346 BELL SYSTEM TECHNICAL JOURNAL 



unit e.m.f. between terminals 11. Let Vzi{t) denote the resultant 

 voltage between terminals 33 measured in the direction of the arrow, 

 and /,-, the current flowing between the networks. We have then the 

 two following expressions for the current I^. 



h = S,,{t)-jJv,y{T)Sri{t-T)dr (255) 



and 



h = ^f'Vs,{T)T^,{t-r)dr. (256) 



dUo 



Equating we get 



■j'Vn(T)[S,2{t-r) + T,,{t-T)]dr==S2,{t). 



(257) 



By precisely similar reasoning, if terminals 11 are short circuited 

 and a unit e.m.f. inserted between terminals 22, and the correspond- 

 ing voltage across terminals 33 denoted by F32, we have ^ 



^ rVs2{T)[S22{t-T)i-Tnit-T)]dT = Ti,{t). (258) 



dtJo 



Equations (257) and (258) are integral equations of the Poisson 

 type which completely determine F31 and F32 in terms of the indicial 

 admittances 6* and T. We shall discuss the solution of these equations 

 presently. 



If UiuU22,U2i= U12 denote the indicial admittances of the com- 

 pound network we have at once 



C/ii = >Su(0-4 rVs,ir)Su{t-T)dr (259) 



at Jo 



U22 = T22{t)-j^£Vs2(.T)T2lit-r)dT (260) 



U2l=U,2=^, l'v3l{r)T2l(t-T)dT 



dtJo 

 = |: rV^2{r)Su(t-T)dT. 



dtJo 



and 



(261) 



If, therefore, equations (257) and (258) are solved for F31 and F32, 

 the required indicial admittances of the compound network are given 



8 F32 being opposite to T'31 in direction. 



