200 MKTHODS OF PETROGRAPHIC-MICROSCOPIC RESEARCH. 
or the coordinate micrometer ocular described above. This ocular coin- 
bined with the method of projection of Professor Wulff, or with the gradu- 
ated hemisphere of Professor Nikitin, is a general extension of the Mallard 
method, and like the Bccke method utilizes the rule of Biot and Fresnel, 
which defines the planes of vibration for any direction of wave propagation. 
With this ocular the probable errors of determination on sharp interference 
figures should not exceed i if both optic axes are visible, nor 3 if only one 
optic axis appears in the field. 
(b) In parallel polarized light the methods involving the Fcdorow-Fuess 
universal stage are used and furnish satisfactory results, provided the posi- 
tion of one optic axis can be determined directly. If both optic axes are 
outside of the field of vision, the results obtained are usually unsatisfactory 
and inaccurate. Theoretically, it is possible to measure the optic axial 
angle of any biaxial transparent mineral on any section by means of the 
universal stage. If both optic axes appear within the field of vision, the 
error of determination should not exceed 1, and if only one of the opt it- 
axes be visible the accuracy may decrease to ==5. The exact location of 
a visible optic axis is assisted somewhat by use of the method of optical 
curves. Having once fixed the location of one optic axis, that of the second 
is determined by the method of extinction curves. If both optic axes lie 
entirely outside of the field, special methods must be resorted to, but in 
general without marked success, owing to the great difference in the value 
of 2 V caused by a very slight deviation in the measured extinction angle. 
The range of the field of vision of the universal stage is greater than that 
of any possible interference figure; the Fedorow universal-stage methods 
arc, therefore, applicable to a greater number of sections than the methods 
with convergent polarized light and may furnish results on sections other- 
wise useless for ordinary methods. 
Both experience and theory show that for all these methods the accuracy 
of the determination varies considerably with the section and mineral in 
question. The most accurate results can be obtained on sections for which 
both optic axes appear within the field of vision; less accurate but still 
satisfactory measurements can be made when only one optic axis appears, 
particularly when it is situated about midway from the center to the margin 
of the field. 
