THEORY OF MIXED COLOURS. 71 



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 inquiry. 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 he W— w. If now we add another unit 

 of the black, it might at first sight appear that the re- 

 maining whiteness would be W — iw i and that, after the ad- 

 dition of n units, 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 quan- 

 tity of BaS0 4 being 10 grams in each case and the carbon 

 increasing from o*oo6 gram to 0*048 gram. The differ- 

 ence in tint between the successive mixtures seemed to 

 diminish more rapidly than seemed consistent with such 

 a law of diminution of whiteness. The difference between 

 the seventh and eighth mixtures 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 

 following 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 constant fraction of the initial whiteness. Suppose M 

 to be the mass of the white, and W its initial whiteness; 

 let m be the mass of the black. After mixing with the 



