64 



Vol XLIII.. Art. 6. — S. Tsuboi : 



n,- = 



J. / 1 

 2 



{--jryM^-jry^i.-.,' 



(2) 



Specially when N coincides with B, we have 



<f = 2ß <p' = 0° 



where /^ is the angle between the Z-axis and one of the [optic 

 binomials, (2) may therefore be written as 



/?-= 



(3) 



Now, as we have in the spherical triangle ABN (Fig. b3) 



it follows that 



cos {<p — ^') ^ cos 2i2 ^ cos {<p-^(p') (4) 



for any values of ç-<f', <f + <p', and 2 i?, within the hmit of 0°-1807^ 

 and accordingly from (2), (3), and (4) we have 



Moreover, as ni, U:, and ß are positive, we have 



n.^ß^n, (r>) 



Applying the principle jnst proved, the limiting values of ß 

 were determined as follows : — 



The finely crushed fragments of a biaxial mineral were im- 



1) We have here no necessity to consider any angles out of this limit. 



