330 BELL SYSTEM TECHNICAL JOURNAL 



In the subsequent analysis /„ (?) of the solution for the solid wire 

 case is replaced by 



M&-{^-lK„{i) = Mn{i), (10) 



and Jn (?) is replaced by 



A'(^)-^^/^n'(?) =-!/„'(?). (in 



Otherwise the formulation of the alternating current resistance of 

 the conductor proceeds exactly as in the solid wire case. For the 

 electric force at the surface r=a in the conductor, we write 



R..=Ao{Mo{i)+hiMM) cose+/7o.Uo(t) cos 29+ . . .] (12) 



and determine the fundamental coefficient Ao in terms of the current 

 in the conductor. The resistance R of the tubular conductor per 

 unit length is defined as the mean dissipation per unit length (li\ided 

 by the mean square current where the mean dissiiiaiion is calculated 

 by Po)-nting's theorem. Accordingly, we get 



' ..=1 ' 



To determine the harmonic coefficients h\ . . . hn or Ai . . . An, 

 the total tangential magnetic force and the total normal magnetic 

 induction at the outer surface of a conductor are expressed in terms 

 of the coordinates of that conductor alone, and the conditions of 

 continuity at the surface are applied. This leads to the set of equations 



q„ = {-\r2p„k"-^=^ p„k"^J.q) (14) 



= 1.2,3 ... « 



where 



<7, = (?ilV (O-WMMn (?))/{ M'ii), 



p, = (^l/»'(f)-WMM,(?))/(.l/„'(f)+M/i.U„(?)), 

 Qn = trjln. 



