On the Estimation of Aperture. By Prof. E. Ahhe. 413 



the details of a structure are so minute, that wide-angled (or even 

 moderate angled) systems are required for its delineation, there 

 remains only one reason which accounts for a radiation of the object 

 in other directions than those embraced within the incident pencil, 

 and that is the diffraction of the light by the structure. By virtue 

 of the diffraction effect attendant upon the transmission or reflec- 

 tion of light by any structure (whatever may be its composition) 

 the incident beams are scattered over a larger or smaller part of 

 the hemisphere above the object ; and thus a radiation is obtained 

 which, in the case of very minute elements, may fill the whole hemi- 

 sphere (even in a dense medium), and utilize any wide aperture. 

 Owing to the diffraction effect, microscopical objects radiate, in a 

 certain sense, in the manner of self-luminous bodies, and this the 

 more so as their elements become smaller and smaller. What is 

 generally (and erroneously) called " diffused " radiation of micro- 

 scopic objects is — with the exception probably of a few particular 

 cases which have no practical importance for the Microscope — 

 nothing else but radiation by means of diffraction beams expanding 

 the incident pencils above the object. 



From this point of view a proper estimation of the actual 

 importance of aperture in the Microscope, and of the 'practical 

 value of a correct definition of apertures, is entirely based upon the 

 consideration of the phenomena of diffraction in the Microscope. 

 All aperture-equivalents or aperture-angles beyond a very moderate 

 extent would be meaningless and dead things, if there did not 

 exist a general physical process by virtue of which the objects 

 emit those rays which can be admitted by wide apertures. At the 

 same time it is evident that the original idea of aperture as the 

 capacity of an objective of gathering-in rays from the objects, means 

 but one function practically, that of gathering-in a greater or less 

 portion of the diffracted rays scattered by the objects. There 

 cannot be any other general benefit of large apertures, because there 

 is no other general cause of a dissipation of light by the objects 

 without which the utilization of wide-aperture cones would not be 

 possible. Diffraction, however, is universal whenever the strictly 

 uniform propagation of luminous waves (transmitted or reflected) 

 is disturbed by the interposition either of opaque or semi-opaque 



portion of the vnlve which is optically conjugate to the area of the pupil. 

 Provided the mid-rib is not just projected on the eye, the flame or the diaphragm- 

 hole is seen as well defined as if through a plate of glass ; you do not see the least 

 deflected or scattered light except the bright diffraction spectra arranged around 

 the direct image. 



Whilst it is not my opinion that the an/M^a^um- valve is composed of spherules, 

 yet even if such should exist, they would not have a different effect. We may 

 infer from observation and from theory, that very minute spherules, or cylindrical 

 threads, have entirely lost the characters of refract'tirj bodies, which are sn 

 distinctly exhibited by air-bubVjles, fat-drops, &c., of larger size. The residual 

 effect of such objects is solely retardation or acceleration of the transmitted 

 waves, by virtue of the difference of tlieir own refractive index and that of the 

 surroimding medium ; and this is one among the conditions of diffrartidu. 



Ser. 2.— YOL. I. 2 F 



