7 
opaque colour, red for instance. Suppose we start with a 
white area A, then the quantity of white light given 
off normally may he denoted by juA. Suppose now a great 
number of red points to fall upon this surface and to be 
equally diffused, so that the eye does nob perceive detached 
red and white points, but a surface uniformly tinted of a 
light red colour. Let a be the area occupied by the red 
points ; then the quantity of red light we may denote by 
li X a, and the uncovered white area will be A ~a, and the 
quantity of white light given off will be ja(A — a). Suppose 
now a second series of red points to fall upon the surface, 
and that they distribute themselves without bias, and also 
that there is no chemical action. Then the uncovered 
white area will be - ^ - and the red area will be 
A ( A — 4 
A 
Hence after the second operation the light 
ju(A— a ) 2 
given off will consist of white light 
and of red 
light 
| A— ^ ^ - 1 or as we may write them /u AR 2 and 
jUiA(X— R 2 ), where R=X— If the operation be repeated 
n times the residual whiteness will become juAR w and the 
redness will become /u a A(X — R w ). If n becomes infinite the 
whiteness vanishes and the red becomes ju x A, being the red 
light that would be given off if we supposed the surface to 
be covered with red points only. 
A method for experimentally testing the foregoing theory 
relative to the intensity of the residual whiteness, after 
admixture with a perfect black, would be as follows. Take 
three surfaces of different degrees of whiteness (A, B, C), 
due to admixture with p, q , r units of black ; look at the 
surfaces through some fluid containing in solution some 
soluble black substance, adjust the columns so that the 
intensity of the transmitted light shall be the same. 
