144 METHODS OF PETROGRAPHIC-MICROSCOPIC RESEARCH. 
K is a small fraction not greatly different from zero, as shown in Figs. 69 to 
71. Plates showing interference colors from first-order red to second-order 
blue are the least favorable, therefore, for the measurement of extinction 
angles by methods based on intensity differences. Plates, on the other hand 
showing interference colors gray to yellow of the first order are best suited 
for such measurements. If the methods involving interference tints (chro- 
matic intensity) be used, however, these objections do not hold with equal 
force. Experience has shown that in case the mineral plate does show red or 
blue interference tints of the first and second orders the best determinations 
can be made either by the method of rotating the upper nicol or by the bi- 
quartz wedge plate, and the extinction direction is fixed by noting the 
absence of abnormal interference colors on rotating the nicol very slightly 
or on inserting the wedge. 
After this digression on the most suitable sections for the measurement 
of extinction angles, Fig. 74 may again be considered and the relative 
accuracy of the different methods under the same conditions of experiment 
deduced. 
The heavy curve (Fig. 74) indicates that for the assumed threshold value 
sensitiveness, 0.05 per cent of the total intensity, an error of at least =*= 38' on 
a single determination is possible if the crystal plate alone be rotated under 
crossed nicols. On the other hand, if the crystal plate remains stationary 
and the upper nicol alone is rotated, the other intensity curves of Fig. 74 
are valid, each curve indicating the intensity of illumination of the crystal 
plate for a specified angular distance from its position of total extinction 
during the rotation of the upper nicol from 88 to 92. These curves in- 
dicate that the probable error with this method is less than half as great 
as in the preceding method, for if the crystal be only =*= 15' distant from its 
position of total extinction, differences in intensity can even then be detected 
on rotating the upper nicol. 
The changes in intensity of illumination of the microscopic field on rota- 
tion of the analyzer are indicated by the o' curve, while for the crystal 
plate the 15' curve is applicable for illustration. At 8843' (Fig. 74) the 
field is just beginning to show detectable illumination (0.05 per cent of total 
intensity), while for the same angle the crystal is illuminated with 0.097 
per cent of the total intensity, nearly twice as great and easily noticeable. 
In this position the crystal plate appears, therefore, decidedly lighter than 
the field. On the other side of 90 the crystal plate passes the threshold 
limit of vision under the assumed conditions at 9i42', while for the same 
angle the microscopic field is illuminated by 0.097 P er cent of tne total 
intensity ; in this case the field is appreciably brighter than the crystal and 
the difference can be readily detected by the eye. 
If white light be used, these differences are accentuated by the abnormal 
interference colors which appear in the crystal plate when it is not precisely 
in the position of total extinction. This method of rotating the upper nicol 
has the advantage, furthermore, of not being dependent on the accuracy 
with which the nicols are crossed, since all data are referred at once to the 
plane of the polarizer. It is not, however, so advantageous in very weakly 
birefracting or deeply colored mineral plates; and for such plates may 
become less sensitive than the ordinary method. 
