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_. Let _p_ = ɑ_a_, _q_ = β_b_, _r_ = ɣ_c_, Then we may write (ii.) as-- ɑ_aR_ + β_bG_ + ɣ_cV_ = _zZ_--(iii.). Now either ɑ, β, or ɣ must be smaller than the other two. As an example, if ɑ be the smallest, we multiply (i.) by ɑ when we get-- ɑ_aR_ + ɑ_bG_ + ɑ_cV_= ɑ_wW_--(iv.) Subtracting (iv.) from (iii.) and we get-- (β-ɑ)_bG_ + (ɣ-ɑ)_cV_ = _zZ_ - ɑ_wW_. Now it has already been stated that between _V_ and _G_ there is some ray which gives the same sensation of colour, mixed with a very small quantity of white light, as the above mixture of _V_ and _G_--let us call it _X_ and its luminosity _x_ [_x_ being evidently equal to (β-ɑ)_b_ + (ɣ-ɑ)_c_], and μ the luminosity of the small quantity of white added. We then get _zZ_ = _xX_ + (μ + ɑ) _W_. Here we have the colour _Z_ in terms of a single ray, and of white light.