TRANS. OF PROF. ABBE’S PAPER ON THE MICROSCOPE. 123 
a misdirection of my labours towards aims-of very problematical 
worth. 
As, then, it was important above all things to ascertain more 
exactly than has been hitherto set forth the actual facts respecting 
the operation and effect of angular aperture, I endeavoured to de- 
termine by experiment in what cases a distinct advantage resulted 
from larger angular aperture, and in what cases no such advantage 
could be perceived. For this purpose a series of objectives, differ- 
ing widely in focal length and angular aperture, were constructed, 
according to my calculations, and their accuracy tested, so as to 
afford a certainty of correctness. The test-objects employed in- 
cluded prepared insect scales of various kinds, diatom valves, 
striped muscle fibre, diamond-ruled lines on glass, groups of lines 
on silvered glass, fine and coarse powdered substances, and, be- 
sides these, the minute optical images of natural objects (lattice 
bars, wire-net) obtained by means of air-bubbles, or, preferably, by 
objectives of short focus, fitted to the stage of the microscope. 
These experiments yielded the following results : 
(i.) So long as the angle of aperture remains within such limits 
that no noticeable diminution of sharpness of image results from its 
diffraction effect, no sensible improvement in the delineation of the 
outlines of the object takes place, provided these parts are not of 
less size than zg inch. 
(ii.) On the other hand, the difference is wholly in favour of 
the larger aperture for every object which yields details minuter 
than the limits above given; and this quite irrespective of the 
question whether such details are due to unevenness of surface or 
to unequal transparency in an infinitely thin layer, or whether 
the detail takes the form of striation, granulation, trelliswork, or 
images of natural objects reflected from bubbles or produced by 
refraction of lenses. 
(uii.) The smaller the linear dimension of such details, so much 
the larger must be the angle of aperture of the objective, if they 
are to be made out with any definite kind of illumination, e. g. 
whether purely central or very oblique: and this irrespective of the 
more or less marked character of the delineation and of the focal 
length and necessary amplifying power of the objective. 
(iv.) When the detail in the real object appears in the form of 
striation, groups of lines, &c., a given angular aperture always 
reaches ‘much finer details with oblique than direct illuminations, 
and this irrespective of the circumstance that the constitution of 
the object admits or excludes the possibility of shade effects. 
(v.) A structure of the supposed kind, which is not revealed by 
an objective used with direct illumination, will not be rendered 
visible by inclining the odject ztsedf at any angle to the axis of the 
microscope, even when lying at right angles with the axis, it is 
