622 Mr. J. R. Carson on 



It will be remembered, of course, that 



b = as/4,7r\fjbp 

 and J n (i*/ib) = iia + ivn. 



If the foregoing is substituted in (20), some easy 

 simplifications give 



SlV^ (Si 



C = 1 + ^V2( S i-"¥ 2 S 2 ),. . . (44). 



where 



& x =2 w n k 2n s 2n , (45). 



n-l 



S 2 = I mc n k 2 »s 2n s n4 -\ (46) 



?i-i 



R^^M ^-'V o (47) 



= resistance of wire icith concentric return, 



and w w is the auxiliary function 



11 V — U V 



u n 2 -i-< 2 -i 



Equation (44) is the formula for the correction factor C 

 for non-magnetic conductors, the evaluation of which is 

 discussed in section III. For the purposes of numerical 

 calculation, the following asymptotic expressions are useful. 

 For values of the argument b equal to or greater than 5, 



i^S^-v* m 



Consequently for b>5, 



= l + 2(vT-l/&) (S } -^0PS\ . . (50) 



From the asymptotic expansions of J n it is easy to show 

 that for b>^n 2 



ic, 



l/*/2-(2n-l)/26 (51> 



