6 Mr. J. J. Thomson on the Magnetic Effects 



G, H the components of the vector potential, and o the 

 specific resistance of the metal. 



d¥ (hjr 

 dx ' 



<ru= —bco€ ipt rr — 



crv = 



GW — 



awe 



ipt 



dt 



dG 

 dt 



<m 



dt 



dty 



dy' 



d-^r 



dz~ ; 



(2) 



and therefore 



4:7T/j} 



V 2 F = 



7 . , d¥ d^ 



4z7T/Jb' 



y V 2 G=aft)6^ 



Air/X 



>V 2 H = 



dR 

 dt 



da 



dt 



dijr 



dz' 



d^r 



In the dielectric outside the sphere, if /, g 9 h are the elec- 

 tric displacements, K the specific inductive capacity, and if 

 'd/'bt denote partial differentiation with respect to the time, 

 the equations are 



K 7 " dt dx" Xht dz) dx' 



dG d^ 



K 9 dt dy \*t dz) 



dy \bt 



47r _ dR dty _ _ f"d 



G 



(0€ l 



>~ 



dyjr 

 Ty' 

 d^fr 

 ~dz~ 



and therefore 



i^-d-'-i^-d-^f. 



(») 



with a similar equation for G. 



From the form of these equations we see that the solution 

 will take the form 



^ = ^0 + ^6^ + ^/ e-^ + yfr 2 e 2i Pt + yfr 2 ' e~ 2 ^ + . . . 

 F = F 1 &* + F/ e-^ + F 2 e 2 ^ + F 2 ' e" 2 ^. 



If we substitute these values in the above equations, we see 

 that we may put 'v/r/ yjr 2 ' ... F/, F 2 ' all equal to zero. 

 If e is the quantity of electricity on the sphere, 



^o = 



Kr 



