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, or _x_ parts of X can be matched by _a_ parts of A, combined with _b_ parts of B and _c_ parts of C. If the sign of one of the quantities _a_, _b_, or _c_ is negative, it indicates that that colour must be combined with X to match the other two. Now Maxwell was able to show that, if A, B, C be properly selected, nearly every other colour can be matched by positive combinations of these three. These three colours, then, are primary colours, and nearly every other colour can be matched by a combination of the three primary colours. Experiments, however, with coloured discs, such as were undertaken by Young, Forbes and Maxwell, were not capable of giving satisfactory results. The colours of the discs were not pure spectrum colours, and varied to some extent with the nature of the incident light. It was for this reason that Helmholtz in 1852 experimented with the spectrum, and that Maxwell about the same time invented his colour box.