EXTINCTION ANGLES. 137 
into longitudinal halves, the ellipsoidal axes of the two halves including an 
angle of 5 to 10. With such a combination wedge all interference colors 
from complete darkness to second-order colors can be obtained and the 
most sensitive conditions obtained for accurate measurements under the 
given conditions of illumination. 
All of the preceding plates, the Bravais-Stober, the Koenigsberger, and 
the Traube, the selenite twin plate, the quartz double combination wedge, 
and the artificially twinned quartz plate and wedges of the last paragraph, 
can be made possibly somewhat more sensitive by dividing the field into 
quadrants instead of halves, after the example of Bertrand in his rotatory 
polarizing quartz plates described below, but the attendant increase in 
difficulty of construction and in cost would probably offset any advantage 
gained thereby. 
BI-NICOL OCULAR. 
In the practical application of these different types of plates the angle 
has been small (2 to 4) and found to furnish good results, but in each case 
there is a particular angle 6 which is best adapted for the observations ; the 
limit of sensitiveness of different eyes introduces, moreover, a variable ele- 
ment of such wide range that the angle 6 can not be calculated and fixed 
once for all. In order, therefore, to have control over all angles 6 and thus 
in each instance to be in a position to procure the best possible conditions, 
the bi-nicol ocular* was constructed, but after completion was found to 
suffer from a defect which it was difficult to overcome satisfactorily, namely, 
the depolarizing effect of the total reflecting prism pairs on the transmitted 
light-waves when the planes of the rotating nicols are not parallel with the 
planes of the polarizer and analyzer. As a result, a certain amount of false 
light is introduced into the field and tends to veil the sharp contrast of the 
two halves and thus to decrease the sensitiveness of the instrument. 
BERTRAND PLATB. 
In place of birefracting plates, which introduce an entirely new set of 
conditions in the path of light-waves and which complicate the expression 
for the relative intensity correspondingly, Kleinf and BertrandJ have used 
the rotatory power of quartz plates, cut normal to the principal axis, on 
the plane of polarization of normally incident, plane polarized waves. As 
shown above, the total effect of such a quartz plate in monochromatic light 
is merely to increase the angular distance 6 in the intensity formula (6). 
This power of rotation of quartz varies with different wave-lengths and 
with the thickness of the plate. If white light be used, interference colors 
result, as indicated in Figs. 69, 70, and 71. In Fig. 70 the change in in- 
tensity of different colors with change in thickness of the plate is shown, 
while in the dotted line of Fig. 7 1 the distribution of intensity for different 
wave-lengths throughout the spectrum is indicated for a quartz plate normal 
to the optic axis and 3.6585 mm. thick, for which the angle of rotation for 
the color 555 nn is 90; this color accordingly suffers total reflection in the 
*Amer. Jour. Sci (4). 26, 374, 1908. 
tNeues Jahrbuch, 9. 1874. 
IZeitschr. Kryst.. I, 69. 1877; Bull. Soc. Min.. I, 27. 1878. 
