| 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.