194 METHODS OF PETROGRAPHIC-MICROSCOPIC RESEARCH. 
are not, in general, microscopic methods, although the total refractometer of 
Walle'rant is attached directly to the microscope and is employed on thin 
uncovered and polished sections of rocks. Unfortunately, the writer has 
had practically no opportunity to work with the total refractometer of 
Walle'rant and is, therefore, not in a position to judge personally of its 
fitness for optic axial-angle determinations. With the Abbe-Pulfrich total 
refractometer the probable error of the values obtained with monochro- 
matic light on highly polished crystal plates of at least i sq. mm. surface 
area should not exceed 3 in the fourth decimal place. From these refractive 
index values the optic axial angle can be calculated by the usual formula 
and a check on the direct measurements of the optic axial angle can be thus 
obtained. 
THE RELATIVE ACCURACY OF THE DIFFERENT METHODS. 
In this section only a brief summary of the results of observation with 
the different methods will be given, together with a short statement of the 
relative accuracy and applicability of the several methods under test. 
Different minerals (as aragonite, topaz, muscovite, etc.) were first chosen 
and oriented sections cut to show the different phenomena required by the 
several methods. The correct optic axial angle for each mineral was then 
measured in sodium light on a Wulfing-Fuess axial angle apparatus,* the 
angle obtained thereby being adopted as the standard of comparison for all 
methods. For each mineral a series of measurements of the optic axial angle 
was taken for different sections and by the different methods ; the rela- 
tive degree of accuracy of each method was judged, not only by the results 
obtained, but also by the factors, on which the method itself is dependent, 
and by their influence under the different conditions of observation. 
MEASUREMENTS WITH THE AXIAL-ANGLE APPARATUS. 
The optic axial angles obtained in sodium light on the Wiilfing axial-angle 
apparatus varied slightly and the average of five determinations of each 
angle is given below: 
Topaz, Willard Co., Utah: 2= 126 13'. 2^ = 66 42'. 
Aragonite, Bilin, Bohemia: 2 = 3io9'. 2F=i822'. 
Muscovite: (a) 2 = 7i4o'; (6) 2 = 5942 ; . 
MEASUREMENTS WITH THE BECKE DRAWING-TABLE. 
To economize space, the results are given below in their reduced form 
ready for plotting directly in projection, the angle # denoting the equatorial 
angle from the horizontal line of the projection and p the polar distance; 
A i, as usual, denotes the visible axial point and Pi any point on the dark 
axial bar. 
Topaz. 
<t> o 
A l o 5 .o 
Pi +65 20.5 
E. A. WQlfiuf. Neue Jahrb. Beil. Bd.. 12, 403-446. 1898; Rosenbusch-Wiilfing, Mikros, Physiogr 4 th 
ed.. I, i. 217. 1904. 
