104 BELL SYSTEM TECHNICAL JOURNAL 



(40) 



The quantities <^ and a have the same significance as in equations 

 (36) and (37). 



The tangential magnetic field intensity in the sea water at the 

 surface of wire " zero " is, therefore, 



''^ = rp^' = Wa -^o+cos^[-g./f-f(^+5n^.)+Jl2.] (41) 

 + 2 cos 20[- ga/f^ + ^ (^ + 522 Bo) — |y S2] 



+ n cos ncj, \ - qj^n + LJ> (^ + 5^^^^) _ ( ^^ 2„1 



L w n! J 



To satisfy the condition of continuity of electric and magnetic 

 field intensities at the surface of the armor wire it is necessary that 

 the coefftcients of the corresponding terms of (36) and (38) and of 

 (37) and (41) be equal. This gives 



Co Jo (^) = (^ + NBo) K-A logc - 5olog {ac, . . . c„) - 2o, (42) 



C„/„(^)=g„/r«+^^^(^ + 5„„5o)-^:^2„,n = l,2,...oc (43) 



^J'o (^) Co = - tiBo, (44) 



Un (I) Cn= - m r?»/f" - ^^^ (^ + Sn„Bo) 



-^^S„].« = 1,2, ...00 (45) 



From these expressions the quantities Bi . . . Ci . . . can be de- 

 termined. Multiplying (43) by tui and subtracting (45) gives 



r = ^^^g" \ (A(\\ 



r« ^M/n (^) - ^// (I)' ^''''^ 



