same word, it may be observed, is often used by artists in an entirely different sense: they will remark of a painting that it is noticeable for the purity of its color, meaning only that the tints in it have no tendency to look dull or dirty, but not at all implying the absence of white or gray light.
Next let us suppose that in our study of these matters we have presented to us for examination two colored surfaces, which we find reflect in both oases eight-tenths red light and two-tenths white light. In spite of this the tints may not match, one of them being much brighter than the other, containing, say, twice as much red light and twice as much white light; having, in other words, twice as great brightness or luminosity. The only mode of causing the tints to match will be to expose the darker-colored surface to a stronger light, or the brighter surface to one that is feebler. It is evident, then, that brightness or luminosity is one of the properties by which we can* define color; it is our second color-constant. This word luminosity is also often used by artists in an entirely different sense, they calling-color in a painting luminous simply because it recalls to the mind the impression of light, not because it actually reflects much light to ​the eye. The term bright color is sometimes used in a somewhat analogous sense, but the ideas are so totally different that there is little risk of confusion.
The practical determination of the second constant is possible in a great many cases; it presents itself always in the shape of a rather troublesome photometric problem, capable of a more or less accurate solution. The relative brightness of the colors of the solar spectrum is one of the most interesting of these problems, as its solution would serve to give some idea of the relative brightness of the colors, which, taken together, constitute white light. Quite recently a set of measurements were made in different regions of the spectrum by Vierordt, who denoted the points measured by the fixed lines, as is usual in such studies. The following table will serve to give an idea of his results:
| Color. | Degree of Luminosity. |
| Dark red | 800 |
| Red | 4,930 |
| Red, slightly orange | 11,000 |
| Orange red | 27,730 |
| Orange | 69,850 |
| Yellow | 78,910 |
| Green | 30,330 |
| Cyan blue | 11,000 |
| Blue | 4,930 |
| Ultramarine blue | 906 |
| Violet | 359 |
| " | 131 |
| " | 58 |
| " | 9 |
These measurements were made on a spectrum obtained by a glass prism, which, as has been mentioned in a previous chapter, contracts the red, orange, and yellow spaces unduly, and hence increases their illumination disproportionately. It is to be hoped that a corresponding set of measurements will soon be made on the normal spectrum, furnished by a ruled plate. If we should multiply the luminosity of the colors in either kind of spectrum by their extent or areas, we should obtain measures of the relative amounts of these several tints in white light.
By the simple method of rotating disks we can very roughly determine the second constant in the case of a colored surface, for example, of paper tinted with vermilion. A circular disk, about six inches in diameter, is cut from the paper, and placed on a rotation apparatus, as indicated in Fig. 3. On the same axis is fastened a double disk of black-and-white paper, so arranged that the proportions of black-and-white can be varied at will. When the whole is set in rapid rotation, the color of the vermilion paper will of course not ​be altered; but the black-and-white will blend into a gray. This gray can be altered in its brightness till it seems about as luminous as the red. If we find, for example, that with the disk three-quarters black and one-quarter white an equality appears to be established, we conclude that the luminosity of our red surface is twenty-five per cent, of that of white paper. This is of course based on the supposition that the black paper reflects no light; it actually reflects from two to five per cent., the reflecting power of white paper being put at 100. The results thus obtained are always inexact, and the same observer
will often obtain different results on different days, though those of a single day may agree pretty well among themselves. In the appendix to this chapter, a peculiar photometer will be described, which has been contrived by the author for the purpose of comparing more accurately together the relative luminosity of different colored surfaces, or that of colored and white surfaces.
But to resume our search for color-constants. We may meet with two portions of colored light, having the same degree of purity and the same apparent brightness, which nevertheless appear to the eye totally different; one may excite the sensation of blue, the other that of red; we say the tones are entirely different. The tone of the color is, then, our third and last constant, or, as the physicist would say, the degree of refrangibility, or the wave-length of the light. It has in a previous chapter been shown that the spectrum offers all possible tones except the purples, well arranged in an orderly series; and the purples themselves can be produced with some trouble, by causing the blue or violet of the spectrum to mingle in certain proportions with the red. Rutherford's automatic six-prism spectroscope can very conveniently be employed for the determination of the tone. (See Fig. 5.) A peculiar eye-piece is to be used, which isolates a little slice of the spectrum in its upper half, as indicated in Fig. 6. In the lower half of the field the fixed lines are seen, and the tone selected as ​matching the color under examination can be located by their aid. Afterward, if it is considered desirable, white light can be added to the spectral tint, till it is subdued sufficiently to render exact comparison possible.
Fig. 5.—Facsimile of Rutherford's Drawing of Six-Prism Spectroscope.—{American Journal of Sciences and Arts, 1865.)
The experimental determination of the color-constants is beset with a considerable amount of difficulty, even in the simplest cases, such as cardboards covered with pigments. The best mode of proceeding appears to be to call the luminosity of white cardboard 100, and then to determine photometrically the comparative luminosity of the colored cardboards. The measurement of the amount of white light reflected along with the colored is still more troublesome, and the result likely to be somewhat less exact, while the determination of the tone, or third constant, is moderately easy under favorable circumstances. One of the uses of such determinations is the ​production of a set of standard colored disks with known constants, which can afterward be combined with each other, as well as with standard black or white disks, so as to generate at will, with ease and certainty, an immense number of tints whose constants will be known. If we make a record of the constants involved in such experiments, we can afterward reproduce the tints just as they originally were, or alter them to any desirable extent. To carry out the letter of this it will of course be necessary to view the standard disks under similar illuminations at different times, a point which can be secured with the
Fig. 6.—Eye-Piece for isolating the Tints of the Spectrum.
aid of the photometer above referred to. The standard disks can also be used for building up a set of standard charts, containing a vast variety of tints of known composition, arranged methodically with regard to purity, luminosity, and tone. These matters will be considered at some length in a separate chapter, and are now only hinted at as a justification for the trouble we have been at in defining the constants of color.
There is another point to be touched on in this connection. One of the most noticeable things about colors is their difference in intensity. Colors are intense when they excel both in purity and brightness; for it is quite evident that, however pure the colored light may be, it still will produce very little effect on the eye if its total quantity be small; and, on the other hand, it is plain that its action on the same organ will not be considerable if it is diluted with much white light. Purity and brightness, or luminosity, are, then, the factors on which intensity depends. We shall see hereafter that this is strictly true only within certain limits, and that an inordinate increase of luminosity is attended with a loss of intensity of hue.
Having defined the three constants of color, it will be interesting to inquire into the sensitiveness of the eye in these directions. This subject has lately been studied with care by Aubert, who made an extensive set of observations with the aid of colored disks. It was ​found that the addition of one part of white light to 360 parts of pure colored light produced a change which was perceptible to the eye; smaller amounts failed to bring about this result. It was also ascertained that mingling pure colored light with from 120 to 180 parts of white light caused it to become invisible, the hue being no longer distinguishable from white. Differences in luminosity as small as $^1$⁄$_{120}$ to $^1$⁄$_{180}$ could under favorable circumstances be perceived. It hence followed that irregularities in the illumination or distribution of pigment over a surface, which were smaller than $^1$⁄$_{180}$ of the total amount of light reflected, could no longer be noticed by the eye. Experiments with red, orange, and blue disks were made on the sensitiveness of the eye to changes of tone or refrangibility; thus the combination of the blue disk with a minute portion of the red disk altered its hue by moving it a little toward violet; on reversing the case, or adding a little blue to the red disk, the tone of the latter moved in the direction of purple. Similar combinations were made with the other disks. Aubert ascertained, in this way, that recognizable changes of tone could be produced by the addition of quantities of colored light as small as from $^1$⁄$_{100}$ to $^1$⁄$_{300}$ of the total amount of light involved. From such data he calculated that in a solar spectrum at least 1,000 distinguishable tones are visible. But we can still recognize these tones when the light producing them is subjected to considerable variation in brightness. Let us limit ourselves to 1,000 slight variations, which we can produce by gradually increasing the brightness of our spectrum, till it finally is ten times as luminous as it originally was. This will furnish us with a million tones, differing perceptibly from each other. If each of these tones is again varied 300 times, by the addition of different quantities of white light, it carries up the number of hues we are able to distinguish as high as 300,000,000. In this calculation no account is taken of the purples, or of colors which are very bright or very faint, or mixed with very much white light. For these it will hardly be extravagant to demand another 100,000,000; we reach thus the astonishing conclusion that the human eye under favorable circumstances is able to distinguish as many as 400,000,000 different hues!
* ↑ C. Vierordt, Poggendorfs Annalen, Band cxxxvii., S. 200.
* ↑ Aubert, "Physiologie der Netzhaut," Breslau, 1865.