Vortex Theory of Electromagnetic Action. 413 



and reducing, becomes 



du dy ^dot dy dot. d$ __ du djS 

 dx dy dy dx dz dx dx dz 



And this expression vanishes whenever a, /3, y are functions of 

 the same function of x, y, and z. This is, of course, satisfied 

 if «, jS, 7 are constants or components of a wave of magnetic 

 force crossing the medium. 



Hence, whenever a wave is traversing a field of magnetic 

 force, the electrokinetic energy is 



[Vf + Gg + Wi+167r*C{f( 7 g-ph)+ 9 (*h-yf) 



+ h(Bf-ctg)\ ] dx dy dz. . (26) 



The terms in C are in general small ; and if, with Mr. Fitz- 

 gerald, we are considering a wave in a field of strong uniform 

 magnetic force components «, £, y, we may put a, J8, y for 

 a, /3, 7 in the above terms and treat them as constant. Then, 

 from the equations 



we get 



p= _'d f?T_rfT 

 dt df df 



P=-§-327r 2 C( y #-/3A), 



(27) 



And these agree exactly with (21), remembering that 



^=4ttC, 

 P 

 and that in the present case we have neglected quantities like 

 a', /3', y' '. Thus, the additional term assumed by Mr. Fitz- 

 gerald leads to Mr. Hall's additional terms in the electromo- 

 tive force. Of course, if we start from Mr. Hall's terms in 

 the electromotive force, and work backwards to find the elec- 

 trokinetic energy, we shall arrive at Mr. Fitzgerald's term ; 

 and if, further, we assume the hypotheses of the molecular 

 vortex theory, we shall get Maxwell's additional term. Mr. 

 Fitzgerald's term is a direct consequence of Hall's experi- 

 ments; Maxwell's term is a consequence of them on some 

 theory of the action between light and magnetism. 

 Phil Mag. S. 5. Vol. 11. No. 70. June 1881. 2H 



