258 Wisconsin Academy of Sciences^ Arts, and Letters. 



scalar. Hence this velocity must be in the same direction as n, or 

 in the opposite direction, that is, it must be an angular velocity 

 about the axis of z. 



Again, this velocity cannot be independent of the magnetic 

 force, for if it were related to a direction fixed in the medium, the 

 phenomenon would be different if we turned the medium end for 

 end, which is not the case. 



We are therefore led to the conclusion that this velocity is an 

 invariable accompaniment of the magnetic force in those media 

 which exhibit the magnetic rotation of the plane of polarization. 



We have been hitherto obliged to use language which is, per- 

 haps, too suggestive of the ordinary hypothesis of motion in the 

 undulatory theory. It is easy, however, to state our result in a 

 form free from this hypothesis. 



Whatever light is, at each point of space there is something 

 going on, whether displacement or rotation, or something not jet 

 imagined, which is certainly of the nature of a vector or directed 

 quantity, the direction of which is normal to the direction of the 

 ray. This is completely proved by the phenomenon of inter- 

 ference. 



In the case of circularly-polarized light, the magnitude of this 

 vector remains always the same, but its direction rotates round 

 the direction of the ray so as to complete a revolution in the peri- 

 odic time of the wave. The uncertainty which exists as to whether 

 this vector is in the plane of polarization or perpendicular to it, 

 does not extend to our knowledge of the direction in which it rotates 

 m right handed and left> handed circularly-polarized light respec- 

 tively. The direction and the angular velocity of this vector are 

 perfectly known, though the physical nature of the vector and 

 its absolute direction at a given instant are uncertain. 



When a ray of circularly-polarized light falls on a medium un- 

 der the action of magnetic force, its propagation within the me- 

 dium is affected by the relation of the direction of rotation of the 

 light to the direction of the magnetic force. From this we conclude 

 that in the medium, when under the action of magnetic force, some 

 rotatory motion is going on, the axis of rotation being in the direc- 

 tion of the magnetic forces ; and that the rate of propagation of cir- 



