On the Estimation of Aperture. By Prof. E. Abbe. 405 



beams in balsam than in air ; and if the elements of the structure 

 are very minute a solid cone exceeding in balsam the angle of 82^ 

 will contain beams which do not exist at all when the same 

 structure is in air, because they cannot be originated except with 

 waves of shorter length than are in air. 



Experiments, which have been fully described, demonstrate 

 ad oculos the admission of these beams of diffracted light to 

 the Microscope and the effects which are attendant upon the 

 admission of more or less of them in regard to the microscopical 

 image. It is shown that the diffracted light emanating from the 

 objects may utilize the whole aperture of a system, although the 

 incident cone of light, if it were simply transmitted (in the absence 

 of an object), would fill only a small portion of the aperture. In 

 particular it may be seen experimentally, that with a narrow 

 illuminating pencil a wide-angled immersion glass may gather in, 

 and collect to the image, rays from an object in water or balsam, 

 which are not met with in the whole hemisphere when the object 

 is in air, and consequently can never be utilized by a dry lens 

 of any aperture-angle whatever. 



Owing to the general principle of physical optics mentioned 

 above, homologous diffraction beams from one and the same struc- 

 ture — for instance, the first, or second . . . maximum in the case 

 of a periodic structure — are the same rays physically, notwith- 

 standing their different obhquity, and diffraction beams which 

 show the same obliquity in different media are different rays 

 physically. Thus the phenomena of diffraction in the Microscope 

 afibrd another experimental proof of the validity of the inference 

 from the principle of the aperture-equivalent : that there is an 

 unequal angular distribution of radiation in different media, and 

 that a given solid cone from a radiant in balsam may contain more 

 rays than the same cone from a radiant in air, because the same 

 rays are closer together, and others are introduced. 



The above considerations lead to the following conclusions : — 



(1) The unequal equivalent of equal aperture-aw^Zes in- 

 dicates a different number of rays, as conveyed by equal 

 cones in different media consequent upon a different density 

 of radiation in such media ; and this is quite distinct from 

 any photometrical estimation of the quantify of light in these 

 cones, which may vary independently according to the illu- 

 mination of the object, the change of its surface by different 

 media, &c. 



(2) An aperture-cone exceeding twice the critical angle 

 of the medium to which it pertains, embraces a surplus 

 of rays which do not exist, physically, when the object is in 

 air, because tbey are not emitted into air. A wide-angled 

 immersion glass, therefore, may utilize rays from an object in 



