174 METHODS OF PETROGRAPHIC-MICROSCOPIC RESEARCH. 
direction, the writer modified* the Fedorow-Fuess universal stage by having 
a brass disk, L, constructed in the workshop of the Geophysical Laboratory 
to fit in the Fedorow-Fuess stage (large model) in place of the inner ring 
bearing the glass with cross-hair (Plate 6, Fig. 2). Into this ring the upper 
lens of the ten Siethoff condenser lens system is inserted. The partially 
beveled upper surface of this condenser lens has a radius of 1.5 mm., and 
permits, even with a No. 9 Fuess objective, angular movements of about 
30 on either side of the normal. By means of a proper cylinder of brass 
resting on the cylinder containing the lower nicol, the remaining lenses of 
the condenser system are raised to the required distance from the upper 
lens. This type has proved extremely serviceable in work with artificial 
preparations, since by its use sections can be so placed that the most 
favorable measurements possible can be accomplished with the cross-line 
micrometer ocular; in case the optic axial angle is small, it can be measured 
directly by means of the universal stage in convergent polarized light. 
Wladimir Arschinowf has recently described a glass hemisphere, 50 to 
60 mm. in diameter, which rests on the microscope stage and carries two 
graduated metal semicircles attached on pivots above the plane surface of 
the hemisphere. The mounted section is placed on the centered glass hemi- 
sphere and the coordinate angles of tilting are read off on the graduated semi- 
circles. By means of this device the section can be readily tilted into any 
position, but can not be turned about any axis after having been tilted, as 
is the case with the universal stage. 
The writer has recently had constructed a graduated hemisphere (Fig. 
108, a, actual size 63 mm. in diameter)! which rests on the microscope stage 
after the manner of the Schroeder van der Kolk hemisphere!) an d on which 
the crystal plate or mounted thin section is placed. In the writer's micro- 
scope the edge of the circular opening of the stage in which the glass hemi- 
sphere rests coincides exactly with the 20 circle of the hemisphere. Two 
notches (Fig. io8,c) cut in the edge of this stage opening serve as points to 
indicate the zero meridian, and the polar and longitudinal angles of tilting 
are read off directly from these points through the hemisphere, 20 being 
subtracted from the polar angle thus determined. The graduations on the 
spherical surf ace of the hemisphere are indicated in Fig. 1 08, a (orthographic 
projection). The divisions are 5 apart and i intervals can be readily 
estimated. On the flat surface of the hemisphere fine cross-lines are cut 
(Fig. 1 08, 6) and aid in centering the hemisphere and in adjusting a crystal 
plate in the primary position. This graduated hemisphere may well serve, 
in place of the expensive universal stage, for most measurements of the 
optic axial angle and of extinction angle in zones, and for tilting crystal 
plates any desired angle. It may also be used to advantage as an apertom- 
eter (refractive index of the glass n^ a = i .5 19) for ascertaining the numerical 
aperture of objectives and for determining the angular equivalent of the 
divisions of the cross-line micrometer ocular. To increase the angle of view, 
a small glass hemisphere may be attached with cedar oil above the section 
or crystal plate after the method suggested by Fedorow. 
Ainer. Jour. Sci. (4). 24. 343. 1907. 
tXeitschr. Kryst . 48, 925-229, 1910. 
FThis hemisphere was ground and graduated by the Bausch & Lomb Optical Co.. of Rochester. N. Y., 
and has been found satisfactory. 
||Z wissen. Milcroskop . 12, 188. 1895. 
