On the Estimation of Aperture. By Prof. E. Abhe. 33 



rather on those of speculation and analogy. Microscopists have 

 adhered to the angles not because a peculiar benefit from a greater 

 range of obliquity at the object has been found, but because such 

 a benefit is supposed to be an inevitable necessity with regard to 

 the facts of ordinary vision. The prominences of a wall are seen 

 more distinctly in an oblique direction, or when an oblique incidence 

 of rays makes them project their shadows. It is supposed that 

 in the Microscope a similar efiect must also be connected with 

 oblique vision and with oblique incidence of the illuminating 

 beams, and that consequently a wider range of obliquity in the 

 aperture-cone must be a benefit in microscopical vision, even though 

 we may not be able to observe it directly. This opinion, moreover, 

 seems to have a strong support in the well-established fact that in 

 many objects we see minuter details with an obhque incident pencil 

 than we can see with the same lens by means of direct hght. 

 Moreover, with a wider aperture-angle there is a greater variety of 

 the directions under which delineating pencils emanate from the 

 object ; and it is supposed that the greater variety of perspective 

 aspects which seem to combine in the microscopical image must 

 tend to the exhibition of the structural details, and enhance the 

 impression of solidity in the image in a similar way as is done by 

 binocular vision, and the more so as the objects are closer to the 

 observer and the angle formed between the eyes is increased. By 

 the expression of "all-round" vision the idea is suggested that 

 in observing objects with wide-angled lenses a hundred eyes are 

 arranged around the preparation, and join their different views 

 of the same object in the microscopical image. These benefits, if 

 they exist, must, of course, depend on the angles qua angles, and 

 not on the aperture-equivalents. 



These suggestions reveal a very contented view of the peculiar 

 operations of wide apertures. But it is necessary to say that all 

 these opinions belong to the venerable relics of the past naive 

 period of microscopical science, which was characterized by an 

 unshaken conviction in the validity of the hypothesis that micro- 

 scopical vision is in all essential respects the same thing as ordi- 

 nary vision, that is, governed by the same laws, and based upon 

 the same conditions as those revealed by the optical phenomena 

 with any large bodies. The investigation into the subject of 

 microscopical vision, which the author began some years ago with 

 his friend Dr. Zeiss, and has continued ever since, at once disproved 

 this hyj)othesis by the exhibition of irreconcilable facts, and proved 

 that it is in direct contradiction to the best-established principles 

 of physical optics. 



The observations and experiments mentioned in my first paper 

 (of 1873) establish the fact that, in so far as aperture is effective in 

 microscopical vision, we have nothing hke shadow efiects or other 

 indications of solidity in the image. The advantage of obhque 



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