34-4 jF. E\ Wright — Measurement of the Optie Axial Angh 



that axis. By plotting these directions graphically in projec- 

 tion, and by determining extinction angles in given zones, it is 

 possible not only to measure the optic axial angle, but also to 

 determine the exact position of the optic axes with reference 

 to the crystal plate, even though it may happen that neither 

 optic axis appears within the field of vision. 



The values for 2Y thus obtained on different sections, how- 

 ever, are not all of the same order of exactness, as will appear 

 later in the more detailed discussion of the different sections. 

 It should be noted that in the Fedorow methods, as in the pre- 

 ceding, the measured angles are reduced b} T means of the aver- 

 age refractive index fi to true angles within the mineral before 

 plotting in stereographic projection. Here also the combina- 

 tion of tracing paper with stereographic projection plat as a 

 base, as suggested by Wulff, is to be recommended as the best 

 and most efficient scheme for obtaining results rapidly and 

 accurately. 



In these methods the rule of construction of Biot-Fresnel, 

 that the planes of vibration of light waves propagated in any 

 given direction bisect the angles between the two planes" con- 

 taining one of the two optic axes and the given direction, is 

 used constantly, since the two factors, on which the universal 

 stage methods are practically based, are the directions of the 

 optic axes, as they may be determined directly, and extinction 

 angles for certain zones and directions. Fedorow has also 

 shown how it is possible with his methods to measure the 

 refractive indices and also the birefringence approximately of 

 a mineral from any section. These methods are not, however, 

 germane to the purpose of this paper, and will not be discussed 

 further. It may be stated that, although the methods of Fedo- 

 row involve the use of a stereographic projection plat and are 

 in part graphical in nature, they are not difficult of applica- 

 tion and often furnish results where other methods fail. In 

 ordinary microscopic work, it frequently happens that one 

 method will yield more accurate data in a shorter time than a 

 second, and. that particular method should then be chosen in 

 preference to all others. 



In general, the Fedorow methods are indirect methods and 

 frequently involve a large expenditure of time to complete the 

 observations on a single plate. For these reasons chiefly, 

 penologists have not adopted them so rapidly and generally as 

 might have been anticipated, particularly as the old tested 

 methods accomplish about what is desired, by the busy penolo- 

 gist who uses the microscope simply as a means to an end — to 

 aid him in interpreting geological phenomena and relations. 



When attached to the microscope, the Fedorow-Fuess stage 

 (fig. 20) possesses, when in the 0° (primary) position, three 



