ßß Vol. XLTII., Art. G. — S. Tsuboi : 



centre of the stereogram, XX' and YY' the vibration directions 

 of niçois, A the position of the observed optic axis, XAX' the 

 great circle representing the optical plane, and MN the direction 

 of extinction. The straight line OA was then drawn to cut the 

 stereographic circle at A', and taking the point B' on the same 

 circle so that A'N=NB' and connecting B' with 0, the position 

 of tlie other optic axis B was determined as the point of inter- 

 section of the straight line BO with the great circle XAX' 

 (Biot-Fresnel's law). 



The azimuth (^') and the central angular distance {p') of the 

 second pole were calculated as follows : — 



f'=B'ON-\- Y'ON=A'ON^ Y'ON 

 = ^+F'0.Vx2 (1) 



In spherical triangles, OAD and OBD, we have the rela- 

 tions : — 



sin ^i> — sin (f sin f) (2) 



tan 01) — cos <p tan /> (8) 



cot o' = cos (p' cot OD (4) 



tan^D^sin ODta.n(p' (5) 



and from the formulae (1), (3), and (4), the values of <p' and />' 

 were obtained. 



The inclination of the optical plane with respect to the side 

 pinacoid, i.e. O.P. Ail/(010), was determined by subtracting the 

 value of angle OD from 90°. 



Optic Axial Angle.'^— rCalculating the values of AD and BD 

 witli tlie formulae (2), (3), and (5), the optic axial angle was de- 

 termined {AD-^BD). 



1) S. Tsuboi, " On the Methuilj of MeasureTnent of the Optic Axial Angle of ;i Mineral ia 

 Eock Slicj," Jour. Geol. Soc. Tô'rijô, Vol. XXIV.. p. 14D, iai7 (in Japiinese). 



