Dr. W. E. Sumpner on the Diffusion of Light. 83 



light-sources within a room, and if Q! is the total amount of 

 light falling on the walls, 



Q'=Q+*?Q' (2) 



For of the quantity Q', a portion ^Q' must be reflected, and 

 the rest absorbed, and the rate at which light is absorbed by 

 the Avails must be equal to the rate at which it is produced. 

 The average illumination V of the walls of the room must 

 hence be related to I, the illumination due to the direct action 

 of the lights, by the equation 



l '=ih l (3) 



Thus if jj = -90, r = 10I, and if i| = '50, I' = 2I, so that the 

 illumination due to the walls of the room may become far 

 more important than that caused by the direct rays of the 

 lights. 



The truth of this relation may be also seen as follows : — 

 The light Q falling on the walls is partially reflected, and a 

 quantity ^Q is sent back into the room. This light falls on 

 the walls again and a portion rj x ?;Q is reflected a second 

 time. The total quantity of light Q' falling on the walls 

 owing to successive reflexions is given by the equation* , 



Q' = Q + 7? Q + ^Q + ... = T ^-Q. 



Or, again, as the illumination l p ' of the walls at any point P 

 is made up of a portion I p due to the direct rays of the lights, 

 together with a part caused by radiation from the walls, we 

 have 



V = I P+J Bcos< M n > .... (4) 



where B is the brightness of the walls, and cj> is the inclina- 

 tion of the solid angle dfl to the normal to the surface at the 

 point P. Assuming that the brightness is the same all over 

 the bounding surface of the room, the value of the integral is 

 readily seen to be 7rB, and this, as already shown, is equal 

 to rjV, where I' is the average illumination of the walls. 



When the bounding surface of a room or enclosure consists 

 of portions whose reflective powers are different, the average 

 reflective power may be taken as 



*, — *7A+77 2 A 2 + &c. . . . ,-. 



"m— J^ , . . . . {OJ 



* Since writing this paper I have discovered that this relation has 

 been already pointed out by Mascart [see Palaz, Traitc dc Photomitrte 

 Indus tr telle, p. 2(58]. 



G2 



