250 Scientific Proceedings, Royal Dublin Society. 



XXII.— NOTE ON MR. J. J. THOMSON'S INVESTIGATION OF 

 THE ELECTRO-MAGNETIC ACTION OF A MOVING ELEC- 

 TRIFIED SPHERE, BY GEORGE FRANCIS FITZGERALD, 

 Fellow of Trinity College, Dublin, and Erasmus Smith's 

 Professor of Natural and Experimental Philosophy in the 

 University of Dublin. 



[Read, November 21st, 1881.] 



In the April number of the " Philosophical Magazine " for the 

 present year Mr. J. J . Thomson has given an interesting investi- 

 gation of the electro-magnetic action of a moving electritied 

 sphere. 



On the fourth page (I.e. p. 232) of this investigation, he makes 

 an assumption which he does not justify in order to make the 

 components of the vector potential of electro-magnetic induction 

 satisfy the condition — 



dx dy dz 



As it seemed very likely that they ought to satisfy this con- 

 dition, I thought it v^orth while bringing before the Society 

 a justification of his assumption which, however, leads to slightly 

 different equations from his, though his final result is unaffected. 

 Mr. Thomson has not touched the question of the discontinuity 

 at the surface of the sphere, nor what becomes of the displace- 

 ment when the sphere passes over a point. We may a.ssume that 

 the point remains in its displaced position, and this is practically 

 what Mr. Thomson assumes, but if we do the above condition is 

 not fulfilled. We may assume that it returns to its original 

 position, so that no permanent displacement takes place in the 

 track of the sphere as would occur on Mr. Thomson's assumption. 

 This, however, does not satisfy the condition either, and I have 

 been led to assume that the particle does return to its original 

 position, but that in some way or other the discontinuity at the 

 surface acts as if a moving q^uantity of electricity acted like a^ 



