538 WRIGHT: MEASUREMENTS OF REFRACTIVE INDICES 



-^^ = y COS rp — a cos r^ and sin i = ^- sin r^ . . . .d (fig. 2) 

 d 



■ - = /3 cos ry - a COS r^ and sin z = 7- sin r^ . . . .e (fig. 2) 



— '— = a cos Ty — /3 cos r^ and sin i = y sin r-y ... ./ (fig. 2) 

 d 



For uniaxial minerals these equations reduce to the following, 

 in which the positive of the =t sign should be used for a positive 

 mineral, the negative sign for a negative mineral. 

 (1) Section normal to the principal axis 



± — = 0) (cos r^ — cos rj and sin i = e- sin r^ g (fig, 2) 



d 



(2) Section parallel to the principal axis 



± — ^ = (e - w) cos r^ h (fig. 2) 



d 



=1= = e COS fj — o) cos r^j and sin z = e sin r^ i (fig. 2) 



It is of interest to note that in the case of normal incidence 

 {i ^ r = 0) all of the above equations reduce to the ordinary 



k "X 

 expression for the birefringence — 1— = ^2 — ?ii (i.e., path- 

 difference varies with thickness of plate and with the birefringence.) 

 In the case of a section normal to a bisectrix the path-difference 

 for waves along an optic axis (binormal) is zero and the angle 

 of refraction is half the optic axial angle (r^ = V); thus from 

 equation a we find 



= 7 cos a — j8 cos Va OY 



cos Va = -■ COS r^ (7) 



1^_ J. 



from which the usual expression cos^ Y^ = — can be easily 



Q,2 <y2 



