intensity of the mixture of masses of differently coloured light is equal to the sum of the intensities of the separate components.

But to resume our search for colour-constants. We may meet with two portions of coloured 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 hues are entirely different. The hue of the colour is, then, our third and last constant, or, as the physicist would say, the degree of refrangibility, or the wave-length of the light. In the preceding chapter it has been shown that the spectrum offers all possible hues, 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.

For the determination of the hue, an ordinary one-prism spectroscope can be used; it is only necessary to add a little contrivance which enables the observer to isolate at will any

small portion of the spectrum. This object is easily attained by introducing into the eye-piece of the instrument

FIG. 10. Rutherfurd's Automatic Spectroscope.

a diaphragm perforated by a very narrow slit (see Fig. 9). The observer then sees in the upper part of the field of view the selected spectral colour; in the lower part of the field the scale is visible, and with its aid the precise position of the prismatic hue can be determined. Instead of using a

scale divided into equal parts, it is often advantageous to employ the plan suggested by Dr. J. C. Dalton, and used by him for determining the position of certain absorption bands. Dr. Dalton employs as a scale a minute photograph which shows the positions of the fixed lines, and divides up the spaces between them conveniently. Fig. 9 exhibits the appearance of the field of view and the scale. For more accurate work Rutherfurd's automatic six-prism spectroscope can be employed (see Fig. 10*). A diffraction grating can also be used-in those cases where the student of colour is so fortunate as to possess one. With a very perfect grating of this kind, for which the author was indebted to Mr. Rutherfurd, the third constant was determined for a number of coloured disks. The following table gives their positions in a normal spectrum having from A to H 1,000 parts; the corresponding wave-lengths are also given :

We have seen that the first colour-constant has reference to the purity of the colour, or indicates the relative amount of white light mixed with it. This constant is in all cases

* Fig. 10 is a facsimile of Rutherfurd's drawing of his six-prism spectroscope ("American Journal of Science and Arts," 1865).

+ See Chapter iv. for an account of the grating.

difficult to determine; probably something might be effected by carrying out practically the idea suggested in Fig. 6, by making the necessary additions to the apparatus there indicated. It would be necessary to measure the relative luminosity of the selected spectral hue and the white light, and then to mix them in proper proportions, till the mixture matched the colour of the painted paper, etc. The second and third colour-constants can be more easily determined. It may be well here to refer to the terms used to indicate these constants. For the first constant, the word purity, in the sense of freedom from white light (or from the sensation of white), is well adapted. The term luminosity will be employed in this work to indicate the second constant ; the third constant will generally be referred to by the term hue. Colours are often also called intense, or saturated, when they excel both in purity and luminosity; for it is quite evident that, however pure the coloured light may be, it still will produce very little effect on the eye if its total quantity be small; 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 luminosity are, then, the factors on which the intensity or saturation 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 or saturation.

Having defined the three constants of colour, it will be interesting to inquire into the sensitiveness of the eye in these directions. This subject has been studied by Aubert, who made an extensive set of observations with the aid of coloured disks.* It was found that the addition of one part of white light to 360 parts of coloured light produced a change which was perceptible to the eye; smaller amounts failed to bring about this result. It was also ascertained

* Aubert, "Physiologie der Netzhaut," Breslau, 1865.

that mingling the coloured light of a disk with from 120 to 180 parts of white light (from white paper) caused it to become imperceptible, the hue being no longer distinguishable from that of the paper.* Differences in luminosity as small as to could also, under favourable circumstances, be perceived. It hence followed that irregularities in the illumination, or distribution of pigment over a surface, which were smaller than 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 hue or wave-length; thus, the combination of the blue disk with a minute portion of the red disk altered its hue, moving it a little toward violet; on reversing the case, or adding a little blue to the red disk, the hue 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 hue could be produced, by the addition of quantities of coloured light, as small as from too of the total amount of light involved. From such data he calculated that in a solar spectrum at least a thousand distinguishable hues are visible. But we can still recognize these hues, when the light producing them is subjected to considerable variation in luminosity. Let us limit ourselves to 100 slight variations, which we can produce by gradually increasing the brightness of our spectrum, till it finally is five times as luminous as it originally was. This will furnish us with a hundred thousand hues, differing perceptibly from each other. If each of these hues is again varied

*To obtain correct results it is of course necessary to know the luminosity of the coloured disk as compared with the white disk, for in the above results by Aubert they are considered to be equal. With the aid of the table of luminosities previously given, this correction can be made, and it will be found that four or five times as much white light is actually necessary as is indicated above.

Compare Chapter x.