﻿of Radiation in any Material System. 535 



the element from the origin. This assumes that e~ kz is 

 sensibly constant throughout dV. 



Instead of (85) and (86) consider the functions 



yjr 1 =\ 1 ^ i(nz-pt)d v (87) 



fa=z\^e<™-Pt)dv (88) 



And $ = J F 1 ^_ 1 + 6ri^_ 2 ; 



where the integration in (87) and (88) is supposed to be 

 over unit volume of the medium and ^_i, yjr_ 2 are the 

 conjugates of fa and fa. Then (84) becomes 



Z\ z x 



or ^V 1 + (^ + m) 2 i^ 1 + 47r^ 1 = . . . (89) 



c 



and 



^G 1 + (k + in) 2 G x + lirSfa = 0. . . . (90) 

 And by (59) 



£ 7 r$fa = F 1 <i> n + G&2, ±Tr$ylr 2 = F 1 ® 21 + G^ 22 , 



2n 2n 



. . . (91) 



2 n 2n 



. . . (92) 

 With similar definitions of <1> 21 and <S> 22 (89) and (90) 

 reduce to 



£F 1 +(k + inyF 1 + ® n F 1 +<P la G 1 = . . (93) 



c 



^Gi + ik + inYGi+^nFx + ^Gt^O . . (94) 



I reserve the further consideration of these results. Where 

 there is no rotation of the plane of polarization 



^12 = ^21 = 0. 



Where the medium is isotropic the defining equations (87), 

 (88), (93) and (94) show that 3> n = <I> 22 . 



