106 BELL SYSTEM TECHNICAL JOURNAL 



Having shown that the constants A, B^ . . . of the series (35) are 

 proportional to I^, we can express the electric field intensity at the 

 inner surface of the return conductor in the form 



£2 = — Z^Io- 



The computation of Z2 is facilitated by transforming the terms of 

 (35) to the axis of the core conductor ^ and placing r = c — a. We 

 thus obtain 



E2=-Z2lo={A+NBo)K-A\og{c-a)-NBo\ogc-N{qi-q2 + qz...) 

 + (terms containing cos d, cos 26, etc., as factors). (53) 



We have, by applying the curl law to an elementary contour which 

 links the core conductor and the return. 



where 



1^ - £i + £2 = - ip^,,, (54) 



U _ 7 T - ^t^otp J o (y y 



ILi — L,\ lo — I Ji (l-\ ■''" 



?0 Jo \Xo) 



(55) 



*12 = ^12 lo = 2 lo log , 



do 



and 



^o = aoi'v4:ir\o(Jio'ip, 



>o and Ho being the electrical constants of the core conductor and 

 Oo its radius. The value given above for $12 holds only for the con- 

 tour on which £2 is independent of the angle d, that is, when the terms 

 of (53) that contain cos 6, cos 26, etc., vanish. The value of Z2 to 

 be used in (54) is therefore determined from 



£2 = - Z2 7o = (^ + NBo) K - A\og{c - a) - NBo log c 



- iV (gi - 22 + . . .) (56) 

 As before, 



- U" = (i? + ipL) lo, (57) 



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

 the cable, including the sea return. 

 We have then from (54), 



R + ipL = Zi + Z2 + ipLn, (58) 



from which R and L can be determined. 



See Note II. • 



