FRESNEL OX DOUBLE REFRACTION'. 323 



sections of the two surfaces are sensibly coincident. For topaz 



the ratio — is 0*9939 ; for anhydrous sulphate of lime, one of 



the bi-axal crystals whose double refraction is most powerful ; 

 this same ratio, according to the observations of M. Biot, is 

 equal to 0-9725 *. 



Observations on the route of the Waves and luminous rays in 

 the direction of the optic axes. 



It is to the circular sections of the surface of elasticity that a 

 plane wave must be parallel in the interior of a crystal, in order 

 that it may be there susceptible of only one velocity of propaga- 

 tion ; and this condition is satisfied when the plate of crystal, 

 cut parallel to the circular sections of the surface of elasticity, is 

 presented perpendicularly to the luminous beam. But it is to 

 be remarked that the ordinary and extraordinary rays resulting 

 from it do not follow- the same direction, and deviate a little, 

 both the one and the other, from the normal to the circular sec- 

 tion of the ellipsoid. This is more easily seen by a reference to 

 fig. 14, which represents the intersection of the plane of .r z with 

 the two sheets of the wave surface, and in which the ellipticity 

 of one of them is exaggerated to render the divergence of the 

 rays more perceptible. 



This intersection is composed of a circle and an ellipse, whose 

 equations are 



.1-2 + ^2 = V^, and «2 .^.2 + ^2 _j2 ^ ^2 ^2^ 



The plane T S, drawn parallel to the circular section of the sur- 

 face of elasticity, and distant from the centre A by a quantity 

 equal to [b], touches at the same time the circle and the ellipse 



* According to tlie observations of M. Biot, the angle between the two optic 

 axes iniimpid topaz is G;5°14'2", and in anhydrous sulphate of lime 41°41'22", 

 which gives 31° 37' 1" and 22° 20' 41" for the value of the angle whose tangent 



is represented by — . / ^ „ ; it results from the same measures that the 



I g^i iji 



angle which has for its tangent . / — is in the former crystal31°46'25", 



and in the second 22° 54' 43". Hence the difference of direction between the 

 circular sections of the ellipsoid and of the surface of elasticity is only 9' 24" for 

 topaz and 34' 2" for anhydrous sulphate of lime. 



Note. — The seconds marked in the value of the angles given by M. Biot, 

 and which we have here transcribed, do not signify that the precision of measure- 

 ment can be carried to this extent; for it is difficult even to determine the 

 angle of the optic axes within half a degree ntarly. 



