M. Helmlioltz on the Theory of Electrodynamics. 531 



exhibit differences. The plan of my memoir was principally to seek 

 out those differences which it might be possible to discover byprac- 

 ticable experiments. It must here be remarked that the various 

 potential-expressions which I formed differ from one another only 

 by a constant (in my memoir, denoted by k) , We obtain Neu- 

 mann's expression if we put ^= + 1, MaxwelFs if ^ = 0, W. We- 

 ber's if k= — \. The investigation showed that the expressions 

 with k negative led to impossible consequences — namely, to an 

 unstable equilibrium of the electricity in conductors, which, once 

 disturbed, might give rise to infinitely great current-intensities 

 and unlimited charges. On the other hand, the expressions 

 with k positive, or with ^ = 0, gave stable equilibrium, and, even 

 for open currents, only such differences as, with our present ex- 

 perimental means, can hardly be detected j so that what is yet 

 doubtful in the mathematical conception of the law, viz. the 

 value of the constant k, appears to have no effect in the applica- 

 tion of it to experiment. 



These expressions for the potential of each two current-ele- 

 ments, however, are manifestly not elementary expressions of the 

 last acting forces ; for they lead, if we imagine each current- 

 element as a solid body, to at least two forces for each, or to a 

 force and a pair of forces ; and the quantity and partly the di- 

 rection of these forces depend not merely on the situation of the 

 elements, but also on the velocity of the electric currents. The 

 phenomena of induction are only indirectly derived from the 

 electrodynamic potential, through the interposition of the law of 

 the conservation of energy. 



Among the further-penetrating hypotheses which seek to 

 ascertain the elementary forces that lie at the base of electrody- 

 namic phenomena, two especially must be mentioned. Mr. 

 Clerk-Maxwell drops the assumption of action at a distance, and 

 assumes that all magnetic, electrostatic, and electrodynamic 

 actions are translated to a distance by the propagation of mole- 

 cular motions and forces in an elastic medium vv^hich fills space. 

 As the theory finally gives for this medium the capability of 

 executing oscillations which are perfectly similar to those of light 

 and have also the velocity of propagation of light, this medium 

 must be identified with the luminiferous sether. It is true that, 

 for the reciprocal action of neighbouring volume-elements of this 

 medium, he assumes laws considerably different from those of 

 the elastic bodies known to us ; but he has shown that a kind 

 of reciprocal action, such as he attributes to the ?ether, can indeed 

 be produced by a mechanical combination of solid elastic bodies. 

 For this purpose a system of cells with elastic walls and cylin- 

 drical cavities must be taken, in which elastic balls can rotate 

 and be flattened out by the centrifugal force. In the walls of 



2 M 2 



