782 Prof. J. H. Jeans on the 



in air : and in the metallic medium 



_K^dX „ , 



- c a ' &c- - " • • ! - ' 



where K 2 ' is given by equation (14). 



The velocity V 1 o£ radiation in medium 1 is given by 

 V 1 2 = C 2 /Ki/x 1 . We introduce an angle 6 2 and a velocity V/ 

 given by 



1 



sinW _K7^ 2 _Y 2 /2 rm 



sm 2 ^ nr ~ v^ l± ' ; 



Clearly both sin # 2 ' and V 2 ' will be complex, but their ratio 

 is real. 



The exponential through which the time and space- 

 coordinates enter in the radiation in medium (1) may be 

 taken to be 



exp. ip ( t — ^r- [x cos 1 -f y sin ± ) ) ; 



the corresponding factor in medium (2) will be 



. / cos# 2 ' sin0 2 '\ / 1Q x 



exp. ip^w-YT—y-yn-J • - • (18) 



sin t) / 

 Remembering that -^fft~ ^ s f^al, we see that it will be 



V 2 



possible to introduce two new quantities 6 2 an( l V 2 , both real, 

 such that 



sin 6 2 sin 6 2 



V. 



«jOS t/ 2 



2 



COS#< 



The exponential (18) now becomes 



— ?e. 



e -epz 



exp. ip ( £ — ==- (x cos # 2 + ?/ sin 9 2 ) J . 



and we now see that 6 2 an d V 2 are the angle of refraction and 

 velocity of the radiation in medium 2. 



14. We introduce a new complex quantity u 12 , associated 

 with radiation passing from medium 1 to medium 2, and 



