Notes on some Points in the Theory of Light. 207 



does not remain the same, can never differ much from unity ; 

 since it must become exactly equal to unity, ivhatever be the 

 direction of the ray, when the crystalline structure is sup- 

 posed to disappear, and the medium to become a rotatory 

 fluid. 



That a theory involving so many inconsistencies should 

 have been advanced by a person of M. Cauchy's reputation 

 would, perhaps, appear very extraordinary, if we did not re- 

 collect that it was unavoidably suggested by the general prin- 

 ciplas which he had previously adopted, and which were 

 supposed, not merely by himself, but by the scientific world 

 generally, to have already afforded the only satisfactory ex- 

 planation of the laws of double refraction in the common 

 and well-known case where the vibrations are rectilinear. 

 This supposed explanation was obtained, as has been said, 

 by restricting the application of M. Cauchy's principles to 

 the hypothesis of a vibrating medium arranged symmetrically, 

 in which case it was shown that the vibrations were neces- 

 sarily rectilinear; and of course the removal of this restric- 

 tion was the only way in which it was possible, on those 

 principles, to account for the existence of circular and ellip- 

 tical vibrations. Accordingly, when M. Cauchy perceived 

 that, on the hypothesis of unsymmetrical arrangement, the 

 existence of rectilinear vibrations became impossible, and that 

 of elliptic vibrations, generally speaking, possible, he found 

 it very easy to persuade himself that he had obtained a new 

 proof of the correctness of his views, and a new and most im- 

 portant application of the fundamental equations by which 

 his general principles were analytically expressed. To have 

 supposed otherwise would have been to admit that his general 

 principles were false. If the elliptical or gws&-circular vibra- 

 tions which he was now contemplating were not capable of 

 being identified with those which had been recognized in the 

 phenomena presented by quartz and the rotatory fluids if 

 their laws were essentially or very considerably different his 

 theory would be inconsistent with a wide range of well-known 



