Professor Abbe's Paper on the Microscope. 249 
Now to anyone who clearly realizes in his own mind what are 
the assumptions upon which a similitude between an object and its 
optical image is commonly accepted, the foregoing facts must 
suffice to lead to the conclusion that, under the circumstances above 
indicated, such acceptance is a purely arbitrary supposition. As a 
positive instance of the contrary stands the conclusion to which 
experiments lead by rigorous deduction, namely, that different 
structures always yield the same microscopic images as soon as the 
difference of diffraction effect connected with them is artificially 
removed from the action of the microscope ; and that similar 
structures as constantly yield different images when the diffractive 
effect taking place in the microscope is artificially rendered dis- 
similar. In other ivords, the images of structure arising from the 
operation of the diffractive process stand in no constant relation 
with the real constitution of the objects causing them, but rather 
with the diffraction phenomena themselves, which are the true 
causes of their formation. As this is not the place to enter into a 
physical exposition of such phenomena, it may suffice to say in brief, 
that the conclusions here deduced from facts won by direct observa- 
tion, are fully substantiated by the theory of undulation of light, 
which shows not only why microscopic structural detail is not imaged 
according to dioptric law, but also how a different process of image 
formation is actually brought about. It can be shown that the 
images of the illuminating surface, which appear in the upper 
focal plane of the objective (the direct image and the diffraction 
images), must each represent, at the point of correspondence, equal 
oscillation phases when each single colour is examined separately. 
The delineation of structure seen in the field of the microscope is 
in all its characters, — those which are conformable with the real 
constitution of the object as well as those which are not so — nothing 
more than the result of this process of interference occurring where 
all the image-forming rays encounter each other. The relation 
existing between the linear distances from the axis of the micro- 
scope of constituent elements of the aperture image, and the 
various inclination of rays entering the objective, taken together 
with the dioptric analysis of the microscope, afford all the data 
necessary for complete demonstration of the above positions. From 
them may be deduced that in an achromatic objective the inter- 
ference images, for all colours, coincide, and yield as a total effect 
achromatism, thus differing from all other known interference 
phenomena. 
The final result of these researches may be thus stated : 
Everything visible in the microscope picture which is not 
accounted for by the simple “ absorption image,” but for which the 
co-operation of groups of diffracted rays is needed — in fact all 
minute structural detail — is, as a rule, not imaged geometrically, 
