172 V + 188 E = 75 Y + 45 W + 240 X. This equation is full of meaning. It tells us in the first place what we have already known, that V and E are one or both impure colours, and that when rotated together in the proportions indicated, they produce at least a luminosity of white equal to 53/360 of a white disc (as the black used reflected just 3·4% of white light). Further, it tells us that we can obtain the luminosity of Y, when we know the luminosities of V and E. At page 186, the luminosities of these colours are given as 36 and 30 respectively, white being 100. This makes the luminosity of the colours on the left hand of the equation 17·2 + 15·67, or 32·87, and on the right =75/360= Y + 14·76, and consequently the luminosity of Y = 86·9. In the same way we can obtain any other colour in terms of these standards. We may here show how we can obtain the luminosity of any colour by means of the three inner discs, and the black and white outer discs. We have already shown that any colour may be matched by the combination of not more than two simple colours, after deducting white from it; and from this we deduce that any coloured pigment will form a grey with some two of the three coloured discs, V, E, and U; and this being done we can then calculate the luminosity. For instance, with an orange-coloured pigment we should proceed to make a disc of the same diameter as that of the three above; an inspection would show us that in this colour red predominates, and therefore we could do without the red disc. We should then alter the proportions of V, U, and O, till they gave a match which was the same as that of a grey given by the rotating black and white sectors. In an experiment with an orange of this kind, the following results were obtained-- E 115° } U 150° } = { W 85° O 95° } { X 275° We can now from these deduce the luminosity of the orange employed in this case. The luminosities of E and U, as already found, were 30 and 4·4, whilst the black (X) reflected 3·4% of white light; we thus get the following equations-- 115 × 30 + 150 × 4·4 + 95 O = (85 + 3·4 × 275) 100. This gives 95 O = 9435 - (3450 + 660). O = 56. That is, the luminosity of the orange is ·56 that of white; by direct measurement it was ·57. In a similar way the luminosity of chrome yellow (Y) is found. In this case-- E 35 } U 204 } = { W 101 Y 121 } { X 259 Similar equations were formed as the above. 35 × 30 + 204 × 4·4 + 121 Y = (101 + 3·4 × 259) 100 whence Y = 77·6. That is, the luminosity of the chrome yellow is ·78; the same as was obtained by direct measurement.