Dr. W. E. Sumpner on the Di fusion of Light. 93 



easiest way to represent these facts is to assume that, of the 

 light transmitted, a portion Tj passes through without change 

 of direction, and that the rest r 2 is diffused in accordance 

 with the cosine law. The case is analogous with a reflecting 

 surface such as white enamelled iron, which reflects a portion 

 ij 1 of the incident light in accordance with the regular law 

 of reflexion, and diffuses another portion rj 2 according to the 

 law of cosines. On referring to equations (8) to (11) it will 

 be noticed that they are still true for the illumination due to 

 diffusion if we substitute for rj either t 2 or rj 2 (according as 

 we are considering transmission (fig. 3) or reflexion (fig. 2) 

 respectively). The additional illumination at the photometer 

 due to regular, *. e. direct, transmission (transparency) is 



K nn 



T W (17) 



and a similar expression holds for regular reflexion if we 

 substitute rj x for tj. 



The whole illumination must, as before, be equal to &/?/ 2 , and 

 by (11), (12), and (17) we have 



whence the value of Y in (16) is equal to 



Y=T a + ^X; (19) 



and a similar expression holds for reflexion if we replace t } 

 and t 2 by 7} 1 and rj 2 respectively. The true values for the 

 transmitting and reflecting coefficients are 



T = Tl ! T2 ' 1, (20) 



rj = r] 1 + r} 2 , J 



and the reason the values found for Y were too high, and 

 became greater and greater as x increased, was simply that 

 the values used for X (see 12) were always greater than 4, 

 and increased rapidly with x. 



By plotting the numbers found for Y with the corresponding- 

 values of X, a straight line is obtained from which the values 

 represented by the symbols in (20) can all be determined. 

 The straightness of these lines, and the verification of the 

 fundamental formula 



^-f-a + T = 1, 



