197 
Professor Abbe's Paper on the Microscope. 
amplification, so that every detail that can he possibly delineated by 
an objective in its “ virtual ” image is certainly accessible to any eye 
possessing normal vision, when the tube and ocular, taken together, 
represent a telescopic magnifying power of eight times. Even this 
performance is only reached in the case of low and middle power 
objectives ; for when the focal length is less than i inch, the rela- 
tive perfection of construction perceptibly fails, on account of the 
rapidly accumulating technical difficulties, and there certainly does 
not exist an objective of inch focus whose optical capacity 
exceeds a fivefold angular amplification. 
From all this may be gathered how utterly futile any efforts to 
obtain disproportionately high amplifications by means of specially 
constructed eye-pieces must prove ; and, as regards any expectation 
of exalting the performance of the instrument by further shortening 
of the focal length of the objective, there stands in the way one 
objection, which, in the present state of our knowledge, is absolute 
and insuperable — namely, that the imperfections resulting from 
residual aberrations and defective technical manipulation increase 
with every addition of magnifying power. This form of diffraction, 
likewise, turns the image of each point in an object into a dispersive 
circle of greater or less diameter ; but the resulting diminution of 
optical capacity, while scarcely noticeable in objectives of moderate 
power, compared with the effect of residual aberrations, becomes 
very serious with the higher powers. Assuming the magnitude of 
angle of aperture 180° in air, which cannot be exceeded beyond a 
few degrees, even by immersion systems, we find, e. g. for an 
amplification of 1000, the diameter = sV inch, and for amplifica- 
tion of 5000 = 2 “§w inch, without reference to the mode in which 
the amplification is obtained (through objective and ocular). And 
if we would know what conditions are involved in such amplifica- 
tions — as, for instance, 5000 fold — we have only to make a 
puncture of Aso inch diameter with a needle in a card or piece of 
tinfoil, and through this opening to look at some brightly illumi- 
nated object, which has well-defined edges (e. g. a candle flame), and 
we shall have before our eye of what must be the appearance of the 
outlines of a microscopic object magnified 5000 times, even if the 
microscope itself were absolutely perfect, the diffractive effect 
excepted.* 
Taking all these circumstances into consideration, it must be 
concluded that no material exaltation of the absolute power of the 
microscope, beyond what is attainable at present with objectives of 
aV inch focal length, is to be expected in the future, either by 
shortening of focus or by further improvement of construction. 
And as there exists at this moment no microscope whose serviceable 
* Due to smallness of aperture of a minute lens, and to be carefully distin- 
guished from the diffraction which is caused by the structure of objects. 
P 2 
