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On the Estimation of Aperture in the Mieroseo])e. 

 By Professor E. Abbe, Hon. F.E.M.S.f 



{Bead 9th March, 1881.) 



In originating tlie " numerical " definition of aperture, my special 

 aim was to signalize the all-important fact, so long overlooked and 

 even denied, of the existence of an unequal equivalent of equal 

 aperture-angles in different media; to propound a simple and 

 exact expression by means of which this unequal equivalent 

 could be estimated ; and thus to afford a definition of aperture for 

 the practical comparison of objectives, which should exhibit the 

 true relation of aperture to the actual performance of the Micro- 

 scope, a relation which is entirely concealed by the angular 

 expression. 



As some little time must probably still elapse before my more 

 extensive paper " On the Function of Aperture in Microscopical 

 Vision " can be completely printed (a great part of which was laid 

 before the Meeting of the Society in June 1880 i), it has been 

 suggested to me that it may be useful if I here summarize the 

 principal considerations which bear upon the determination of the 

 aperture-equivalent in the Microscope. 



I. — Definition of Aperture hy the Ratio of "Opening" and Power. 



The general notion of "aperture," which everyone forms j^r^r 

 to attempting any distinct definition of the term, unquestionably 

 refers to the greater or less number of rays which are collected and 

 utihzed by an optical instrument— consequently, to the opening of 

 the lenses or lens-systems, and to that alone. Every definition of 

 the term must conform to this primary idea. 



In the case of a telescope-objective the absolute opening of the 

 lens is itself the proper expression of aperture ; because in the 

 depiction of distant objects by parallel (or approximately parallel) 

 rays, no other element can have any influence on the larger or 

 smaller number of rays admitted from an object at a definite dis- 

 tance. This is a matter of general agreement. 



If we consider the case of the Microscope, however, the matter 

 is not quite so simple. 



(1) In a single-leria Microscope it is evident that the number of 

 rays admitted within one meridional plane of the lens increases in 

 the proportion of its clear diameter, provided aU other circum- 

 stances are the same. For if the lens projects a distinct image to a 



t The original paper is written by Prof. Abbe in English.— Ed. 

 X See this Journal, iii. (1880) p. 735. ' 



B 



