TRANSMISSION Ol'ER SUIi.M.tRINE CABLES 



99 



being conducted by the sea water alone. As in the preceding case, 



2Mit> Jo{x\) 



Z, = 



Xi J'o{Xi) 



TVie expression for Z2 simplifies considerably. The electric field 

 intensity in the sea water may be written, from (4), 



£2 = B2 Ko (pi), 



(30) 



the term in J^ being absent in order to permit £2 to vanish at infinity. 

 Also, from (6), 



2 tJL.ip 



From (30) and (31) we have 



y2 



/l. 



, _ 2/x2tp Ko {yi) J. 

 yi K'o {yi) 



from which the return impedance can be written, 



2ij.2ip Ko {ji) 



We have then 



Z = R + ipL = 



^' y^ K'oiy,) 



2fj.iip Jo {xi) _ 2iX2ip Ko (^2) 

 Xi Jo (xi) y-i K'o (^2) 



(31) 



(32) 



(33) 



+ ipLn. 



The resistance and inductance of the sea return of a submarine 

 cable were calculated from formula (28). employing the following 

 values for the constants: 



Copper 



Iron 



Sea Water 



ai = .226 cm. 



61 = 



Ml = 1 



Xi = 6.06 X 10-" 



a2 = .990 cm. 



62 = -737 cm. 

 M2 = 100 



[ X2 = 8 X 10-6 



as = «> 



bs = .990 cm. 



M3 = 1 



X3 = 5 X lO-'i 



