70 Mr. 0. Heaviside on the 



condition is satisfied at all the faults if 



V^ =SAsin(y + M, 

 V^ 2 =Y^ + 2Bsin^£L) 3 



. a(x — x 2 ) 



V, 



V^ + ZCsin 



. (3) 



and so on. The second condition is satisfied at all the faults 

 l g 



by making 



<V 



-ci-j . / Q\X 2 



z 2 a 



; -n(y +h ) 





= — -< sm(- 1 —+b i )+ sin ( -7-^ + &,• 1 



z 2 a t I \ I 7 z x a { \ I 



Di= — Ismt -V^ +&,•)+ —sin 



*3«» \ t / ^i 



sm 



ai(x 2 — x x ) \ 



Bj ^ajQ 3 — a? x ) , C t - . ^OiCfar: £2) 



—y - i bill v , 



W 



and so on, where 



1- H' * 2_ 



U 



12. The terminal arrangements have next to be considered. 

 By the theory of the condenser, at the beginning P we have, 

 at time t, 



v i pi d v i v i — v _ 1 dv 



Hence, if 

 we have 



Si dt B-i 



k dx 



Ri Si Ci 



,rh= M> n ^M> n= d- 



, dv 



00 



as the relation between the potentials of Ci and the beginning 



of the line, and 



r\ / \idv w d 2 v 7 od 3 v /c ,\ 



Q = v -( mi + n 1 )l^+n 1 r 1 l 2 — 2 -m 1 n 1 r 1 l s ^ 3 . (5) 



as the equation to be satisfied by the potential at x = 0. 

 At the end Q we have 



-££-*=£+<ra .... (6) 



k dx 



8 



2 _j n dv 2 

 da 



dt 



v — v 2 =g~R 3 + L-^ 



(J) 



