On the Estimation of Ajoerture. By Prof. E. Abbe. 25 



V.e conceded that an objective of 120'^ air-angle aliows more than an 

 objective of 6U°, and that it does so because it admits more rays 

 than the latter. Nobody can deny, then, that a system of UO" 

 balsam-angle must have the same preponderance over the system of 

 60° air-angle, because it also admits more rays — quite apart from 

 the question, why does a lens show more if it admits more rays ? 



At the same time, however, it will not be without interest to 

 refer here to the considerations which show how the subject of 

 aperture in the Microscope becomes one of general practical 

 importance. 



It is evident that the increase of the aperture-equivalent 

 would not be the basis of progress in the performance of the 

 instrument, if there did not exist a general cause by virtue of 

 which such wide apertures are utilized. Now, it is quite certain 

 that the illumination of the objects by wider incident pencils 

 of light, does not afford such a general utilization. In the prac • 

 tical use of wide-angled objectives, we are for the most part 

 confined to an illumination by rather narrow pencils, which occupy 

 only a small portion of the aperture-cone. If we throw upon a 

 delicate object a cone of light sufficient to fill the whole aperture 

 of such a system (which of course can always be done by means 

 of a suitable illuminating apparatus) we should in most cases 

 see nothing, or next to nothing. Wide-angled glasses, as is well 

 known, show more than narrow-angled, although the direct trans- 

 mitted rays from the illuminating pencil utilize a small portion 

 only of the clear opening ; and in many cases show the more, the 

 more the incident pencil is reduced. Consequently, another reason 

 is required in order to account for the fact, that there is a general 

 benefit with the wider aperture. 



"With regard to rather coarse objects, which are perfectly de- 

 lineated by low-power and narrow-angled lenses, we find several 

 efiects which produce an angular expansion or dissipation of the 

 incident pencil above the object — particularly deflections of the 

 transmitted rays by prismatic or lenticular action of the elements. 

 These effects, however, do thot continue when we have objects with 

 minute detail of any kind. Theory and observation unite in the 

 conclusion, that spherical, cylindrical, or prismatic elements not 

 exceeding a few wave-lengths in diameter cannot yield and do not 

 yield anything like lenticular or prismatic deflections.f Whenever 



t By way of example I may refer to the phenomena of the valve of Pleurosiijiaa 

 angulatum first pointed out eight years ago. The more general oinuion among 

 microscopists is that it is composed of spherules. Inspect now through such a valve 

 a bright well-defined luminous object and observe the optical effects of the spherules 

 on the transmitted rays. Notwithstanding the minuteness of the diatom, this may 

 be readily done. With an i objective, focus a good specimen at the ceutre of 

 the field, and after having withdrawn the ocular, bring the pupil of the eye on 

 the air-image of the valve as projected by the system. You will then see the 

 illuminating flame or the clear diaphragm-hole of the condenser ihruugh the 

 valve, because no ray can reach the eye, which has not passed through that 



