86 Dr. "W. E. Sumpner on the Diffusion of Light. 



the other a glow-lamp run generally at about 20 candle- 

 power, placed at Pj. A Lummer-Brodhun photometer was 

 slid along the bench to a point P 2 at which the illumination 

 due to reflexion from the surface OR was equal to that due 

 to the Methven standard at L. At first the lamp P x was 

 permanently situated a little to one side of the bench, and 

 the rays from it in the direction of the photometer P 2 were 

 screened off. Subsequently the points P x and P 2 were made 

 to coincide, the lamp being fixed to the same slider as the 

 photometer and suitably screened from it and from the eyes 

 of the observer. In some experiments the distance OL was 

 kept fixed and the position of balance OP was determined 

 for each surface tested. In other cases both OP and OL 

 were varied. 

 Let:— 



A = area of diffusing surface on screen OR (centre at 0). 

 O l5 X2 2 = solid angles subtended by A at P 1? P 2 respectively. 

 x ± , x 2 = distances 0P l7 OP 2 respectively. 

 y = distance P 2 L. 



K = candle-power of the glow-lamp at P 1# 

 k = candle-power of Methven standard at L. 



Then :— 



The quantity of light falling on the area A is KHj, 

 the average illumination of A is KXlj/A, 

 the average brightness is ^KHi/VA, by (1), 

 the illumination at P 2 is 7)K.£l 1 £l 2 /' 7r A, 

 and also the illumination at P 2 is k/y 2 ; 

 whence 



_ k 7rA _ k itx 2 x 2 

 V ~Kll^ 2 ~K~Af~ 7 (8) 



provided the dimensions of A are small compared with x x or 

 x 2 . When this is not the case, the equation (8) is not suffi- 

 ciently correct, and a more accurate formula may be obtained 

 as follows, by taking note of the inclination of the rays to 

 the surfaces. 



The illumination of the surface at the point R due to the 

 lamp at P x can be easily shown to be K cos 3 fa/x 2 , where fa 

 is the angle between RP X and OL, the line of centres of the 

 bench. The bifightness B of the surface at R is therefore 

 rjKco^fa/TTXi 2 by equation (1). An element of area dA at 

 R subtends at P 2 a solid angle dX2 2 equal to co^fadK/x 2 2 y 

 and the illumination at P 2 due to this element is Bc/f2 2 = 

 7]KGO^faco^fadAl'rrx^x 2 2 on any area placed perpendicular 

 to RP 2 . As the photometer screen is perpendicular to the 



i 



