2 
so by additional water, but the painter in oil or distemper, if 
he wishes to accomplish a similar object, has to mix with 
some opaque white. This, then, is the matter which I first 
propose to consider. A coloured powder and a white powder 
are intimately blended ; what is the law of the intensity of 
colour ? As a typical case, I take the mixture of black 
and white, because it was such a mixture that suggested 
this enquiry. In what follows I suppose the powders 
to consist of indefinitely small particles, which do not exert 
any chemical action on each other. Suppose that we take 
a mass of some white substance, and add to it a small 
quantity of some black substance ; then we shall take away 
some portion of its whiteness — if w denote the whiteness 
lost, and W the initial whiteness — then the remaining 
whiteness would be W — w. If now we add another unit of 
the black, it might at first sight appear that the remaining 
whiteness would be W— 2 w, and after the addition of n units, 
that the remaining whiteness would be W —nw. For some 
experiments which I was making, I had prepared eight grey 
tints by mixing BaS0 4 with carbon ; the quantity of BaS0 4 
being 10 grms. in each case, and the carbon increasing from 
0‘006 grms. to 0-048 grms. The difference in tint between the 
successive mixtures seemed to diminish more rapidly than 
seemed consistent with such a law of diminution of white- 
ness. The difference between the seventh and eighth 
mixture was almost inappreciable, but according to the 
foregoing supposition, the difference between successive 
pairs should be the same. 
On considering the matter further, I was led to the fol- 
lowing train of reasoning. If we take equal masses of 
white of different intensities and to each add the same bulk 
of black, then in each case the whiteness lost will be a con- 
stant fraction of the initial whiteness. Suppose M to be 
the mass of the white, and W 0 its initial whiteness, let m 
be the mass of the black. After mixing with the white it 
