406 Transactions of the Society. 



a denser medium, which are entirely lost for the image — 

 which, in fact, do not exist — when the same object is in air 

 or is observed through a film of air. This loss can never he 

 compensated for hy inct'ease of illumination, because the raya 

 which are lost are different rays, physically, to those obtained 

 by any illumination however intense in a medium like air. 



It is not surprising that a notion of aperture — the angular 

 notion — which is so incomplete and so misleading in regard to 

 the most characteristic feature of the performance of the Micro- 

 scope should have been abandoned. Adhering to the angles merely, 

 and disregarding the influence of the medium, has entirely con- 

 cealed from many microscopists even those plain truths which have 

 long ago been settled by the practical use of the instrument. 

 Inasmuch as the experience of two decades has established beyond 

 any doubt the fact, that immersion objectives readily depict minute 

 structures which are not shown by the most perfect dry lens, what- 

 ever may he the illumination, it is strange that it can still be 

 Bupposed anywhere at this day that the true advantage of the 

 immersion method cannot be anything beyond greater convenience 

 in regard to working distance and some (very moderate) gain of 

 light from the abolition of front-reflection — hecause the aperture- 

 angle of these objectives cannot be greater than with dry lenses. 



If any person, who agrees that a rational definition of aperture 

 can only be established on the basis developed here, should yet 

 dislike the expression " numerical aperture " — for any reason what- 

 ever — I certainly do not object to another term, if a hetter can be 

 found. In point of fact, I was obliged to introduce this term for 

 the mere sake of preventing confusion. It is in reality objection- 

 able, as the word " numerical " conveys the idea that a particular 

 description of aperture, among others on an equal footing, is 

 intended to be denoted. From my point of view, the aperture- 

 equivalent should be called " aperture " sans phrase, because it is 

 " aperture sa7is pilirase." 



YI. — Tlie Photometrical Equivalent of different Apertures. 



Difference of aperture must of course always correspond to a 

 difierent quantity of light admitted to the objective, provided all 

 other circumstances are equal ; and thus the question of aperture 

 has necessarily also a photometrical aspect which leads to the 

 consideration of the photometrical equivalent of difierent aper- 

 tures or aperture-angles. But it is clear that this point of view 

 does not meet the real essence of the aperture problem. The 

 brightness of the image (which of course alone will depend on the 

 photometrical equivalent) is certainly a matter of practical importance 

 in the Microscope ; but if a greater aperture signified nothing more 



