On the Estimation of A^perture. By Prof. E. Abbe. 399 



elementary truth that a hemisphere of refractive index n amplifies 

 an object at its centre by exactly n diameters. Consequently the 

 hemisphere or extra front has changed the original objective into 

 one of ^i-times higher power or shorter focal length, hut it never- 

 theless utilizes the full opening of the loiver power. Consequently 

 the aperture is also increased in the proportion of 1 : w, whilst 

 the aperture-aw^Ze remains the same. 



If, for instance, a | of, say, 60° air-angle has the extra front of 

 crown glass, it would be converted into a ^ of 60^ &aZsam-angle, 

 utilizing the full original opening of the \. But a ^ of 60° air- 

 angle would of course have a smaller opening than a ^ ; for such an 

 objective would be obtained by reducing all elements of the former 

 I in the proportion of 3 : 2, whereby the opening for the air-angle 

 of 60° would be reduced in the same proportion. 



Thus it is shown that equal angles pertaining to different 

 media are different apertures. 



(3) The other inference from the principle of the aperture- 

 equivalent — that an immersion objective can have a greater 

 aperture than the widest-angled dry lens — also admits of a direct 

 experimental demonstration. Mr. Stephenson t has already pointed 

 out the remarkable experiment (and has given due prominence to 

 its bearing on the aperture problem), by which it is shown to every 

 one's eyes that the aperture of a wide-angled immersion glass is cut 

 down, when it is made to act as a dry lens even with an angle of nearly 

 180°. Take any immersion objective of balsam-angle exceeding the 

 double of the critical angle, and focus it on a balsam-mounted object 

 which is illuminated by any kind of immersion condenser, in such 

 a way, that the whole range of the aperture-angle is filled by the 

 incident rays. Eemove the eye-piece and place the pupil of the eye 

 at the place where the air image is projected by the objective, and 

 look down on the lens. You see a uniformly bright circle of well- 

 defined diameter which is the true cross-section of the image- 

 forming pencil emerging from the Microscope (for the eye receives 

 now all rays which have been transmitted through a small central 

 portion of the object — that portion which is conjugate to the pupil 

 — and receives no other rays). After this, focus the same objective 

 on an ordinary dry-mounted preparation (or on one which is con- 

 nested with the slide, the cover-glass being put on dry), and repeat the 

 observation ; you will now see again a well-defined circle, a cross- 

 section of the emergent pencil, but of less diameter than in the 

 former case, surrounded by a dark annulus, visible by faint diffused 

 light only. 



The diameter of the emergent pencil in both these experiments 

 may be accurately measured if the " auxiliary Microscope " of the 

 author's apertometric apparatus is used with an eye-piece micro- 



t See this Journal, ii. (1879) p. 267. 



2 B 2 



