546 BELL SYSTEM TECHNICAL JOURNAL 



unit length between two cylindrical conductors is 



Y = ^"fe +Jr^ ^ G + i^C, (43) 



logy 



the symbols G and C being used in the usual way to designate the 

 distributed radial conductance and capacity. Writing these sepa- 

 rately, we have 



r> ^TTg 27re . . 



G = ^ , C = ^, . (44) 



logy log-y 



Returning to (40), we find that F can be written in the form 



But the ratio of the transverse electromotive force V to the longitudinal 

 current / is known as the longitudinal characteristic impedance of the 

 coaxial pair. Its value is obviously F/F. 



The External Inductance 



In dealing with parallel wires it is customary to use the term 

 "external inductance" for the total magnetic flux in the space sur- 

 rounding the pair.^^ We shall adopt the same usage in connection 

 with coaxial pairs. Strictly speaking, we must therefore consider it 

 as being composed of two parts : one being the flux between the cylinders, 

 the other the flux in the space surrounding them. But the longi- 

 tudinal displacement current is negligible by comparison with the con- 

 duction current, and effects due to it have been consistently ignored 

 throughout this part of our study. To the same order of approxima- 

 tion, the flux outside the pair is negligible by comparison with that 

 between them, whence we find the "external inductance" to be 



M j ^ H^dp ^„ 



Le = ^' J = TT- log ^T henries/cm. (45) 



1 ATT 



" While this definition is very descriptive, it is not strictly accurate unless the 

 wires are perfectly conducting. The correct definition should read as follows: 

 The external inductance of a parallel pair is the measure (per unit current) of mag- 

 netic energy stored in the space surrounding the pair. The reason the simpler 

 definition fails for imperfectly conducting parallel wires is because some of the lines 

 of magnetic flux lie partly inside and partly outside the wires. This does not happen 

 in connection with coaxial pairs even when they are not perfectly conducting. 

 Hence we are warranted in using the simpler idea. 



