127 



sions are insulated in symmetrical positions within a cylindrical con- 

 ducting sheath of circular section. 



CASE I. Two-wire Cable. 



In the general equations (according to the notation of the first part 

 of this communication) we have k^ = k 2 ; GJ l M=.m^; andOT 2 ( 1 )=tr/ 2 ): 

 and it will be convenient now to denote the values of the members of 



these three equations by k, -, and 4 respectively ; that is, to express 



by k the galvanic resistance in each wire per unit of length, by c the 

 electrostatical capacity of each per unit of length when the other is 

 prevented from acquiring an absolute charge, and by f the propor- 

 tion in which this exceeds the electrostatical capacity of each when 

 the other has a charge equal to its own ; or in other words, to assume 

 c and f so that 



.=-j-.4*l 



** ^Jfcrti; 



if 0, and 8 be the potentials in the two wires in any part of the 

 cable where they are charged with quantities of electricity respectively 

 q l and q% per unit of length. The equations of electrical conduction 

 along the two wires then become 



. ' . . (2). 



From these we have, by addition and subtraction, 



d_ l+fd 



dt ~ kc d 

 where $ and w are such that 



_ and _- 



dt ~ kc da*' dt ~ kc dx* 



Vz=$ uj ....... (4). 



If both wires reached to an infinite distance in each direction, the 

 conditions to be satisfied in integrating the equations of motion would 

 be simply that the initial distribution of electricity along each must 

 be whatever is prescribed ; that is, that 



r, = p,(a?), and t s = ft(a?) 1 (r . 



when *=0 / 



