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



The solution of this is 



H' = 



where I (#0 is the Bessel's function of zero order which vanishes 

 when x is infinite. We may by symmetry, since there is no current 

 in a plane at right angles to the wire, put 



dx 9 dy 



iTjV JC* 1 7TT' 



, as a(jc cud 



where since - I- : \- = 0. 



dx dy dz 



and F', G', H' all satisfy differential equations of the same form we 

 have in the wire 



X = ~^AJ (mr), 



and in the dielectric 



im - f 



Again if ' and to are the velocities of propagation of the electro- 

 static potential in the wire and dielectric respectively, we have in the 

 wire 



= CJ (igr), 



where 2 2 = m 2 --^; 

 and in the dielectric = DI (/<j'r), 

 where ^' 2 = m 2 j^' 



(M) 



Since is continuous as we cross from the wire to the dielectric, we 

 have if a be the radius of the wire 



................ (8), 



and since H is continuous, we have 



AJ (ma) -BI (^a,) = - MiCJ (ga) ........ (9), 



where v and v' are the values of v in the wire and dielectric respec- 

 tively. Since F and G are continuous, we have 



-~gCJ '(2a) = ^BV^a) 4-~ 



