ZOOLOGY AND BOTANY, MICROSCOPY, ETC. 
513 
obliged to Lave regard to the greatest possible angle of aperture or to 
the highest “ numerical aperture ” of Abbe, of which the expression is 
a = n sin u (where u is the refractive index). Accordingly they give in 
their price lists with dry systems the angle of aperture or the numerical 
aperture, and with immersion systems the latter. Whether these data 
correspond to the facts must be subjected to experiment. Herr Kayser 
received from a well-known firm an oil-immersion (1/16 in.), which 
he had required to be capable of resolving Ampliipleura pellucida in 
oblique light. The system supplied did not answer to the requirements. 
The maker having ascribed the non-resolution to “ badness of the pre- 
paration, defects in means of illumination, stand, &c.,” it remained for a 
time doubtful whether these circumstances were really to blame. Herr 
Kayser was at that time engaged on the construction of apertometers. 
The apparatus resulting from his investigations, which serves for the 
examination of dry systems, has the following arrangement. Round a 
horizontal divided circle a vernier can be turned, and an upright, on 
which is fixed a Microscope directed horizontally, is set up in the centre. 
In front of the objective of the latter is a ring attached by a pin to the 
same upright. This ring can be rotated about the axis of the upright 
by means of side pieces which reach to the horizontal scale and carry a 
second vernier. With the plane of the ring at right angles to the axis 
of the Microscope, which passes through its centre, the reading on the 
second vernier is 90°, when the direction of the Microscope corresponds 
to the reading 0°. The system whose aperture is to be tested is placed 
in the ring. The Microscope is then displaced along its axis until the 
combined optical apparatus, which acts as a non-inverting telescope, 
shows the images distinctly. When by suitable turning of the whole 
apparatus the cross wires of the Microscope have been adjusted on an 
object not too near, the first vernier is displaced, without moving the 
second, both to right and left, until the image in each case just vanishes 
on the edge. The sum of the two angles read off is the angle of aperture. 
The angle thus given for an objective system, No. 7, of about 4 mm. 
focal length, was greater than the value given for it and found by the 
Abbe apertometer, in which the identity of an optician’s systems of 
equal members is assumed. The author, attributing the magnification 
to his apparatus objective, tried the apertometer objective of Zeiss, 
specially made for the Abbe apertometer ; but even with this the result 
remained unaffected. 
The second apertometric apparatus constructed by Herr Kayser can 
be used for both dry and immersion systems. It consists simply of a 
glass plate of which one face is silvered and has scratched upon it a 
system of concentric circles which come into observation according to 
the dimensions of the apertures to be determined. The plate is laid on 
the stage with the silvered side downwards, and carries on its upper face 
in the middle of the rings, a small cover-glass, on the under side of 
which is a small mark. The Microscope containing the objective to be 
tested is first adjusted on this mark. Then without moving the body- 
tube the eye-piece is withdrawn, and again replaced in the tube when 
combined with the apertometer objective. The eye-piece is then adjusted 
so that the rings near the edge appear quite distinct ; the extreme ring 
is counted, and if it does not exactly coincide with the edge, an estima- 
