FRESXEL ON DOUBLE REFRACTION. 325 



traversing the plate t st' s', although both following different 

 directions, again become parallel to each other outside the cry- 

 stal. When the face of emergence of the refracting medium is 

 made to vary its inclination, the ray E A, and that one of the 

 two rays L A which belongs to the same sheet E L, are refracted 

 conformably to the law of Descartes, whilst the ray O A, and 

 the other ray directed along L A which answers to the second 

 sheet L O, are refracted extraordinarily. This establishes a yet 

 further difference between the characters of the optic axes of 

 uni-axal and bi-axal crystals; for in the former all the rays 

 parallel to the optic axis in the interior of the crystal are refi'acted 

 according to the law of Descartes, whatever be the direction and 

 inclination of the face of emergence, because these rays being 

 then parallel to one of the axes of elasticity, are perpendicular at 

 the same time to the two sheets of the wave surface. 



Having dwelt on distinctions which the theory shows clearly, 

 but which escape in most observations, and were not capable of 

 being made evident by those of M. Biot, we proceed to consider 

 for a moment the planes of polarization in a less rigorous man- 

 ner, and adopt the rule which he has given for determining 

 their direction, without any alteration of his enunciation, in 

 order that we may be enabled to explain ourselves in a more 

 simple and clearer manner. 



The rays named Ordinary by MM. Biot and Brewster are those 

 whose variations of velocity have the least extent. 



As we have already remarked, there is no longer any ordinary 

 ray, properly so called, in crystals with two axes, since neither 

 of the two beams of light traverses the crystal with the same 

 velocity in all directions ; but that which is called the ordinary 

 beam, by analogy with the term adopted for uni-axal crystals, is 

 that whose variations of velocity are the least sensible. Now 

 it is easy to see that this is the one whose plane of polarization 

 bisects the acute dihedral angle comprised between the planes 

 drawn through the direction of the luminous rays and the two 

 optic axes ; whilst the plane of polarization of the beam which 

 undergoes the greatest variations of velocity, bisects the obtuse 

 dihedral angle which is the supplement of the former. 



In fact, whatever be the direction of the first beam, its plane 

 of polarization passing within the acute angle QAP (fig. 15) 

 of the two optic axes, its trace on the plane of the figure is con- 



