Crystalline Reflexion and Refraction. 59 



w, = w + ^cosV = 60° 42', 

 which is the maximum value of the polarising angle. 



2. When \=0, the axis lies in the face of the crystal, and formula (55) 

 becomes 



w,=xir — ArsinVcos^a, 



showing that w,=w, when a is either 90° or 270°. But when a is or 180°, we 

 have 



Tsr, = w — A;sinV=54°2', 

 which is the minimum value of the polarising angle. 



3. For the natural fracture-faces of the crystal the value of \ is 45° 23'. 

 Hence, when a= or 180°, 



^,= ^—k (sinV— sin^) = 57° 26' ; 



and when a = 90° or 270°, 



,^,=zir+^cosVsin^ = 59° 50'. 



These values of the polarising angles agree very well with the experiments of Sir 

 David Brewster, and still better with those of M. Seebeck. 



If we wish to know in what azimuths w, is equal to ■nr, on a given surface of 

 the crystal, it is obvious from (55) that we must make 



sinV— sin^\ = sinVcos^AsinV 

 whence we have, simply, 



tanX ,,„. 



COS a = ± ^ , (59) 



tans- ^ ■' 



which shows that the thing is impossible when \ is greater than ot ; and that, 

 when \ is less than m, there are four such azimuths ; as indeed there are, gene- 

 rally speaking, four values of a corresponding to any other particular value of the 

 polarising angle. If a' be the least of these azimuths, the others will be 180° — o', 

 l80°-f-«', and 360° — a. On a natural face of the crystal, the value of a', answer- 

 ing to the supposition Tir,z=w, is found to be 52° 22'. 



Next, let us trace the changes which the deviation undergoes In some 

 remarkable cases. 



1 . When the face of the crystal is perpendicular to its axis, there Is evidently 

 no deviation. Ljl^i) 



