TRANS. OF PROF. ABBE’S PAPER ON THE MICROSCOPE. I7I 
upon the performing power of the instrument is 7/#zs—that parts 
which belong together in the object shall also appear as belonging 
together in the microscopic image, it follows that uniform correction 
of spherical aberration throughout the whole area of aperture must 
be the absolute criterion and rule of guidance in the construction 
of a microscope. Now, it has been shown that with a dry objective 
an adequate compensation of spherical aberration is, as a matter of 
fact, impossible when the angular aperture exceeds 110°. Hence, 
it must be concluded that a dry objective will be less suited for 
ordinary scientific use in proportion as it renders visible such finer 
systems of lines as exceed the limits of resolving power answering 
to that angle (namely, 0°35 for oblique light). The greatest 
possible increase of resolving power can be obtained in a rational 
way only by means of immersion objectives, as these alone admit 
of the largest possible (¢.e., technically practicable angular) aperture, 
without contravening the very first requirement of corrected spherical 
aberration. * 
A mode 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, in- 
deed, 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 but moderately well centered, 
can always be made to work with ome 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 striz 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 striz 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 
* The dry objectives made on Abbe’s calculations, founded upon the princi- 
ples before explained, have only 105° to 110° of angular aperture for the highest 
powers, and cannot pretend therefore to compete, in resolving diatoms, &c., 
with objectives of much higher angle. The immersion lens is constructed with 
a free aperture of about 100° in water, z.¢., somewhat more than would corres- 
pond to 180° in air, because this is attainable without serious disadvantage. 
Professor 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!” 
