34S F. E. Wright — Measure rm nt of the Optic Axial Angle 



any given but fixed position, then turning- IT., through angles 

 of 5° respectively, and for each position of H„ determining 

 the angle of inclination about Y, for which the section is in 

 the darkest position (0° extinction) (fig. 21 ) ; the same results 

 can also be attained by first turning the preparation about V , a 

 specified angle and then about H„ until darkness ensues. By 

 this method, those directions in the crystal are obtained (after 

 proper reduction of observed angles to crystal directions by 

 means of the refractive index) for which the extinction is zero 

 for a given position of the nicols. The curve uniting these 

 directions in projection is the optical curve for the particular 

 position of the nicols to the axes of revolution. Analogous 

 curves for other and different positions of the nicols are to be 

 obtained and plotted in similar manner. All such curves pass 

 through the optic axes and also the center of the projection. 

 Their points of intersection in the projection determine, 

 therefore, with considerable accuracy, the exact position of the 

 optic axis or of both axes, in case both axes can be brought 

 within the field of vision. Since such optical curves are 

 intended solely to increase the accuracy of the determination 

 of the positions of the optic axes, their approximate positions 

 being known from the preliminary determination, it is neces- 

 sary, in actual practice, to take readings of IT., only 5° or 10° 

 on either side of the approximately correct position of the 

 optic axis as determined by the preliminary direct observations. 

 Convenient positions of the nicols for optical curves are at 0°, 

 45°, 15° and 30° from the X 1 axis of revolution. If both 

 optic axes appear within the microscopic field of vision, the 

 most satisfactory method of measuring the optic axial angle by 

 means of the universal stage is to determine the exact position 

 of each axis by the above method and to plat the same in stere- 

 ographic projection, in which the angle can be measured 

 directly by graphical methods rather than by calculation, from 

 the cosine formula, cos 2Y=cos Y ia " cos Y l6 + sin X lCl sin Y l6 

 cos (H 10 — H ]6 ) in which 2Y designates the optic axial angle ; 

 Y ia ,H 1(Z , the readings for the one optic axis ; and Y l6 ,H l6 , 

 those for the second. 



The results obtained by the use of optical curves can be 

 checked and verified by several of the methods described 

 below, which are of general application and can readily be 

 applied to this special case. 



Fedorow has shown that in actual practice with minerals of 

 weak to medium birefringence, the errors can be disregarded 

 which are due to the reduction of all observed angles by means 

 of the average refractive index of the crystal in place of the 

 true refractive indices for each given direction ; and likewise 

 those errors which may arise from slight deviations in planes 



