Moving Electrons and Electric Charges. 203 



This theory was, however, shown long ago by Lord Kelvin 

 and Professor von Helmholtz to be untenable, on account of 

 its violating the principles of the modern theory of energy ; 

 now, of course, direct action at a distance is altogether out of 

 court. The present question is whether a theory of electrons 

 which act on each other, not directly according to a law of 

 force, but mediately by propagation of the effect across the 

 intervening aether, suffices to avoid the discrepancies of earlier 

 theories and give a consistent account of electrical and optical 

 phenomena ; and it is maintained that the answer is altogether 

 in the affirmative. This question is, presumably, sufficiently 

 important and fundamental to justify the present detailed 

 explanation. 



At the end of the first of the two papers referred to, 

 building chiefly on the analytical results of previous theorists, 

 the steady aethereal disturbance carried along by a moving 

 electron had been investigated, and also the law of the force 

 exerted on each other by two moving electrons through the 

 intervention of the aether between them. This was on the 

 hypothesis that each electron carried along with it a steady 

 trail of aethereal disturbance, but that no sensible derange- 

 ment of this steady motion ever occurred such as would lead 

 to loss of the energy of the system by the starting of waves. 

 If the velocities of the electrons remain always small compared 

 with that of radiation, then, however their mutual influences 

 alter their motions, this steady trail will instantaneously adjust 

 itself to the new conditions without sensible excitation of 

 radiation, and the theory will apply. But if any of the elec- 

 trons are moving with velocities comparable with that of 

 radiation, a change in velocity will involve derangement of 

 this steady trail of aethereal strain and motion, giving rise to 

 wave-motion which will carry off some of the energy bv 

 radiation. Accordingly in such a case it is altogether nuga- 

 tory to speak of laws of action between electrons : the complete 

 theory must then take account not only of the positions and 

 velocities of each of the electrons at each instant, but also of 

 the state of each volume-element of the surrounding aether. 

 And the theory of mutual actions of electrons as expressed in 

 the memoir was in fact thus restricted to cases in which their 

 velocities were small compared with that of radiation : unless 

 that condition is satisfied there is no such theory at all. 



In the second paper (§ 15, segg.) the general problem is 

 attacked : it is now not a question of a set of electrons by 

 themselves, each with a definite steady trail, but of the 

 aethereal medium in general, including such electrons as exist 

 in it. The analysis there given determines from foundations 



