DOUBLE REFRACTION. 109 



the property of double refraction ; and arrived at the conclusion 

 that this property belonged to all crystals, excepting those whose 

 primitive form was the cube or regular octahedron. Most organized 

 substances, whether vegetable or animal, were found to possess the 

 same properties. 



In Iceland spar the extraordinary refractive index is less than 

 the ordinary. The extraordinary ray consequently is always re- 

 fracted from the axis of the crystal ; and the same law had been 

 supposed to belong to all double-refracting substances. M. Biot 

 made the important discovery that, in many crystals, the extra- 

 ordinary index was greater than the ordinary, and the extraordi- 

 nary ray therefore refracted towards the axis. Crystals of the latter 

 kind he called attractive, while those of the former were called re- 

 puhive ; the extraordinary refraction being ascribed, in the theory 

 of emission, to attractive or repulsive forces which act as if they 

 emanated from the axis.* These crystals are now generally dis- 

 tinguished by the denominations positive and negative. The Huy- 

 genian law applies to positive as well as to negative crystals ; the 

 spheroid being prolate in the former case, and oblate in the latter. 



The construction given by Huygens for the direction of the 

 two refracted rays is, it has been stated, an immediate consequence 

 of the assumed form of the wave-surface. It easily appears, from 

 the principle of Huygens already adverted to, that the same con- 

 struction will apply in all cases, whatever be the form of the wave, 

 or the law of the velocity of propagation within the crystal ; so 

 that the law of direction is determined when that of velocity is 

 known. A similar connexion between the velocity of the molecule 

 and its path is established, in the theory of emission, by the law 

 of least action. This principle, we know, holds generally in the 

 motion of a point subjected to the action of attracting or repelling 

 forces; and in applying it to the case of a luminous molecule, 

 acted on by forces emanating from the particles of the body which 

 it meets, we may leave out of consideration the insensible curvi- 

 linear portion of the trajectory described in the passage from one 

 medium into another of different density, provided we assume, 

 with Newton, that the forces exerted by the molecules of body on 

 those of light are sensible only at insensible distances. In this 

 simplification of the problem we have to deal only with straight 



* Jffiii. Intl. 1814. 



