OPTIC AXIAL ANGLE. 153 
ing drawing-table fixed in position relative to the microscope. Accurate 
drawings of the interference phenomena are then prepared and serve in place 
of the actual interference figure. This method has been fruitful in its 
results, and with practice the necessary manipulative skill can be acquired 
to obtain trustworthy axial-angle values. The accuracy of the method is 
dependent on several factors the accuracy with which the drawing is pre- 
pared, the exactness with which the drawing- table is centered, and the care 
with which measurements are made on the finished drawing. 
The actual field of the projection does not measure over 25 mm. in diame- 
ter, and a difference of i of E corresponds to a difference in D of about 0.25 
mm., a distance which is easily measurable. With unusually sharp axial 
bars and nice adjustment of the optical system, it is theoretically possible 
to obtain an accuracy of about \ to %\ in practice, however, a greater 
accuracy than i to 2 can not be claimed for the method. 
The writer has not seen the revolving drawing-table described by Pro- 
fessor Becke, and has used in his work a small rotating disk graduated in 
degrees and supported by an arm which, in turn, is attached to the micro- 
scope stand by means of a collar.* This device was constructed in the 
mechanical workshop of the Geophysical Laboratory. The results obtained 
with it have proved satisfactory and the manipulation with the same 
convenient. f 
Having once fixed the position of this table so that its axis of rotation 
coincides (after reflection in the camera lucida) with the optical axis of the 
microscope and is also at the proper distance from the eye for distinct vision, 
its constant K, corresponding to the K of the microscope in the formula 
D = K sin E, can be determined by one of the methods described above. 
With the drawing of an interference figure thus properly prepared, it is 
possible to determine the angular distance polar angle p and longitudinal 
angle <, of any point in the projection and to plot the same in stereographic 
or orthographic or angle projection, and thus to measure the angular dis- 
tance between any two points, as those between optic axes occurring in the 
field of vision. 
In a recent article, t Professor Becke has described an ingenious method 
by which any section, in which only one optic axis appears in the field, can 
be used for the measurement of the optic axial angle, although the values 
obtained are only close approximations to the correct value of 2V. He 
utilizes the fact that sections of biaxial minerals, cut approximately normal 
to an optic axis, exhibit, in convergent polarized light, dark axial bars which 
resemble hyperbolas in the diagonal position and whose degree of curvature 
is dependent on the optic axial angle 2 V. For any given position of the 
stage, the points along the dark bar of the interference figure correspond to 
those directions of light-wave propagation in space whose lines of vibration 
are contained in the principal plane of the lower nicol (polarizer) and for 
which the extinction angle is zero. 
To measure graphically the optic axial angle of a given mineral from the 
degree of curvature of its dark axial bar (zero isogyre) on a section approxi- 
Amer. Jour. Set. (4). 24. 333. 1907. 
fH. Tertsch (T. M. P. M. 29, 171-172. 1910) has described recently an ocular which is so arranged that 
the image of the interference figure is projected by the Bertrsmd lens on a glass surface on which it is traced 
directly. 
IF. Becke. Tschermak's Min. petr. Mitth.. 24, 35-44. 1905. 
