ROTATORY POLARIZATION. 243 



crystal, of the same thickness, one of them being right- 

 handed, and the other left-handed. 



In order to complete the experimental investigation of this 

 subject, it remained to determine the velocities of the two 

 elliptically-polarized rays, and the ratio of the axes of the 

 ellipses, as dependent on the inclination of the rays to the 

 axis of the crystal. This has been effected by M. Jamin, by 

 measuring the amplitudes, and the differences of phase of the 

 two component pencils, when the incident light is polarized 

 in the plane of a principal section. From these data the 

 quantities sought are deduced by calculation. 



(247) All these complicated facts have been linked toge- 

 ther, and their laws deduced, by Professor Mac Cullagh. In 

 this remarkable investigation the author sets out by assuming 

 the form of the differential equations of vibratory motion in 

 rock-crystal ; and from this assumed form he has deduced the 

 elliptical polarization of the two pencils; the law of the 

 ellipticity as depending on the inclination of the ray to the 

 axis ; the interval of retardation in the direction of the 

 axis ; and the peculiar form of the wave-surface. 



The ratio of the axes of the two ellipses is found to be 

 equal to unity in the direction of the axis of the crystal. In 

 all other directions it is given by a quadratic equation 

 whose constant term is equal to unity ; so that this ratio 

 has two values, one of which is the reciprocal of the other. 

 Hence the ratio of the axes is the same in both ellipses ; and 

 the greater axis of one coincides with the smaller axis of the 

 other. 



When the ray traverses the axis of the crystal, the rota- 

 tion of the plane of polarization is given by the formula 



CO 



