250 CONNECTION OF ELECTRICITY AND MAGNETISM. 



certain motions of electricity, as, for instance, radial oscillations in 

 a conducting- sphere, ought to grow without end in intensity and to pro- 

 duce an infinite quantity of motion and of heat, which, of course, must 

 be regarded as impossible. This inference was of some importance for 

 our choice between the different theories of electro-dynamics, because it 

 showed that the laws of induced currents derived from the hypothesis 

 of W. Weber, and in the same way those derived from the different 

 hypothesis which Prof. 0. ISFeumaun, jr., has proposed, are inadmis- 

 sible, leading, as they do, to unstable equilibrium of electricity. I 

 do not think that my objections have been invalidated by the argu- 

 ments brought against them by my opponents, but this I must leave 

 to the judgment of my mathematical readers. 



I may omit here, perhaps, another i)oint of discussion. Mr. C. Neumann 

 believed that the law of the forces derived from the value of the poten- 

 tial led to inferences opposed to the results of experiment in those cases 

 where one part of the conducting wire slides along the surface of another 

 part of the same circuit. I have striven to prove that there is no 

 contradiction between the law of the potential, rightly interpreted, and 

 the observed facts. 



The potential theory, when applied to the calculation of the pondero- 

 motoric forces, produced by and acting on unclosed circuits, gives 

 not only forces acting between two linear elements of electric cur- 

 rents, according to the law of Ampere, but also other forces acting be- 

 tween the end of the current and a linear element of another, and forces 

 acting between two ends. At the extremities of an open stream-line, 

 quantities of free electricity are either appearing or vanishing. We may 

 say, therefore, that those forces are acting between electricity in statu 

 nascendi and streaming electricity. 



It was not difficult to prove that the law of the electro-dynamic poten- 

 tial was in accordance with the principle of conservation of energy, even 

 for currents with open ends. It was to be questioned if the same is the 

 case for the original law of Am^Dere. This question has been investi- 

 gated by Mr. Neuuiann, jr. He bases his reasoning on the suppo- 

 sition that forces, one of which acts between every pair of linear 

 elements of currents, are the only pondero-motoric forces existing. Be- 

 sides, he supposes that the forces of superimposed currents are sim- 

 ply superimposed themselves, and that the principle of conservation 

 of energy is valid. He concludes from a very clever and skillful analy- 

 sis that these assumptions are sufiicient to determine all the ques- 

 tionable points. But the law of induction produced by change of inten- 

 sity, which results from his analysis, corresponds to an unstable equilib- 

 rium of electricity, and to a negative value of the constant, introduced 

 by myself. I infer, therefore, from the results arrived at by Prof. C. 

 Neumann that his hypothesis is inadmissible, and that there must exist, 

 in reality, other pondero motoric forces at the ends of currents besides 

 those of Ampere. I think that the theory based on the existence of an 



