Wave-trains through a Conducting Dielectric. 315 



b is a function of the period and damping of the wave- 

 train as well as of the properties of the reflector. If the 

 wave-train be not damped, we have 



X=90°, T . 



. . . P= V 1 + (^ft)'' \ . . . (14) 



1 



cos#= — , 



p J 



so the expression for b remains unaltered in form, b being 

 still a function of the period. 



But if the conductivity of the electrolyte or a 2 De zero, the 

 angle 6 becomes likewise zero, p is unity, and we get the 

 ordinary value for b, namely, 



6= — ^f, (15) 



the period and damping of the incident ray having vanished 

 from the expression. 



The phase-change >/r is zero for either a perfect insulator 

 or a perfect conductor ; becoming indefinitely small in the 

 first case, and r in the second. 



The refracted wave is dealt with in exactly the same 



manner. Taking the value of -^ from (8), and substituting 

 in it the value of X from (11) we have 



id 



Bo 2\ 2re r 



1 +re* 



— / 6 6\ 



2re 2 1 1 -f r cos ■= ri sin -~ ) 



1 + r 2 + 2r cos -x 



If we write . 9 



r sm - 

 tam//= ^ 5 .... (16) 







1 + r cos ~ 



then B< 



'l + r 2 + 2rcos| 



g t(«/2 -* 



