On the Estimation of Aperture. By Prof. E. Ahhe. 31 



They establish therefore a most general signification of the 

 aperture-equivalent. The value of a ( ^ w sin u) indicates the 

 number of rays which an objective can admit. The rays which 

 are admitted (in such a way that the aperture-cone is truly 

 utiUzed) are greater or smaller portions of the diffraction pencils 

 originating from the objects. The greater or smaller the admitted 

 or utilized portion of these rays, the greater or less similarity 

 hetween the image and the object. The aperture-equivalent measures, 

 consequently, the very essence of microscopical performance. It 

 measures the degree in which a given objective is competent to 

 exhibit a true, complete delineation of structures of given minute- 

 ness, and conversely the proportion of a in different objectives is 

 the exact measure of the different degree of minuteness of structural 

 details which they can reach, either with perfect similarity of the 

 image, or with any equal degree of incompleteness of the image — 

 provided, of course, the purely dioptrical conditions of the delinea- 

 tion (defining- quahties, amplification, &c.) are the same. 



Numerical aperture is thus the true and general expression of 

 the " delineating power " of the Microscope.! 



YIII. — The Indifference of the Angles qua Angles in 

 Microscopical Performance. 



The foregoing considerations establish that from all the points of 

 view which have been investigated, the angle is not the true basis 

 of comparison for objectives. It is not so either in regard to aper- 

 ture in general, as far as this idea has any relation to opening ; nor 

 is it so in regard to the number of rays (geometrically) or of the 

 quantity of light (photometrically) which is admitted to a system; 



t In order to have a brief expression for the capacity which depends on the 

 aperture-equivalent of objectives, the author uses the term " dehneating power." 

 The word " resolving-power," as applied in Englaud, is too restricted in meaning ; 

 the general idea being that it aims merely at the depiction or non-depiction of 

 striations, field-markings, and similar things. Eesolving-power io this restricted 

 sense is the particular exhibition of the general aperture-function on periodic 

 structures, whose diiFraction groups consist of a number of isolated beams (maxima 

 of second order) around the direct beam (which is the maximum of first order 

 according to Fraunhofer's terminology). 



The other term " definition," by which some microscopists convey the idea of 

 a more general optical virtue of the objectives, is better reserved — as is done in 

 Germany — for denoting the " defining quality," or the more or less perfect collec- 

 tion of all admitted rays to sharp foci. This quality — which at all events requires 

 some definite name— is based on the purely dioptrical perfection of a system (the 

 good correction of spherical and chromatic aberration, &c.). It is exhibited by 

 the distinctness of all elements in the image, large as well as minute, and has, of 

 course, nothing to do with aperture. An objective may possess the best definition, 

 but nevertheless a low delineating power, if its aperture is relatively small. Ou 

 the other hand, the actual manifestation of a great delineating power, or the utiliza- 

 tion of a great aperture, must evidently require good definition, just as it requires a 

 certain amplification. Otherwise the minuter elements whicli could be delineated 

 by means of the wide apertuie-cone, would be obliterated by the cii'cles of indis- 

 tinctness in the image, just as they would remain invisible with lack of 

 amplification. 



