OPTICAL, CHARACTER OF BIREFRACTING MINERALS. 8 1 
After the direction of the acute bisectrix has been found by this method 
its value, C or it, can be readily ascertained by ordinary methods either in 
parallel or in convergent polarized light.* 
The isochromatic interference curves which appear in the interference 
figure from a plate parallel with the plane of the optic axes can also be used 
to locate the direction of the acute bisectrix, as was first shown by F. Becke. f 
It can be proved in several different ways that the acute bisectrix is gen- 
erally a direction of less birefringence than the obtuse bisectrix. The bire- 
fringence of any section can be calculated approximately by means of the 
usual formula 
7' a' = (7 a) sin 0i sin 2 
where 7' and a! denote the maximum and minimum refractive indices of the 
given section, 7 and a those of the mineral, 0i and 2 the angles between the 
normal to the section or direction of wave propagation and the two optic 
axes respectively (Plate 5 is a graphical solution of this equation). This 
standard formula indicates clearly that except in the limiting case of 2 V = 90, 
the birefringence for sections in the alternate quadrants containing the acute 
bisectrix is less than that for corresponding sections in the two remaining 
quadrants. The rule resulting from this fact is that the interference colors 
for points in the quadrants containing the acute bisectrix are lower than 
those for corresponding points in the direction of the obtuse bisectrix. J 
Having once determined the direction of the acute bisectrix by this method, 
either by observing the interference figure directly or by using a sensitive 
tint plate or quartz wedge, the relative value of the acute bisectrix, whether 
C or rt, is determined most readily in parallel polarized light by the ordinary 
methods. 
G. Ce"saro has described several methods by which the optical character 
of the mineral can be determined directly on such sections in convergent 
polarized light by observing, on the insertion of a quartz wedge, (i) that 
the black curves of exact compensation appear first in the quadrants con- 
taining the acute bisectrix; (2) that the isochromatic hyperbolas cross in 
the lower or in the upper part of the field, depending on the optical char- 
acter of the mineral and the direction of elongation of the wedge; (3) that 
if the point at which the hyperbolas cross be not visible in the field, the 
direction of the point toward which they converge or from which they 
diverge on inserting the wedge can be seen and thus the character 
determined. 
These methods of Ce"saro are implied by Becke in his paper on the 
Skiodroms, 1 1 wherein a very useful rule for determining the sign of reaction 
of a section is given. More recently J. W. Evans, ^ in discussing this rule, 
This method was first described in 1904 by the writer (Amer. Jour. Set. (4), 17. 388. 1904)- It has 
since been described by G. Ce^saro (Bull, de 1'Acad. roy. de Belgique (class* des Sciences), pp. ago, 392, 
459. 493. 1906; also p. 161, 1007) and evidently without knowledge of the description by the present writer. 
tTschermak's Miner. Petro. Mitteil.. 16, 181. 1897. 
JF. Becke, T. M. P. M. 16, 181. 1897; also in Rosenbusch-Wulfing, Mikroskopische Physiog. (I). I, 
315 and 335. Compare also F. E. Wright, Amer. Jour. Sci. (4), 17, 389-300. 1904; (4), 20. 295, 1905. 
{Bull, de 1'Acad. roy. de Belgique (Classe des Sciences) 290. 392. 459, 493, 1906: 159-161. 1907. 
|)T. M. P. M. 24, 1-34, 1905. In this paper Becke (see also T. M. P. M. 27, 177. 1908) directs attention 
to the difference in behavior of the zero isogyres of uniaxial and biaxial crystals. The black brushes in the 
interference figures from uniaxial crystals are essentially straight lines and are always parallel with the 
polarization plane of the nicols. In biaxial crystals these dark achromatic bars turn as the stage is rotated 
and may include any angle with the principal planes of the nicols. This fact serves to distinguish a uniaxial 
crystal from a biaxial crystal, even in sections in which no optic axis is visible in the interference figure. 
*[Miner. Mag., 14, 231-234, 276-281, 1907. 
