DOUBLE REFRACTION. 115 



-extraordinary ray from the principles of either theory. Indeed 

 the general law of the velocities was itself unknown, even as an 

 experimental fact, although an important relation between the 

 velocities of the two pencils had been discovered by the labours of 

 Sir David Brewster and M. Biot. But this was not all. It was 

 evident that no physical theory of double refraction could be re- 

 garded as complete, which did not at the same time account for 

 the attendant phenomenon of polarization. In this branch of the 

 subject, however, nothing had been accomplished; and all that 

 had been said in explanation of the phenomenon of polarization 

 did not go further than some vague speculations as to its cause. 

 The theory of Fresnel to which I now proceed, and which not 

 only embraces all the known phenomena, but has even outstripped 

 observation, and predicted consequences which were afterwards 

 fully verified, will, I am persuaded, be regarded as the finest 

 generalization in physical science which has been made since the 

 discovery of universal gravitation. 



Fresnel* sets out from the supposition that the elastic force 

 -of the vibrating medium is, in general, different in different 

 directions. This is, in fact, the most general supposition that can 

 be made; and whether we suppose that the vibrating medium 

 is the ether within the crystal, or that the molecules of the body 

 itself partake of the vibratory movement, there will be obviously 

 such a connexion, and mutual dependence, of the parts of the solid 

 and those of the medium in question, that we cannot hesitate to 

 admit for the one what has been already established on the clearest 

 evidence for the other.f Now if a disturbance be produced in a 

 medium so constituted, and any particle displaced from its position 

 of rest, the resultant of the elastic forces which resist the displace- 

 ment will not, in general, act in the direction of that displacement 

 (as in the case of a medium uniformly elastic), and therefore will 

 not drive the displaced particle directly back to its position of 

 equilibrium. Fresnel has shown, however, that there are three 

 directions at right angles to each other, in any of which, if the 

 particles are displaced, the elastic forces do act in the direction 



* " Mcmoire sur la Double Refraction," Mem. Inst., torn. vii. 



t M. Savart has shown that the elasticity of crystals, determined by means of 

 their sonorous vibrations, is, in general, different in different directions. The optic 

 axis of Iceland spar is the axis of least elasticity: that of rock crystal is the axis of 



greatest elasticity. 



1 2 



