Vortex Theory of Electromagnetic Action. 409 



In his paper Prof. Rowland remarks, after showing that 

 Mr. Hall's discovery leads to the same expressions for the 

 rotation of the plane as Prof. Maxwell's, " the conclusion we 

 draw is that the effect discovered by Mr. Hall is the same or due 

 to the same cause as the rotation of the plane of polarization of 

 light." The previous investigation, I think, may supply a 

 connecting link between the two. 



As has already been stated, equations (19) and (23) agree 

 in form with Mr. Fitzgerald's equations ; and in fact (23) is 

 identical with his. For let us put 



P = *', q = P, r=</; 



then p, q, r are the same as Mr. Fitzgerald's f , rj, f, and his 

 final equation is 



&c . ; +V^ = 0, . . (24) 



and differentiating these with respect to t and substituting, we 

 get (23). 



Now Mr. Fitzgerald's equation has been deduced, without 

 any assumption as to the connexion between the motions of 

 matter and sether, from the hypothesis that the electrokinetic 

 energy of the medium contains a term 



where 



d d d d 



de =Ci olv + Pd-y +r/ dz' 



Professor Maxwell's additional term depends on the displace- 

 ments of the medium which constitute light. The potential 

 energy in his case is that which arises from the state of strain 

 of the medium, while in Mr. Fitzgerald's paper the potential 

 energy is the electrostatic energy of the field. The foregoing 

 investigation shows that the two assumptions lead to the same 

 equations for the electric and magnetic disturbance. 



If we suppose that we have in the field light-motion in ad- 

 dition to electrical and magnetic displacements, and assume 

 with Prof. Maxwell his additional term in the kinetic energy, 

 then, on the molecular vortex theory, the electrokinetic energy, 

 or that part of the kinetic energy on which electrical and mag- 

 netic effects depend, will contain a term of the form supposed 

 by Mr. Fitzgerald. The kinetic energy being 



^(t + V 2 + t 2 )dvdydz, 



