192 
METHODS OF PETROGRAPHIC-MICROSCOPIC RESEARCH. 
for the exact determination of the optic axial angle the method of extinction 
angles on different faces in the same zone is not well adapted to optic axial- 
angle determinations, especially when the optic axial angle of the mineral 
is small. In certain cases it is possible to express this relation, as Lane 
has shown, in a slightly different form better adapted for measurements. 
Lane's method, as applied to the pyroxenes and amphiboles, consists in 
measuring the angle between the clinopinacoid and that face of the prism 
zone which has the same extinction angle. The trigonometrical relations 
which obtain for this particular case can be readily deduced from Fig. 1 1 8, 
in which the plane of the optic axes is represented by the vertical line LM , 
FIG. i i 8. 
the optic axes by A\,Ai, the zonal axis by C, and a given plane by P which 
includes the angle v with the normal CN; let the angle CA i = X and CA* =/*; 
also CPAi = a', CPA t = P', CPD = and by construction AiPD = A 2 PD = a. 
Then in the triangle PA \C 
tg a' = cos v . tg X ; 
similarly in triangle 
But 2 = 
('; accordingly 
tg 2{ - * ' 
cos v (tg X+tg M) 
i-cos s t>.(tgXtg/i) 
i-tga'tg/3' 
For that section for which 2$ is equal to the extinction angle 
(i) 
