ELECTROMAGNETIC THEORY OF LINES AND SHIELDS 577 



He = ;;j-^— ^cos 9, 



in excess of the concentric resistance Ra — {lllaj^nflirg given by 

 (84). The relative increase is, therefore, 



The magnetic field (139) is partially reflected from the outer tube, 

 impressed upon the inner conductor, partially refracted into it and 

 dissipated there. Using (110) and (1 1 1) we can show that the reflected 

 field is 



ll_ 

 27ra2 



^^ = '^ — 2^ P COS 6. 



This field converges to the axis of the outer conductor. In order to 

 estimate its effect upon the inner conductor, it is convenient to replace 

 it by an equivalent field converging toward the axis of the inner 

 conductor. By properly changing the origin of the coordinate system 

 this equivalent field can be shown to be 



E, = - y— 2 (/ + P cos if), 



■ti^ = — ;s 5 cos (f. 



Apptying once more (138) (replacing there a by the radius b of the 

 inner conductor), we find that the power loss due to this field is given 

 by the real part of 



/)/2 



so that the absolute increase in resistance of the inner conductor is 



^R.='^J^ (146) 



which must be add ed to the concentric resistance of the inner con- 

 ductor Rb = {ll2b)yl/xf/Tg. The relative increase is therefore 



It is unnecessary to carry the process further. 



