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tion (5) as only approximate in the case of rays inclined to 

 the axis ; for the last term of that equation, if it does not re- 

 main the same, can never differ much from unity ; since it must 

 become exactly equal to unity, whatever be the direction of 

 the ray, when the crystalline structure is supposed to disap- 

 pear, 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 

 principles 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 rectihnear ; 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 ex- 

 istence 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 important 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 

 <7Masi-circular vibrations which he was now contemplating 

 were not capable of being identified with those which had 

 been recognized in the phenomena presented by quartz and 



