RELATION OF APERTURE AND POWER IN THE MICROSCOPE. 189 
of them are so constructed that this sieve cannot be cleaned. Such 
a filter rapidly becomes a foul mass of dead and decaying matter 
through and over which every drop of water must be passed before 
some people will drink it. The consequences may be better 
imagined than described. It is not unfrequently urged that a 
microscope in the hands of an ordinary observer is just so much 
power allowed to run to waste. If, however, the present remarks 
lead to the temporary diversion of the microscopic power re- 
presented by this Society from the very natural and by no means 
useless study of things beautiful to things merely useful, something 
will have been done to remove the stigma, and results be attained, 
the value of which it is scarcely possible to overestimate. 
_ We cannot agree with all the opinions expressed in this paper, 
and shall refer to it again in a future issue-—Ep. 
THE RELATION OF APERTURE AND POWER IN 
THE]. MICROSCOPE. 
By PRoressor E. Agger, Hon. F.R.M-.S. 
(Read 14th June, 1882). 
L1.—The Rational Balance of Aperture and Power. 
(22.) Division of the Entire Process of the Microscope between 
Ocular and Objective. 
AVING determined—as definitely as the circumstances will 
permit—what total power of the Mvcroscoge is necessary or 
useful for the utilization of a given aperture, the next question can 
now be discussed, which is: What power of the odjective is required 
for the same purpose ? 
From the principles on which the former discussion was based, 
this question has raised a distinct issue. If we find that with an 
aperture of 0°50 (60°) a total amplification of 265 diameters is 
required, in order to display the smallest dimensions which are 
within its reach under a visual angle of 2’, it follows that for the 
actual effectiveness of that amplification the microscope-system 
(objective and ocular combined), must so collect the rays in the 
ultimate image that the image-points shall have sufficient sharpness 
for the distinct exhibition of details of that small visual angle. The 
question will therefore be: What composition of the microscope 
must be used, and in particular, what power or focal length of the 
objective is necessary and sufficient, in order to obtain these 265 
