Now, in this experiment, black is not a colour; practically no light reaches the eye from a dead black. We have, however, to fill up the circumference of the top in some way which will not affect the impression on the retina arising from the mixture of the blue and yellow; this we can do by using the black disc.
Thus we have shown that 66·6 parts of red and 33·4 parts of green produce the same chromatic effect as 29·1 of yellow and 24·1 of blue. Similarly in this manner a match can be arranged between any four colours and black, the black being necessary to complete the circumference of the discs.
Thus using A, B, C, D to denote the various colours, a, b, c, d the amounts of each colour taken, we can get a series of results expressed as follows: a parts of A together with b parts of B match c parts of C together with d parts of D; or we may write this as an equation thus:—
a A + b B = c C + d D,
where the + stands for “combined with,” and the = for “matches in tint.”
We may also write the above—
d D = a A + b B - c C,
or d parts of D can be matched by a proper combination of colours A, B, C. The sign - shows that in order to make the match we have to combine the colour C with D; the combination then matches a mixture of A and B.
In this way we can form a number of equations for all possible colours, and if we like to take any three colours A, B, C as standards, we obtain a result which may be written generally—
x X = a A + b B + c C,