Prof, A. Schuster's Electrical Notes. 3 



MM 7 is equal and opposite to the total reaction of the magnet 

 on the electrified parts of the ring. 



The first of these assumptions is supported by experiment, 

 for since Rowland showed that electric convection did produce 

 a magnetic field, he and others have proved that the field 

 cannot differ much in intensity from that of an equivalent 

 current, and is probably identical with it. Both J. J. 

 Thomson's and Heaviside's investigations agree on this point. 

 As regards the second of the above assumptions, it is tacitly 

 made, I believe, by everyone, although the possibility has been 

 pointed out that part of the reaction may take hold of the 

 " medium ; " but so far we have no ground to doubt the truth 

 of Newton's third law as applied to matter alone. 



The current ~Nep will produce a force on a magnetic pole 



of strength ?n, placed at M, which is equal to Rep. This 



will also be the force with which the pole will act on the ring 

 tending to drive it in a direction parallel to its axis ; as the 



magnetic force H at the ring due to this pole is — 2 and the 



ixr , 



total number of particles is 2irNr, it is seen that each particle 

 must be acted on by a force equal to fiKep, which is Heavi- 

 side's result. 



To trace the cause of the discrepancy it is necessary to 

 enter somewhat fully into J. J. Thomson's first paper ; but 

 in criticising the correctness of some of its deductions I wish 

 specially to guard myself against the supposition that I do not 

 appreciate the high value of that paper. Criticism after a 

 lapse of years is an easy task compared with the opening out 

 of a new line of thought, when errors of detail are of compa- 

 ratively little importance. I begin with an independent 

 calculation of the magnetic forces acting on the sphere, 

 assuming J. J. Thomson's values for the magnetic forces 

 which are due to the sphere. 



3. If the surface charge of the sphere is q, and the velocity 

 is along the axis of X and equal to iv } the components of 

 magnetic force are 



a= — qwg/r*, fi = qwx/r z , 7 = 0,. . . . (1) 



where the velocity id is supposed to be small compared to the 

 velocity of light. 



To obtain the force which acts on the sphere in a magnetic 

 field H, we may imagine that field to be homogeneous and 

 produced by magnetic matter covering a concentric sphere S 

 of radius R, with a surface-density a = 3fiR cos y/^rr, where p 

 is the permeability and 7 the angular distance between P and 



B2 



