252 Scientific Proceedings, Royal Dublin Society. 



These are the components of the electro-magnetic 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 



3R 511^ ^ ^^ 



G. = - -i—^ cos a . sm a . cos e. 



-tr epa^ 



Hg = — ^^— ^ cos a . sm a . sm t. 



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

 as due to the external displacement currents, and given by him 

 {I.e. p. 233), namely — 



Ge = /^g (5R2 — 3a^) cos a sin a cos e. 

 He = _^ (5R2— 3a^) cos a sin a cos e. 



we get as the resultant values of the components produced by 

 the displacements assumed — 



^d = 7^^ 0^^ - ^^) COS a sin a cos e. 



Ha = -^ (E,2 - a"^) cos a sin a sm e. 



which however do not satisfy the condition — 



dx dy dz 



Now it is very easy to calculate the action of the superficial 

 moving electricity if it be assumed to act like an electric current. 

 Each element of the surface will act as if it had an electric 

 l.^ on it, and the x components of the electro-magnetic potential 

 will evidently be the same as the electrostatic potential, while 

 the y and z components will vanish. Hence — 



Fe = ^ G. = H, = 0. 



