OPTIC AXIAL ANGLE. 177 
On the original stage described by Fedorow and made by Fuess, the partial 
scales F a are wanting and have been attached by the writer.* These 
scales have been found essential and of practical service in several of the 
methods described below, especially those involving the principal sections 
of the triaxial ellipsoid of any mineral. Each partial scale of Vt is accurately 
divided and carefully adjusted to the instrument. When not in use, the 
scale segments of Vt can be inclined to a horizontal position V& (Plate 6, 
Fig. 2) and are then entirely out of the way. Measurements given below 
will be referred to this modification of the Fedorow-Fuess universal stage. 
To increase the angle of vision of the field, two glass hemispheres, A\ 
and A 2 (in Plate 6, Fig. i, AI only appears, A z being hidden by H^), are 
usually employed; between these the preparation is placed, either cedar- 
wood oil or glycerin being used to stick the same together and to reduce the 
effects of total reflection. For general work with the universal stage, it is 
advisable to follow the suggestion of Fedorow and use special circular (2 cm. 
diameter) object-glasses on which to mount the preparations in place of the 
ordinary rectangular (26 X 46 mm.) thin-section object-glasses. 
With the universal stage of this type it is possible not only to bring a 
crystal section to any given position, but also to rotate the section about 
any axis; in short, by its use one has control over all possible directions 
and zones or axes of rotation of a crystal. 
THE DETERMINATION OF THE CRYSTAL SYSTEM OF A GIVEN MINERAL BY 
MEANS OF THE UNIVERSAL STAGE. 
The fact that the universal stage allows the observer to study the different 
effects of a given mineral section on light- waves transmitted through it in 
different directions enables him to determine at once the crystal system to 
which the crystal belongs. This is accomplished most readily by means of 
extinction angles along certain directions, since the term extinction angle 
implies a definite relation between a given crystallographic and a given 
optical direction in any mineral. These relations vary with the crystal 
system of the mineral, and in fact are such definite functions of the same 
that, as Brewsterf was the first to show, it is possible from extinction 
angles alone to determine definitely the crystal system of a given mineral. 
Briefly, an isometric mineral is isotropic for all directions of light-wave 
propagation. Uniaxial minerals (hexagonal and tetragonal) appear isotro- 
pic for light-waves passing along the principal crystallographic axis. For 
all other directions they are anisotropic, but even then can generally be 
distinguished from biaxial minerals at once by the fact that every section 
of a uniaxial mineral contains the co ellipsoidal axis, parallel with and normal 
to which it extinguishes. If the section be placed, therefore, in the position 
of darkness between crossed nicols and be rotated about a horizontal axis, 
Vi, it will continue to remain dark if the ellipsoidal axis co coincides with 
the axis of rotation, while if the ellipsoidal axis co be normal to the latter 
the crystal will exhibit interference colors of polarization on rotation except 
for sections of the prism zone. Biaxial minerals, on the other hand, do not 
*Amer. Jour. Sci. (4), 14, 345. 1907. The improved form of universal sUge is now furnished by R. Fuess 
& Co.. Germany. 
tD. Brewster. Phil. Trans., 187-218. 1814; 199-173, 1818. 
