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II . — Measurement of Angular Aperture. 
By J. W. Stephenson, F.B.A.S., Treasurer K.M S. 
( Head before the Royal Microscopical Society, June 2, 1875.) 
Plate CVIII. 
The necessity of an easy method of determining the angles of 
aperture of object-glasses has long been apparent, and the want 
has recently been more than usually felt, when the relative angles 
of different constructions have been more prominently brought 
before the Society. 
The object of the scale for the measurement of angular aperture 
which I have placed on the table (with some lithographic copies) 
is to supply this want, and its merits, if any, are the simplicity of 
its construction and its strict adherence to the piinciple of esti- 
mating angles which has hitherto been usually adopted. 
Being merely a scale of the cotangents of half the angles indi- 
cated, it may be laid down from any ordinary trigonometrical 
tables. 
It is hardly necessary to point out that the distance A B being 
constant, the line A cl is always the cotan. of the angle Ad B ; but 
as the angle to be measured is twice the angle AcZB, it is so 
marked on the scale. 
The method of using the scale is this : some small and narrow 
body, readily visible, such as a flame or a strip of white paper on a 
black ground, is accurately placed at each of the points A and C, and 
viewed through the back of the object-glass to be measured, which 
is placed above, with its axis parallel to the line A D. By gradually 
advancing the objective from D towards B, the images of the flames 
(or any other objects employed) separate, until at a certain point 
each is seen on the opposite margins of the posterior lens of the 
combination. At this point the angle of the glass is seen imme- 
diately beneath the front lens. 
It will be observed that for the lower angles a side scale has 
been introduced. This is necessary in consequence of the very 
rapid increase in the length of the cotangents of small angles. In 
using this reduced scale, which is only half that of the principal 
scale, the objects to be viewed are placed on the points A and B, 
instead of the points A and C. 
With high powers it is desirable to view the images with an 
ordinary hand magnifier, but with low powers this is quite unne- 
cessary. 
A convenient, but by no means necessary, form of object-glass 
holder is shown in Fig. 1, in which the Society’s screw is fixed at 
right angles to a brass plate, cut out to facilitate the reading off 
with objectives of different lengths. 
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