CIRCUIT TIIF.OKy .1X1) OPERATION Al. CAI.CVI.VS 741 



Mcavisiile's procedure at iliis point w.is as rem.irkaWe as it was siic- 

 rcssful. Me first disoardetl the second series in inteRral powers of p 

 as meaningless. He then identified \ p with 1/'\/t/ anil replaced 

 p" by d' /dt" in the first series, getting 



-('+'^i.S+-): 



1 rf , 1 (f . \ 1 



(94) 



or, carrying out the indicated differentiation, 



1 /. 1 . 1.3 1.3.5 



V = - 





V^V 2at ' {2atr {2aiy 



which agrees with (91). 



This is a typical example of a Heaviside divergent solution for 

 which he offered no explanation and no proof other than its practical 

 success. His procedure in this respect is quite unsatisfactory and in 

 particular his discarding an entire series without explanation is in- 

 tellectually repugnant. We shall leave these questions for the present, 

 howe\er; later we shall make a systematic study of his divergent 

 solutions and rationalize them in a satisfactory manner. First, 

 however, we shall take up a specific problem for which Heaviside 

 obtains a divergent solution without discarding any terms. 



Problem C: Current Entering a Line of Distributed L, R and C 



Consider a transmission line of distributed inductance L, resistance 

 R. and capacity C per unit length. The differential equations of 

 current and voltage are 



(95) 

 it dx 



Ki'placing d/dl \)\ p, we get 



(96) 



Equations (96) correspond exactly with (58) for the non-inductive 

 cable: except that we must replace R by pL-\-R. For the infinitely 



