342 BELL SYSTEM TE.CIINICAL JOURNAL 



tation. This, however, is merely answerable to the complexity of the 

 physical problem, and no simpler general solution can possibly exist. 



The foregoing method when applied to the differential equations of 

 the transmission line, leads to the following differential equations 



(Lp-hR)J = -j-^ + LP, 



(11) 

 {Cp + G)^ = -A/+ CV\ 



Here / and ^ are Laplace transforms of the current I and voltage V 

 and /", V'^ are the initial values of / and V at reference time / = 0. 

 /, <I>, P, V^ are functions of x but of course independent of /. 

 The formal solution of equations (11) is as follows: write 



Lp -\- R = Z{p) = Z, 



Cp + G = Y(p) = Y, (12) 



Also 



Then 



[ZY = y, ^ZjY = K. 



LP-^lv^ = Fi.) = F. 





i^S) 



A and B are constants of integration determined by the relations 

 between / and $ at the physical terminals of the line. 



