On a Large-angled Immersion Objective. By J. W. Stephenson. 55 
using an illuminating pencil of extreme obliquity, incident at right 
angles to the axis of the valve, and a “ perfect -network,” sharp 
and distinct, when the incident ray from a paraffin lamp is in- 
clined at an angle of about 45° to the longitudinal and transverse 
striae. 
The more easy test "of Amphipleura pellucida on Holler’s 
Probe-Platte is readily seen, but as this diatom is in balsam an 
“ immersion condenser ” is of course necessary ; that used by me 
is a non-achromatic triplet of 138° balsam angle = 1 • 40 of numerical 
aperture, made for me by Mr. Zeiss, under Professor Abbe’s direc- 
tions ; but I find that another non-achromatic condenser of very 
large angle, which I have used for many years, is perfectly effective 
when similarly attached to the slide by a drop of water or oil. 
The preceding observations, in which the expression “ nume- 
rical aperture ” has been more than once adopted, not unnaturally 
leads to some remarks on the more common measure of “ angular ” 
aperture. 
It has long been evident that the time has arrived for a more 
rational definition of the resolving power of a microscope than 
that now in use. Even before the introduction of immersion 
objectives, the expression “ angle of aperture” was deceptive as an 
indication of resolving power, inasmuch as resolving power is pro- 
portional to the sine of the semi-angular aperture of the objective, 
and not to the angle of aperture itself; and it is needless to 
dwell on the fact, that having regard to the small progressive 
increase in the sines of large angles, the ratio of resolving power 
can bear no proportion to the mere number of degrees. 
But, since the invention of the immersion system, the present 
measure has become still more objectionable ; it not only fails to 
give the relative resolving powers, but suggests apparent differences 
where there is no essential difference, and gives an appearance of 
identity where none exists. 
In the last number of our ‘ Transactions,’ a paper, by Mr. 
Zeiss, on Abbe’s Apertometer, explains the meaning of the expres- 
sion “ numerical aperture.” 
Briefly stated, it is equal to the product of the refractive index 
of the medium in front of the objective, multiplied into the sine of 
the semi-angular aperture = n sin. ic. 
This definition of “ numerical aperture ” offers at once a means 
by which all objectives, whether dry, water, or oil immersion, can 
be directly compared. It is based on the theory whence Professors 
Ahbe and Helmholtz deduced the limit of visibility. 
The wave-lengths of the various coloured rays composing the 
diffraction spectrum being shortened on entering different media 
in front of the objectives, in the ratio of their respective indices of 
refraction, affords one of the most complete, as it is one of the most 
