TR.-INSMISSION OVER SUBMARINE CABLES 



93 



We liave now succcecled in cxpressin;j; tlu' electric forces in the 

 conductors as linear functions of the currents /i . . . /„, the coeffi- 

 cients being of the nature of inipxxlances, by a method which is simply 

 an application of the principle of continuity of magnetic field intensity. 

 The remaining boundar\- condition, continuity of the tangential 

 component of electrical field intensit\- gives, where two consecutive 

 cylinders are in electrical contact, 



EAr-Ey - [t;:-,: - 7/, ]/, + ... + [z;+..^-z^] 



/,■ + Z'j+,,j+Jj+, = 0. (9) 



This gives m relations between the n currents of the system, m 

 being the number of contacts between successive cylinders. In the 

 case where the j and (_; + l)st conductors are separated by a layer 

 of dielectric material, a relation between the boundary values of 

 electric field intensity may be obtained as follows: 



If Er is the radial electric field intensity in the dielectric, then 



Vi 



^ / . 



Erdr 



is the potential difference between the j and {j + l)st conductors, 

 in the sense employed in ordinary circuit theory. If we now apply the 

 law 



curl h = — jj. -y: 

 at 



(j + 1)^' Conductor 



f' Conductor 

 Fig. 1 



