16 
On the Limits of the 0])tical 
profound knowledge. This point of view had not been neglected 
by Dr. Abbe, but in my translation two short sections of his essay, 
which referred to brightness of image, and to certain inquiries 
connected with illumination of the image, were, for reasons 
mentioned in the preface, omitted. It is therefore so much the 
more satisfactory that Professor Helmholtz's essay enters fully into 
the subject. The peculiar conditions under which objects are seen 
when magnified by the microscope, can only be understood by 
studying both aspects, physical and physiological, in connection 
with each other. The laws of formation of optical images (when 
amplified by interposition of lenses), and the laws of dispersion of 
the rays by which these images are formed, help us to an interpre- 
tation of the physical agencies at work, and show us also why the 
extreme amplifications employed render vision through the micro- 
scope more imperfect than through any other optical instrument, 
such as telescope or camera. But the analysis of these physical 
agencies and efiects involves the consideration of the eye itself, as 
an optical instrument through which the microscope image must 
pass to reach the perceiving organ. And apart from the imperfec- 
tions arising from aberrations and dispersions of rays in the instru- 
ment, other imperfections of the retinal image will be found in 
considering the more or less favourable conditions under which the 
microscope image enters the eye. The area into which the micro- 
scope image is collected at the eye spot (over the ocular), varies in 
size with the amplification, and is smaller in proportion as the 
ampHfication is greater. And this variation of size is accompanied 
by variation in brightness of image and distinctness of detail. If 
the area of illuminated image entering the pupil is smaller than 
that of the pupillary aperture, loss of brightness is felt. For the 
condition of most effective illumination (brightness of image) is that 
which obtains when the area of image at the eye spot, and the area 
of the pupil, are equal. On the other hand, a small and intensely 
bright spot of light in front of the pupil presents the exact con- 
dition under which entoptic shadows obscuring the image are 
thrown with it on the retina. But as brightness of image is as 
necessary to distinct vision as any mere amplification of detail can 
be, it follows that a suitable relation of " aperture " to " magnifying 
power " must be maintained in every good objective ; for " aperture " 
in this particular case means the measure of light admitted with 
the image-forming rays ; and as a larger measure of light is re- 
quired in proportion to the increase of magnifying power, so it is 
only when these two factors are suitably proportioned that details 
in the objective will be rendered clearly visible in its microscope 
image. And again, as respects the bundle of rays collected into a 
smaller or larger area at their entrance to the pupil, the regulation 
of illumination from without is better maintained with a large 
