176 METHODS OP PETROGRAPHIC-MICROSCOPIC RESEARCH. 
of vision. Fedorow has also shown how it is possible with his methods to 
measure the refractive indices and the birefringence approximately of a min- 
eral from any section. 
The values for 2 V thus obtained on different sections, however, 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 convergent polarized light methods, the measured angles 
are reduced by means of the average refractive index /3 to corresponding 
angles within the mineral before plotting in stereographic or angle projec- 
tion. Here also the combination of tracing-paper with the 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. The 
new graduated hemisphere of Nikitin can also be used for the same purpose 
and is equally efficient. 
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 containing an optic axis 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. If the crystal plates be observed, as is usually the case, 
mounted in Canada balsam between the object-glass and cover-slip, the 
rotatory effects of the boundary surfaces on the planes of vibration of the 
transmitted waves become noticeable and render the results inaccurate to 
just that extent. In case the Fedorow glass hemispheres described below be 
used above and below the crystal mount, the rotatory effects of the bound- 
ary surfaces are decreased and the results obtained are correspondingly 
more accurate. Even under these favorable conditions elliptic polarization 
is often noticeable on steeply inclined plates, even in monochromatic light, 
but it is usually so slight that it may, in general, be neglected. 
It may be stated that, although the methods of Fedorow involve the use 
of a stereographic or angle projection plat and are in part graphical in nature, 
they are not difficult of application 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, petrologists 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 petrol- 
ogist 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 (Plate 6, 
Fig. i) possesses, when in the o (primary) position, three horizontal 
circles, H\ (microscope stage), HI, and Hi, each circle graduated into degrees 
with verniers attached to HI and # 2 ; each of these circles can be rotated 
about a vertical axis ; the horizontal axes of rotation and equivalent vertical 
circles are V\ and V* (also divided into degrees) and Vi with vernier attached. 
