2 7 o HERMANN VON HELMHOLTZ 



reciprocal action, and directly proportional to the product of 

 the two quantities, with repulsion between like, attraction 

 between unlike charges, was supplemented by Weber by the 

 hypothesis that the velocity with which the two electric charges 

 approached, or receded from each other, as well as their 

 accelerations, must have some influence on the magnitude of 

 the force between them. This assumption of forces which are 

 dependent, not only on the position, but also upon the motions, 

 of the acting points, seemed to contradict Helmholtz's 

 observations, since he was led by his inquiry into the conservation 

 of energy to the view that forces depending on distance and 

 velocity are contrary to the universal law of the conservation 

 of energy, which had been thoroughly confirmed for the 

 phenomena of electrodynamics also. It is true that Helmholtz 

 had not at that time taken into consideration the more compli- 

 cated case of Weber's law, in which the forces further depend 

 on acceleration, and it was in fact shown that Weber's law 

 admits of no cyclical process by which work can be evolved 

 out of nothing. 



Along with Weber's hypothesis were a whole series of 

 others, all having this in common, that they regarded the 

 magnitude of Coulomb's force as modified by the influence of 

 some component of the velocity of the moving electrical 

 charges. Such were the hypotheses of F. E. Neumann, of his 

 son C. Neumann, and other physicists, but the observed facts, 

 and conclusions from theories that were not well founded, all 

 ran confusedly together. Helmholtz undertook to clear up 

 the region of electrodynamics, and to search for crucial results 

 of the several theories, so as, wherever possible, to decide 

 between them by means of suitable experiments. He found in 

 the first place that all the phenomena incident on the passage 

 of fully closed currents in their circulation through closed 

 metallic circuits, in which during the passage of the current 

 there was no perceptible change in the electric charges 

 accumulated in any part of the conductor, were equally well 

 accounted for on any of the above hypotheses. The results 

 agreed as well with Ampere's law of electromagnetic action 

 as with the theorems discovered by Faraday, and amplified by 

 F. E. Neumann. With incompletely closed circuits, however, 

 these hypotheses led to essentially different results, since 



