278 Prof. J. J. Thomson. The Resistance of [Jan. 17, 



where log 7 = 0'577 log 2, 



so that equation (14) becomes 



the solution of which (see * London Math. Soc. Proc.,' vol. 17, p. 316) 

 is 



if** ~~" 



and therefore 



P" p<T / ^TTflp 



~~~ o H T~ 'V / 



V* 47rv'"a V a 



(1-0 



Thus in this case, since the second term on the right-hand side is 

 small compared with the first, the disturbance is propagated along the 

 wire with the same velocity as that of electrodynamic action through 

 the dielectric. The amplitude of the vibration will sink to 1/e of its 

 original value after traversing a distance 



8va 



If, however, v v does not vanish, and if we suppose qa small, 

 which will be the case unless the velocity of propagation of the 

 electrostatic potential is exceedingly small compared with that of 

 electrodynamic action, since in this case 





_^ 

 " q 



_ __ _ 

 J^iqa) wi log (cy/ 



K ) 

 becomes, remembering that na is large, 



and since - - -- is very large compared with unity, equation (14) 



r 



m 1 (IKCL) op in 



ap 



mv v ^ 

 ~ - - ta log 



____ (16) ; 



and unless (v i/)/v be very small, the right hand side in this equation 

 is very large compared with the first term on the left, and the equa- 

 tion becomes 



m 



ia log 



