Theory of Faults in Cables. 

 and the current arriving at m-=-l is 



Ti 2E 2? 



i^n 



■^ 4 cos^7^e 



16V 



(34) 



19. To find the limiting forms of the solutions when z = Q. 

 In equation (29), when i is odd, a i =i'jr; and when i is even, 

 including 0, and z finite, a { lies between iir and (z' + l)7r, and 

 ultimately becomes (i-\-X)ir when z = 0. The 2ith and 

 (2z + l)th terms in (29) are 



2E^ 



CtiiX' 



WH / __ («s^f 



— cos v j 1 e t 



-j . sm a 2i 



>. (35) 



This vanishes when z=0, and (29) takes the form 



^=0 + + + ... 



each representing a pair of terms. Now, when z is infinitely 

 small 



a 2{ = (l-4^)(2i + l)7r 



by (30). Expanding (35) in powers of z, neglecting squares, 

 &c, it becomes 



. rtT , , (a/ . ax' 1 ax' , 2 at ax'-) _^ 

 2ho\z . Aa < y sin -^ cos -y + -pp- cos y v e t . 



where a stands for (2i + l)7r. The same result is reached by 

 finding the limiting ratio of the expression (35) to z when 

 a 2 i = (2i + l)7r, making 



1 , a 

 Z =2~a C0t 2' 



and multiplying the result by z. Hence (29) finally becomes 



a „ ™C4ax' . ax' , /Sa 2 t A ax' 1 -^ , 0fl . 

 v = 2Eo\zX< -y-sin-^- + (-m 4 ) C0S T~ i e T? ( ^ 



where a £ = (2i + 1)tt. 



The potential v 2 of the receiving condenser is 



f (2i + l) 2 7rH 1> _(*+i)^ 



v a = 16Er 1( sS- 



^} 



and the current T entering the receiving condenser is 

 r 16E »/ (2«+l)V( 3,.,,..,,! -fflffl 



(37) 



(38) 



Curve 3, fig. 2, is calculated from (37), and curve 3, fig. 3, 

 from (38); curve 2, fig. 2, from (29), making a/=0j and 



N2 



