258 FRESNEL ON DOUBLE REFRACTION. 



culations of the intensities of the ordinary and extraordinary 

 images, for a homogeneous light, or that of tlie tints developed 

 by polarized white light, always lead us back to the considera- 

 tion of rectilinear vibi-ations and to the employment of the for- 

 mulae of interference which refer to them. 



In indicating the mechanical cause of the altogether peculiar 

 double refraction exerted by rock-crystal on light in the direc- 

 tion of its axis, we have wandered from the object of this memoir, 

 in which we shall treat solely of the case in which the particles 

 of the vibrating medium have their homologous faces parallel, 

 and thus exhibit the same molecular arrangement from right to 

 left and from left to right. We hope the reader will pardon us 

 this digression on circular polarization, to which we were natu- 

 rally led by what we had just said on rectilinear polarization. 

 It is, besides, useful to familiarize ourselves with these different 

 modes of luminous vibrations, the whole of which we find in 

 the most simple kind of double refraction, such as that of uni- 

 axal crystals, as soon as we, instead of separating in thought the 

 ordinary from the extraordinary w^aves, consider the complex 

 effect which results from their simultaneous existence. 



After having proved that the transversal direction of the lu- 

 minous vibrations is a necessary consequence of the absence of 

 the ordinary phaenomena of interference in the reunion of rays 

 polarized at right angles, it is necessary to show that this hypo- 

 thesis established by facts, in the wave-system, is not contrary 

 to the principles of mechanics, and to explain how such vibra- 

 tions may be propagated in an elastic fluid. 



Possibility of the propagation of Transversal Vibrations in an 

 Elastic Fluid. 



An elastic fluid is by all philosophers conceived as the assem- 

 blage of molecules or material jjoints separated by intervals 

 which are very great relatively to the dimensions of these mole- 

 cules, and kept at a distance by repulsive forces which are in 

 equilibrium with other contrary forces resulting from the mutual 

 attraction of the molecules or from a pressure exerted on the 

 fluid. This being established, let us, for the sake of fixing our 

 ideas, imagine the regular an-angement of molecules represented 

 by fig. 2, and consider the case of a plane and indefinite wave 

 Avhose surface is parallel to the plane projected in A B. If the 

 portion of the medium above this plane has undergone a small 



