OPTIC AXIAL ANGLE. 173 
(3) Draw a great circle, DAiE, in stereographic or angle projection or on 
the Nikitin graduated hemisphere, through A\ (Fig. 88) parallel with the 
direction of vibration of the lower nicol in the first position. This is the 
plane of the optic axes. 
(4) Draw the plane of vibration FOI of the lower nicol in the second 
position (after rotation through some known angle, as 30 or 45). 
(5) Draw the polar circle PK to H and let the point of its intersection 
with FI be C; draw the great circle HA\ and let A \ be its point of inter- 
section with PK. 
(6) Lay off on PK the angular distance CA'z = CA\. Draw the great 
circle HA\\ its point of intersection A z with the great circle DA\E deter- 
mines the position of the second optic axis. The angle AiA 2 is the optic 
axial angle, 2 V. 
MICHEL-LEVY METHOD. 
For sections normal to the acute bisectrix of a mineral with a large optic 
axial angle, Michel-LeVy has suggested a method which, although theoreti- 
cally interesting, is not of great practical value, owing to the indistinctness 
of the phenomena to be observed. His method consists in reading the angle 
of rotation of the stage necessary to bring the interference figure from the 
crossed position to that in which the emerging axial bars of the interference 
figure are tangent to a given circle.* 
H. Tertsch has recently f described a method, requiring the Becke drawing- 
table, with which approximate results of a fair order of accuracy can be 
obtained on a section cut normal to one of the bisectrices. The accuracy 
of the method, however, at best is not great, as is emphasized by Tertsch, 
and it decreases rapidly if the section be not cut precisely normal to a 
bisectrix. In view of the limited application of these methods and the low 
degree of accuracy obtainable by their use, they will not be described further. 
METHODS WITH THE UNIVERSAL STAGE. 
In practice it frequently happens that a given section is not favorably 
cut to show the optical phenomena to the best advantage, and that by 
tilting it a certain angle the interference figures can be improved materially. 
This is particularly the case with fine-grained artificial preparations where, 
although individual crystals and cleavage fragments can frequently be 
obtained, they do not rest in the section in the most advantageous position. 
Such crystals and crystal plates can be tilted either by means of an axial 
angle apparatus for the microscope, as that described by Bertrand J many years 
ago, or by use of the glass hemisphere of Schroeder van der Kolk,| | or by the 
new upper condenser lens of ten Siethoff. The last two methods are quali- 
tative methods only, while that of Bertrand, although quantitative, permits 
of rotations in one plane only. To supply the want of a universal condenser 
lens on which angular movements can be accomplished and measured in any 
*Michel-L<vy et Lacroix, Les MincVaux d. Roches. 94-95, 1888. For a modification and simplification 
of his formula, see P. E. Wright, Amer. Jour. Sci., 22, 289, 1905. 
tT. M. P. M.. 27, 589-594. 1908. 
: K Bertrand. Bull. Sco. Min. I'r . 3. 97-100. 1880. 
l|Schroeder van der Kollc, Zeitschr f. wiss. M kroskopie, 8, 459-461. 1891. and 12, 188-189. 1895. 
IE. G. H. ten Siethoff. Centralblatt f. Min.. 657. 1003 
