THEORY OF MIXED COLOURS. 75 



If we allow a third series of black points to fall upon 

 the surface and to be equally distributed, the remaining 

 white area will be AR ? , and if W 3 denote the quantity of 

 white light, 



W ? =W R 3 . 



If we suppose the operation to be repeated n times, the 

 expression for the remaining white light will be W R\ 

 Hence the ratio of the initial to the final whiteness would 



be p^. Both trains of reasoning concur in giving a similar 



expression for the intensity of the whiteness. In some 

 papers which I have contributed to this Society I have 

 pointed out that the law expressing the intensity of trans- 

 mitted light when we dissolve Q units of colouring-matter 

 in a transparent medium, is of the form XuiS. Hence we 

 have this curious result : when the intensity of an opaque 

 white is diminished by mixture with an opaque black, the 

 mathematical expression for the intensity of the whiteness 

 is of the same form as if we had dissolved the black in a 

 transparent medium and surveyed a white area through it. 

 In the foregoing reasoning I have supposed the particles, 

 after admixture, to distribute themselves without bias. It 

 becomes a question of much interest, when we mix 

 particles of heterogeneous matter, is this always the case ? 

 Under some circumstances they may be brought within 

 the sphere of molecular attractions, and these may have 

 some influence in the distribution ; in other words it is 

 possible to conceive that the particles will distribute them- 

 selves with some bias. Here, again, it seems to me that 

 so far from such speculations on the intensity of colour 

 of mixtures being fruitless, they may even extend the ap- 

 plication of colorimetry ; for while experimental agreement 

 with the theory would strengthen the theory, even negation 



