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tallized medium, imagine the ellipsoid to be described as above, and 

 let it be cut through its centre by a plane parallel to that of a pla7ie 

 wave of light incident on the crystal ; then if the vibrations of the 

 light be parallel to either of the axes of the section, the plane con- 

 taining the direction of the vibrations and that of the elastic force 

 arising from them will be perpendicular to the plane of the wave 

 (No. 4, preceding) ; and therefore, according to Fresnel's theory, the 

 direction of the vibrations will remain parallel to itself, while the 

 wave is propagated. But if the light be common light, or if it be 

 polarised, and the plane of polarisation be not perpendicular to either 

 of the axes of the section, the wave will be divided into two others 

 having the directions of their vibrations parallel to the semiaxes of 

 the elliptic section, and their planes of polarisation perpendicular to 

 them : their velocities of propagation — measured in a direction per- 

 pendicular to their plane — will be different, and will be in the sub- 

 duplicate ratio of the elasticities in the direction of their respective 

 vibrations, and therefore (by No. 3.) inversely as the semiaxes of the 

 section to which those vibrations are parallel. ;; jo - - 



If a wave be propagated m all directions from an origin O 

 within a crystal, its surface will at each instant be touched by the 

 simultaneous position of a plane wave which passed through O at the 

 instant when the former began to be propagated (Memoir, p. 127.) 

 Hence, to find the- surface of the double wave in a crystal, let the 

 abovementioned ellipsoid be cut by any plane through its centre O, 

 and imagine two other planes parallel to this section, and at distances 

 from it which are third proportionals to its semiaxes OR, Or, and any 

 given line k : the double surface which touches these planes in all 

 their positions will be the surface of the wave. 



Now conceive another concentric ellipsoid, having the directions 

 of its semiaxes the same, but their lengths a, b, c, inversely propor- 



M 2 



