E,/ dR\ H <m r , 



Self-induction of Wires, 343 



gitudinal, the energy-transfer in them would be exactly radial, 

 and EC and — FC would be precisely equal to the Joule heat 

 per second plus the rate of increase of the magnetic energy, 

 in the inner and the outer conductor, respectively. But as 

 there is a small radial current, there is also a small longitu- 

 dinal transfer of energy in the conductors. Thus, E r and E* 

 being the radial and longitudinal components of the electric 

 force, in the inner conductor, for example, the longitudinal 

 and the radial components of the energy- current per unit area 

 are 



E r H/47r and E^H/4tt, 



the latter being inward. Their convergences are 



^^BJE and 1 d E 2 H 



dx Ait ' r dr Air 



or 



E gg E, <ZH H dE z 



Air Ait dr Air dr 

 or 



E,r *^,andE,r.+ £^-', 



Air dz ' Air dr 



if T r and Y % are the components of the electric current-density. 

 The sum of the first terms is clearly the dissipativity per unit 

 volume ; and that of the second terms is, by equation (13), 



Part I., H/xH/47r, the rate of increase of the magnetic energy. 



The longitudinal transfer of energy in either conductor per 

 unit area is also expressed by — (Airh)~ ll 3.{d^ / dz) ; or, by 

 — {Airkfi)" 1 (dTx / dz) across the complete section, if T x tempo- 

 rarily denote the magnetic energy in the conductor per unit 

 length. 



Now let E„ Fu Oi, Vi, and E 2 , F 2 , C 2 , Y 2 refer to two dis- 

 tinct normal systems. Then, if we could neglect the longi- 

 tudinal transfer in the conductors, we should have 



U^-T^J^VA-VAKCPi-M • • (122) 



the left side referring to unit length of line ; and, in the whole 

 line, 



U 12 -T 12 =[V 1 C 2 -V 2 C 1 ]^(i' 1 -i> 2 ). • • (123) 



Similarly, for a single normal system, 



2 (U-T)=^C^J, (124) 



