540 BELL SYSTEM TECHNICAL JOURNAL 



mental equations (13) which assume the following simple form: 



ii^eE, = TH^, ii^ull^ = TE„ "EeEA = 0, (22) 



if Eg vanishes identically. Either of the first two equations determines 

 the ratio of the electromotive intensity to the magnetomotive; the 

 two ratios are consistent only if the condition (21) is satisfied. Then, 

 we have also 



r _ t .. , ^^ A 



Ep =-^ H^ = ^p 11^ and H^ = - , (23) 



tcoe \ € p 



where A is some quantity independent of p. This constant can be 

 readily calculated from Ampere's law. The magnetomotive force 

 acting along the circumference of any particular cross-section of the 

 inner cylinder equals l-wpH^ amperes, i.e., lirA; since this M.M.F. 

 should equal the total current I flowing in the inner conductor through 

 the cross-section, the quantity A equals 7/2 tt. Reintroducing the 

 implied factor e"~^^, we have 



■'■■'■ V rj ^ ) 



/xp 



27rp \ e 



In practical measurements we are concerned with the total potential 

 difference (F) between the cylinders, rather than with the transverse 

 electromotive intensity. The former is merely the integral of the 

 intensity. 



This voltage and the current I vary as voltage and current in a semi- 

 infinite transmission line whose propagation constant is T and whose 

 characteristic impedance is 



At any point z the intensities Ep and H^ have the same values as ivould 

 the voltage and current at the same distance z from the end of a trans- 

 mission line whose propagation constant and characteristic impedance are 

 respectively icoVcAi and ^ult. 



