METHODS OF PETROGRAPHIC-MICROSCOPIC RESEARCH. 
two colors, but only for two, red and blue being selected generally for visual 
purposes. The part of the spectrum lying between the red and blue is 
brought to focal points nearer the lens, while the colors beyond red and 
blue focus at points farther from the lens. The spectrum is folded, as it 
were, on itself, the red and blue parts being brought to coincidence, while 
the center or yellow-green part is focussed at points near the lens. This 
remnant of chromatic aberration is called secondary spectrum and results 
from the fact that the dispersion of crown and flint glasses is not propor- 
tional throughout the spectrum. The secondary spectrum may be dimin- 
ished by a suitable choice of glasses, but with the material at present 
available at least three lenses are required, for a reasonably high aperture, 
to bring to the same focus three different colors and thus to eliminate the 
secondary spectrum. 
Even after this has been done and there is practically no chromatic differ- 
ence in image distance, the magnification of the different colored images at 
the image point may be different (Fig. 26). The E. F. of the lens for blue 
rblue 
red 
FlG. 26. 
is less than that for red and consequently the blue image is larger than the 
red image. There is a chromatic difference in magnification of the images, 
which increases as we recede from the axis. Achromasy in the axis and 
freedom from chromatic difference of magnification can not be obtained 
in an objective of high aperture; microscope objectives (and in fact all 
objectives of high aperture) show this defect near the margin of the field. 
Magnifiers, on the other hand (in which the aperture of the image forming 
pencils is limited by the pupil of the eye and hence small), are not sensitive 
to chromatic aberration in the axis, but are seriously affected by chromatic 
differences of magnification, especially near the margin of the field. They 
are corrected, accordingly, not for axial achromatism (as is the objective), 
but to give equal focal lengths for two colors. This correction is attained 
in ordinary achromatic eye-pieces with two lenses of the same kind of glass 
by mounting them at a distance d = apart. The images may then be 
2 
viewed at infinity; the angles which they subtend at the eye are identical 
for the two colors, and they appear, therefore, to be of the same size. By 
changing this distance d it is possible to give the eye-piece chromatic over- 
correction or undercorrection, thus making the image for red larger or 
smaller than that for blue. By proper chromatic overcorrection of the eye- 
