142 METHODS OF PETROGRAPHIC-MICROSCOPIC RESEARCH. 
symmetrical interference figure than proportionate changes in intensity or 
color. Theoretically these methods suffer from serious defects which it 
is difficult to remedy. Convergent polarized light postulates a cone of 
obliquely incident light; the plane of polarization of each wave impulse of 
this cone suffers at the boundary surfaces of the crystal plate more or less 
rotation, depending on the angle of incidence, the optical constants of the 
crystal, the azimuth of the crystal section, and the enveloping medium. 
The lenses of the microscope, moreover, rotate the plane of polarization of 
all oblique waves whose line of propagation is not contained in the principal 
nicol planes. These factors together tend to modify the phenomena which 
appear in the interference figure so that the observed positions of total 
extinction may not be precisely correct for the section under investigation. 
Plane parallel polarized light should be used as far as possible in all such 
determinations. 
The practical application of such methods, moreover, is not entirely satis- 
factory. The first method of this type was proposed by Kobell* in 1851, 
who used a plate of calcite normal to the optic axis as his test plate. The 
microscope was arranged for convergent polarized light and the crystal 
plate with the calcite test plate above it placed on the microscope stage 
and turned until the interference figure appeared perfectly normal and 
undistorted. Practically, the following objections apply to this method. 
The optical system of the microscope requires changing each time to meet 
the new conditions; during the observations the crystal itself is lost sight 
of, and in the case of minute crystals or crystals with undulatory extinction 
this is a serious drawback. Moreover, it is tacitly assumed that in the 
crystal plate itself for directions other than normal to its surface the planes 
of polarization remain parallel, which in general is only approximately true 
even for small fields which include only a small angle with the normal. 
In the Brezinaf method a more complicated interference figure is pro- 
duced by two calcite plates cut at a small angle with the optic axis and 
cemented together one above the other in such a way that the optic axes 
of the two are in the same plane and at equal angles with the normal. The 
interference figure from such a combination is noteworthy because of a dark 
vertical bar through the center of the field. A slight rotation of an inter- 
vening crystal plate displaces this bar noticeably, but the same objections 
noted in the Kobell method apply with equal force to this method, with 
the result that neither method is made use of at the present time by working 
petrologists. Both these methods, in fact, were suggested before the petro- 
graphic microscope had come into general use. 
THE RELATIVE SENSITIVENESS OF THE DIFFERENT METHODS. 
The term position of extinction or extinction direction means practically 
that position of a birefracting plate for which light-waves are transmitted 
without changing their plane of vibration and for which no light passes the 
upper nicol, i.e., the field is actually just as dark as though no birefracting 
crystal plate were there. A rotation of the plate through a very small 
angle from its position of total extinction allows a small percentage of the 
total amount of incident light through the upper nicol and the field is very 
dimly illuminated. For a given angle of rotation, the actual amount of 
Ann.. 95, 330. 1853. fDocribed in Schraufs Lehrb. d. Phys. Min , 2, 219-930. 1868. 
