OPTIC AXIAL ANGLE. 
screws as the stage was turned about its horizontal axis from degree to 
degree on both sides from the horizontal position. By means of the two 
plates a continuous set of readings was obtained for D for angles E ranging 
from o to 47. These values were ascertained for both scales (horizontal 
and vertical) of the double-screw micrometer ocular described on page 155 
and are listed in table 7. 
The values for D listed under the heading "calculated" in this table were 
calculated from Mallard's formula by taking the average value of K for both 
the horizontal and vertical scales of the double-screw micrometer ocular; 
for the vertical micrometer scale, ^ = 412.3; for the horizontal, ^ = 422.4. 
The agreement between theory and practice for this objective (Fuess 
No. 9) as indicated in table 5 is remarkable.* The screw of the horizontal 
micrometer registered 0.005 mm. for each division on the head, while the 
vertical scale screw, which was constructed later and on a different lathe, 
was a trifle coarser and registered a slightly greater movement for one 
division on its head. For this reason the values K v and K h are slightly dif- 
ferent. On an average a movement of 6 divisions or 0.03 mm. corresponded 
to i, so that with the bi-micrometer ocular the probable error is nearly 10' 
from the setting alone and in ordinary work with interference figures differ- 
ences of i may be expected. 
If only a single-screw micrometer ocular be used, the section should be 
cut very nearly normal to the acute bisectrix; otherwise the values become 
much less certain, but with a double-screw micrometer ocular, or microm- 
eter ocular with coordinate scale, this error can be eliminated directly and 
equally good values can be obtained on sections only approximately normal 
to the acute bisectrix, as will be shown on page 155. In all measurements of 
optic axial angles, it is highly essential that the lens system of the micro- 
scope be perfectly centered, otherwise errors of considerable magnitude are 
possible. 
Instead of solving the Mallard equations (D = K . sin E and sin E = /3 sin F) 
by logarithms, graphical methods may be used which are sufficiently accu- 
rate for the purpose. The method of Fedorow,f which is a graphical solu- 
tion of the proportion 
sin E sin V A B 
= or = 
i j_ i C 
ft 
is of general application and is satisfactory in practice. An accurate draw- 
ing (Plate 7) is made, which serves for all possible angles and all refractive 
mineral indices to be encountered. To solve the equation D = K sin E 
*In the Mikroskopische Physiographic I. 1, 330. 
by Rosenbuscb and Wvilfing. the latter gives a series 
of measurements with an a-monobromnaphthalene 
immersion objective of R. Winkel and finds differ- 
ences as high as 8 between observed and calculated 
values as indicated in the table herewith. The 
angles under // are half the axial angles for these 
minerals obtained from measurements on an optic 
axial angle apparatus, while the angles under //i 
were calculated by Mallard's formula on the as- 
sumption that the K obtained for topaz (1.075) is 
valid for all angles. The differences between observation and calculation are large and indicate, in accord 
with the observations by the writer, that the determination of the positions of optic axes near the periphery 
of the field is less accurate than that for more centrally located points. 
tZeitschr. f. Kryst.. 26, 225-261. 1896. Compare also Souza-Brandao. Comm. d. Serv. Geologico de 
Portugal, 5, 118-250, 1903. F. E. Wright, Amer Jour. Sci. (4), 24, 330. 1907. 
H 
D 
K 
Hi 
Aragonite. . . 
Muscovite. . 
Topaz .... 
n33' 
2443 
39 5 
o-35 
0.700 
i .075 
1.633 
1.674 
i .705 
IO X 
24 1 4' 
CJ905') 
Calcite 
6o5i 
I 590 
1.821 
683o' 
