OPTIC AXIAL ANGLE. 163 
and during each set of observations neither the optical system nor the crystal 
plate was touched. Experience showed that if the upper nicol remained in 
the tube, as is ordinarily the case, and was then rotated, a shift of the optical 
center resulted, which, although almost negligible, was still distinctly notice- 
able. The cross-line micrometer ocular described below served to locate 
accurately the different points in the field. The axial bars of the inter- 
ference figure were plotted directly on cross-section paper as they appeared 
for different angles of rotation of the crossed nicols. The interference figures 
were sharp and the dark axial bars clearly defined, although not perfectly 
dark, and readings could be made to one-half of one division (about i in 
angular coordinates) of the coordinate scale of the ocular. 
MUSCOVITE. 
Several fresh cleavage flakes of this mineral were observed in convergent 
polarized light and the positions of the axial bars determined for different 
angles of rotation of the crossed nicols. The results are plotted in the stere- 
ographic projections (Figs. 950 and 95 b), in which the axial bars are drawn 
for the two positions of the extinguishing plane of the upper nicol (10 
and +15) as indicated by the dotted lines. The observations were made 
by using the cross-grating ocular as shown in the photomicrograph (Plate 2, 
Fig. 3). The observed coordinate values were reduced to their angular 
equivalents by use of the apertometer, and these in turn were reduced to 
the corresponding crystal angles by means of the sine formula and the 
refractive index /3. The use of the refractive index /3 for all directions intro- 
duces an error, but experience has shown that this error is not great and, in 
general, may be disregarded. 
Points were located as accurately as possible along each axial bar and 
then plotted in projection (indicated by small circles, Figs. 95*1 and 956). 
Although the axial bars were not perfectly sharp, they were well defined and 
the points were taken along the central line of the bar, the position of each 
point being determinable to within about i, or less for certain positions. 
In Fig. 95 a the results obtained from an unmounted cleavage plate are rep- 
resented; in Fig. 956 the interference figure is that from the same plate 
mounted in Canada balsam between cover-glass and object-glass. In each 
of these figures the positions of the line of vibration were determined graphi- 
cally, both by the method of Professor Becke (indicated by small crosses) 
and by that of the writer (indicated by small circles). A comparison of the 
relative positions of these small circles and crosses relative to the dotted line 
which represents the position of extinguishing plane of the upper nicol shows 
that in a few instances the points as determined by Professor Becke's method 
are slightly more accurate than the equivalent points of the writer's method ; 
in the majority of instances, however, the small circles are more nearly cor- 
rect than the small crosses. As a general rule, it may be stated that the 
order of accuracy of the two graphical methods is about the same, the 
writer's method having the single advantage of greater simplicity. 
A critical comparison of the results of observation on mounted flakes 
with those on unmounted flakes shows clearly the effects of rotation by the 
glass surface, causing the axial bars and axes to shift slightly, so that the 
direct reading of the optic axial angle is not quite the same in the two cases. 
