the new Action of Magnetism. 

 North Pole above. 



433 



North Pole below. 



It is seen that all these effects are such as would happen 

 were the electric current to be rotated in a fixed direction with 

 respect to the lines of magnetic force, and to an amount de- 

 pending only on the magnetic force and not on the current. 

 This fact seems to point immediately to that other very im- 

 portant case of rotation, namely the rotation of the plane of 

 polarization of light. For, by Maxwell's theory, light is an 

 electrical phenomenon, and consists of waves of electrical dis- 

 placement, the currents of displacement being at right angles 

 to the direction of propagation of the light. If the action we 

 are now considering takes place in dielectrics, which point 

 Mr. Hall is now investigating, the rotation of the plane of 

 polarization of light is explained. 



I give the following very imperfect theory at this stage of 

 the paper, hoping to finally give a more perfect one either in 

 this paper or a later one. 



Let .£) be the intensity of the magnetic field, and let E be 

 the original electromotive force at any point, and let c be a 

 constant for the given medium. Then the new electromotive 

 force E' will be 



E'=c.0E, 



and the final electromotive force will be rotated through an 

 angle which will be very nearly equal to c.f). As the wave 

 progresses through the medium, each time it (the electromo- 

 tive force) is reversed it will be rotated through this angle; so 

 that the total rotation will be this quantity multiplied by the 

 number of waves. If X is the wave-length in air, and i is the 

 index of refraction, and c is the length of medium, then the 



ci 



number of waves will be — , and the total rotation 



