TRANS. OF PROF. ABBE’S PAPER ON THE MICROSCOPE. 93 
which the track of any ray occupies, the direction which it took be- 
fore entering the microscope. Consequently the aperture images 
formed above the objective, when examined with a suitable micro- 
meter eye-piece, can be used for measurement of the divergence 
which the rays coming from the object undergo. 
In the next place, we need a more characteristic exposition of 
the optical functions which, in the case of images formed under 
larger angles, by rays having a grea¢ inclination to the axis, differ 
greatly from the abstraction by which theory represents the action 
of a set of lenses in forming an image. And such an exposition 
offers itself when we can define by axioms of general validity the 
mode in which an image is focused and spread out on the focal 
plane of an optical system, and distinguish the focusing function 
and the extension of image over a surface as the two principal 
factors of the image-forming process, alike independent in their 
abstract idea, and distinct in actual specific function. Apart from 
the fact that no exhaustive analysis of a faulty image nor any 
means of perfect correction are possible until such characteristic 
distinction can be laid down, we have no other means of determin- 
ing the part taken by each constituent element of a compound 
system of lenses in the joint performance of the whole. When 
then we define the function of the objective to be the production 
of a real image, and the function of the eye-piece the amplification 
of this image,—such explanation does not by any means reach 
the essential principle of action of the compound microscope. 
This is obvious at once when we consider that by such a definition 
the combination of objective and eye-piece is made only to in- 
dicate magnifying power, whereas on the contrary the remarkable 
superiority of compound over simple microscope consists in the 
guality of its performance. By the objective an image is formed 
and spread out in what is an almost perfect accordance with the 
laws by which images of infinitely small elements of a surface are 
formed. By the eye-fzece a displacement of focus is effected ; that 
is to say, a change of divergence of each separate pencil of light 
takes place till the divergence is almost imperceptible, and the 
pencils infinitely fine. 
The first step or act in the image-forming process consists, not 
in the production of a reversed image by the objective in front of 
or within the ocular, but rather in the production of a “ virtual” 
image at an infinite distance with parallel rays. The second act 
comprises the last refraction through the posterior surface of the 
objective, and the several refractions taking place in the ocular 
by which the image is re-formed at the distance of clear vision with 
diverging visual angles. The first act answers plainly to the 
- function of an ordinary “magnifying glass”; while the second, 
taking all the changes comprised therein together, answers as obvi- 
