214 Faraday. 



In the year following Faraday's discovery, Airy* suggested 

 a way of representing the effect analytically; as might have been 

 expected, this was by modifying the equations which had been 

 already introduced by MacCullagh for the case of naturally 

 active bodies. In Mac Cullagh's equations 

 |8^F =c2 8 2 2 r + VZ 



d^Y 



the terms 8 3 ^/8# 3 and 8 3 F/8# 3 change sign with x, so that the 

 rotation of the plane of polarization is always right-handed or 

 always left-handed with respect to the direction of the beam. 

 This is the case in naturally-active bodies ; but the rotation due 

 to a magnetic field is in the same absolute direction whichever 

 way the light is travelling, so that the derivations with respect 

 to x must be of even order. Airy proposed the equations 

 /8 2 F 2 8 2 F a 



I *-, * o 1 <*N 9 r^ *"\ / 



dx* dt' 



where p denotes a constant, proportional to the strength of the 

 magnetic field which is used to produce the effect. He remarked, 

 however, that instead of taking p dZ/dt and fj. 8 Y/dt as the additional 

 terms, it would be possible to take 8 3 ^/8 3 and /u 8 3 F/8^ 3 , or 

 im() 3 Z/dz?dt> and ju8 3 F/8^ 2 8^, or any other derivates in which the 

 number of differentiations is odd with respect to t and even with 

 respect to x. It may, in fact, be shown by the method pre- 

 viously applied to Mac Cullagh's formulae that, if the equations 



are 



, 8 2 F 8 r+s ^ 



8 r+s F 



where (r + s) is an odd number, the angle through which the 



* Phil. Mag. xxviii (1846) p. 469. 



