1895.] of the Electric and Luntiniferous Medium. 223 



from the principle of energy, as the work of the surplus energy in 

 the field, the motions of the bodies in the field being thus supposed 

 slow compared with radiation. It was seen that in order to obtain 

 the correct sign for the electrodynamic forcives between current 

 systems, we are precluded from taking a current to be simply a 

 vortex ring in the fluid aether; but that this difficulty is removed by 

 taking a current to be produced by the convection of electrons or 

 elementary electric charges through the free tether, thus making the 

 current effectively a vortex of a type whose strength can be altered 

 by induction from neighbouring currents. An electron occurs 

 naturally in the theory as a centre or nucleus of rotational strain, 

 which can have a permanent existence in the rotationally elastic 

 nather, in the same sense as a vortex ring can have a permanent 

 existence in the ordinary perfect fluid of theoretical hydrodynamics. 



In the present paper a further development of the theory of elec- 

 trons is made. As a preliminary, the consequences, as regards pon- 

 deromotive forces, of treating an element of current < as a separate 

 dynamical entity, which were indicated in the previous paper, are 

 here more fully considered. It is maintained that a hypothesis of 

 this kind would lead to an internal stress in a conductor carrying a 

 current, in addition to the forcive of Ampere which acts on each 

 element of the conductor at right angles to its length. Though this 

 stress is self-equilibrating as regards the conductor as a whole, yet 

 when the conductor is a liquid, such as mercury, it will involve a 

 change of fluid pressure which ought to be of the same order of 

 magnitude as the amperean forcive, and therefore capable of detec- 

 tion whenever the latter is easily observed. Experiments made by 

 Professors FitzGerald and Lodge on this subject have yielded purely 

 negative results, so that there is ground for the conclusion that the 

 ordinary current-element ? cannot be legitimately employed in 

 framing a dynamical theory. 



This result is entirely confirmed when we work out the properties 

 of the field of currents, considered as produced by the convection of 

 electrons. There can be no doubt that a single electron may be 

 correctly taken as an independent element of the medium for dynamical 

 purposes ; so that electrodynamical relations deduced from a statistical 

 theory of moving electrons will rest on a much surer basis than those 

 derived from the use of a hypothetical current-element of the ordi- 

 nary kind, in cases where they are in discrepancy. 



Now it is shown that an intrinsic singularity in the aether, of the 

 form of an electron e, moving with velocity (a-, y, z) relative to the 

 quiescent mass of ajther, is subject to a force e (P, Q, R), given by 

 equations of the form 



VOL. LVT11. 



