white light with the various prismatic hues. The general effect of this proceeding will be to diminish the action of the coloured light; the mixture will indeed present to the eye more light, but it will be paler; the colour-element will begin to be pushed into the background. Conversely, if we now should subject our mixture of white and coloured light to analysis by a second prism, we should infallibly detect the presence of the white as well as of the coloured light; or, if no white light were present, that would also

be equally apparent. Taking all this into consideration, it is evident that, when a particular colour 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 clue toward a classification of colours: our pure standard colours are to be those found in the spectrum; the coloured light coming from the surfaces of natural objects, or from painted surfaces, we must compare with the hues 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 coloured light will be found quite marked. To illustrate by an example: if white paper be painted with vermilion, and compared with the solar spectrum, it will be noticed that it corresponds in general hue with a certain portion of the red space; but the two colours 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 from the mirror (Fig. 6), it will become possible to match the two colours; and, if we know how much 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, mixed with twenty per cent. of white light. If we make the experiment with a surface painted with "emerald green," we shall obtain about the same result, while we shall find that artificial ultramarine-blue reflects about twenty-five per cent. of white light. In all of these cases the total amount of light reflected by the coloured paper is of course taken as 100, and the results here given are to be regarded only as approximations. In every case some white light is sure to be present; its effect is to soften the colour 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-grey, bluish-grey, or reddishgrey. If one part of red light is mixed with sixteen parts of white light, the mixture appears of a pale pinkish hue. The specific effects produced by the mixture of white with coloured light will be considered in Chapter XII.; it is enough for us at present to have obtained an idea of one of the constants of colour, 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 colour, 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 grey light.

Next let us suppose that in our study of these matters we have presented to us for examination two coloured surfaces, which we find reflect in both cases 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, perhaps, 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-coloured 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 colour; it is our second colour-constant. This word luminosity is also often used by artists in an entirely different sense, they calling colour 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 colour" is sometimes used in a somewhat analogous sense by them, but the ideas are so totally different that there is little risk of confusion.

The determination of the second constant is practicable in some cases; it presents itself always in the shape of a difficult photometric problem. The relative brightness of the colours 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 colours which, taken together, constitute white light. Quite recently a set of measurements was made in different regions of the spectrum by Vierordt, who referred the points measured to the fixed lines, as is usual in such studies.* Reducing his designations of the different regions of the spectrum to those of our spectral chart, which includes 1,000 parts from A to H (see previous chapter), and supplying the colours. from the observations of the present writer, we obtain the following table:

* C. Vierordt, Poggendorff's "Annalen," Band cxxxvii., S. 200.

TABLE SHOWING THE LUMINOSITY OF DIFFERENT REGIONS OF THE PRISMATIC

Let us suppose

The author finds that with the aid of rotating disks the second constant can often be determined.* that we wish to determine the luminosity of paper painted 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. 7. On the same axis is fastened a double disk of black and of white paper, so arranged that the proportions of the black and white can be varied at will. When the whole is set in rapid rotation, the colour of the vermilion paper will of course not be altered, but the black and white will blend into a grey. This grey can be altered in its brightness, till it seems about as luminous as the red (Fig. 8). 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 the white paper. This

* "American Journal of Science and Arts," February, 1878.
+ See Maxwell's "Disks," chapter x.

is of course based on the assumption that the black paper reflects no light; it actually does reflect from two to six per cent., the reflecting power of white paper being put at 100. The black disk used by the author reflected 5.2 per

cent. of white light; to meet this a correction was introduced, and a series of measurements made, some of the more important of which are given in the following table:

These results were afterward tested by the use of a set of disks, the colours of which were complementary to those mentioned in the table, and these additional experiments and calculations showed that the original measurements differed but little from the truth. This agreement proved also the correctness of Grassmann's assumption, that the total

* In thick paste. Washed on as a water-colour. Artificial, as a paste.