1 38 M. Rudberg on the Refraction of the differently-coloured 



rallel to both of these axes, and consequently undergo every 

 change of velocity of propagation which the difference of elas- 

 ticity in these two directions admits. 



If therefore we cut a prism in such a manner that its edge 

 is parallel to one of the axes of crystallization, that of the two 

 rays whose plane of polarization is perpendicular to the axis 

 ought to have a constant velocity, and follow in its refraction 

 the law of Descartes (Snellius). The velocity of the other 

 ray depends on its direction in reference to the other two axes 

 of crystallization. Having thus cut three prisms, each of 

 which had its edge respectively parallel to one of the axes of 

 crystallization, and determining in each prism the index of re- 

 fraction of the ray whose velocity remains invariable, we shall 

 have the three elements on which the double refraction of the 

 crystal depends. 



The exposition of the results of the mathematical theory of 

 Fresnel will illustrate still better what we have said. Calling, 

 in the spirit of the system of emanation, f', v" the velocities of 

 the two rays, s', s" the angles which the two optical axes form 

 with the common direction of the rays, we shall have the 

 velocity of one of these by the equation 



'/^ = A + B . sin^ i (e' - e"), 

 and that of the other by the equation 



x/'' = A + B . sin i (/ + e")> 

 in which A and B are constants. 



It has already been remarked, that two of the axes of cry- 

 stallization are situated in the same plane as the optical axes, 

 and that the third is perpendicular to this plane. I shall in 

 the sequel call the axis of crystallization which bisects the 

 acute angle of the optical axes the axis A, that which bisects 

 the obtuse angle the axis B, and that which is perpendicular 

 to the plane of the optical axes the axis C. From the pre- 

 ceding observations we conclude, 



1. If the edge of the prism is parallel to the axis A, and if 

 the two rays are consequently refracted in a plane perpen- 

 dicular to this axis, we shall always have, if the angles b' and s" 

 are reckoned from the axis A, e' + n" = 180°, and therefore 

 i/^ = A + B . cos^ e", and t/'^ = A + B. 



This last velocity is constant, and is that of the ray whose 

 plane of polarization is perpendicular to the axis A. 



The velocity of the other ray depends on the value of the 

 angle e", which may vary from 90^ to 90° — \ a, calling a. the 

 acute angle of the optical axes. The value of the square of this 

 velocity will thus vary 



between A and A + B sin^ i a. 



I 



