OPTICAL CHARACTER OF BIREFRACTING MINERALS. 77 
are not in focus at the same time with the vertical, while oblique lines are 
never strictly in focus. This phenomenon of astigmatism is due to the fact 
that the radius of curvature of the lens on which the oblique rays impinge is 
shorter in the horizontal plane than in the vertical; the lens appears fore- 
shortened in the horizontal plane. (Figs. 21,22.) 
A still further defect is the fact that it is not possible to correct a lens 
for the sine condition for more than one image plane ; the rear focal plane of 
the objective is not plane but curved ; it consists in fact of two coaxial sur- 
faces which are more or less spherical or paraboloidal or irregular and wavy 
in shape, even when monochromatic light is used. To bring into accurate 
focus all the points on these two surfaces at one and the same time is ob- 
viously impossible, and a compromise is made by using a small stop in the 
eye-point of the ocular if the observations be made with a Bertrand lens, 
thus reducing the parallax and the effect of astigmatism as much as possible ; 
points midway between the center and margin of the field are brought to 
the sharpest possible focus, in which case the focus over the entire field is 
fair. If the interference figure be examined without the Bertrand lens, a 
stop should be placed in the image plane and all but the central, axial por- 
tion of the object cut out, thus reducing the astigmatic errors. For the same 
reason a stop should be introduced either in the upper focal plane of the 
Bertrand Jens, or in the conjugate image plane of the upper focal plane of 
the objective as formed by the Bertrand lens, and the image narrowed down 
to the axial portion. A third and more important factor is the distortion 
due to the analyzer, which tends to disturb the symmetry of the interference 
figure and thus to render the measurements less exact. 
Another factor in the interference figure is the chromatic error of the 
objective. Although in designing an objective the optician strives to 
reduce the chromatic aberrations to negligible limits in the image plane, 
this is not the case for the focal plane of the objective and the image there 
formed is not achromatic. As a result, the colors in the interference figure 
are not strictly pure, but are more or less modified and veiled by the chro- 
matic aberration colors of the objective itself. In testing for dispersion of 
the optic axes the chromatic errors of the objective should be taken into 
account. 
These factors indicate clearly that an interference figure in the micro- 
scope is so encumbered with disturbing elements that measurements of 
a high degree of precision are not possible under any conditions. The 
approximate results obtained, however, are sufficiently correct for practical 
purposes, data of a higher order of accuracy being rarely required.* 
*The following method of artificial illumination has proved satisfactory in petrographic microscopic 
work. The source of light (acetylene or Nernst light) is placed in the principal focal plane of a large con- 
denser lens from which parallel rays then emerge and pass to the substage reflector and into the microscope. 
A pale blue glass disk with one side finely ground is placed in the lower focal plane of the condenser approxi- 
mately, and serves two purposes: (i) to reduce the intensity of the red and yellow from the artificial light 
and thus to render the light more nearly like daylight; (2) to furnish by means of the finely ground, lower 
surface of the blue glass disk a series of radiant points in the lower focal plane of the condenser from which 
light rays arc refracted in all directions. This insures uniform illumination over the field and for ordinary 
purposes, especially observation of interference figures, has proved more satisfactory than the usual method 
of placing the ground blue glass between the suhstage reflector and the lower nicol. TheVfTectsof depolari- 
zation at the finely ground surface are not serious and in general not noticeable. By using a concave mirror 
(attached to the arm of the microscope) in conjunction with the artificial light source, excellent illumination 
for the study of minerals in reflected light can be obtained. By means of colored glass screens it is. moreover, 
possible in certain instances to illuminate the surface of the preparation with light of such a hue that the 
difference in aspect between two minerals, as hematite and magnetite, which resemble each other closely 
and are not always easy to distinguish under the microscope in ordinary light, is accentuated in a measure 
and their determination facilitated to that extent. 
