INTRODUCTION. 
The most efficient and useful tool in petrographic research is the petro- 
graphic microscope, and since its introduction by Sorby, half a century 
ago, the science of petrology has been largely dependent on it for further 
development. During these years the microscope itself, together with micro- 
scopical methods, has undergone frequent change and improvement to meet 
adequately the requirements made by the rapidly advancing science. As 
a result, the modern petrographic microscope is admirably suited to the 
purpose for which it is intended, namely, the examination of thin sections 
of rocks. It is satisfactory and convenient, and for most observers serves 
merely as a means to an end ; and only when new conditions arise is the need 
for special microscopical devices felt. 
During the past six years the work with artificial silicate preparations in 
the Geophysical Laboratory has imposed new and difficult problems to be 
solved by the microscope. Not only are such preparations very fine-grained, 
but the degree of accuracy of each measurement must be definitely known 
if it is to be applied without reserve to geophysical problems. To meet these 
new conditions it has been necessary to devise new methods, involving 
extensive alterations in the microscope, and also to test the different 
methods available for the determination of the optical constants of minerals 
in the thin section and to ascertain their relative accuracy and general 
applicability. As a result of these tests, the methods best adapted for work 
with artificial and all fine-grained preparations are now fairly well known 
and their application is in large measure a matter of routine. 
Minerals are determined under the microscope by means of their crystal- 
lographic and optic properties; the more accurately such properties or 
constants can be ascertained for any given mineral, the more reliable and 
satisfactory is the determination. The optical properties thus made use 
of in the practical determination of minerals under the microscope are, 
briefly, refractive index, birefringence, optic axial angle, optical character, 
extinction angle, color, and pleochroism. By means of these properties alone 
it is not only possible to ascertain the crystal system to which a given 
mineral belongs, but also by a short process of elimination to determine 
definitely the mineral in question. This process has been carried to such 
refinement in certain instances, as in the isomorphous series of the plagio- 
clase feldspars, that by optical properties alone the actual chemical com- 
position of the particular plagioclase under observation can be obtained 
with considerable accuracy. 
The optical and crystallographic characters which thus serve in the 
microscopical examination of minerals can be grouped into two classes, 
those of the first class (crystal habit, color, pleochroism and absorption, optical 
character of elongation, optical character of the mineral, and dispersion of the 
optic axes and bisectrices) being ascertained usually by direct observation 
