TRANSMISSION OVER SUBMARINE CABLES 



101 



protective covering of jute, surrouiuied !)>• a riiij^ of N armor wires 

 immersed in sea water. The method of solution is essentially similar 

 to that given in the preceding pages, and consists in determining the 

 values of electric field intensity at the outer surface of the core con- 

 ductor and the inner surface of the return conductor, from which the 

 internal impedances of the two conductors can be found. 



Fig. 4 



The main dif^culty in the analysis is caused by the lack of uniaxial 

 symmetry in the return conductor. This was overcome by employ- 

 ing a method developed by one of the authors^ in a study of trans- 

 mission in parallel wires. 



The electric field intensity in the sea w^ater satisfies the differential 

 equation 



^ + — -x- + ^:rTi-- 4:Tr\fipiE = 0, 



the solution of which is a Fourier-Bessel expansion, 



E = AoKo (ja) -[- AiKi {ra) cos4> + A2K2 {ra) cos 2(^ + . . . -{-, 



r and <^ being referred to the axis of the particular wire. 



Assuming that the current distribution in the core conductor is 

 independent of the angle 0, that is, neglecting the individual char- 

 acter of the armor wires only in their efifect on the current distribu- 

 tion in the core, the effect due to the current in the core is represented 



'"Wave Propagation over Parallel Wires; The Proximity Effect." John R. 

 Carson, PJiil. Mag., vol. xli, p. 607 (1921). 



