of Minerals in the Thin Section. 333 



of the optic axial angle, although the values obtained are only 

 close approximations to the true value of the 2 V. 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 2V. For any given position of the stage, 

 the points along the dark bar of the interference figure corre- 

 spond to those directions of light wave propagation in space 

 whose planes of vibration coincide with 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 min- 

 eral from the degree of curvature of its dark axial bar (zero 

 isogyre) on a section about normal to an optic axis by this 

 method, the axial bar is first drawn when in a position parallel 

 to the horizontal cross hair (fig. 8, the straight line A 1 C in this 

 position being the trace of the plane of optic axes) ; the micro- 

 scope stage and drawing table are 

 then revolved in the same direction 

 about some convenient angle 30° or 

 45° and the axial bar drawn in the 

 new position (A 1 P of fig. 8).* 

 These drawings are repeated after 

 revolution of the microscopic stage 

 or drawing table alone through 180° 

 (A/.C and A/ P 7 ). 



The point P in the projection is 

 any convenient point on the dark 

 curve or zero isogyre, and is there- 

 fore a direction in the crystal in its 

 given position relative to the nicols along which light waves 

 are propagated without changing their original plane of vibra- 

 tion. The plane of vibration for the point P is thus known, 

 and the law of Biot can be applied directly^ to find by con- 

 struction the second optic axis A 2 . 



A convenient form of construction is shown in fig. 9, the 

 details of which are the same in every case. After plotting 

 the observed points P and A 1 on tracing paper above the pro- 

 jection plat, the great circle A/CA/, of which P is the pole, 

 is first found by revolving the tracing paper about the center 

 O until P coincides with the vertical diameter of the under- 



*In his work the writer has found it more convenient and accurate to 

 revolve the nicols instead of the stages, which remain stationary except for 

 revolutions of 380°. 



Am. Jour. Sci.— Fourth Series, Vol. XXIV, No. 142.— October, 1907. 

 23 



