ANGULAR APERTURE. 
evident, therefore, that by the mere effect of this increased illumi¬ 
nation, the lineaments showing the structure of the object, which 
were altogether imperceptible in c and d, began to be developed 
but very imperfectly in e, were more visible in f, and became 
quite distinct in a. 
The great and manifest importance, therefore, of the angle of 
aperture to the efficiency of the microscope, renders it indispen¬ 
sable that easy and practicable means should always be attainable 
for determining it. If the distance of the object from the object- 
glass, and the virtual opening or diameter of the object-glass 
could be always exactly measured; and if all the rays which 
fall on the object-glass could be assumed to pass through it, and 
to converge upon the image, then the angular aperture would be 
an element of very easy calculation. But it is not practicable to 
obtain these data, and it cannot be assumed that all the rays 
which are incident upon the object-glass will pass through it, 
and be made to converge upon the image. 
16. Instead, therefore, of calculating the angular aperture in 
this manner, it is determined by immediate experiment. 
The greatest angle of aperture of which a given lens is capable* 
will be found by determining the greatest obliquity with which 
it is possible for rays to fall upon the object-glass, so as to be 
refracted by it to the eye-glass. The following method of ascer¬ 
taining this, for any given object-glass, was contrived and 
practised by Mr. Pritchard, at an early epoch in the pro¬ 
gress of the improvement of the microscope, when the importance 
of the angular aperture was demonstrated by that eminent artist 
and Dr. Goring. The same method, with but little modification, 
is that still practised by opticians. 
Let m m, fig. 9, be the microscope, the object end being fixed 
upon a pivot, so that the eye end can be moved over a graduated 
semicircle. Let a small luminous object, such as the flame 
of a candle, be placed in the direction r r, at the distance of 6 or 
8 feet, so that the rays proceeding from it to the object-glass may 
be considered as parallel. If the microscope be directed towards 
the candle, all the rays will fall perpendicularly on the object- 
glass, and will evidently pass through it to the eye-glass. If the 
microscope be then turned on the pivot to the left, the rays will 
fall more and more obliquely on the object-glass, and a less and 
less number of them will pass to the eye-glass. 
When such a position as m m is given to the microscope, those 
rays only which fall upon the border of the object-glass upon the 
right of the observer, will arrive at the eye-glass, and the field of 
view will then appear, as shown at f, half illuminated and half 
dark. If the microscope be moved beyond this position, the field 
13 
