and the Magnetic Rotation of Polarized Light. 255 



were rotated around the lines of force in the same way as the 

 electric currents are rotated in metals ; but I now find that 

 this is not necessary, but that we only have to apply the 

 rotation to the displacement currents of Maxwell, and we get 

 a complete explanation of the magnetic rotation of the plane 

 of polarization of light. 



As Sir W. Thomson has shown that the latter effect must 

 be due to some rotation in the magnetic field, so by connect- 

 ing the new discovered action with the old, we prove that it 

 also is due to rotation in the field. For Maxwell's equations 

 merely express the facts of the case, and give no explanation. 



Let a 1 ', V ', e' be the components of the electric current in 

 the direction of the axes, and a, b, e the components of the 

 magnetic force. Let also c be the coefficient of the new effect. 

 Under these circumstances, electromotive forces will be set up 

 in the medium whose components are 



0" = z{a l b f -a f b l ). 



To apply these results to Maxwell's theory of light, we must 

 assume that the same action which takes place in conductors 

 with reference to conducted currents, also takes place in di- 

 electrics with reference to displacement currents. It is almost 

 impossible to detect this action experimentally; but we shall 

 here follow out the consequence of its existence. I shall follow 

 the method of Art. 783 of Maxwell's ' Treatise,' with the ad- 

 dition of this new action*. 



Assume at once C = 0, yjr = 0, and J = 0, as they are after- 

 wards taken or proved to be. 



Let P, Q, and R, be the components of the electromotive 

 forces acting at any point. The electromotive force will be 

 composed of two parts : — first, the rate of variation of the 

 vector potential, as on the old theory ; and, second, a term 

 depending on the new action, and whose components we 

 have designated by A", B", and C". Adding these together, 

 we have 



P=-f+c(V-^). 



Q=-^ + c(V L « / -c / a 1 ), 

 R=-^ + c(« 1 Z/-a / £ 1 ). 



,72 J2 /p 



* I use the expression A 2 to signify the operation — a +_-[- _, while 

 Maxwell uses it (in his ' Theory of Light ') with the opposite sign. 



