34: 
On the Limits of the Optical 
aberrations appear to exert but an inconsiderable influence, in spite 
of the very large angles of incidence and divergence of rays. Con- 
sidering tlie extreme care expended on calculation and execution of 
lenses for telescopes and the photograph camera, it is justly a 
matter of surprise that with the lenses of the microscope, which 
are so much more difficult to construct according to prescribed 
dimensions, and which have so large an aperture, spherical aberra- 
tion makes itself so little felt. I have, however, already pointed 
out that when there is water between the object and covering glass, 
and also between this and the objective, the divergence angle is not 
87^°, as usually stated, but only 48^°. With dry mounted objects 
an angle of 87 J° can indeed be in action, but only through the 
minute distance hettveen the ohject and covering glass, so that the 
Spherical aberration arising therefrom is of no importance. 
As wide pencils of light are needed to keep diffraction within 
moderate limits, the illuminating apparatus should also be capable 
of emitting pencils of the same angle, in order to show clearly the 
contour lines of dark objects. 
If there happen to be particles in the object which act like lenses, 
these may of course convert a small illuminating pencil of rays into 
strongly divergent rays, and so become clearly visible. Otherwise 
nothing is seen but a confusion of diffractions at and in the object 
on one part, and in the (optical) aperture of the microscope on the 
other part. 
Here lies obviously the explanation why microscopes, otherwise 
good, but whose illuminating apparatus is not specially arranged for 
the purpose, yield, with artificial illumination, e. g. a flame, such 
unserviceable images of the outlines of dark objects. For an 
immersions lens, the best illuminating apparatus is one constructed 
according to the same principle — that is to say, a lens of the same 
kind reversed. The readiest mode of finding whether the illumina- 
ting apparatus gives sufficiently wide pencils of light is to examine 
the ocular image with a magnifying lens after the instrument has 
been focussed. 
I must now relate here the failure of an attempted improvement, 
the negative result of which is significant. I thought myself 
justified in inferring theoretically that the diffraction of the micro- 
scope might be neutralized if the points of the narrow aperture 
which causes this diffraction were made singly and separately 
luminous, and that this could be effected by causing a sharply 
defined optical image of the source of light (e. g. sun illumined 
cloud) to be thrown by a lens on the plane of this aperture. 
Years ago I tried experiments of this kind on a Nobert microscope, 
provided with immersion lenses, giving excellent definition. The 
result of this trial showed that it was perfectly indifferent whether 
the image of the source of light fell on the plane of the object or 
