RELATION OF APERTURE AND POWER IN THE MICROSCOPE. 231 
sider a super-amplification of about 6 as that which will just raise 
the inherent aberrations up to the threshold of vision, for an aperture 
of about 1°30.* It appears quite intelligible that the total (or 
nearly total) suppression of the front-aberrations should not only 
compensate for the increased aperture but in fact should leave a 
surplus benefit, as is indicated in the higher value of v. 
(3) Regarding the lower apertures of the dry system, my com- 
parisons show a relatively s/ow increase of the critical v, as the 
apertures diminish. This may be sufficiently accounted for by the 
circumstance that these lower apertures are always made with 
relatively greater working-distance (the clear air-space between 
the front surface and the radiant being a greater fraction of the 
focal length) than is adopted in the wide-aperture systems. 
The relief to the front-aberration, and the corresponding 
reduction of the residuary aberrations, which is due to the reduction 
of the angle of the pencil, is therefore partly compensated by the 
increased aberration attendant upon a relatively thicker air-space 
in front of the system. Considering the medium-power objectives 
as they are generally (and properly) made with the view to a 
convenient working distance, I cannot admit of a higher number 
for the critical vy than 5 to 6, even for apertures down to about 
0'40 (47°). If the aperture is reduced below this, the increase of 
v becomes decidedly more rapid, in so far that for o°15—-0°20 N.A. 
(17°-23°), 8 to 10 appears to me to be the correct super-amplifica- 
tion which very good objectives will bear without a perceptible loss 
of definition (under the condition, of course, that the total powers 
obtained thereby are not empty powers in regard to the delineating 
capacity of the aperture in question). 
Similar indications for still lower apertures would be of very 
subordinate interest ; and, besides that, they could not be given on 
* If any one should wonder at the /ow super-amplifications assigned here, and 
should consider the above statements to be poor evidence of the present con- 
dition of microscopical optics, I would ask him to reflect upon what it means, that 
objectives even of rather short focal length should bear a super-amplification up 
to 4 and 6, without any perceptible injury to the sharpness of the image. This 
means nothing less than that the Microscope is capable of showing objects 
enlarged to more than 800 diameters under the same conditions, so far as the 
geometrical precision of the observation is concerned, as if the microscopic 
objects could be enlarged in that degree corforeally, not optically, and were then 
seen with the naked eye at a distance of 250 mm., without the interference of 
any optical apparatus. Up to those high figures of amplification the modern 
Microscope maintains therefore the undiminished sharpness of naked-eye vision, 
and performs without any perceptible difference in the same way as if material 
bodies, instead of mere enlarged images, were depicted upon the retina, The 
time is not long past when no system, except very low-angled lenses, could bear 
even its own proper power without any super-amplification, and not 100 
diameters could then be obtained without great inferiority when compared with 
direct vision. 
