212 THE MICROSCOPICAL NEWS. 
quantity “ would be =o. In that case the dissipation of the light 
at the ultimate image of the microscope would also = 0, z.z., the 
image would retain its full ideal perfection, with every amount of 
super-amplification; and it would, therefore, be entirely unim- 
portant whether a certain total power had been obtained by an 
objective of long or short focal length. If, however, the objectives 
in question are afflicted with certain defects, however small, the 
quantity z will obtain a certain value; and the dissipation of the 
rays corresponding to that value, being more and more enlarged as 
the super-amplification is increased, there must always exist a 
certain maximum super-amplification or value of v which the objec- 
tive will bear without a visible or an objectionable loss of sharpness 
or perfection of image. Consequently, we have a maximum of the 
total amplification N which can be obtained with a given focal 
length under the condition of a certain degree of sharpness of the 
image; and, conversely, a maximum focal length which admits of 
a given amplification under the same conditions. If, for example, 
the inherent dissipation of a certain kind of objective were confined 
to an angle of 15”, no eye would recognise the dissipation-circles if 
such a system were used only under its own normal amplification 
(using it as a simple microscope). The dissipation would, how- 
ever, become visible, and would introduce a perceptible indistinct- 
ness of the image, if the super-amplification much exceeded 4, and 
the deterioration would become very great should it amount to 16, 
because in these cases the circles of indistinctness would be dis- 
played in the respective ultimate images under a visual angle of 
more than 1’ and of 4’. If now acertain amplification, say 320 
diameters, is required with objectives of that degree of perfection, 
a 1-8th inch would yield that number with a super-amplification of 
4, but a 1-2 inch would require 16; the perfection of the image in 
the latter case being very much less than in the former. 
It would be useless to attempt to assign by way of example 
numerical values of the constant w for different kinds of objectives, 
and of the limit of U which would be consistent with a sufficient 
perfection of the image, in order to compute theoretically the 
amount of super-amplification which every objective would bear. The 
circumstances on which the first two elements depend, are much 
too complicated for a theoretical estimation of their influence in 
regard to the actual performance of the microscope. Nevertheless, 
the foregoing considerations indicate the aim of the problem, which 
is to determine the adequate focal length for every aperture. It 
will be quite sufficient for our purpose to determine the limits of 
admissible super-amplification drectly by practical observations, 
without further caring for the elementary conditions on which it 
depends ; and if this is done, we have obtained all necessary data 
for the problem under consideration. 
