DOUBLE REFRACTION . 113 



resultant. Thus, then, the laws of uniaxal crystals, as well as of 

 singly-refracting media, are embraced in this hypothesis The case 

 of two resultant axes is reducible to that of two unequal polariz- 

 ing axes ; and it has been shown to be a consequence of the rule, 

 that the difference of the squares of the velocities of the ordinary 

 and extraordinary rays within the crystal is proportional to the 

 product of the sines of the angles which the latter makes with the 

 resultant axes. M. Biot was led to the discovery of this beautiful 

 law by analogy,* and he afterwards observed that it was implicitly 

 contained in the law proposed by Sir David Brewster. 



The term " polarizing force" seems to have been adopted by 

 Sir David Brewster without any reference to the law which go- 

 verned the planes of polarization of the two pencils, a law 

 which, in biaxal crystals, still remained unknown. In the case 

 of uniaxal crystals, it could not fail to be observed, the plane of 

 polarization of one of the pencils contained the direction of the 

 ray and the axis ; while that of the other was a plane passing 

 through the ray at right angles to the former. Conceiving that 

 these planes, in biaxal crystals, must be symmetrically placed with 

 respect to the planes passing through the ray and the two axes, 

 M. Biot was led to the simple and elegant law that the plane 

 of polarization of one of the pencils was that passing through the 

 ray, and bisecting the dihedral angle contained by these planes ; 

 while that of the other was perpendicular to the former, or bisected 

 the supplemental dihedral angle.f 



When a ray of light enters a crystal, the component molecules 

 are supposed, in the theory of M. Biot, to receive different motions 

 round their centres of gravity, dependent on the nature of the 

 forces exerted upon them by the particles of the body. Sometimes 

 the molecules of the ray are turned by the operation of these 

 forces, so as to have certain lines in each, denominated axes of 

 polarization, all in the same direction ; and this arrangement of 

 the molecules is maintained throughout the whole of their future 

 progress. There are other cases, however, according to this author, 

 in which the molecules oscillate round their centres of gravity in 

 certain periods, during their entire progress through the crystal ; 



* " Memoire aur lea Lois generates dc la Double Refraction, &c.," &* /'> 

 torn. iii. 

 t Ibid. 



I 



