142 REPORT ON PHYSICAL OPTICS. 



interference of two circularly polarized pencils which are propagated 

 along the axis with unequal velocities, one revolving from left to 

 right, and the other in the opposite direction. A plane-polarized 

 ray, in fact, is equivalent to two circularly polarized rays of half 

 the' intensity, in one of which the vibrations are from left to right, 

 and in the other in the opposite direction. When a plane-polar- 

 ized ray, therefore, is incident perpendicularly upon a plate of 

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

 into two such circularly polarized rays. These are supposed to be 

 transmitted with different velocities ; so that when they assume a 

 common velocity at emergence, one of them is in advance of the 

 other. 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 through an angle proportional to the 

 interval of retardation of the two pencils, and therefore measured 

 by the thickness of the crystal. But this interval varies also with 

 the colour of the light ; and we are obliged to suppose that it is 

 the same for a given number of waves, whatever be their length, 

 so that, for a given thickness of the crystal, it varies inversely as 

 the length of the wave. From this supposition it will follow that 

 the deviation of the plane of polarization of the emergent ray is 

 inversely as the square of that length, agreeably to the experi- 

 mental results of M. Biot.* 



The laws of rotatory polarization were thus completely ex- 

 plained ; and it only remained to prove the truth of the hypo- 

 thesis, that two circularly polarized pencils, whose vibrations are 

 in opposite directions, will actually be transmitted along the axis 

 of quartz with different velocities. This supposition is easily put 

 to the test -of experiment, since such a difference of velocities must 

 give rise to a difference of refraction, when the surface of emer- 

 gence is oblique to the direction of the ray. According to the 

 hypothesis, therefore, a plane-polarized ray, transmitted through a 

 prism of rock-crystal in the direction 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 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 com- 



* Annale* de Chimie, torn, xxviii. p. 147. 



