1889.] Conductors in the Neighbourhood of a Wire. 



Thus the rate at which heat is generated in the outer conductor is 

 approximately 



and is therefore approximately independent of the resistances of the 

 wire and of the outer conductor, and large compared with the heat 

 developed in the wire. 



The case of an iron wire would differ from that investigated in the 

 case when though na is large, /(/na is also large ; in this case equation 

 (9) becomes approximately 



v v* I na J 



which represents a vibration travelling with a smaller velocity than 

 that of the electrodynamic action through the dielectric, and dying 

 away to 1/e of its original value after traversing a space comparable 

 with a wave-length. When the rate of alternation of the currents 

 gets sufficiently rapid, n'h gets large, and ^ijna small, and we get 

 Case III. na and n'h booh large. 



In this case, since J '(ma) = <J (ma) and I '(m'&) = — il (m'b) 

 and equation (9) reduces to 



m 3 » _ £ ( i _(JL + 4 \ _j l 



v v~ I \na n'bj log (bja) J 



_ »H ~* IV W/ t V V6 2 //log.(&/o)J " 



m = » V7 { 1+ 2A§^) { \/ &) + \/ {if) } hiW) ) ■ 



This represents a vibration travelling with the velocity v ^ (vjv') s and 

 dying away to 1/e of its original value after traversing a distance 



4<v 



p 



From this equation we see that if <r/a 2 is very much greater than 

 ff'/fr 3 , the decay of the disturbance will be due chiefly to the resistance 

 of the wire, but if, on the other hand, a' /b' 2 is very much greater than 

 <7/a 2 , the decay will be due chiefly to the resistance of the outer con- 

 ductor. This case includes that of a wire surrounded by a metal 

 tube, the space between the tube and the wire being occupied by any 

 dielectric, in this case the electrical conditions are perfectly definite, 

 and we see that the velocity of propagation along the wire will be 

 vV (f/V)> where v is the velocity of propagation of the electrodynamic 

 action through the dielectric. Thus if v = v, as in Maxwell's theory, 

 the velocity along the wire will be the same as that through the 



