by a Magnet in a Rotating Conductor. 507 



induced currents, upon which the true explanation of the pheno- 

 menon in question depends, our knowledge of the same, from 

 an experimental as well as from a theoretical point of view, is 

 still very deficient. The paths of the currents induced in the 

 rotating conductor have by no means been experimentally de- 

 termined with certainty ; for, as I shall elsewhere show, the 

 methods employed in investigating the curves described by these 

 currents do not attain the object in view. These methods, in 

 fact, are based upon the inadmissible assumption that the cur- 

 rent-curves, and the lines of level of the potential of the free 

 electricity, constitute two orthogonal systems. In a theoretic 

 point of view, however, the treatment which the problem has 

 hitherto received is still more imperfect, as will be evident from 

 the following resume. The laws of currents excited by magnetic 

 induction in linear conductors were completely established by 

 Neumann, Weber, and others, and reduced by Weber to the 

 general principle of the mutual action of moving quantities of 

 electricity. Kirchhoff* afterwards exhibited the general differ- 

 ential equations for the variable electro- dynamic condition of 

 stationary solid conductors, taking into consideration the in- 

 ductive action produced between the several parts of the con- 

 ductor by the variations in the intensity of the current; and he 

 deduced from these equations certain general conclusions. With 

 respect to the induction in solid conductors moving under the 

 influence of a magnet, however, the general differential equa- 

 tions, upon whose integration the solution of the problem 

 depends, have not as yet even been exhibited. Shortly after 

 the publication of Arago's experiment, Poissonf, it is true, 

 sought to explain the phenomenon by the action of magnetism 

 at its moments of appearance and disappearance, — an action 

 which might be very appreciable even in metals which, like cop- 

 per, exert no action on the magnetic needle as soon as equili- 

 brium in the magnetic condition of their molecules has been 

 established. Since Faraday's discovery, however, Poisson's 

 theory, notwithstanding its ingenuity and elaborate develop- 

 ment, must be regarded as antiquated. Besides the experi- 

 mental researches of Faraday J, Nobili, Antinori§, and Mat- 

 teucci||, to which I shall elsewhere return, a theoretical memoir 



* Poggendorff's Annalen, vol. cii. p. 529. 



t " Sur la Theorie du Magnetisme en mouvement," Mem. de VAcad. des 

 Sciences, annee 1823, vol. vi. (Paris, 1827). 



| Phil. Trans. 1832. 



§ Antologia di Firenze, No. 134 ; Poggendorff's Annalen, vol. xxiv. 

 p. 621. 



|| Annates de Chimie et de Physique, 3 ser. vol . xxxix ; and Cours special 

 sur Vinduction, le magnetisme de rotation, fyc. Paris, 1853. 



