It will often be—more often than not—necessary, however, to dilute the spectrum colour thrown on the white half of the patch with a trace of white light. By reference to our previous experiments we arrive at what may appear an unlooked-for result, that no matter what the colour may be, we can refer it to one ray of the spectrum, together with a percentage of added white light. It is worthy of remark, that the place in the spectrum where the simple and the compound colours match, varies according to the kind of light with which the pigment is illuminated. This we can show in a very simple way.
To persons who are totally colour-blind to one sensation, viz. the green or the red, the matching of a compound colour with a simple one in the spectrum should possess no difficulties. Taking the trichromic theory of three sensations for the normal-eyed person, it is evident that only the following classes of sensations are possible in the normal-eyed, the green colour-blind and the red colour-blind—
| Normal-eye. | Green colour-blind. | Red colour-blind. |
| Red | Red | — |
| Green | — | Green. |
| Violet | Violet | Violet. |
| Mixtures of red and green | — | — |
| Mixtures of red and violet | Mixtures of red and violet | — |
| Mixtures of green and violet | Mixtures of green and violet. | |
| Mixtures of red, green and violet | — |
If we take as a type of colour-blindness the green colour-blind person, we see that every colour in the spectrum must be either pure red or violet, or else these colours mixed with more or less white light, since these two sensations when excited in certain proportions give the sensation of white. At one place, which is commonly called the neutral point, the proportions of the two colours are such that the impression there given is only white; hence it follows that, between this neutral point and each end of the spectrum, the rays are mixtures of violet and white, or red and white, the dilution of the colours varying from no white to all white. As every compound colour must be a mixture of the same two colours in certain proportions, it follows that the green colour-blind person can match every compound colour with some one ray of the spectrum, and that every colour must to him be either red or violet, diluted with different proportions of white light.
In the same way, a person who is colour-blind to the red can also match any colour with a single spectrum colour, and he will see it as green or violet diluted with more or less white light. This can be readily understood, but it is not quite so plain how any colour sensation felt by the normal eye can be referred to the spectrum.
If we take three rays in the spectrum—one in the red between C and the red Lithium line which we will call R, another in the green between F and b which we will call G, and a third in the violet near G but on the H side of it, and which we may call V—then by varying their intensities (which is equivalent to varying the luminosities) and mixing them, we can give the same impression to the eye that any compound colour gives; and that any intermediate simple spectrum colour gives, if very slightly diluted with white light. With these same three colours, but in different proportions, we can also give the impression of white light to the eye. The intermediate spectrum colours between the green and the violet rays selected when slightly diluted are imitated by mixing these rays together in different proportions, and similarly those lying between the red and the green by mixing together these rays in different proportions—and there is some ray present in the spectrum which, when very slightly diluted with white light, has the same colorific effect on the eye as the mixtures of the pairs v and b, and G and R, in any proportions whatever.
Let the luminosities of the rays R, G and V, which give the impression of white light, be a, b and c units respectively, and p, q and r those which give that of the colour which has to be registered and reproduced. We then get the following equations—where W is white, w its luminosity, Z the colour, and z its luminosity—
aR + bG + cV = wW—(i.);
pR + qG + rV = zZ—(ii.);
Then evidently—
(a + b + c) = w; and (p + q + r) = z.