On the Estimation of Ajperiure. By Prof. E. Able. 27 



elements, or of transparent elements of tmeqnal refraction, vrhich 

 originate nneqtial retardations of the waves. 



Bearing in mind what has been said above fSec. Y.) in regard 

 to the different angular expansion of horaologous diffraction fans in 

 different media, and remembering that this holds good for every kind 

 of diffracting stmctnreS; whether of regular or irregular composition, 

 it will be easily seen that whilst numerical aperture indicates the 

 relation of opening and focal length, it also indicates at the same time 

 the true equivalent of different apertures in regard to the smaller 

 or greater portion of the diffracted Hght, from any given structure, 

 which an objective can admit and collect to the image. 



The practical importance of the admission of more or less 

 diffiraction beams in regard to the image which is depicted by an 

 objective has been shown already by many experiments with 

 various microscopical preparations. Experiments of this kind 

 must, of course, be confined to those structures which permit the 

 direct observation of the diffraction beams and of the influence 

 exercised by their admission or exclusion. This is the case only 

 with regular periodic structures composed of a multitude of similar 

 elements, because these alone yield hrigkt and distinct diffraction 

 spectra, composed of isolated well-defined portions of hght with 

 characteristic colours. Irregular structures, or objects composed 

 of a few elements only, produce diSraction effect also, with no less 

 angular expansion of the rays, but these do not yield distinct 

 spectra nor sufficiently bright beams for convenient observation. The 

 experimental investigation of the subject must therefore be confined 

 to that particular action of the aperture-function in the Micro- 

 scope, which is exhibited in the delineation of lines, striations, field- 

 markings, and similar regular structures, and is known as the 

 "resolving power" of objectives. The study of this particular 

 exhibition of the diffraction phenomena, and of their influence on the 

 microscopic image, affords, however, at the same time an exempli- 

 fication of the aperture function in its general features. It is 

 shown in this way that the admission or exclusion of different 

 portions of the difiraction pencU emanating from an object can 

 have a real influence on the image which is delineated, because 

 it has such influence, as a matter of feet, with certain kinds of 

 objects. 



As, therefore, ^q 'practical value of increase of aperture is the 

 increased admission of diffracted hght from the objects, it is a 

 matter of special importance, for the due appreciation of aperture 

 from this practical point of view, to have a clear answer to the 

 question, Wliat is the benefit of this increased admission in the 

 general performance of the Microscope, apart from the delineation 

 of lines and field-markings in diatoms and similar objects, which 

 may be said to be of interest only to a few ? The definitive 

 outcome of the author's investigation into this subject is fully 



