ELECTRIC CIRCUIT Til TORY 3^7 



At x = we have 



V=E-ZJ 



whence 



(l + PiM + (l-Pi)5=£, (242) 



where pi = Zi/Ki. 

 From (241) and (242) we get 



^ = (1 + Pi)(l+P2)-(1-Pi)(l-P2)e-2T^'^ 



_(l-p,),-27. 

 ^-(l + Pl)(l+P2)-(l-pi)(l-P2)^-2^^ 



and finally 



g-7--^_|_ ?^ £?g-7(25-;«;) 



7, = _J? ?^te? . (243) 



K-i-Zi 1 — pi 1 — P2 2ys 



1+Pl 1 + P2 



If we replace £ by a unit e.m.f. we get the operational formula for 

 the indicial admittance Ax', thus 



where 



^^~i^ 1-M1M26-2T. Z.(/>) ^ ^ 



x=x/(i^+zo, 



^^ 1+Pi X+Zi' 



1 — P2 K — Z2 



M2 = 



1+P2 K + Z2 



i^,7,Zi,Z2,Mi and iU2 are, of course, functions of the operator p. 



The integral equation corresponding to the operational formula 

 (244) is 



1 r°° 



