60 Mr. Mac Cullagh on the Laws of / //yj 



2. When the axis lies in the face of the crystal, the deviation vanishes in the 

 azimuths 0, 90°, 180°, 270°. In the intermediate azimuths, differing 45° from 

 each of these, the deviation is a maximum; for if vpe put \=:0 in formula (55) 

 the result will be 



03= — - sinwsin2a; f^yt' 



and this quantity (neglecting its sign) is a maximum vi^hen 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 vanishes in the azimuths 

 and 1 80°, as also in two other azimuths for which 



tan A 



COS a = — r- — , 

 tannr 



and in which therefore *, is equal to -a,. 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 polarisation 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 crystal 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 azimuth have unlike algebraic signs ; and they will be on opposite sides of 

 that circle when those quantities have like signs. Therefore if the crystal be 

 supposed to revolve in its own plane, beginning at the azimuth 0, the points t and 

 A will lie on the same side of XY until A reaches the position A', where the 

 angle A'Yi is equal to 127° 38' ; the point t will then pass over to the side oppo- 

 site A, at which side it will remain until A arrives at the azimuth 232° 22'. 

 Thenceforward, to the end of the revolution, both points will be found on the 

 same side of the circle XY. 



