Equations of a Moving Material Medium. $c. 367 



actions of adjacent molecules determine the structure of the medium, 

 and any change therein involves change in its local physical constants 

 and properties, which may or may not be important according to 

 circumstances : but such local action contributes nothing towards 

 polarising or straining the element of mass whose structure is thus 

 constituted, and therefore nothing to mechanical excitation, unless at 

 a place where there is abrupt change of density.* In the memoir 

 above mentioned this molecular principle was applied mainly to 

 determine the mechanical stress in a polarised material medium. It 

 necessarily also enters into the determination of the electro dynamic 

 equations of a moving medium treated as a continuous system, and 

 even of a magnetised medium at rest, from consideration of its 

 molecular constitution. It is here intended only to record in precise 

 form the general scheme that results from it, details of demonstra- 

 tion being for the present reserved. Everything being expressed in 

 a continuous scheme per unit volume, let (u')V',iv') denote the 

 current of conduction, (u,v,w) the total current of Maxwell, (/,#, h) 

 the electric displacement in the aether and (/', g', h f ) the electric 

 polarisation of the molecules so that the total so-called displacement 

 flux of Maxwell is (/+/, g+g'> h + ti) ; let p be the volume-density 

 of uncompensated electrons or the density of free charge, let (A, B, C) 

 be the magnetisation, and (p, q, r) the velocity of the matter with 

 respect to the stagnant sether. As before explained ( 13, footnote), 

 the convection of the material polarisation (/', #', h') produces a 

 g^ast-magnetisation (rg'gh 1 , ph' if, 2jP~-jPflO which adds on to 

 (A, B, C). Also, as before shown, the vector potential of the 

 Bsthereal field, so far as it comes from the molecular electric whirls 

 which constitute magnetisation, is given, for a point outside the 

 magnetism, by 



dz dy/ r 



(Imn) being the direction vector of cS, and therefore is that due to 

 a bodily current system (-5 ,...,...) together with current 



sheets on the interfaces. When the point is inside the magnetism, 

 there are still no infinities in the integral expressing F, and this 

 transformation of it by partial integration is still legitimate. But 



* This exception explains why the mechanical tractions on nn interface, deter- 

 mined in 36 as the limit of a gradual transition, are different from the forces on 

 the Poisson equivalent interfacial distribution. 



