372 Dr. Barton and Mr. Lownds on Reflexion and 

 incident wave-train be represented by 



f = e-W-*/»)-Mcos^(/- x/v), . . . (27) 

 wliich accordingly becomes at the electrometer 



fy^e-kptcospt (28) 



The notation previously used for the various wave-trains 

 and for the coefficients of reflexion and transmission will be 

 retained, and the following abbreviations used : — 



IJv = U, 2pl 2 /v = 2pt 2 = 6, 



Ae~ 2 h' T = s, a-\-y = K ; 



CAe-afr=r, CAe-*V=r„ 



l-2r 2 cos 2K + r i = D, l-2 n 2 cos 2 K + r l i = D 1 . 



37. Then we have as before, if d be the electrometer-throw 

 with no condenser on the line, 



Ed= \ [e-*P* cos ptydt, 



«. o 

 whence 



Mp{l + k*)Ed=\ + 2k% ..... (29) 



or, neglecting k 2 , 



4kpEd=l (30) 



38. Now suppose the condenser placed on the line and 

 consider the effect at the electrometer of a single interference 

 of the initial wave-train incident on the condenser with that 

 reflected from the condenser. This is obviously represented 

 by the following integrals : — 



| ^tfdt+i" (<£,+■ $)*dt 



/■*<» n„ r<x 



= 1 <f>i-dt+\ $Ht + 2\ fafldt 



J J% J% 



4Ap(l + A s ) ' K J 



F, 



where -n — r= r^r represents the integral under which it is 



4£/?(l + F) l & 



placed; and the same remark applies to Gri and H^. 



39. But here again, as in the transmitted system already 



dealt with, the wave-train first reflected at the condenser 



returns along the wires, suffering attenuation during its 



transit, is reflected at the oscillator, and is again attenuated 



in passing along the line to the electrometer. This second 



wave-train produces a second interference phenomenon, like 



that due to the initial wave already treated ; but phase changes 



