408 FRED. EUGENE WRIGHT 
The quotient of the two values thus obtained—path difference 
divided by thickness of plate—is the birefringence. The probable 
error of the determination under these conditions with good sections 
may be ro per cent; for ordinary minerals this means an error of 
one or more units in the third decimal place. 
The extinction angle for a given crystal face is the angle between 
a definite crystallographic direction on the face and one of the 
axes of its optic ellipse. With sharply developed crystallites or 
with minerals exhibiting sharp cleavage lines the error resulting 
from incorrect setting of the crystallographic direction parallel 
with the vertical cross-hair in the ocular is practically negligible; 
with less sharply defined crystallographic directions, the settings 
are of course less accurate; but as this is due to the crystal develop- 
ment and not to the method, the observer can only accept the 
situation as he finds it; the only probable error over which he has 
direct control centers essentially in the determination of the 
position of extinction. Since the eye is sensitive only down to a 
certain limit (threshold value, on an average about o.oor meter- 
candle), it is evident that for all positions of the crystal plate 
between crossed nicols for which the intensity of the emergent 
light is below this limit, the plate will appear dark. In ordinary 
microscope work the angular range of this area of darkness varies 
from 1° to 2°, depending on the conditions of illumination and the 
eye of the observer; the error of a single determination may amount 
to 1° under certain conditions. By repeating such determinations 
the probable error can be materially reduced. But more accurate 
results can be obtained by using special devices which have been 
constructed for the purpose. Of these the bi-quartz wedge plate’ 
has the advantage of adjustable sensibility to meet the different 
conditions of observation which arise. It is a combination of a 
right-handed quartz plate with a left-handed quartz wedge, and 
of a left-handed quartz plate with a right-handed wedge, all cut 
normal to the axis and so mounted that the points of exact com- 
pensation in each half are in alignment. The position of extinc- 
tion of a mineral is determined with this device by noting that, on 
its insertion, the parts of the mineral plate covered by the adjacent 
tF, E. Wright, Amer. Jour. Sci. (4), XXVI, 377-78, 1908. 
