1887.] Electric Time-constant of a Circular Disk. 295 

 F = 0, G = 0, 



dB. dR 

 a = Ty> h =~^ C = °- 



In the spaces on each side of the stratum — 



dm dm 

 d& + df ; 



whilst in the conductor itself — 



dm. dm 



The equation of electromotive force is — 



the time-factor, as before, being e~ xt . Let us further assume that 

 x enters into the value of H only through a factor sin mx. We shall 

 then have, in the conductor — 



where W = ^Tr/xXlp — m 3 , 0-5-)' 



and in the external spaces — 



— -— — m^H = 0. 



The solutions of these equations, appropriate to our present 

 problem, are 



H = D cos hj, * 



and H = D'e=w, 



respectively, the upper or lower sign being taken in the latter expres- 

 sion according as y is positive or negative. At the surfaces of the 

 conductor we must have — 



a = fia', b = b', 



when the accented letters relate to points just outside, the unac- 

 cented to points just inside. These conditions give — 



