of the FAectric and Luminiferous Medium. 273 



rigid circuit and the complete circuital current to the geometrical 

 elements of which they are composed. The way was prepared for 

 this by F. Neumann, by his discovery of the electrodynamic potential 

 formula, from which he deduced by a uniform analytical process the 

 mechanical and electric forces in complete rigid circuits, as previously 

 formulated by Ampere and Faraday. Then Helmholtz took up and 

 extended Neumann's theory, introducing Maxwell's principle that 

 the formula of Neumann represents the kinetic energy of the system 

 of current elements, to which Lagrange's general dynamical equa- 

 tions, or more precisely the action method, can be applied. His 

 main aim was to include in this potential theory the conception of 

 dielectric currents introduced by Faraday : but he was at the same 

 time led to generalise Neumann's formula so as to include the possi- 

 bility of waves of electric compression as well as transverse electric 

 waves in dielectric media : the existence of the former type of 

 waves Hertz's discoveries have disproved. 



This theory of von Helmholtz thus originated by way of eluci- 

 dating, from the older standpoint, the aether scheme advanced by 

 Maxwell in the shape of a system of analytical relations, which were 

 the mathematical formulation of Faraday's views, and involved also a 

 unification of the electrical and optical functions of the aether. 

 The equations of Maxwell include implicitly a definite theory of 

 all electromotive phenomena in open circuits at rest, a fact which is 

 not very obvious for the form into which they were thrown in 

 Maxwell's " Treatise," but which is plainer for the form of two con- 

 jugate circuital relations into which he had previously cast them as 

 being the simplest and most direct formal expression of the theory,, 

 but which he left aside in favour of a conception of electrodynamic 

 momentum or vector potential that was intended to connect the 

 equations directly with dynamical principles : this simple formal 

 specification of ethereal relations has since been restated and utilised 

 by Heaviside and Hertz. These Maxwellian fundamental equations,, 

 being purely electromotive, gave no direct explanation of pondero- 

 motive forces : for that purpose the theory had of necessity to take 

 on a dynamical form. A formula for the distribution of the electric 

 energy throughout the aether was suggested by various considerations, 

 and from it an attempt was made by the methods of general dynamics 

 to establish the laws of the force exerted by the aether on the different 

 parts of conductors conveying currents : and it was natural that the 

 same procedure should be extended to an attempt to place the funda- 

 mental formal equations of the aether itself on a dynamical basis. But 

 what was lacking for the satisfactory accomplishment of this purpose 

 was a definite and consistent idea of how the electric charges and 

 currents in the matter established a hold on the aether. In the 

 absence of this, Maxwell had to rely, when actions on portions of 



