5 
(2) we have ■- ^ C ~ -=a—-q } whence q— Cl ^ A a \ and for the 
remaining white area we have the expression 
A — a— a ( A ~ a ) = A^l— 0= AR 2 
and the quantity of white light given off will he juAR 2 ; 
also this quantity of light will appear equally distributed 
over the whole surface; hence, if W 3 denote this white 
light we may write W 2 =pAR 2 ~WoR 2 . 
If we allow a third series of black points to fall upon the 
surface, and to be equally distributed, the remaining white 
ones will be AR 3 , and if W 3 denote the quantity of white 
light 
W 3 = W 0 R 3 
If we suppose the operation to be repeated n times. The 
expression for the remaining white light will be W 0 R n . 
Hence the ratio of the initial to the final whiteness would be 
l 
Both trains of reasoning concur in giving a similar expres- 
sion 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 transmitted light 
when we dissolve Q units of colouring matter in a trans- 
parent medium, is of the form Eat c Q . Hence we have this 
curious result : when the intensity of an opaque white is 
diminished by mixture with an opaque black, the mathe- 
matical expression for the intensity of the whiteness is of 
the same form as if we had dissolved the black in a trans- 
parent 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 be- 
comes 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 
