TRANSMISSION OVER SUBMARINE CABLES 115 



in which Cu, etc., are numerics. This solution is effected by retain- 

 ing a finite number of equations and an equal number of variables 

 and solving by the usual methods. It will be found that except in 

 extreme cases, a very good approximation can be gotten by ignoring 

 all the p's except the first four. The qs may then be obtained by 

 the relation 



Qn = pn + d„ 

 d„ being defined by 



d„ = (X„ - l)p„ - ( - 1)«X„ ^ 2„((f). 



This system is easily adapted to solution by successive ap- 

 proximations, 



d„ = c/'»' + rf',i' + rf<^' + 



in which 



d'^' = (l - ^) C„,p, + . . . + (l - 1^ C„„p„, 



C„i, etc., being the numerical coefficients which appear in the ex- 

 pressions for pi, p2 . . . . 



A very good approximation which holds in most cases is 



d„ = (X, - 1) Cni pi + (X2 - 1) C„2 />2 4- . . . + (X„ - l)C„„p„. 



