EXTINCTION ANGLES. 145 
More sensitive methods can be obtained with devices which allow the 
phenomena on both sides of the 90 position to be observed simultaneously. 
This is the purpose of the Bravais-Stober plate, the double combination 
wedge, the Koenigsberger plate, the Calderon plate, the Traube plate, 
the artificially twinned quartz plates and wedges described above, and most 
effectively by the new circularly polarizing bi-quartz wedge plate ; also by 
the bi-nicol ocular, though less satisfactorily. In each of these last two 
devices the plane of polarization of the incident waves is turned through 
equal angles on both sides of the junction line between the two halves, so 
that the field appears equally lighted throughout, while if the crystal plate 
be not in the position of total extinction it will appear lighter than the field 
in the one half and darker in the second. Since, however, there is an angle 
best suited under the given conditions to show these differences most clearly, 
it follows that the best results can be had with a plate or apparatus in which 
the angle <f> can be varied at will. This condition of variable sensibility is 
met by both the circularly polarizing wedge plate and the bi-nicol ocular ; 
by use of the bi-quartz wedge plate the probable error of the determination 
of the extinction position of any crystal plate is at least one-fourth that of 
a determination after the usual method by rotating the crystal plate under 
crossed nicols. Experience has shown that with favorable sections extinc- 
tion angles can be determined by the use of the bi-quartz wedge with a 
probable error of less than =*= 10' on a single trial. 
Still another method for obtaining the most favorable conditions of 
experiment with a given plate is that suggested on page 136 with the arti- 
ficially twinned quartz wedge. The two halves of this wedge extinguish 
at a small angle (e. g., 3) on opposite sides of the line of junction, and by in- 
serting the wedge that particular interference color, or phase difference if 
monochromatic light be employed, can be produced for which the given 
angle of revolution (3) is the best. This wedge, however, is less favorable 
than the circularly polarizing bi-quartz wedge, since its twinning line must 
be inserted precisely parallel with the plane of the polarizer, while with the 
circularly polarizing bi-quartz wedge the rotation of the planes of polariza- 
tion of transmitted waves is entirely independent of the line of junction of 
the adjacent halves. 
In the preceding pages special emphasis has been placed on those methods 
for measuring extinction angles which are of general application and which 
are based on intensity differences. The other methods, which are of limited 
application and can be used only in white light on favorable sections, depend 
on differences in interference colors produced by slight deviations of the 
crystal plate from its position of total extinction. Although these methods 
are serviceable in many instances, their application and the results obtained 
thereby are so dependent on the conditions of experiment that they are 
difficult to treat satisfactorily in a general way. Experience has shown that 
they are not more sensitive than the other methods and usually much less so. 
This is true both of the selenite sensitive-tint plate and of all combinations 
of the same. 
EXPERIMENTAL TESTS. 
To test the different methods under different conditions, different mineral 
plates were chosen and the position of complete extinction on each deter- 
mined by the different methods under precisely the same conditions of 
