Currents along a Number of Parallel Wires, 569 



Put V 2 = ^ and the right-hand side may be written 



2 loo- — - 

 ° a 



Thus the effective capacity is 



K 



2 1og^ 



The effective inductance, when p is small, approaches the 

 value 



L = 2 log— + 2 - 

 the general value being for small frequencies 

 L = L - 



1 /J?p 2 



as in Lord Rayleigh's formula. 



With high frequencies, using the appropriate approxima- 

 tions for the J functions, we get the corresponding expression 



L n - 



fi /fj,R 



^o 



2 V 2p ' 

 2r V 



approaching the limit L — ~ = 2 log 



The resistance agrees with Lord Rayleigh's well-known 

 expression. 



8. It is easy to extend these results to take leakage into 

 account. If the dielectric be supposed to have a finite 

 resistance p it can be shown * that the constant k-f is altered to 



ft 2 4o/j,ip 



This leads to the value S = 



V 2 p' 



2tt 



2rrj 



p 



* Cf. J. J. Thomson, ' Recent Researches/ p. 262 ; Soinmerfield, Wied. 

 Ann. lxvii. p. 233 (1899) ; Gray & Mathews, ' Bessel Functions,' chap. 13. 



Phil. Mag. S. 6. Vol. 1. No. 5. May 1901. 2 P 



