360 F. F. Wright — Measurement of the Optic Axial Angle 



binomials respectively ; and v the angle between a plane of 

 the zone and plane of optic binomials. For the plane con- 

 taining- the optic axes v = and the extinction angle becomes 



tan A + tan u, 



tan 2 x = — . 



1 — tan A tan ft 



For that plane which shows the same extinction angle, the 



equation 



tan A + tan /a _ ( tan A + tan /x ) cos v 

 1 — tan A tan jx 1 — tan A tan \x cos 2 v 



or 



cost; = — cot A . cot fi (3) 



is evidently valid. In order that equation (3) be valid, 

 cot A cot fx, must be less than unity, or 



A + /*> 90°. 

 But the values 2 V, the optic axial angle, and 2a?, twice the 

 extinction angle on the plane of optic binomials are related to 

 A and jm by the equations 



A + fi = 2 x 



A — [i = 2 V 



Substituting these values in (3), we find 



cos 2 x + cos 2 V fl . 



COS V = 7r^r~- I 4 ) 



COS 2 X — COS 2 V 



or 



XX ~ cos v — 1 . , 



cos 2 V = cos 2 x. (5) 



COS V + 1 w 



In table 2, the values of v are given for different optic axial 

 angles (2V) and different extinction angles (a?), the extinction 

 angle being considered taken invariably to the acute bisectrix of 

 the optic binomial angle. It is evident from this table that for 

 small optic axial angles this method has no practical value for 

 even rough measurements. The larger the axial angle, how- 

 ever, the more sensitive the method becomes. 











Table II. 











Xj 



50 



55 



60 



65 



70 



75 



80 



85 



£C 2 



40 



35 



30 



25 



20 



15 



10 



5 



2V 



















10 



134°27' 



118°58' 



109°03' 



102°08' 



97°10' 



97°37' 



91°21' 



90°00' 



20 



133 29 



117 47 



107 47 



100 49 



95 50 



92 10 



90 00 



88 39 



30 



131 45 



115 42 



105 32 



98 31 



93 31 



90 00 



87 40 



82 23 



40 



129 05 



112 30 



102 08 



94 01 



90 00 



86 29 



84 10 



82 50 



50 



125 04 



107 47 



97 10 



90 00 



85 59 



SI 29 



79 11 



77 52 



60 



118 58 



100 49 



90 00 



82 50 



77 52 



74 28 



72 13 



70 57 



70 



109 03 



90 00 



79 11 



72 13 



67 30 



64 18 



62 13 



61 02 



80 90 00 70 57 61 02 54 56 50 55 48 15 46 31 45 33 



