318 FRESNEL ON DOUBLE REFRACTION. 



Planes of Polarization of Ordinary and Extraordinary Waves. 



According to \vhat we have said at the commencement of this 

 memoir, in deducing our hypothesis as to the nature of luminous 

 vibrations from the phsenomena presented by the interference of 

 polarized rays, the plane of polarization must be parallel or per- 

 pendicular to the direction of the luminous vibrations. It re- 

 mains only to choose between these two directions that which 

 agrees with the usual acceptation. Now the name plane of 

 polarization of the ordinary beam in uni-axal crystals is given to 

 the plane drawn through this beam parallel to the axis of the 

 crystal ; and it is clear that the ordinary vibrations, that is to 

 say, those which always call into play the same elasticity, are 

 the vibrations perpendicular to the axis of the crystal ; in fact, 

 in the case of crystals with one axis, the surface of elasticity be- 

 comes a surface of revolution, and each diametral section has 

 always its greatest or least radius vector situated on the inter- 

 section of its plane with the equator ; it is therefore this radius 

 vector which remains constant, since the equator is a circle, and 

 which consequently gives the direction of the ordinary vibra- 

 tions ; whence we see that these vibrations are always perpendi- 

 cular to the axis of the crystal. Hence the plane drawn through 

 this axis and the ordinary ray is perpendicular to these vibra- 

 tions, since they are also perpendicular to the ordinary ray by 

 reason of the sphericity of the wave to which they belong ; but 

 this plane is precisely, as we have just said, that which it has 

 been agreed to call the plane of polarizatioii of the ordinary ray ; 

 hence we shall give the name oi plane of polarization of a lumi- 

 nous wave to the plane normal to the direction of its vibrations. 

 This theoretical definition agrees with the meaning attached to 

 the expression ''plane of polarization'' in the emission system, 

 so long as the wave is spherical and its vibrations perpendicular 

 to the luminous ray, because then the plane of polarization 

 always passes through the ray; but when the vibrations are 

 oblique to the ray, the plane of polarization, which ought to be 

 perpendicular to them according to our definition, no longer 

 contains the luminous ray, whilst in the emission system it is 

 supposed to be always directed along this ray. Hence, the same 

 direction precisely would not be assigned in the two theories to 

 the planes of polarization of luminous rays in media where their 

 waves no longer have the spherical form. But, in the first place. 



