Wave-trains through a Conducting Dielectric. 335 



wire circuit — reduction coefficients covering loss of energy 

 due either to damping by the imperfectly conducting wires or 

 to imperfect reflexion at the ends of the circuit. 

 If then 



T n is the intensity of the n th train emerging from B 



towards C, 

 R n is the intensity of the n th train reflected from B 



towards A, 

 we have 



T n+1 = edR,, + r X 1 n l 



»•+. = « + «!!„/ {L) 



The effect on the electrometer is proportional to 



" ~" } (2) 



71 = 



so we have to sum a finite-difference series. 

 Let T n = Ah" 



K = B6» 



Rewriting (1) with these values of T n and R n , we have 

 Ab = eel B + r% A,l 

 Bb = d x A + re B ; J 

 whence, eliminating A and B, 



b 2 -'br{e+x) + e X (r 2 -d 2 ) = 0. ... (3) 



This is an equation to determine b. Suppose b x and b 2 to he 

 the roots ; A Y A 2 , B x B 2 being the corresponding values of A 

 and B. We have then 



b 1 + b 2 =r(e + x ), bib 2 ={r*-d*)ex. . . . (4) 

 T n = AiftJ + A 2 &» "J 



r^Aa^+^a^ (5) 



Oi—re l b 2 —re 2 ) 

 From this last equation, 



1 = dl = A x + A 2 , ~\ 



i3 t j ( A i , A 2 \ ?• • • • ( 6 ) 



The total effect on the electrometer is consequently pro- 



