'50 
METHODS OF PETROGRAPHIC-MICROSCOPIC RESEARCH. 
The results of the calibration of a 4 mm. Zeiss apochromatic objective by 
this method (with Bertrand lens and cross-line micrometer disk* in the 
focal plane of the Ramsden ocular and with a small aperture stop in its eye- 
circle) are given in table 6, from which it is evident that the Mallard formula 
obtains throughout practically the entire field, the appreciable differences 
being confined to the margin of the field, where the measurements at best 
are less satisfactory because of (a) increasing indistinctness of the dark axial 
brushes, (6) the crowding together and decreasing distance between succes- 
sive equal angular intervals, (c) the distortion caused by the analyzer. 
TABUS 7. 
Observed. 
Calculated. 
Observed. 
Calculated. 

D* 
Dk 
Df 
Dk 
E 
D* 
Dk 
Dt 
Dk 

1 
2 
3 
4 
I 
8 
9 
10 
n 
12 
3 
"4 
15 
16 
17 
9 
20 
21 
22 
23 
24 
25 

85 
l6. 5 
23 
*l 
36.5 
44- 
52 
f 5 
65 
7 5 
78.5 
85- 
92-5 
100.5 
107.5 
113.5 
119.5 
125.5 
"32. 
'39 5 
146.5 
54 
160. 
166. 
73- 
o 
8. 
16. 
22.5 
30. 
V 
5- 
K\ 
& 5 
87.5 
94 5 
102. 
109.5 
II 7 . 
124.5 
131.5 
138. 
44 5 
152.5 
158.5 
164.5 
171. 
79 
O 
,6- 
11 
29 
30 
3' 
32 
33 
34 
11 
H 
39 
40 
4' 
42 
43 
44 
$ 
9 
49 
50 
181. 
187.5 
'94-5 
199. 
205.5 
213.5 
219. 
225. 
230.5 
236.5 
243- 
249. 
254 
259. 
264. 
269. 
273. 
279 5 
286.5 
290. 
295. 
300. 
186. 
192.5 
199. 
206.5 
212.5 
218.5 
225. 
230.5 
237-5 
243 5 
250.5 
256.5 
261 .5 
266.5 
272. 
277. 
283. 
288. 
293 5 
299. 
303-5 
308. 
206. 1 
211.2 
35 9 
36.8 
236.5 242.3 
71.6 
73-4 
265. 
271.5 
106.7 
109.3 
291.5 
298.7 
141.0 
44 5 
316.6 
323.6 
174.2 
.78.5 
The validity of the formula was furthermore checked for another micro- 
scope with another lens system (No. 9, Fuess, with Amici-Bertrand lens, 
system 7 to 9, and double-screw micrometer ocular with Ramsden ocular) 
and by another method. Two polished plates of calcite were used, the one 
cut after oooi and the second at an angle of 23! 7' with oooi as measured 
on a two-circled goniometer, the adjustment on the goniometer having been 
accomplished by means of fresh cleavage faces along the edge of the plate. 
These plates were placed successively on a carefully adjusted Fedorow-Fuess 
universal stage (large model) fitted with a special universal condenser lensf 
and the positions of the optic axis were measured on the micrometer ocular 
Amer. Jour. ScL (4). 24, 341. 1907. 
tAmer. Jour. Sci. (4). 24, 33*. 1907. 
