146 METHODS OF PETROGRAPHIC-MICROSCOPIC RESEARCH. 
illumination with white light. On an anhydrite plate showing white inter- 
ference tints of the higher orders the maximum error of a single deter- 
mination by rotating the crystal plate under crossed nicols was found 
to be about 1.1; by revolving the upper nicol alone, 0.4; by inserting the 
bi-quartz wedge plate, about o. i ; by using the Calderon ocular, about 0.5 ; 
by means of the Bertrand ocular, about 0.1; with the anhydrite section 
the sensitive-tint plate is of no value, since the interference color of the 
anhydrite plate itself is so high that the violet of the inserted plate has no 
effect and any occurring differences in intensity are in a strongly lighted 
field and not easily discernible. 
Similar measurements were made on an apatite plate parallel to the prin- 
cipal axis and showing the interference tint, red of the first order. The 
maximum error of a single determination of the position of total extinction 
on turning the crystal plate alone under crossed nicols was found to be 0.9 ; 
on rotating upper nicol about 0.2, accurate because of abnormal interfer- 
ence colors which appear when the plate is turned only a slight distance from 
its correct extinction position ; on inserting the bi-quartz wedge 0.2 to 0.3 ; 
with the Calderon ocular, about 0.3 ; with the Bertrand ocular, about 0.3 ; 
the sensitive-tint plate is again of no value, since the interference color 
changes comparatively slowly as the crystal is rotated. 
A section of nephelite parallel to the principal axis and showing the inter- 
ference color, yellow first order, gave the following results : On turning the 
crystal plate alone, possible error 0.4; on rotating upper nicol, less than 
0.1; with bi-quartz wedge plate less than 0.1; Calderon ocular about 0.2; 
Bertrand ocular less than o. i; sensitive violet plate still of very little value 
as a method ; only slight changes in color for large angles of rotation of plate. 
On a plate of colorless gehlenite of very low interference color, dull gray 
of the first order, the sensitive-tint plate proved as satisfactory as any other, 
and more so than the method of turning the crystal plate under crossed 
nicols or of rotating the upper nicol or the Calderon ocular. The Bertrand 
ocular and the bi-quartz wedge plate proved about as favorable, the prob- 
able error being slightly less than 0.5. 
A plate of strongly pleochroic tourmaline was also used and the following 
results obtained : Probable error of determination on turning crystal plate 
alone, about i . 6 ; the method of rotating the upper nicol is of little value 
because of deep natural color of mineral and consequent inability to match 
fields; with the bi-quartz wedge plate 0.3; Calderon ocular, about 0.4; 
Bertrand ocular, about 0.5. The sensitive-tint plate is useless because 
of the strong natural color of mineral which veils the true interference colors. 
The results of these tests show that the theoretical deductions from the 
general equations are in general valid, but that in certain instances other 
factors (as natural color and very low birefringence) become dominant and 
tend to render some of the methods less sensitive and to favor the use of 
other (for general purposes, less suitable) methods. The bi-quartz wedge- 
plate, however, seems to apply in all cases with equally favorable results and 
to equal in sensitiveness any of the methods, whether of limited or of general 
application. 
