1 20 On tJie Laws of Crystalline 



1. When the face of the crystal is perpendicular to its axis 

 there is evidently no deviation. 



2. When the axis lies in the face of the crystal the devia- 

 tion vanishes in the azimuths 0, 90, 180, 270. In the inter- 

 mediate azimuths, differing 45 from each of these, the deviation 

 is a maximum ; for if we put A = in formula (55) the result will 

 be 



3 = - - sin CT sin 2a ; 



and this quantity (neglecting its sign) is a maximum when sin 

 2a = 1. The coefficient of sin 2a is equal to 3 54', which is 

 consequently the greatest value of the deviation. According to 

 the experiments of M. Seebeck, the value is 3 57'. 



3. On the fracture-faces of the crystal the deviation va- 

 nishes in the azimuths and 180, as also in two other azi- 

 muths for which 



tan A 

 cos a = - , 



and in which, therefore, wi is equal to w. In the azimuth 45 

 the deviation is -3 35'; in the azimuth 90 it is -2 32'; and 

 in the azimuth 127 38' it vanishes; after which it attains a 

 small maximum with a positive sign, and vanishes again in 

 azimuth 180. The calculated values of the deviation agree 

 pretty well with the values observed by M. Seebeck. 



The sign of the deviation shows at what side of the plane 

 of incidence the plane of polarization lies. But the position of 

 the latter plane is best indicated by that of the transversal of 

 the reflected ray. If this transversal and the axis of the crys- 

 tal be produced from the origin, towards the same side of the 

 plane of xz, until they intersect the sphere in the points t and 

 A respectively, these points will be on the same side of the 

 great circle XY when the deviation and the sine of the azi- 

 muth have unlike algebraic signs ; and they will be on opposite 

 sides of that circle when those quantities have like signs. There- 

 fore if the crystal be supposed to revolve in its own plane, be- 



