■626 Mr. J. R. Carson on 



true resistance R* and reactance X of the circuit are defined 

 by the relation 



~R + iX = 2Z + ipJj (64) 



Having calculated q 1 . . . q n and li x . . . h n in accordance 

 with methods discussed above, it is a straightforward process 

 to calculate Z, L, R, and X from (60), . . . (64), the only 

 operations involved being the evaluation of the Bessel 

 functions appearing in the formulas. For very low fre- 

 quencies, Z and L approach the limit Z and L respectively. 

 On the other hand, when the frequency is sufficiently high 

 they approach upper limits corresponding to 



h n J n /J r~ 2k n s n when n is even. 

 Consequently, 



(i + /i 2 J 2 /J + ^ JV Jo + • - •) ~ i_/.2 g * = ^™> 



where C m is the upper limit of the correction factor C. 

 It may also be shown that 



2Z + ipL— 2C m Z + tip log Q- ). 



The limiting values of Z and L correspond to the surface 

 distribution of currents which would exist if the wires were 

 of infinite conductivity. 



The calculation of Z and L from the foregoing formulas 

 and tables of Bessel functions is not a difficult matter. The 

 writer, however, hopes when time permits to prepare nume- 

 rical tables and the theoretical data for the computation 

 of Z and L, similar to those given in section III for the 

 correction factor C. The latter function is, however, of 

 much the greater engineering importance. 



III. Formula for Correction Factor C for 

 Non-Magnetic Conductors. 



List of Symbols, 

 a = radius of wire in cm. 



c = interaxial separation between wires in cm. 

 k = ratio ale. 



\ = conductivity of wire in elm. c.G.s. units. 

 ix = permeability „ „ „ 



p = 27T times frequency in cycles per second. 



b = a x/4zir\fip, 

 * The circuit resistance is, of course, twice that of the wire. 



