92 THE MICROSCOPICAL NEWS. 
deed, for certain cases, capable of definite verification, but for the 
generality of objects, and particularly for those objects on which the 
microscope is supposed to exhibit its highest quality of performance, 
it appears that the production of microscopic images is closely con- 
nected with a peculiar and hitherto neglected ‘physical process, 
which has its seat in and depends on the nature of the odvect itself, 
although the measure of its effect stands in direct dependence upon 
the construction of the odjective. It is hence possible not only to 
fix the limits of the visible, beyond which no further resolution of 
structure could be expected, but also to bring to light the fact 
that a microscopic image which may be entirely free from error in 
itself, and therefore be supposed to represent in all cases the true 
structure of an object, nevertheless does zo¢ do so for a whole class 
of objects and observations. 
In addition to those images of ¢he object which are thrown off by 
the lenses of the microscope, a series of associated images of the 
aperture are simultaneously thrown off, which together form an 
image of the outwardly projected plane of aperture. This latter 
(aperture image) is thus associated with the final virtual image of 
the object, and appears at the eye-point, so called, above the ocular 
where it may be examined witha lens. But the image of the object, 
so far as it is produced by the objective alone, lies in or close to the 
upper focal plane of the objective, where also it may be seen by 
looking down the tube of the microscope with the naked eye. These 
two sets of images are interconnected by common relations, the de- 
termination of which affords a key to the solution of questions 
scarcely to be approached by any other means. All the character- 
istics of the object mages hang together with certain characteristics 
of the aperture images, and vice versa. 
The principle on which is founded the study of these aperture 
images leads to various results, depending for their full development 
upon a principle which constitutes at the same time a law of fruitful 
application throughout the whole theory of the microscope, and 
which may be thus formularized. 
When an objective ts perfectly aplanatic for one of its focal planes, 
every ray proceeding from this focus strikes the plane of the conjugate 
Jocus at a point, whose lineal distance from the axis ts equal to the 
sum of the equivalent focal length of the objective x the sum of the angle 
which that ray forms with the axis. 
Now as this condition must be fulfilled in every correct instru- 
ment, both for the objective and for the whole optical part of the 
microscope, the formula above given establishes a relation of quan- 
tity between the angle of aperture of the microscope and the lineal 
diameter of the aperture images above the objective and ocular. 
Moreover, it is thus possible to determine, by micrometric mea- 
surement of the position in the upper focal plane of the objective 
