200 Extracts from Mr. H. E. Fripjp's Translation of 
the operation and eJBfect of angular aperture, I endeavoured to deter- 
mine 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, differing 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 included pre- 
pared 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, besides 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 ^gVo- 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. 
(iii.) 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 ohject itself at any angle to the axis of the 
microscope, even when, lying at right angles with the axis, it is 
perfectly resolved by oblique illuminations. Eesolution, however, 
follows at once when the incident light is directed perpendicularly 
to the plane of the object, as it lies inclined to the axis. Hence 
the increased effect of oblique illumination depends solely on the 
