300 Transactions of the Society. 



YIII. — The Relation of Aperture and Poiver in the Microscope* 



By Professor Abbe, Hon. F.R.M.S. 



CBead 10th May, 1882.) 



I. — General Considerations as to Wide and Narrow Apertures. 



The question of tlie relative values of high and low apertures has 

 been much obscured by the one-sidedness with which it has been 

 treated. One party of microscopists — the " wide-aperturists " — 

 having recognized that high apertures are capable of exhibiting 

 minuter details than low apertures, conclude therefrom that all 

 microscopical work must be done with very wide apertures, and 

 that low-angled systems are worthless. Another party, relying 

 upon the fact that there are many cases in which low or moderate 

 apertures perform decidedly better than wide ones, generalize this 

 experience and deny that there can be any essential benefit in very 

 wide apertures, asserting that all observations, with the possible 

 exception of resolving diatom striae, can be done as well with low- 

 angled objectives. The premises of both these views may be said 

 to be true, but true under conditions only ; and by disregarding 

 these conditions both parties arrive at conclusions which are equally 

 remote from a proper estimation of the requirements of scientific 

 work with the Microscope. My view of the question t is based on 

 the following considerations : — 



1 . Every given degree of minuteness of microscopic detail requires 

 a given aperture in order to obtain a complete (or perfect) image, 

 i. e. an image which is a true enlarged projection of the structure, 

 exhibiting all elements in their true form and arrangement. The 

 minuter the dimensions of the elements the wider an aperture is 

 necessary — the larger these dimensions the narrower an aperture 

 is sufieient. Structures whose smallest elements are measured by 

 considerable multiples of the wave-lengths of hght are perfectly 

 dehneated with low or very moderate apertures, and their examina- 

 tion with wide apertures does not improve their recognition. On 

 the other hand, if we are dealing with objects whose dimensions (or 

 structural elements) are equal to a few wave-lengths only, even the 



* The paper (received Sth April) is written by Professor Abbe in English. 



t As some suggestion appears to have been made when the above paper 

 ■was read as to my views having undergone a change, I beg to remind my readers 

 that the views above explained are those which I have professed since 1873— the 

 date of my first paper on the subject. My advocacy of wide apertures for 

 minute objects appears to have been interpreted as an advocacy of wide apertures 

 for all purposes — a misapprehension which I am at a loss to account for, as 

 nothing I have ever said oi- written could justify any such a supposition. 



All the catalogues of Mr. Zeiss issued since 1872 give practical evidence of 

 this, as the objectives there specified (and stated to be constructed according to my 

 principles and under my direction) include no low and medium powers, except 

 with low or very moderate apertures. — E. A. 



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