Intelligence and Miscellaneous Articles. 303 



Hence calling the displacement D, we have 



C IR dt= — a . dx ds . cos 0. 

 dt 



Hence 



D=_g /I^.ds. cos0. 



Now — =p, the velocity of the sphere which is supposed to be 



moving along x. Hence the components of I) are /, g, h ; and 

 observing that ds = a 2 dp. d<j>, where cos 6=fx, and a is the radius of 

 the sphere, while 4wa 2 . d = e, the total quantity of electricity on the 

 sphere, 



fdcc dy dz= — -j- fi 2 djj, d<p, 



g dx dy dz= — -±-\l cos (p dp dip, 



h dx dy dz=— -^ n sin <p dp df. 



47T 



Hence the components of the electromagnetic potential are at a 

 point at a distance 



d\xd<p. 



H^- e 2>CCl* sh 



4 *JJ ' 



These are the components of the electromagnetic potential due 

 to this superficial change of displacement that I have assumed. 

 When integrated over the surface of the sphere, they give at a 

 point distant E from its centre, and whose polar angles are a and e, 



r{ epa 2 



^S= — ^D3" C0S * ' Sm a ' C0S *> 



O-tv 



-^•s = ~ f^r cos a . sin a . sin e. 



If we add to these the components calculated by Mr. Thomson 

 as due to the external displacement-currents, and given by him (loc. 

 cit. p. 233), namely 



Pe = I^ (5E2_3ft2)(COS2a ~ i) ' 

 G- e = ^* (5E 2 — 3a 2 ) cos a sin a cos e, 



H e = -^j^ (5E 2 — 3a 2 ) cos a sin a cos e, 



