1 68 
METHODS OF PETROGRAPHIC-MICROSCOPIC RESEARCH. 
isogyre AHR, the positions of the two optic axes A and B (optic axial 
angle 2 V in this particular case measuring 30) being definitely fixed, as 
well as the plane of vibration DE of light- waves from the lower nicol. To 
find this point H of the great circle THM, the stereographic projection 
plane is first rotated about TM until the great circle THM coincides with 
the straight line TH'M. By this process A is transposed to A' and the 
position of B is changed to B'. The projection is then rotated about DE as 
an axis until H' coincides with H" and radii H"A"K and H"B"N include 
equal angles with the nicol plane DE. The angle of revolution required 
to bring A' to A" or B' to B" is noted and the projection then rotated 
back to its original position, the center H" passing thereby first to H' 
and then to H , which is the desired 
point. That H is actually the 
correct point can be proved, further- 
more, by drawing the great circles 
through HAF and II BL and noting 
that the angles FC and CL on the 
great circle FCL polar to H are 
equal. 
This method of construction is 
perfectly general. After the stereo- 
graphic plats had been finished they 
were transferred to equivalent ortho- 
graphic plats. (In these figures the 
position of the plane of vibration is 
indicated by arrows pointing NE ) 
In Figs. 99 to 101 the directions in 
the orthographic plat were corrected 
for the passage of the light-waves 
from the crystal plate to air by means 
of the usual sine relation sin i=n sin r, 
FIG. 99. This figure illustrates the posi- 
tions in the interference figure of the dark 
curves of total extinction (axial bars) as 
they would appear in the field were obser- 
vations made in air on a series of biaxial 
minerals having a mean refractive index 
of i .60 and the optic angles indicated, and 
cut normal to one of the optic axes (bi- 
normals). From the figure it is evident 
that the radius of curvature of the axial 
bar increases with the optic axial angle, 
so that for 2 V = go, the axial bar is prac- 
tically a straight line. 
where * = the angle of incidence, 
r = angle of refraction, and n = aver- 
age refractive index; for minerals of 
medium birefringence the error aris- 
ing from substituting /3 for the cor- 
rect refractive index is negligible.* 
In figures 99 to 101 the dark lines represent the curves of total extinction 
(zero isogyres or axial bars) of the interference figure in orthographic projec- 
tion, the plane of the optic axes making an angle of about 45 with the plane 
of vibration of light- waves from the lower nicol. In the construction of the 
figures neither the rotation of the boundary surfaces on the plane of polar- 
ization of the transmitted light-waves nor the elliptic polarization phe- 
nomena, due to repeated total reflection within the crystal plate, was taken 
into account. For this reason the figures do not represent interference 
figures as actually observed under the microscope, but rather as they would 
appear were the Biot-Fresnel rule strictly valid. At a distance from the 
See Uo Arner. Jour. ScL (4), 24, 338-340. 1907. 
