176 The Aether as an Elastic Solid. 



*he ambiguous sign being determined according as the circular 

 polarization. ^ ri^ht-handed or left-handed. 



Substituting in ^ e above differential equations, we have 



or 



Since I// denotes the velocity of propagation, it is evident that 

 the reciprocals of the velocities of propagation of a right-handed 

 and left-handed beam differ by the quantity 



from which it is easily shown that the angle through which the 

 plane of polarization of a plane-polarized beam rotates in unit 

 length of path is 



rV 



If we neglect the variation of Ci with the period of the light, 

 this expression satisfies Biot's law that the angle of rotation 

 in unit length of path is proportional to the inverse square of 

 the wave-length. 



MacCullagh's investigation can be scarcely called a theory, 

 for it amounts only to a reduction of the phenomena to 

 empirical, though mathematical, laws ; but it was on this 

 foundation that later workers built the theory which is now 

 accepted.* 



* The later developments of this theory will be discussed in a subsequent 

 chapter ; hut mention may here he made of an attempt which was made in 1856 by 

 Carl Neumann, then a very young man, to provide a rational basis for MacCullagh's 

 equations. Neumann showed that the equations may be derived from the 

 hypothesis that the relative displacement of one aethereal particle with respect to 

 another acts on the latter according to the same law as an element of an electric 

 current acts on a magnetic pole. Cf. the preface to C. Neumann's Die 

 Drehung der Polarisationsebene des Lichtes, Halle, 1863. 



