Theory of Faults in Cables. 171 



At time t, 



^ . . ax -^ 

 v=2,Asm-j-e t, 



where the a's are the + roots, including imaginary roots with 



+ real parts, of 



tan a , 9 



= —m + sar, 



a 



and 



m 



a 





\m 2 -j-dx— , 

 2E 



/- asm 2a 2 \ 



all s 2?n cos" 5 a J 



V 2a J 



For simplicity, put m=0, then 



K 1 — 2^-J 



where 



tana 2 /icr v 

 =sa z . (45) 



a ? v y 



When s is large, there is no trouble with imaginary roots. 

 There is a root of (45) a little above zero, another a little 



under 77 ; and the rest are nearly — , — -, .... Hence, when 



2 J 2 2 



5 is large, (45) becomes 



l = sa 2 



to determine the lowest root, or 



- 1 T.kl 

 s L 

 Therefore (44) is nearly the same as 



Ex -» «p 2E . (i-i>« -tf-Pw 



I 1 (l — ^)7T £ 



and the current nearly the same as 



E -*2 



This case corresponds to a short land-line, the self-induction 

 of the receiving instrument causing greatly more retardation 

 than the electrostatic capacity of the line. The current at 



