white area will be VXJ " . **' , and the red area will be 



THEORY OF MIXED COLOURS. 77 



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 

 /^a, and the uncovered white area will be A— a, and the 

 quantity of white light given off will be /a (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 



(A-a) 

 A 



A— — -r — -. Hence after the second operation the light 



a ( A — a) % 

 given off will consist of white light » — - , and of red 



light //,, | A— - — ~-jr-^- \ y or > as we ma y write them, //AR* 



and /^(i— R 2 ), where R=i — -r-. If the operation be 



repeated n times, the residual whiteness will become /juAR n 

 and the redness will become /^A(i — R w ). If n becomes 

 infinite, the whiteness vanishes and the red becomes /^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 y 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. 

 Suppose first we compare A and B. Let t and t 1 be the 

 lengths of the columns. Then 



WoRtt^WoIW (3) 



