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



for H to make 



dF dG + dH_ 



dx dy dz ~~ 



Inside the sphere the differential equations for F x and G } are 

 of the form 



if X x 2 = — 47T/L6^p/<7, the solution of this equation is 



where 



3 sin X x r 3 cos X^ sin X^ 



S 2 (V): 



Similarly 



(V) 3 (Vr V 



G^D^SaCXr)! 



dy dz r ' 

 the differential equation for H^ is 



So that 



where 



a , v sinX^ 



and is introduced to make 



^ dG dH =Q 

 (/#? dy dz 



Since F l5 Gj, Hi are continuous when r=a, if a is the radius 

 of the sphere we have 



CE 2 (^)^DS 2 (X 1 «) + ^=^ ^ _ (5) 



-20B (i\o) -2DS (Xia) + ^ =0. 



Since, on the assumption discussed above, the electrification 

 on the surface of the moving sphere is equivalent to a tangen- 



tial current-sheet whose intensity is ft>e^sin#-r — g, we have 



as another surface-condition that the difference between the 



