Professor Abbe’s Paper on the Microscope. 253 
A inode of testing which turns upon the determination of the 
utmost limit of “ resolving power,” whether tried upon a “ Nobert ” 
plate, a diatom, or an insect scale, brings into play a quite excep- 
tional direction of rays of light into the microscope, such as is, 
indeed, required for this purpose by the physical condition of the 
problem. Theory and practice teach us that every objective which 
is not a total failure — however imperfect in respect to correction of 
spherical aberration — if its lenses be hut moderately well centered, 
can always be made to work with one of its zones, e. g. the outer- 
most, if during its construction it has been tried on a similar test. 
The proof that an objective can resolve very minute striae on a 
diatom or Nobert’s test-plate, attests, strictly speaking, nothing 
more than that its angular aperture answers to the calculable angle 
of diffraction of the interlinear distance of the striae on the test, 
and that it is not so badly constructed that a sufficient correction 
of its outer zone is impossible. A trial of this sort offers no means 
of ascertaining what conditions for the correct fusion of aperture 
images such an objective would present in the much more unfavour- 
able case of the ordinary observing position. Nor can the result 
be considered as sufficiently characteristic even of the “ resolving 
power ” in its more general attributes. 
Nor can the test of “ resolving power ” by direct light be 
estimated at a much higher value. In the neighbourhood of the 
limit of resolution corresponding to this form of illumination, all 
direct light passes through the central zone, and all diffracted fight 
through the peripheral zone of the aperture. 
From the point of view presented by the theory here propounded, 
another method offers itself, which, while employing the usual tests, 
brings directly into fight the particular points which mainly in- 
fluence the quality of performance during ordinary use of the 
microscope. If it be desired to test, in a most critical way, the 
conditions of exact co-operation of pencils of fight which pass 
through every part of the aperture, there are truly no better means 
than those afforded by natural objects of the diatom class and 
insect scales, provided that the mere fact of accomplished “ resolu- 
tion ” is not made the chief consideration, but that the exact consti- 
tution of the total image produced by the objective is studied. 
The considerations adduced lead to certain rules respecting the 
objectives of much higher angle. The immersion lens is constructed with a free 
aperture of about 100° in water, i. e. somewhat more than would correspond 
to 180° in air, because this is attainable without serious disadvantage. Pro- 
fessor Abbe is, however, convinced that even the immersion lens would not lose 
any of its value for ordinary scientific purposes, whilst it would be materially 
improved in many respects if its construction were based upon calculations for a 
smaller aperture, “ but,” he adds, “ in view of this universally accepted standard 
of valuation, the practical optician can scarcely be expected to trouble himself 
about qualities of performance which would be very certainly ranked amongst 
those of a secondary order ! ” 
