FRESXEL ON DOUBLE REFRACTION. 319 



this difference would be always very slight, because the surface 

 of the luminous waves does not deviate much from the spherical 

 form even in those crystals whose double refraction is most 

 powerful ; in the second place, it becomes useless to take any 

 account of it for the experiments made by M. Biot and the other 

 experimenters on the direction of the planes of polarization of 

 the ordinary and extraordinary rays, since it is always outside 

 the crystal, and by the direction of the planes of polarization of 

 the incident or emergent rays, that they have judged of the direc- 

 tion of the planes of polarization of the refracted rays. Thus, 

 for example, suppose that we wished to determine the planes of 

 polarization of the ordinary and extraordinary refraction in a 

 crystallized plate with parallel faces perpendicular to the incident 

 rays. For this purpose it is sufficient to employ light previously 

 polarized, and to turn the plate in its plane until the emergent 

 beam, analysed by a prism or rhomboid of Iceland spar, no longer 

 presents any trace of depolarization in consequence of its passage 

 across the crystallized plate. When this condition is fulfilled, 

 we may conclude from it that the plane of polarization of the 

 refracted wave coincides with that of the incident wave. There 

 are always two positions of the plate which satisfy this condition, 

 and thus afford the means of tracing on the crystal the direction 

 of the planes of polarization of the ordinary and extraordinary 

 refraction. In this experiment, the incident wave being parallel 

 to the faces of the crystallized plate, preserves this parallelism 

 in traversing it ; and if the direction of the vibrations of the in- 

 cident wave coincides with that of one of the axes of the parallel 

 diametral section made in the surface of elasticity, they will suf- 

 fer no further deviation in traversing the crystal ; in that case, 

 the incident, refracted and emergent waves have all three the 

 same plane of polarization, and their surfaces are parallel, although 

 moreover the refracted rays may be oblique to their wave, and 

 thus not be found on the prolongation of the incident and emer- 

 gent rays. In this case, the definition of the plane of polariza- 

 tion according to the emission system no longer gives rigorously 

 for the plane of polarization of the refracted rays the same direc- 

 tion as the definition drawn from our theory, although they agree 

 in other respects as to the direction of the planes of polarization 

 of the incident and emergent rays, the only ones which can be 

 determined immediately by observation. 



Considering always as the true plane of polarization that which 



