EXTINCTION ANGLES. 131 
In the Calderon method described below, the calcite plates are purposely 
so thick that they show the white interference colors of higher orders in 
white light, in which case the thickness is so great that for a number of 
different colors throughout the spectrum the path-difference of the emergent 
waves is a whole number of wave-lengths; in other words, in the Calderon 
method it is permissible for practical purposes to consider the plate of such 
a thickness that for white light the expression sin 2 is unity; the angle 0j, 
A 
therefore, should be small in order to secure the best results, so small in fact 
that the illumination of the field is just visible. 
In several of the other methods cited below for the exact location of the 
ellipsoidal axes of a given plate, use is made of quartz plates or wedges, 
which are cut normal to the principal axis, and which rotate the planes of 
vibration of normally incident, plane polarized light. For the purposes of 
this paper it is not necessary to enter into the mathematical discussion and 
theory of the rotatory power of quartz, but simply to apply the known 
laws of rotatory polarization as they were first proved experimentally by 
Arago and Biot on this mineral. A quartz plate perpendicular to the 
principal axis rotates the plane of normally incident, plane polarized waves, 
through an angle which is proportional to the thickness of the quartz plate 
and also approximately proportional to the inverse square of the wave- 
length used.* The rotation effected by two superimposed plates is, more- 
over, the algebraic sum of the rotations produced by each separately. 
By using, therefore, a properly constructed quartz wedge, it is possible 
to counteract exactly the effect, in plane-polarized monochromatic light, 
of any crystal plate in any given position with respect to the nicols, by 
rotating the new planes of vibration, determined by the crystal plate back 
to the original planes of the nicols. 
In the intensity formula (5) 
7i = cos 2 <-sin 26 sin 2(6-4) sin 2 - d(y'-a') 
\ 
this rotation affects the angle 6 only and, if the nicols be crossed, then 
7i = sin 2 2 6 sin 2 - d (7' a') (Equation ( 1 1 ) , page 121) 
A 
In all measurements of extinction angles, however, 6 is a small quantity 
and in place of the sine we may use the angle itself without sensible error; 
accordingly, 
This formula, which for small angles, 6, states that the light intensity is 
proportional to the square of the angle 6, will be employed later in the 
description of a new combination quartz wedge for use in determining 
extinction angles. 
In certain other methods convergent polarized light is employed and the 
disturbing effects of an intervening crystal plate observed whose optic 
ellipsoidal axes are not precisely parallel with the planes of the nicols. The 
intensity formulae applying to such conditions are similar to those for plane 
For more accurate expressions of the relation of the specific rotation of quartz to the wave-length, sec 
P. Drude. Lehrbuch d. Optik. ist ed.. 381. 1900; P. G. Nutting. Phys. Rev., 18, 34. 1003. 
