240 ROTATORY POLARIZATION. 



crystal, cut perpendicularly to the axis, it may be resolved 

 into two such circularly-polarized rays ; and as these are sup- 

 posed to be transmitted with different velocities, one of them 

 will be in advance of the other when they assume a common 

 velocity at emergence. They then compound a single ray, 

 polarized in a single plane ; and this plane, it can be shown, 

 is removed from the plane of primitive polarization by an 

 angle proportional to the interval of retardation, and there- 

 fore to the thickness of the crystal. 



Thus the laws of rotatory polarization are completely ex- 

 plained ; and it only remains to prove the truth of the 

 assumption, that two circularly-polarized pencils, whose 

 vibrations are in opposite directions, are actually transmitted 

 along the axis of quartz with different velocities. This sup- 

 position is easily put to the test of experiment, since such a 

 difference of velocity must produce a difference of refraction 

 when the surface of emergence is oblique to the direction of 

 the ray. According to this hypothesis, therefore, a polarized 

 ray transmitted through a prism of rock-crystal, in the di- 

 rection of the optic axis, should undergo double refraction at 

 emergence ; and the two pencils into which it is divided 

 should be circularly-polarized. This has been completely 

 verified by Fresnel, by means of an achromatic combination 

 of right-handed and left-handed prisms, arranged so as to 

 double the separation; and he has shown that the two 

 pencils are neither common nor plane-polarized light, but 

 possess all the physical characters of light circularly-po- 

 larized. 



(245) The relation between the rotation and double re- 

 fraction of rock-crystal, in the direction of its axis, has been 

 very simply deduced by M. Babinet. 



Let v and v' denote the velocities of the ordinary and 

 extraordinary waves in the direction of the axis of the 



