4 
points to fall on this surface, being equally distributed. 
Then the surface will appear to the eye of a grey tint, but 
grey and white are quantities of the same kind and are 
therefore comparable. What we call grey being a white of 
diminished intensity. Suppose a to be the area occupied 
by the black points. Then A — a will be the uncovered 
white area, and the quantity of white light given off by 
this will be ju(A— a); moreover this quantity of white light 
will appear uniformly diffused over the surface. If we 
denote it by Wx we shall then have 
Wi™ /i (A— a) —fxA(l — — W oR when E is written for 1 — 
A A. 
Now suppose a segond series of black points to fall on the 
surface. It might at first sight appear that the remaining 
white area would be A— 2 a; but on consideration this did 
not seem necessarily the case, for manifestly it supposes 
that the particles distribute themselves with some bias ; 
that is, they prefer to fall upon a white surface ; but suppose 
that they have no such bias, and that they will as readily 
fall upon a black as upon a white surface. Now the surface 
on which they fall is grey or a mixture of black and white. 
So we have this question in the distribution of the second 
black area (consisting of innumerable detached points), how 
much falls on the black surface and how much on the 
unoccupied white area ? Let p be the portion that falls on 
the black surface and q the portion that falls on the white, 
now what will be the ratio of p to q ? If we suppose the 
second series of black points to be fairly distributed, the 
portion which falls on the black surface will be to the 
portion which falls on the white as the areas of those 
surfaces, so that 
a 
q A — a 
also p + q~a, .... 
and the remaining white area will be A—a—q. From (1) and 
•( 1 ) 
,( 2 ) 
