TRANSMISSION OVER SUBMARINE CABLES 97 



t-urface of the iron sht-ath. ("oiiscciikmUK- cfiuation (10) may be 

 written 



1^ - £o' + E[' = - ixip^ = - ipL,.Iu (18) 



where £"i and E'-i are the values of electric field intensity at the 

 outer surface of the core conductor and the inner surface of the iron, 

 respectively, V is the potential difTerence between these two surfaces, 

 and $ is the magnetic flux threading unit length of the gutta percha 

 and jute. Also, from (14) 



- I? = G + WC '' <'«' 



in which Ii is the current in the core and 



G = ^, C = ^, (20) 



2 log - 2 log - 



where gu and ki2 are the electrical constants of the gutta percha, 

 and b is the external radius of the core. It is evident, that G and C 

 are respectively the leakage and capacity of unit length of the cable. 

 Therefore, from (1), 



cTiFc = " + ""■ = ^' ^^'^ 



where R and L are the resistance and inductance of unit length of the 

 cable, including the sea return. Equation (18) may then be written 



Z /i = E[' - £2' + ipLi2 Ii. (22) 



To determine Z we must express E"i and E'2 as functions of /i. 

 We have seen that 



E[' = Zi lu (23) 



where Zi may be termed the " internal impedance " per unit length 

 of this conductor. In fact, when we place Vi = in (8) we obtain 



^„ ^ 2mip Jo (xi) ^24) 



^^ .Tl Jo' (xi)' 



which is the usual formula for the internal impedance of a c\lindrical 

 conductor. 

 Similarly 



£2' = - Z2 /i (25) 



where Z2 is the internal impedance of the return conductor, the 



