

202 



the surface of elasticity ; and that the plane of polarization of 

 the other is perpendicular. This coincides, very nearly, with 

 the rule previously given by M. Biot, namely, that the plane 

 of polarization of one of the pencils bisects the dihedral angle 

 formed by planes drawn through the ray and the two optic axes ; 

 while that of the other is perpendicular, or bisects the supple- 

 mental dihedral angle. 



Thus the two fundamental facts of crystalline refraction 

 namely, the bifurcation of the ray, and the opposite po- 

 larization of the two pencils are completely accounted 

 for. 



Further, the amplitudes of the resolved vibrations are 

 represented by the cosines of the angles winch the direction 

 of the original vibration contains with the two fixed rec- 

 tangular directions ; and, as the squares of these amplitudes 

 measure the intensities of the two pencils, the law of Malus 

 respecting these intensities is a necessary consequence. 



(214) The velocity of propagation of a plane wave in any 

 direction being known, the form of the wave, diverging from 

 any point within the crystal, may be found. For, if we con- 

 ceive an indefinite number of plane waves, which, at the com- 

 mencement of the time, all pass through the point which is 

 considered as the origin of the disturbance, the wave-surface 

 will be that touched by all these planes at any instant. Fresnel 

 has given the following elegant construction for its determi- 

 nation : "Let an ellipsoid be conceived, whose semiaxes are 

 a, b y c (the same as those of the surface of elasticity), and let 

 it be cut by any diametral plane. At the centre of this sec- 

 tion let a perpendicular be raised ; and on this line let two 

 portions be taken, whose lengths (measured from the centre) 

 are equal to the greatest and least radii of the section. The 

 extremities of these perpendiculars will be the loci of the 

 double wave." 



