274 



Dr. J. Larmor. A Dynamical Theory 



circuits were under consideration, on the notion of a current element, 

 and to derive the formulae from that conception with such degree of 

 definiteness as was possible. It was this imperfect dynamical method 

 which it was the aim of Helmholtz to discuss and elucidate in the 

 analysis above mentioned. 



In so far as these theories were dynamical they all involved current 

 ■elements : but the criticism of the second of the present memoirs is 

 held to show that a current element is not a legitimate dynamical 

 entity, in that the forces strictly derivable from that assumption, 

 both mechanical and electric, are in disagreement with experimental 

 knowledge: and the reason is indicated, namely that the method of 

 ■current elements forms an incomplete specification of the phenomena, 

 inasmuch as it gives no account of how a current is induced within 

 an element of volume of the matter by separation of the two elec- 

 tricities under the action of the electric force. This led to the 

 introduction of the mobile electron or atomic charge of electricity as 

 the true physical element, and to a dynamical theory of molecular 

 type which is held to be self-consistent and in full agreement with 

 •experimental knowledge, and which may be regarded as in a manner 

 a final development of the Weberian notion of moving electric 

 particles. The true electric current of moving electrons is thus made 

 up of a current of conduction and a current of dielectric polarisation : 

 it does not flow in closed circuits, but if there is added on to it a 

 ■quantity called the aethereal displacement current, which is not a flow 

 of electricity at all but a flux of elastic displacement of the aether, 

 there is obtained the total circuital current of Faraday and Maxwell. 

 This more precise three-fold specification of the total current, in 

 place of the two-fold specification of Maxwell which ignores the 

 physical distinction between the polarisation current in the dielectric 

 matter and the displacement current in the aether occupying the 

 same space, introduces notable differences as regards ponderomotive 

 forces, moving material media, electric radiation, and in other re- 

 spects. In the main the results correspond with Faraday's geo- 

 metrical mode of specification by means of tubes of induction ; they 

 agree more closely with the scheme derived by Maxwell from direct 

 consideration of his mechanical model of the electric field than with 

 the later analytical theory of his " Treatise." 



The general equations of the electric field, when it contains moving 

 material bodies, dielectric or conducting, are formulated on these 

 principles. They are applied to the problem of the uniform rotation 

 •of a charged conductor, or a dielectric body, in a magnetic field : to 

 the influence of motion of a material medium on the velocity of 

 radiation that is passing across it : and to the influence of steady 

 translation of a material system through the aether on its configura- 

 tion and the distribution of its electric charges. 



