1891.] On the Theory of Electrodynamics. 521 



IV. " On the Theory of Electrodynamics." By J. LARMOR, 

 Fellow of St. John's College, Cambridge. Communicated 

 by Professor J. J. THOMSON, F.R.S. Received May 11, 

 1891. 



The electrical ideas of Clerk Maxwell, which, were cultivated partly 

 in relation to mechanical models of electrodyuamic action, led him to 

 the general principle that electrical currents always flow round com- 

 plete circuits. 



To verify this principle for the case of the current which charges 

 a condenser, it was necessary to postulate an electrodynamic action 

 of the same type as that of a current for the electric displacement 

 across the dielectric, in which the excitation of the dielectric may be 

 supposed, after Faraday, to consist. The existence of such an action 

 has subsequently been deduced qualitatively from the general prin- 

 ciple of action and reaction,* and has also been detected by various 

 experimenters. 



The principle also requires that the electric displacement shall not 

 lead to any accumulation of charge in the interior of the dielectric, 

 therefore that it shall be solenoidal or circuital, f its characteristic 

 equation being of the type 



dx \ dx ) dy\ dy J dz \ dz ) 



where V is the electric potential, and K a dielectric constant. The 

 surface density of the electricity conducted to a face of a condenser 

 must neutralise the electric displacement, and not leave any residual 

 effective electrification on the surface. On taking the displacement 

 and the surface density each equal to KF/4n-, where F denotes the 

 electric force, the value of K becomes unity for a vacuum dielectric ; 

 and K represents the specific inductive capacity as measured by 

 electrostatic experiments. 



When this principle of circuital currents is postulated, the theory 

 of electrodynamics is reduced to the Ampere-Neumann theory of 

 complete circuits, of which the truth has been fully established. It 

 leads, as shown by Maxwell, to the propagation of electrical action 

 in dielectric media by waves of transverse electric displacement, 

 which have the intimate relations to waves of light that are now well 

 known. 



* Cf. J. J. Thomson, 'Brit. Assoc. Report,' 1885. 

 t A term recently introduced by Sir W. Thomson. 



