320 BELL SYSTEM TECHNICAL JOURNAL 



where W is the mean energy transmitted through the cyHnder, T is 

 the mean stored magnetic energy and U the mean stored electric 

 energy, H* denoting the conjugate imaginary of //. Then 



K = Ku+ iKi (16) 



and 



lKn\iV=W, (16a) 



while 



\Ki\I\^ = 2co(r- U), (16b) 



/ being the total current. (In a non-dissipative system T = U and 

 K = Kr.) Rewriting the integral in (15) we therefore have 



W = hKn\I\' = ^\ r rp{E,He* - EeH,*)dpde] - (17) 



^'^L^O Jo J Real Part 



(From equations (1) it readily follows, that for any E- or //-wave, K 

 may be made to depend upon either the transverse electric or transverse 

 magnetic force alone by substituting in formula (17) 



for the £-wave, and 



(18) 



(19) 



for the //-wave, where [£]- and [//]' are defined as 



lEj = |£p|2 + \Ee\'- and [HJ = \H,\^ -f {Hel''.) 

 Consider first the fundamental ii-wave. H^, //p and Eg are zero and 



E, = AJoipX), 



E, = ^AJ,(p\), ■ (20) 



//, = ^,/l/,(pX), 



fico 1 

 where 



X2 = ^2 _^ CO^V^ 



and X = rom/a. (Jo(rom) = 0.) 



From (3) the total axial current /^ in the sheath is given by 



L = ple, P = a. (21) 



