1 86 
METHODS OF PETROGRAPHIC-MICROSCOPIC RESEARCH. 
By this method of determining the positions of the principal sections of 
the ellipsoid, the distinction between uniaxial and biaxial minerals is greatly 
facilitated and the general problem solved for all possible sections. In 
case the position of neither optic axis can be determined directly, both 
optic axes lying outside the field of vision, the methods for measuring the 
optic axial angle are based solely on the determination of extinction angles 
along certain directions, and are of such a nature that by their use only very 
rough approximations to the true value of 2 V can be obtained, errors of 
10 and over being easily within the range of possibility. Fedorow has 
suggested one principal method applicable to such cases and the writer has 
had occasion to use several others. They are not so satisfactory, however, 
as the above methods, and are not of equal practical value. For the sake 
of completeness they are described briefly below. 
FIG. 115. 
SECTION NEARLY PERPENDICULAR TO THE OPTIC NORMAL B- 
In case the section of a mineral is so cut that it makes an angle of 30 or 
less with the plane of the optic axes, neither optic axis appearing, in con- 
sequence, within the field of vision, the above method places the observer 
in a position to measure the optic axial angle without even seeing either 
optic axis. The exact position of /3 can first be determined by this method, 
and then brought to coincidence with the microscopic axis, in which case 
the plane of the optic axis is horizontal. In this position the circles V\ 
and HI are free and the section can be revolved about V\ and extinction 
angles determined on HI (Figs. 115 and 116). 
Since the exact positions of a and y have been determined and the two 
optic axes make equal angles with these bisectrices, it is possible by trial 
to bring one of the optic axes A\ to coincidence with the normal to Vi 
(Fig. 115) and to test the accuracy of its position by means of extinction 
curves for different inclinations of the section about Vi. Thus let a be the 
acute bisectrix (Fig. 115) and assume that one optic axis A\ coincides pre- 
