326 BELL SYSTEM TECHNICAL JOURNAL 



one of the wires and the separation of the wires. The Bessel functions are of 

 order zero to infinity and the argument, h, is given by 



h = ia\/Air\nip (2a) 



where 



a = radius of the wire in cm. 



X = conductivity of wire in c.g.s. units 



ju = permeability of wire in c.g.s. units 



p = 2t times the frequency in cycles per second 



The separation comes in by way of the quantity k, the ratio a/c of the radius 

 to the interaxial separation of the wires, and a function 5 which can be 

 expressed as a continued fraction in k , viz., 



. = ^« (3a) 



1 



1- "' 



1 - ... 



which results in 



from which 



1 



1 - k^s 



(4a) 



2)fe2 ^ ^ 



as given by Carson's equation (38). 



The actual expression for R + iX is as follows: 



R + iX = 2Z-\- ipL 



= - Aip log ks + 2Zo\l + Z i-ksYhnJu/Jo] 



(6a) 



where 



Zo = i?o + iX^ 





 2p UoVo — tloVo , . 2p UqUo + fo^'o /-, a 



— — 2 , 2 + * -f — 9. . •>. (7a) 



A 2 1 2 ' h 2 I 2 



17 



which is the impedance of a wire with concentric return expressed as usual 

 in terms of the ber and bei functions related to the Bessel functions by the 

 formula 



" Russell, "Alternating Currents," Edition 1904, Vol. I, p. 370. 



