Professor Abbe's Paper on the Microscope. 251 
fibre. The manifold changes in the characters of the images which 
present themselves account, to a certain extent, for the notorious 
discordance between the representations of different observers. 
In connection with the foregoing conclusions, which have an 
important bearing on the scientific application of the microscope, it 
appears, further, that the limits of “ resolving ” power are deter- 
minate for every objective and for the microscope as a whole. 
No particles can be resolved when they are situated so closely 
together that not even the first of a series of diffraction pencils 
produced by them can enter the objective simultaneously with the 
undiffracted rays. As even with immersion objectives the angular 
aperture cannot, by any possible means, be increased beyond the 
degree which would correspond, in effect, to 180° in air, it follows 
that whatever improvement may be effected in regard to serviceable 
magnifying power, the limit of resolving power cannot be stretched 
sensibly beyond the figure denoting the wave-length of violet rays 
when direct illumination is used, nor beyond half that amount when 
extreme oblique illumination is used. The last limit is, in point of 
fact, already reached by the finest lines of the Nobert plate and the 
finest known markings on diatom valves, as far as seeing is con- 
cerned. Only in the photographic copy of microscope images can 
resolution of detail be carried any farther. 
From these facts it appears that the microscope image — ex- 
cluding two cases of a similar and exceptional kind — consists, as a 
general rule, of two superimposed images, each being equally dis- 
tinct in origin and character, and also capable of being separated and 
examined apart from each other. Of these, one is a negative image, 
in which the several constituent parts of an object re-present them- 
selves geometrically, by virtue of the unequal emergence of light 
which is caused by their mass affecting unequally the transmission 
of the incident rays. This image may, for shortness sake, be called 
the “ absorption image f because partial absorption is the principal 
cause of the different amount of emergent light. It is the bearer of 
the “ defining ” power, whose amount is determined by the greater 
or less exactitude with which direct incident light is brought into 
perfect homofocal reunion. Consequently, it is always the direct 
light which “ defines,” no matter in what direction it arrives at the 
objective, i. e. whether the central or peripheral zones of the objec- 
tive receive it. But, independently of the “ absorption image," all 
such parts of the object as contain interior structure will be imaged 
a second time, and this time as a positive image, because these parts 
will appear as if self-luminous, in consequence of the diffraction 
phenomena which they cause. Now this “ diffraction image” is ma- 
nifestly the bearer of “resolving” power, that is, the discriminating 
or separating faculty of the microscope. Its development depends, 
therefore, in the first and chief place upon angular aperture, in so far 
