of Minerals in the Thin Section. 353 



thus locating- A 2 afresh with each extinction. By establishing 

 a set of observations about V 2 for each new position of V, it is 

 possible to extend the number of observations indefinitely and 

 thus to locate A 2 with the greatest possible accuracy. In fact, 

 the position of A a in the projection is immaterial so long as 

 this position be definitely known with respect to the axes of 

 revolution [Y, and Y 2 ), since with A/ located at any point in 

 the projection it is still possible to locate A 2 by means of extinc- 

 tion angles for different angles of inclination about V, and Y 2 . 

 This method, involving the use of both Y 1 and Y 2 , is therefore 

 a method of general application and is capable of furnishing 

 reliable data on all sections so cut that one optic axis at least 

 falls within the field of vision. 



Still another method which furnishes trustworthy results and 

 is of general application, consists in determining first the posi- 

 tions of the planes of symmetry and the axes of the ellipsoid 

 within the crystal. (Fig. 26.) In this method, practically all of 

 the graduated circles of the stage are brought into play, since 

 not only must extinction angles be observed, but also the section 

 revolved about the ellipsoidal axes and the exact position of 

 each axis noted. The method of procedure consists in first 

 placing the stage in the zero (primary) position, H 3 , H 19 H 2 , 

 and Yj in zero position, and Y 2 normal to Y x ; the section hav- 

 ing any orientation and position. The section is then inclined 

 about Y 2 until darkness between crossed nicols ensues ; if this 

 be not the case, it is turned about H 3 a small angle, and the 

 attempt made a second time, and so on until at a definite angle 

 of inclination about Y 2 darkness is observed. The preparation 

 is then revolved about Y„ and if by chance the correct position 

 be obtained, darkness will continue for every angle of inclina- 

 tion about Y,. This is usually not the case, and by repeated 

 trial that position of H 3 , H 2 is to be found for which the prepa- 

 ration remains dark for every angle of revolution about Y r 

 The angle of inclination Y 2 and the directive angle H 3 deter- 

 mine then the position of one of the planes of symmetry of the 

 ellipsoid within the crystal, e. g., the plane aft'y of fig. 26, this 

 being fixed by the line 0/3' ; in similar fashion the planes a(3<y' 

 and a f ^ry are located and plotted in the stereographic projec- 

 tion. This method of locating the planes of symmetry of the 

 ellipsoid within the crystal is comparatively rapid and sensitive, 

 and a fair degree of accuracy can be attained by its use. 

 The new circles Y 2 (fig. 20) which were attached in the Geo- 

 physical Laboratory to the large Fedorow-Fuess universal stage, 

 have proved extremely serviceable and time savers in this 

 method. 



Having once determined the position of either a or 7 by this 

 method, and that of one optic axis A 1 by optical 'curves, the 



