358 BELL SYSTEM TECHNICAL JOURNAL 



Also Z.v(o) =sR. We thus get 



A. {I) = -p + -^ > co^'^x.e'^c . (285) 



sR sR-^-^ s 



This is a thoroughly practical formula for computation, owing to 

 the rapid convergence of the series. In fact, for this particular line 

 termination chosen, it is probably the simplest and most easily com- 

 puted form of solution. These advantages depend, however, strictly 

 on two facts. First, the fact that the line is taken as non-inductive 

 and secondly that the terminations chosen are those of a short circuit. 

 In fact, as we shall see, it is only in the case of the non-inductive 

 cable that this type of solution is of any practical value. 



There is one other point which should be carefully observed in 

 connection with this solution (285). This is that it is not expressed 

 in terms of a series of direct and reflected waves, corresponding to the 

 sequence of physical phenomena, but in terms of normal or characteristic 

 vibrations. This point will be returned to later. 



Let us now attempt to apply this type of solution to the trans- 

 mission Hne, L,R,C,G. Writing 



^ 2L^2C 

 '^ 2L 2C' 



v = i/Vlc. 



We have 



whence 



y'-^[(P+py-<^'] 



p,n= —p±V 



\y'n+^ 



\/mTr\~ a^ 



= -p±iv\\[--) — ^, m = l,2, . . . 





V 



\ /W7r\ 2 a- 



