88 Dr. J. W. Nicholson on the Effective 



The values of these functions have been tabulated, yet as 

 Russell has shown *, the tables need revision. But it is 

 preferable, in place of a laborious tabulation, to use the 

 asymptotic formula? for these functions, which Russell 

 develops in the same paper. We may distinguish two im- 

 portant cases, and it is convenient to recapitulate, at this 

 stage, the meanings of the various symbols. The oscillation 

 is assumed to be sine-shaped, and of frequency p/27r, fx and <r 

 are the permeability and resistivity of the wire. The wire 

 has a radius r of section, and is wound on a cylinder of 

 radius a, such that r/a is small. The angle of the helix is a. 

 Let n be the number of turns of the helix in a length z 

 parallel to its axis. Since, in a helix, z~a6 tan a, we have 



■n = 6/27r=z'2'7Ta tan a, 

 and therefore 



a = tan- 1 (^/27r»a) (40) 



Case of Small Frequency. 



When x-=r(4'7rfjLp/a)i is less than 2, we may write 



pi f . _ 1 lm \ 4 13 (x\* 647_ _ (xV 2 \ 



4' r \ 24\2/ + 4320\2/ "~ 12*. 360 . 56\2/ i 



-^^ 2 1 x - + is U) " i«ob) + 1^730(2) ) 



and therefore 



-K 1+ 6(2) 4 -2io(l) 8 }' 



no higher order being necessary in the last two, as they will 

 be multiplied by r 2 /a 2 . 

 The resistance becomes 



* Zoc. cit.\ 



(41) 



