1 66 
METHODS OF PETROGRAPHIC-MICROSCOPIC RESEARCH. 
point P of the zero isogyre, which appears darker than any adjacent lateral 
point for a given position of the nicols, may then be shifted slightly after 
a rotation of the nicols through 90; it should be noted that part of the 
observed shifting may be due to the distortion caused by the analyzer. 
Briefly stated, an obliquely transmitted wave will be extinguished pro- 
vided its direction of vibration after emergence is contained in the extin- 
guishing plane of the analyzer. The direction of vibration of an observed 
dark point on the axial bar of an interference figure is therefore the line of 
intersection of the extinguishing plane of the upper nicol with the polar 
plane of the given point. As noted above, this construction, suggested by 
the writer, does not take into consideration the rotatory effects of the sur- 
faces of the crystal plate and the glass mount and is accordingly only an 
approximate method. The method of Professor Becke is different and con- 
sists in finding the intersection of the polar plane with the great circle in 
stereographic projection which is tangent to a line parallel with the princi- 
pal section of one of the nicols. The points obtained by these two methods 
are slightly different, but not sufficiently different to affect the degree of 
approximation obtainable by such methods. In principle, however, the 
two methods are fundamentally different and the above detailed discussion* 
of the factors entering the problem indicates the general validity of the 
principle on which the method proposed by the writer is based. Neither 
the Becke method nor that proposed by the writer for finding the plane 
of vibration of a point P on the zero isogyre is strictly correct ; but a correct 
method is not feasible in view of the complex conditions of observation 
which obtain. 
Measurements with the double-screw micrometer ocular or the coordinate 
micrometer ocular are relatively free from the personal factor which plays 
an important part in the Becke drawing-table, and the values for 2 V ob- 
tained by its use are correspondingly more accurate. This method is of 
general application to all sections cut in such a way that either one or both 
optic axes appear in the microscopic field. By using projection plats, 
either stereographic or orthographic or angle, results of a fair degree of 
accuracy can be obtained in a few minutes.t 
*See also Amer. Jour. Sci. (4), 31, 156-211. 1911. 
M device to aid in the graphical solution of the above problems. The measurement of the optic axial angle 
by the curvature of the dark bar of the interference figure involves two steps: (i) the measurement and 
location of the optic axis and some point on the dark bar, and (2) certain manipulations in the projection 
plat. In the second part of the procedure a stereographic or angle projection plat serves as base, and the 
angular values are plotted directly on thin transparent paper placed directly above the plat and held in 
center by means of a needle; but 
FIG. 97. 
this needle is not entirely satis- 
factory, since it does not hold its 
place rigidly enough and tends 
thereby to injure the projection 
plat below. To overcome this 
difficulty the writer has construct- 
ed the following little device (Fig. 
97, one-eighth actual size): A 
heavy brass bar fits into two 
bras* end-blocks, C and D; at its center a small brass rod I'., containing a needle backed by a spring, 
is introduced. By this device the needle is supported in a vertical position and rigidly; as the distance 
between the end-blocks C and D is 44 cm., more than sufficient space is available for the projection plat and 
overlying drawing. The writer has used this device for several years and has found it satisfactory and 
a time-saver. 
Recently. Professor Nikitin (C. Leiss. Zeitschr. Kryst. 47, 379. 1909) has had constructed a graduated 
porcelain hemisphere which the writer has found satisfactory in optic axial angle projections and slightly 
more accurate than the projection plats, chiefly because of its lack of distortion toward the margin and 
consequent acute-angled intersections of great circles. This hemisphere has the advantage of serving as a 
model in the study of optical phenomena and is a useful piece of apparatus for the petrological laboratory. 
