OPTIC AXIAL ANGLE. 
157 
reographic (small circles) or orthographic (coordinates) or angle projection. 
Any point H of the dark curved axial bar can then be determined by two 
micrometer readings (coordinates from the center), and, after proper reduc- 
tion to angles within the crystal, maybe plotted in the projection. From the 
projection plot thus obtained, the optic axial angle can be ascertained, 
either by the Becke method described above or by the following simpler 
method,* which differs from the Becke method in the determination of the 
direction of vibration for a dark point H on the zero isogyre in the inter- 
ference figure. 
In the new method two courses of procedure are available for finding the 
great circle which indicates the plane of vibration for a point H of the dark 
brush of an interference figure : (a) it is the great circle passing through H 
and the intersection C of the polar great circle PK (Fig. 88) with the trace 
FIG. 88. In this figure the operations of actual construction are given which are 
required to measure A , A t from the data in the drawing. The points A t and H are first 
located accurately in the drawing, reduced to angular values and plotted directly on 
tracing paper in stereographic or angle projection; the great circle PK polar to H, and 
the horizontal great circle DA t E through Ai are then sketched; the point A \ is the inter- 
section of the great circle HA i, containing H and A t with the polar circle PK, while the 
line OC is the trace of the plane of vibration of the lower nicol (polarizer) as it appears 
on the drawing after the rotation of 30 or 45; the angle MOF indicating directly the 
angle of rotation. By construction A' t C is made equal to A\C, and the intersection 
At of the great circle H A' t with the great circle DAiE determines A t , the second optic 
binormal ; the angle A i A , is the desired optic axial angle 2 V. 
of the principal plane FOI of the lower nicol ; (b) it is the great circle con- 
taining H and tangent at // to the small circle which parallels in projection 
the trace FOI of the principal plane of the lower nicol. In actual work, 
however, it is not necessary to draw this great circle HC, as the point C is the 
point sought and determines at once the direction of extinction for the given 
section. The simplified construction is illustrated in Fig. 88, where C is the 
Am. Jour. Sci. (4), 24, 336, 1907. 
