1889.] Electrolytes to very rapidly alternating Currents. 275 



dF dG dH _ d(f> 



~&c + di + ~dT = di' 



On this theory v is also equal to 1 -I- j-- where e is a quantity such 



that the effect of the polarisation produced in a parallelipipedal 

 element of dielectric by an electromotive force X may be represented 

 by distributions of electricity of surface densities plus and minus e 

 over the faces of the parallelipipedon at right angles to X. 



Let all the variable quantities be proportional to e*(" M[ +**) 1 Then 

 in the conductor since 



d&^ dy*^ dz* ' * dt' 



where /* is the magnetic permeability and a the specific resistance of 

 the conductor, we have 



dx% dy 2 



or, since the axis of the wire is an axis of symmetry, if r be the 

 distance of a point in the wire from this axis 



L' = 0j 



dr* T r dr 



and if r? 



a 



the solution of fche equation is 



H' = AJ (mry<"+i*>, 



where J (ic) represents the Bessel's function of zero order which is 

 finite when x = 0. 



In the dielectric surrounding the wire H' satisfies the differential 

 equation 



J2TJ' 



dx^ 1 dy^ dz^ v^ d$ 



where v is the velocity of propagation of electro dynamic action 

 through the dielectric. Transforming this as before, this may be 

 written 





dr 2 r dr 

 where <c 2 = m 2 



