336 BELL SYSTEM TECHNICAL JOURNAL 



As a check on formulae (V) and (VI), the limiting cases may be 

 arrived at directly as follows. If the conductors are thin tubes, 

 the harmonic coefficients are given by 



/», = (- l)«+'2;t" ^"^ 





4;-i) 



When f is very large 



= (-l)"2/fe"5", (44) 



and 



^-=^' = 1 (45) 



Mo Mo' 



so that 



C=Real[l + igl/.„4;:conj.^,] 



1-ifeV 



(46) 



the same result as for the corresponding liniitiiig case of a solid con- 

 ductor. 



On the other hand, if ^ is not large and J — f is very small, 



(47) 

 (48) 

 (49) 



so that 

 and 



(50) 

 (51) 



