FRES.VEL ON DOUBLE REFRACTION. 243 



agreed In a satisfactory manner with the calculation ; or, at least, 

 the difference which I have observed is sufficiently small to be 

 attributed to some inaccuracy in the cleavage of the crystal or 

 the direction of the rays, and perhaps also to some slight dif- 

 ference of optical properties between my topaz and those of 

 M. Biot. 



But before entering into the detail of these experiments, I 

 shall endeavour to exhibit clearly the reasonings which have led 

 me to it. In this memoir I shall follow the synthetical method. 

 I shall first explain the mechanical theory of double refraction ; 

 and afterwards make known the observations and calculations 

 which have enabled me to verify it, and which form in some sort 

 its experimental demonstration. 



Mechanical Theory of Double Refraction. 



This theory rests on two hypotheses, one relative to the nature 

 of the luminous vibrations, and the other to the constitution of 

 the media possessing the property of double refraction. According 

 to the first, the luminous vibrations, instead of being performed 

 in the direction of the rays themselves, as has been generally 

 supposed by those who have applied the wave system to optics, 

 are perpendicular to the rays, or, more strictly speaking, parallel 

 to the surface of the waves. According to the second hypo- 

 thesis, the vibrating molecules of doubly-refracting media do not 

 exhibit the same mutual dependence in all directions ; so that 

 their relative displacements will give rise to different elasticities 

 according to their directions. 



This second supposition has nothing in it but what is very 

 probable ; it is more general than the contrary supposition, 

 namely that which makes the mutual dependence of the mole- 

 cules, or the elasticity, the same in every direction. If there 

 are many bodies which do not present the phaenomena which 

 ought to follow on this supposition, it is no doubt generally 

 owing to the compensation of opposite effects produced by the 

 molecular groups being turned in all directions. With regard 

 to the hypothesis as to the nature of the luminous vibrations, it 

 appears at first much more difficult to admit, because one does 

 not easily see how transversal vibrations are capable of indefinite 

 propagation in a fluid. 



Nevertheless, if the facts which already furnish so many pro- 

 babilities in favour of the wave system, and so many objections 



