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 U O | 115° 150° 95° | } | = | { | W X | 85° 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 U O | 35 204 121 | } | = | { | W X | 101 259 |