206 THE MICROSCOPICAL NEWS. 
THE RELATION OF APERTURE AND POWER IN 
THE, MICROSCOPE, 
By Proressor E. ABBE, Hon. F.ROMS: 
(Read 14th June, 1882). 
Ll.—The Rational Balance of Aperture and Power. 
(c7.) Division of the Entire Process of the Microscope between 
Ocular and Objective. 
(Continued from page 192.) 
(2) According to a fundamental dioptrical proposition the linear 
amplification N’ of the image, which is projected by a system of 
given focal length f, is s¢rvzc¢ly determined by the formula 
A 
in which A denotes the distance of the image from the posterior 
principal focus of the system (the place where rays are collected 
from distant points in front of the system) ; and this is the same 
whether the image be real or virtual. The objective-image of a 
given system is therefore always amplified in exact proportion to 
the length A; and the linear diameter of the dissipation-circles 
(c) of that image must also be proportional to A, since « is propor- 
tional to N’.. Taking now the angular diameter of these dissipa- 
tion-circles at the posterior principal focus, ze., the visual angle 
under which they would appear at ¢hat place, this angle must 
obviously be the same for every position and amplification of the 
image, because the linear diameter « always varies in direct propor- 
tion to the distance A. We thus arrive at the theorem :— 
If an objective projects a real or virtual image without the 
interference of an eye-piece, the visual angle of the dissipation- 
circles of that image, taken for the place of the posterior principal 
focus, is the same for every position and amplification of the image, 
and is a constant quantity in every system. 
This proposition shows the method of estimating numerically 
the degree of optical perfection in objectives. The constant visual 
angle defined above (which I shall denote by the letter z in the 
following discussion) exhibits an exact measure of the smaller or 
greater dissipation of the rays zzherent¢ in a given construction, and 
one which is independent of the various accidental circumstances 
under which an objective performs. 
(c) Suppose now the angle w (the inherent angular dissipation 
of the light) to be given for a certain objective, and an image pro- 
jected by that objective to a distance A from its posterior prin- 
