Theory of Faults in Cables. 71 



Therefore if 



Ra __ S 2 C 2 __ L 



m *~W n2 ~TV T2 -~d> s -"kLcW 

 we have 



V2 = v + W2 /_ +5 £3__ ? .... (8) 

 giving v 2 in terms of v at a = I, and 



= v + (m 2 + rc 2 )Z -£ + i%raP ^ 2 + (s + m 2 r 2 w 2 )/ 3 -^ 



+w?S ' ' ' (9) 



as the condition held by the potential at x = h In (5), (8), 

 and (9), for — has been substituted -v ^— 2 - 



13. Now the law of formation of the a's and 6's can be 

 found. From ,#=0 to x=x ly 



and from the last fault at #=#„ to ,r = / ; 



V^=SAsin(f +& ) +S Bsin<^l 



Inserting the first of these in (5) and the second in (9), and 

 then making ^ = in the first case and x — l in the second, we 

 find 



tan6j . = K+%)^-^i^ 3 m . m (10) 



^(ai+b^ + q.sina. (l- °^\ +q! sin a. (l- ~ 2 j +^'sina £ A_£jA + 



»s (a* + &,-) + q[ cos a, M - j + yj cos a,, f 1 — -j J ' + ?•" cos a,- (l — ^j j + 



_ (m 2 + n 2 )a { ^(s + m 2 n 2 r 2 )a? + n 2 r 2 sa\ 

 — , .... {lL) 



l—n 2 r 2 at 



where 



Equations (10) and (11) serve to determine the a's and 6's. 



14. Now only the A's remain to be found. This is to bo 



