20 Transactions of the Royal Microscopical Society. 
thickness, polished on the cylindrical edge, and ground to an angle 
of 45° in the direction of the diameter. This disk being put on 
the stage of a microscope, the rays admitted by the cylindrical edge 
of the disk horizontally are directed into the axis of the microscope 
by total reflexion. The centre of the semicircle is formed by a 
little hole in a silvered cover cemented to the upper face of the 
disk. 
Two indices of blackened brass with sharp edges, sliding on 
the periphery of the disk, afford visible marks for observing the 
limits of telescopic field, or microscopic aperture, of any objective. 
On the upper face of the disk there are two engraved scales ; 
one of them showing the angular semi-aperture for air, the other 
the numerical indication of aperture as stated above. 
A 2-inch object-glass, with a specially adjusted diaphragm above 
the lens, is added to the apparatus. It is to be adapted to a draw- 
tube applied within the microscope, in order to get the telescopic 
eye-piece necessary for measuring the higher power objectives. 
The management of the apparatus is as follows : 
The semicircular disk of crown glass is to be put on the stage 
of a microscope, and the objective, the aperture of which is to 
be measured (we will call it x), is roughly focussed to the little hole 
in the silvered cover-glass. In the case of an immersion lens a 
drop of water of course will be applied. 
This done, the eye-piece of the microscope is taken off, without 
altering the position of the objective x. The naked eye, in looking 
down into the open tube, will now see above the objective a small 
air-image of the cylindrical edge of the glass disk and images of 
objects round the microscope, which are brought into the axis 
of the microscope by total reflexion. 
If X is an objective of low power, from J inch downwards, the 
naked eye is sufficient for observing the aperture. For this purpose 
the two indices of black brass are put to the edge of the glass disk, 
and moved to and fro until the points of them as seen in the 
image above x just touch the margin of the illuminated field ; i. e. 
appear or disappear, the pupil of the eye being kept in a central 
position. The position of the indices is read by their straight 
edges on the innermost scale of the disk. The half sum of both 
readings will give the semi air-angle of the objective x. For 
systems of higher power the image above the objective is too small 
for observation with the naked eye. In this case an auxiliary 
microscope is necessary for this observation, which is got by means 
of the draw-tube. The lens belonging to the apparatus (we will call 
it B) is screwed to the draw-tube and combined with one of the 
ordinary eye-pieces. The auxiliary microscope thus obtained, is 
focussed to the image above named, by moving the draw-tube up 
and down until the edge of the disk is seen quite distinctly. Now 
