Vortex Theory of Electromagnetic Action. 403 



let P be tlie electromotive force at the point, and suppose that 



Similarly 









sap 



acity ; then 



P: 



47T, 



Att/ulB 



p ■ 



P = 



d¥ _ 



dt ' 



dx 



Q= 



_dG_ 

 dt ' 



_d^ 



dij 3 



E: 



~ dt ' 



dyjr 

 dz' 



■/} 



(14) 



And thus in a dielectric medium also Maxwell's equations 

 would hold. 



Differentiating (12) and the two similar equations with 

 reference to x, y } z and adding, we have 



dx dy dz 



(15) 



Differentiating (14) with reference to t, and substituting for 

 P from (12), remembering that 



rt 



= F &c, 



we have, of course, Maxwell's equations for F, Gr, H in a 

 dielectric medium, viz. 



Maxwell, § 783 (7). If J is a linear function of t 9 or a con- 

 stant, or zero, 



d_(di + dv + dt\ =0 



dx \dx dy dz/ ' 

 and 



dx ~ 2 * 



Thus the electromotive force at any point due to the free 

 electricity is proportional to the mechanical force exerted at 

 that point in the medium. In addition to this we have the 



