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II. — Description of Professor Abbe's Apertometer, with Instructions 
for its Use. By Carl Zeiss, of Jena. 
{Read before the Eoyal Microscopical Society, by John E. Ingpen, Esq., 
December 5, 1877.) 
Plate II. 
The apparatus in question is intended to enable an exact mea- 
surement of angular aperture of any object-glass, dry or immersion, 
to be made, and to afford a definition of aperture, which is not 
limited by the maximum air-angle, which is independent of the 
medium in front of the lens, and which at the same time, by its 
theoretical signification, may afibrd a direct indication of the re- 
solving power of an objective. 
The principle of the method is stated by Professor Abbe in the 
following manner : — The lens is made to act as a telescopic objective 
by combining it either with the naked eye or with an auxiliary 
microscope equivalent to a terrestrial eye-piece, and by observing 
the images of external objects near the bach focal plane of the lens. 
The angular field of the miniature telescope established in this way, 
is determined by observation, the real area of field in the micro- 
scopic action of the lens, or the central part of this area, being made 
to act as the area of aperture in telescopic vision. By this inver- 
sion the angular field in the telescopic action of the lens is made 
strictly identical with the angular aperture in its microscopic 
action. In order to get a determination of aperture not depending 
on the medium in which it is observed, the angular amount of 
the telescopic field is reduced, by a calculated scale, to a purely 
numerical value — the product of the sine of semi-aperture with the 
refractive index of the medium in which it is observed. This 
product is constant for different media (air, water, or balsam), and 
by its value in any objective indicates the limit of resolving power 
(the minimum distance of separable parts) in relation to the wave- 
length of light. 
The apparatus consists of a semicircular disk of crown glass, 
90 mm. (3 '5 inches) in diameter, and 12 mm. (O’ 5 inch) in 
DESCRIPTION OF PLATE II. 
Fig. 1. — Plan of Apertometer, full size, a, silvered cover with transparent 
centre ; h, b, blackened brass indices. The inner scale shows the air-angle, the 
outer scale the “ numerical aperture,” by which a direct comparison can be 
made between dry and immersion objectives. 
Fig. 2. — Elevation, showing position of one of the indices b. The image of 
the point is made to coincide witli the margin of the field of view. 
Fig. 3. — Section of examining glass, showing the position of its achromatic 
lens and diaphragm. 
Fig. 4. — Diaphragm of examining glass. 
Fig. 5. — One of the indices shown in perspective. 
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