Wave-trains through a Conducting Dielectric. 319 



its history in detail to obtain the expressions for the rays 

 emergent after 0, 2, 4, . . . &c. internal reflexions. Let 

 the incident wave-train be given by 



from the time t = onwards, p being a complex quantity as 

 defined by ' (9). Passing through the first surface and 

 reaching the second the wave becomes (d being the thickness 

 of the electrolyte) 



p(t-qd) 1(0/2-.//) 



Ace e » 



and emerges in the form 



Keff ni e m ' m e^-^\ . . . (I.) 



If we take the instant at which the incident wave first 

 strikes the plate as the origin of time, the wave-train (I.) 

 begins to emerge at time 



d. V .Vfo.Bm( x + £) t _ _ _ (31) 



' 2 ~ ' P, 



by equation (19). 



The wave reflected from the second surface at the time 

 that (I.) emerges is 



—A. bee e e , 



which becomes on reflexion at the first surface 



A . ¥e e~ md /*"** f**+~*\ 



and emerges from the second surface at time 3t 2 as 



Mfy e -^^'-*fr) e M*-*V-*\ m m m (IL) 



This is the second emergent ray, or the ray emerging after 

 two internal reflexions. The third emergent ray will be 



Ab 4 cfe~ 5pqd e^/ 2 - 2 *'- 4 ^^- V|» ^ ^ (III.) 



emerging at time 5t 2 ; and so on for the others. The 

 (n + l)th emergent ray, or the ray emerging after 2n in- 

 ternal reflexions, is 



^n c s e -Vn + l)pqd e i{e\2-2y-2n^ j>{t- V/3,*) 



