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needless to say, that if the accuracy of Fresnel's law of 

 double refraction is to be disputed, it must be on much better 

 grounds than these ; and the results of M. Cauchy are cer- 

 tainly too far removed from that law to have any chance of 

 being consonant with truth. Although, for example, his new- 

 views respecting the direction of the vibrations agree, in a 

 general way, with those of Fresnel, there is yet, in one par- 

 ticular, an important difference between them ; for accord- 

 ing to Fresnel, the vibrations are always exactly in the sur- 

 face of the wave, while, according to M. Cauchy (in his old 

 theory as well as the new), they are only so in ordinary media. 

 In a biaxal crystal he finds — and this is one of the ways in 

 which the "invisible ray" manifests its influence — that the 

 direction of vibration, in each of the two rays that are visible, 

 is inclined at a certain angle to the wave-plane ; but this 

 augle, though small, is by no means inconsiderable, as M. 

 Cauchy seems to intimate, overlooking the fact, which appears 

 from his own equations, that it is of the same order of mag- 

 nitude as the quantities on which the double refraction de- 

 pends. It is true, the deviation measured by this angle can- 

 not, if it exists, be directly observed in the refracted light ; 

 but its indirect effects on reflected light ought to be very 

 great, since the action of the crystal on a ray reflected at its 

 surface differs from that of an ordinary medium by a quantity 

 of the same order merely as the aforesaid angle ; and as the 

 problem of crystalline reflexion has been already solved 

 (Trans. R. I. A. vol. xviii., p. 31) on the supposition (which 

 is an essential one in the solution) that the vibrations are ex- 

 actly in the plane of the wave, it is highly improbable, con- 

 sidering the complex nature of the question, that it will be 

 solved, in any satisfactory way, on a supposition so different 

 as that which is required by the theory of M. Cauchy. How- 

 ever, as the laws of such reflexion are now well known, by 

 means of the solution alluded to, it is possible that M. Cauchy 

 may, as in the case of double refraction, succeed in deducing 



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