1885.] of polarization of light by a moving medium. 253 



so that the ray polarized in the opposite sense to that of the 

 rotation of the medium travels more slowly than the one polarized 

 in the same sense. 



The ray for which the displacements are nearly parallel to x is 

 given by 



f— a sin (nt — Iz) +a sin (nt — l x z), 

 or say f= 2a sin (nt — Iz) 



g = a cos (nt — \z) — a cos (nt — Iz), 



g = 2a sin f ^-= — J 3 cos (nt — Iz) 



= 2x ■-*-= — - ^ cos (w£ — Iz) approximately 



= a . — - z sin (nt — Iz) ; 



or the plane of polarization is twisted in the same direction as the 

 rotation of the body through an angle tojv per unit length. We 

 may state this result rather more neatly by saying that the 

 rotation of the plane of polarization after the light has travelled 

 any distance is equal to the angle turned through by the me- 

 dium in the time taken by light to traverse that distance. To 

 twist the plane of polarization through a third of a minute after 

 traversing 10 metres, the medium would have to make about 500 

 revolutions per second. This seems just to bring it within the 

 limit of experimental verification, as the light might be reflected 

 backwards and forwards. We must however remember that o> 3 is 

 the angular velocity of the ether and not of the moving piece of 

 glass or whatever we may use for the experiment. 



The amount of the rotation of the plane of polarization is 

 independent of the wave-length, so that the theory in this form 

 would not account for the magnetic rotation of the plane of 

 polarization where the magnitude of the rotation varies inversely as 

 the square of the wave-length. An application of this result seems 

 worth noticing ; according to some theories there is a rotation of 

 the ether around the lines of magnetic force, now this will produce 

 a rotation of the plane of polarization whatever the medium may 

 be. Now experiments with negative results have been made to 

 detect the rotation of the plane of polarization in air and we may 

 conclude that if the rotation had been as much as 1' per 

 metre it could not have escaped detection, so that even in very 

 powerful magnetic fields the ether cannot be rotating more than 

 15000 times per second. 



If we go to second powers of co/n we see that the velocity of 

 vol. V. PT. iv. 18 



