508 M. E. Jochmann on the Electric Currents induced 



by Felici* must be here mentioned. Instigated by the observa- 

 tions of Matteucci, this author sought to determine the induc- 

 tion in an infinitely thin and unlimited plane disc, rotating 

 under the influence of one or two opposite magnetic poles 

 situated in the plane of the disc. Although, as will be after- 

 wards shown, this case is only admissible as a limiting one, in 

 consequence of the discontinuity therein involved, and although 

 Felici, in solving the problem, employs several hypotheses the 

 correctness of which requires proof, still, as far as the forms of 

 the current-curves are concerned, the result of applying the fol- 

 lowing theory to this limiting case agrees with that obtained, 

 in a quite different manner, by Felici himself. 



In the following memoir I first exhibit the general equations 

 of the motion of electricity in a conducting solid of revolu- 

 tion, of any form, which rotates with constant velocity around 

 its axis, under the influence of a given magnetic distribution. 

 The only assumptions required in the establishment and reduc- 

 tion of these equations are Weber's law of the mutual action of 

 moving quantities of electricity, and the conditions which follow 

 from the supposition of a constant electro-dynamic condition 

 (Stromungszustand). Applying the equations to the particular 

 case where the given magnetic distribution is symmetrical 

 with respect to the axis of rotation, I then show that in this 

 case the component of the current vanishes at every point of 

 the conductor, consequently that no currents are induced, but 

 that it is possible to assign a distribution of free electricity on 

 the surface and in the interior of the conductor, such that its 

 potential, at each point of the conductor, shall equilibrate with 

 the electromotive force induced by the magnetism. I treat, 

 lastly, the case of a disc of any thickness, bounded by two pa- 

 rallel planes, and rotating under the influence of one or more 

 magnetic poles not situated in the axis of rotation. In so doing 

 I assume, for the sake of simplification, that the velocity of 

 rotation, and hence also the intensity of the currents, is suffi- 

 ciently small to permit of our neglecting the inductive action 

 between the several parts of the disc in presence of the direct 

 inductive action of the magnetic poles. 



1. When a homogeneous conducting solid of revolution 

 rotates around its axis with constant velocity, under the influ- 

 ence of any given distribution of magnetic matter, or under the 

 influence of any given system of closed galvanic currents exter- 

 nal to the conductor, a system of currents is induced in the con- 

 ductor, the direction and intensity of which at every point in 

 space remains constant so long as the inducing magnetic force 



* Tortolini's Annali di Scienze Matematiche e Fisiche, 1853, p. 1/3 ; 

 and 1854, p. 35. 



