THEORY OF MIXED COLOURS. 73 



If we continue the operation n times, then from the 

 above law, if Wn denote the remaining whiteness, we shall 

 have 



Wn=W U n . 



Also the mass will be 



I also used an independent method of reasoning. Suppose 

 we have a white area A, then the quantity of white light 

 given off in any direction, say normal to the surface, will 

 be proportional to A ; so that, if W denote the white 

 light, we may write W =j«A. Suppose now a great 

 number of black 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 /a (A— a) ; moreover this quantity 

 of white light will appear uniformly diffused over the 

 surface. If we denote it by W t we shall then have 



W 



I= MA- a) =/*A(i _!)=WJR, 



where ft is written for 1 — -r-. Now suppose a second series 



of black spots to fall on the surface. It might at first 

 sight appear that the remaining white area would be 

 A — la ; but on consideration this did not seem necessarily 

 the case, for manifestly it supposes that the particles dis- 

 tribute themselves with some bias ; that is, they prefer to 

 fall upon a white surface ; but suppose that they have no 



