198 FRESNEL'S THEORY OF DOUBLE REFRACTION. 



bodies, having two optic axes, or two lines of no separation, 

 Huy gens' law was found not to be general ; and it was ascer- 

 tained that one of the rays, at least, in biaxal crystals, fol- 

 lowed some new and unknown law. 



In this state of the question the problem of double re- 

 fraction was taken up by Fresnel ; and by the aid of a na- 

 tural and simple hypothesis, combined with the principle of 

 transversal vibrations, he has been conducted to its complete 

 solution, a solution which not only embraces all the known 

 phenomena, but has even outstripped observation, and pre- 

 dicted consequences which were afterwards verified by ex- 

 periment. 



(210) Fresnel sets out from the supposition, that the 

 elastic force of the vibrating medium, in every crystal, is 

 different in different directions. It is easy to see, generally, 

 that the phenomenon of double refraction is a necessary con- 

 sequence of this hypothesis, and of the principle of transversal 

 vibrations. 



Let us take, for example, the simple case of a ray of 

 light proceeding from an infinitely distant point, and falling 

 perpendicularly on the surface of a uniaxal crystal, cut 

 parallel to the axis. The incident wave being plane, and 

 parallel to the surface of the crystal, the vibrations are also 

 parallel to the same surface ; and we may conceive them to 

 be composed of vibrations parallel and perpendicular to the 

 axis of the crystal. Now, the elasticity brought into play by 

 these two sets of vibrations being different, they will be 

 propagated with different velocities ; and there will be two 

 waves within the crystal, in which the vibrations are pa- 

 rallel to two fixed directions at right angles to one another, 

 or two rays oppositely polarized. If the second face of the 

 crystal be parallel to the first, the two rays will emerge 

 perpendicularly ; and the only effect produced will be, that 



