Very convenient discs for producing colours by rotation of sectors may be made by the following: vermilion (V), emerald green (E), French ultramarine blue (U), chrome yellow (Y), lamp-black (X), and (zinc) white (W). With these nearly every colour can be produced, or its value derived. The chrome yellow disc is somewhat superfluous, but is sometimes useful. The alteration in the proportions of the colours can be readily made by Clark-Maxwell's plan. From the circumference to the centre he cut the discs open, as at _ab_ (Fig. 42). Any moderate number of discs, similarly cut, may be slipt over one another, and only a sector of each is left visible. It should be remarked that this necessitates the rotating apparatus being viewed with a direct light, as in the case of two or three overlapping discs it is impossible to keep them entirely flat, and shades are apt to be introduced. If we wish to produce a white, or rather a grey, from three colours, we can take three small discs of V, E and U, of equal diameter, and behind them place discs of black and white, of larger diameter, rotating the whole five on a common centre. We shall find that by altering the proportions of the three first we can get a grey which can be exactly matched by a mixture of black and white, X and W. It has already been shown that even lamp-black reflects a certain amount of white light, so this amount of reflected white light has to be added to the white in the outside sectors. In the sectors used in the following experiments it was found that the following proportions of the three colours were required-- V = 124° E = 143° U = 93° ---- 360° and to make the same grey it required X = 278° W = 82° ---- 360° Now the black reflected 3·4% of white light, so that really the proportions of black and white were X = 268·6 W = 91·4 ----- 360·0 These matches were made in the light emitted by the crater of the positive pole of the electric light, and are correct only for this light. The greys here are dark greys, and such greys can be matched exactly by throwing the white light in which the comparisons were made on a white card, and reducing the intensity by means of the rotating sectors. We can prove whether our matches are fairly correct from our previous measures of the luminosity of these three colours, in comparison with that of white. The luminosities of V, E, and U, as found from the measures (pp. 93-95), are 36, 30, and 4·4, white being 100; 124 of V would have a luminosity of (124×36)/360, or 12·4; 143 of E would have 11·92; and 93 of U would have 1·14; which, added to either, give a luminosity of 25·46. The luminosity of 91·4/360 of white, which is that of the mixture of black and white, comes to 25·39, so that we may assume our observations have been fairly correct.