OPTIC AXIAL ANGLE. 
193 
in the plane of the optic axes 
=tg,.c* 
I-COS 2 tgXtgM I- 
(2) 
. ' . cos v = cot X . cot n. (3) 
In order that this equation be valid the product cot X cot n must be less 
than unity and either X or n must be negative and one or both greater than 
45. The optic axial angle, 2 V, and the extinction angle, $ , in the plane of 
the optic binormals are related to X and /z by the equations 
With the aid of these values equation (3) can be written 
v cos 2 V 
fry- _ . ~ m - 
2 COS 2$ 
an equation which is valid only for 2 V or 2$ greater than 90. 
In table 8, the values of v are given for different optic axial angles (2V) 
and different extinction angles (), the extinction angle being considered 
taken invariably to the acute bisectrix of the optic binormal 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, 
however, the more sensitive the method becomes. 
TABLE 8. 
27 
1=50 
1=40 
i=55 
i=35 
t =6o 
=30 
,=65 
, = 25 
1 = 70 
,=20 
i = 75 
. = 15 
,=8o 
, = io 
.=85 
,= 5 
10 
I3427' 
118*58' 
i0903' 
I0208' 
97io' 
934i' 
9 I2l' 
90oo 
20 
133 29 
"7 47 
107 47 
loo 49 
95 50 
92 10 
90 oo 
88 39 
30 
131 46 
"5 43 
105 32 
98 31 
93 31 
90 oo 
87 40 
86 19 
40 
129 08 
112 30 102 08 
94 oi 
90 oo 
86 29 
84 10 , 82 50 
50 
125 04 
107 47 
97 ii 
90 oo 85 59 
81 29 
79 ii ! 77 52 
60 
118 58 
loo 49 90 oo 
82 49 ! 77 52 
74 28 
72 13 70 57 
70 
109 03 
90 oo 
79 ii 
72 13 
67 30 
64 17 
62 13 
61 02 
80 
90 oo 
70 57 
61 02 
54 56 
50 52 
48 H 
46 31 
45 33 
MEASUREMENT OF THE OPTIC AXIAL ANGLE ON THE TOTAL REFRACTOMETER. 
Pulfrich,* Soret.f Viola,| Cornu,|| and Walle'rantl have shown that it is 
possible on a single section of a biaxial or uniaxial mineral to determine, not 
only the three principal refractive indices a, /3, and 7, but also, by observing 
the planes of polarization of each wave corresponding respectively to a/3, 0y 
and ya, to determine accurately the relative position of the principal planes 
of the ellipsoid to the given section; and, from the accurate refractive indices 
thus ascertained, to calculate the optic axial angle with great exactness. 
These methods, however, require specially ground and polished sections and 
*C. Pulfrich. Das Total Reflelctometer. Leipzig. 1890. 
tSoret. Zeitsrhr Kryst., IS. 43. 1899. 
JC. Viola. Zeitschr. Kryst.. 31, 40-48. 1889; 36. 345-251. 1902. 
ilCornu. Compt. Rend.. 133, 135; Bull. Soc. Mia.. 25. 7. 
F. Wallerant. Bull. Soc. Min.. 20, 12-26. 1889. 
