430 SUBMARINE CABLE LAYING AND REPAIRING, 



The mean potential is 



E + e E + E(l-«) ^'>- 



= E(^). ... (2) 



2 2 



Hence the ratio of the initial to the mean potential is 



E 2 



E(2-n) 2-w* 



(B) 



2 



And we have 



2 

 True capacity = apparent capacity X > 



= —r'-R microfarads. ... (4) 



d 2, — n 



The quantity of charge (?) in the cable will be the true 

 capacity multiplied by the mean potential, that is 



_DK ^_ E(2-ro) 



^-T "2^1 2 



, DKE 

 whence g= (oj 



It is convenient to compare the true capacity of the cable with 

 that of the cable assumed as extended in length to include 

 the whole resistance (x +f) as the conductor resistance. The 

 true capacity of this extended cable would be 



— microfarads, 



r 



where r and h are respectively the conductor resistance and 

 capacity per naut, and E is the total resistance of the ex- 

 tended cable («■ + /)• 



Also the quantity of charge on the extended cable, if charged 

 to the same potential E and free at the distant end, would be 



eM. 



r 

 and if earthed at the distant end the quantity (Q) would be 



Q=|.!^^ (6) 



