The Aether as an Elastic Solid. 1 75 



amounts in passing through a given thickness of the substance-: 

 at any stage they may be recompoundecl into a pkne-polarized 

 ray, the azimuth of whose plane of polarization varies with the 

 length of path traversed. 



It is readily seen from this that a ray of light incident on 

 a crystal of quartz will in general bifurcate into two refracted 

 rays, each of which will be elliptically polarized, i.e. will be 

 capable of resolution into two plane-polarized components 

 which differ in phase by a definite amount. The directions of 

 these refracted rays may be determined by Huygens' con- 

 struction, provided the wave-surface is supposed to consist of a 

 sphere and spheroid which do not touch. 



The first attempt to frame a theory of naturally active 

 bodies was made by MacCullagh in 1836.* Suppose a plane 

 wave of light to be propagated within a crystal of quartz. Let 

 (#, ?/, z) denote the coordinates of a vibrating molecule, when 

 the axis of x is taken at right angles to the plane of the wave, 

 and the axis of z at right angles to the axis of the 

 crystal. Using Fand Zto denote the displacements parallel to 

 the axes of y and z respectively at any time t, MacCullagh 

 assumed that the differential equations which determine Y and 



__ _ 

 w "" ** w ^'w 



where /* denotes a constant on which the natural rotatory 

 property of the crystal depends. In order to avoid compli- 

 cations arising from the ordinary crystalline properties of quartz, 

 we shall suppose that the light is propagated parallel to the 

 optic axis, so that we can take c, equal to c 2 . 



Assuming first that the beam is circularly polarized, let it 

 be represented by 



(y f\ 



Y = A sin (Ix - ), Z = A cos (Ix - t), 



* Trans. Royal Irish Acad., xvii. ; MacCullagh's Coll. Works, p. 63. 



