1889.J Conductors in the Neighbourhood of a Wire, 



7 



Since na is large, the second term in the bracket will be small for 

 wires made of non-magnetic metals ; so that for this case (11) reduces 



or, substituting for n the approximate value /\J ^ 7r ^ i l P^ } 



or 



rn-ll^V J lo gWV^) llfi , Z L_ 1 



vlv I I log(6 2 /a 2 ) j 1 T 41og( ff 74V^) i 



This represents a disturbance propagated with the velocity 



1 



V V log(feV) / 



and fading away to 1/e of its original value, after traversing a distance 



7T p \/ V \/ ( ° a 2 ^ 4i7Tfi pofi) ' 



or if X is the wave-length of the electrical vibration, the distance a 

 disturbance travels before falling to 1/e of its original value is 



2X , d 

 lo 



7T 



.2 " & 



Thus in this case, even if v' equals v, that is, if Maxwell's theory is 

 correct, the rate of propagation of the disturbance along the wire will 

 not be the same as that of electrodynamic action through air ; and 

 yet the conditions may be such as to allow a disturbance to pass 

 over several wave-lengths before falling to 1/e of its original value. 

 It will be noticed that the velocity of propagation does not depend on 

 the specific resistance of the wire, and that it increases with the 

 rapidity of the reversal, and that the rate at which the vibrations die 

 away is independent of the resistance of the wire, and only varies 

 slowly with the resistance of the outer conductor, since d only enters 

 in the form log d . 



"We can see the reason of this if we consider the amount of heat 

 produced in the outer conductor. 



If i is the current parallel to the axis of z passing through a 

 section of the wire, then, assuming in the investigation that v — v } 



