10 Prof. J. J. Thomson. On the Effect produced by [May 2, 



dielectric, but it will not be so unless this condition is fulfilled. 

 Thus this case would afford a definite means of testing whether or not 

 Maxwell's theory is true. The thickness of the outer tube would be 

 immaterial, as with these very rapid vibrations the currents are 

 entirely confined to the inner skin of the tube. 



By comparing the results for this case with those of Case II, we 

 see that if the rate at which the electrical disturbances die away 

 depends on the conductivity of the wire, the velocity of propagation 

 through the wire must be the same as that through the dielectric if 

 Maxwell's theory is true. 



The preceding equations can be modified so as to include the case 

 when the outer conductor is replaced by another dielectric ; all that 

 we have to do is in equation (9) to replace n' by where 



v 1 being the velocity of propagation through the outer dielectric. 

 In this case equation (9) becomes 



k2 _ Tl ! m J o(' na ) K ' ioO'fr) 1 I | y, ~ y m 2 



I m 2 — ?i 2 J '(ma) m 2 — ^ I '(t/c'6) / log (bja) v 



If both K r b and na are large, the velocity is the same as before, 

 viz., v V (f/"')- If na i s l ar g e an( i ic'b small, the equation becomes 

 approximately 



v v 2 log {b/a) 



or substituting for I (</c'&) we get 



\ v log (b/a) J v 2 I log {b/aj J ' 

 Thus the velocity of propagation is 



I v' ^ log (b/a) 1 / 



J log (l/ 7 ^6; y 

 I ^ loff(6/a) / 



log {b/a) 



As it has been shown above that if the rate at which the vibrations 

 decay depends upon the nature of the wire, the rate of propagation 

 of the disturbance along the wire will be v^/(v/v'), I thought it would 

 be of interest to determine the rate of propagation in this case, in 

 order to see whether the velocity would still differ as much as in 

 Hertz's experiments from that of the propagation of the electro- 

 dynamic action through air. 



