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 XXXV. Intelligence and Miscellaneous Articles. 



NOTE ON MR. J. J. THOMSON'S INVESTIGATION OF THE ELECTRO- 

 MAGNETIC ACTION OF A MOVING ELECTRIFIED SPHERE. BY 

 GEORGE FRANCIS FITZGERALD, FELLOW OF TRINITY COLLEGE, 

 DUBLIN, ETC. 



TX the April number of the Philosophical Magazine for the pre- 

 ■*- sent year Mr. J. J. Thomson has given an interesting investiga- 

 tion of the electromagnetic action of a moving electrified sphere. 



On the fourth page (loc. cit. 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 electromagnetic induction 

 satisfv the condition 



dec dy dz 



As it seemed very likely that they ought to satisfy this condition, 

 I thought it worth while bringing before the Society a justification 

 of his assumption, which, however, leads to slightly different equa- 

 tions 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 displacement 

 when the sphere passes over a point. We may assume 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 ful- 

 filled. 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, how- 

 ever, 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 quantity of electricity acted like an element of an electric 

 current. This may seem like begging the question ; but it is only 

 doing explicitly what Mr. Thomson does implicitly. It is evidently 

 impossible that the electromagnetic action of moving electricity can 

 be due entirely to the electromagnetic action of the displacement- 

 currents in the dielectric ; for in the case of a plane moving parallel 

 to itself there are none of these displacement-currents, and yet that 

 is the only case that has been experimentally verified. 



To show that my assumption leads to equations satisfying the 

 condition, and leading to practically the same results as Mr. Thom- 

 son's, does not require much work. 



Consider an elementary volume dm ds . cos 0, where ds is an ele- 

 ment of the surface of the sphere, and 6 the angle the radius makes 

 with x. The displacement in this volume is = I, the superficial 

 density, while after the time dt it is zero on my assumption. 



* From the Scientific Proceedings of the Pioyal Dublin Society, vol. iii. 

 part 4, having been read November 21, 1881. Communicated by the 

 Author. 



