This same holds good when in (ii.) ɣ is smaller than ɑ and β; but it does not do so should it happen that β is the smallest, for there is no part of the spectrum which contains simple colours giving the same sensation to the eye as mixtures of red and blue. There is, however, a very simple way in which the registration of such a colour (which it must be remarked must be of a purple tone) can be effected. It can be fixed by its complementary. To do this we must add to (ii.) a certain amount of _R_ and _V_, which will make the whole white. Thus, suppose in (iii.) ɑ to be larger than ɣ and ɣ than β, then we must add ϕ_bG_ + θ_cV_ and we have ɑ_aR_ + (β + ϕ)_bG_ + (ɣ + θ)_cV_ = _nW_ = _Z_ + ϕ_bG_ + θ_cV_; but (β + ϕ), and (ɣ + θ) each equal ɑ ∴ _n_ = ɑ_w_. ∴ _Z_ + ϕ_bG_ + θ_cV_= ɑ_wW_. Now between _V_ and _G_ in the spectrum there is some single colour which gives the sensation of the mixture of _G_ and _V_. Let it be _X_´ with luminosity _x_´, together with white whose luminosity is μ´, which must equal (ϕ_b_ + θ_c_). ∴ _Z_ + _x´X_´ + μ´_W_ = ɑ_wW_ _Z_ = (ɑ_w_ - μ´)_W_ - _x´X´_ which again is the colour expressed in terms of white light less the complementary colour. We have thus arrived at the very simple deduction that the hue and luminosity of any colour, however compounded, may be registered by a reference to white light and a single ray of the spectrum. In practice this dominant ray is very easy to find. Suppose we wish to determine numerically the colour of a signal-green glass in the electric light, we should proceed as follows-- The colour patch apparatus (described in chapter IV.) is employed, and the coloured glass is placed between the silvered mirror which reflects the beam already reflected from the first surface of the first prism of the spectrum apparatus, and the screen, and a square image of that surface of the prism showing the tint of the glass is formed on the screen by means of the lens. Touching this image is a square patch of white light formed by the re-combination of the spectrum by means of another lens. An opaque slide containing an adjustable slit is moved across the spectrum in the manner described in the chapter referred to until the colour of this last patch is approximately the same hue as that of the glass.