On the Estimation of A'perture. By Prof. E. Abbe. 423 



In the binocular Microscope we have, as a matter of fact, 

 a diversity of images which are depicted by pencils of different 

 obliquities at the object ; and this, it is true, is a certain hind of 

 perspective difference. As, however, the above observations show, 

 even in this case the circumstances must be, in essential respects, 

 different to those of ordinary vision. One important element of 

 solid vision with the naked eye, the perspective shortening of lines 

 and surfaces by oblique projection, is entirely lost in the Micro- 

 scope ; there remains only the other element, a relative displace- 

 ment of consecutive planes in the image, which, of course, is 

 still competent to afford sufficient indications for a stereoscopic 

 coalescence of the impressions. But the fact that these displace- 

 ments are seen in the Microscope depends upon a peculiar property 

 of microscopic amplification, which by itself is a strong contrast to 

 macroscopic vision ; for this visibility depends entirely on the fact 

 that the amplification of the depth is largely exaggerated — is 

 always the square of the linear amplification in the other direction 

 reduced in the proportion of the refractive index of the medium in 

 which the object is. 



Taking regard at the same time to the general inferences from 

 undulatory optics, referred to above, it is seen that solid vision — 

 i. e. delineation of objects liJce solid objects — is confined, even in the 

 binocular Microscope, to relatively coarse elements, the dimensions of 

 which are large multiples of the wave-length. Whenever elements 

 require, for being delineated, the utiHzation of oblique rays, that 

 is, of wide (and even moderate) apertures, the arrangement of 

 such elements within a solid space of sufficient dimensions may be 

 seen still with the characteristics of solid vision, but the elements 

 themselves are no longer depicted as solid objects of larger dimen- 

 sions would be depicted. A Pleurosigma valve may be seen as a 

 solid object, by an unconscious stereoscopic impression in the 

 binocular Microscope, or by a mental combination of the images of 

 successive planes in the monocular; but the corjmscules which 

 compose the valve can never be seen as solids, unless we could 

 obtain objectives of a numerical aperture at least = 8 or 10, and 

 could discover an imbedding substance of the same refractive index, 

 in order to gain an image by means of rays of 8 or 10 times shorter 

 wave-length. 



The very first step of every understanding of the Microscope is 

 to abandon the gratuitous assumption of our ancestors, that micro- 

 scopical vision is an imitation of macroscopical, and to become 

 familiar with the idea that it is a thing sui generis, in regard to 

 which nothing can be legitimately inferred from the optical 

 phenomena connected with bodies of large size. 



