produced by Motion in the Electric Field. 3 



? + £ o = ^ («/- ug) -^(un- (w - w )f), 



71+7)0 = fc(( w - w °)9- vh ) -faW-ve)* 



If the motion of the medium is irrotational, these conditions 

 will be satisfied if we suppose that the motion of the dielectric 

 gives rise to magnetic forces whose components u, /3 } y are 

 given by the equations 



« = 4:Tr((w—Wo)g — vh), "j 



/3 = l7r(uh-(w-w Q )f), V. . . . (1) 



y = 4m(vf—ug). ) 



If we suppose that the electric field is due to a number of 

 charged spheres moving wiuh velocities (w l3 v ly iv { ) (w 2 , v 2 , w 2 ) 

 .... respectively, and producing electric displacements whose 

 components are (fij gi, h]) (/i? ^2? ^2)? the component of the 

 magnetic force parallel to x will be 



4ir(wg — vh—\ w x g x + w 2 g 2 + ... — v 1 h i — v 2 h 2 . . \ ), 



where /, g, h are the resultant displacements. 



Thus, since in the general case when the aether is in motion 

 the assumption that the currents are merely due to the changes 

 in the polarization caused by the aether moving from a place 

 where the displacement has one value to another where it has 

 a different one is insufficient if the circuits are closed, it is 

 necessary to replace it by another ; the assumption we shall 

 adopt is that the motion of the polarized aether sets up mag- 

 netic forces whose components are given by equations (1). 



When the aether is at rest this agrees with Maxwell's prin- 

 ciple that the currents are equal to the rate of increase of the 

 electric displacement. We should get these magnetic forces 

 if, in the expression for the mean Lagrangian function of 

 unit volume of the moving aether, there was the term 



a\wg — vh — 2 (i0i#i — vjii ) j- + b j uh — ivf— 2 (iiili x — w lt /i) \ 



+ c\vf—ug-t(v l f 1 -u 1 g l )}\ 



where a, b, c are the components of the magnetic induction. 



This term would show that there is an electromotive force 



parallel to x equal to 7 



cv — bw, 



B2 



