Bays emitted by Substances exposed to y Rays. 627 



have 



dR _ p vHk Line K x m 



and 



dr uric , uBx , Ki ,. a v 



^ = -^ + 2 + 2 + T' • • • ^ 2 > 



when a steady state is reached. 



The first term o£ the right-hand side of equation (1) 

 denotes the absorption of the stream R if there were no 

 secondary radiation; the second and third terms denote the 

 streams of secondary radiation moving in the same direction 

 as the stream R, due to the streams R and r respectively; 

 and the fourth term denotes the stream of radiation dne to 

 the action of the 7 rays, moving in the same direction as the 

 stream R. The terms on the right-hand side of equation (2) 

 have similar meanings. 



The equations may be written 



g=„R_^_N,i • • • • • (3) 



dr 



*L=~_ar+&R+-tf i ...... (4) 



, fl/C -, /JLK „ K x 



where a — jju — r , = { -^-, and JN = ^ • 

 Eliminating r from these equations we get 



JJ=(o»-P)B-(a + 8)N (5) 



The general solution of this equation is 



N 



R = A 1 £-Wa*-^ + A 2 tfW^-^+ _ . . (6) 



a—b 



The amount of radiation Rx per cm. 2 per second from the 

 surface of the layer is obtained by putting x = in the last 

 equation, this giving 



N 

 R 1 = A 1 + A S +^— -^. . . . . . (7) 



It remains to determine the arbitrary constants A, and A 2 . 



Let n denote the thickness of the layer of substance. At 

 the surface where x = we have r — 0, and therefore from 



