TJie Relation of Aperture and Power. By Prof. Abbe. 469 



provided a visual angle of not less than 2' is required for the 

 smallest detail within the reach of every aperture. An increase 

 would be a matter of necessity only if a given observer should 

 consider a smaller visual angle, say 1', as sufficient for distinct 

 observation. On the other hand, it is certain that a surplus of 

 aperture is no drawback by itself, but only in regard to certain 

 practical points, which have been spoken of in the first part of 

 this paper. Among these are some which argue in favour of small 

 apertures (penetration, working-distance, insensibility of the cor- 

 rections, &c), and one which is in favour of increased aperture 

 (brightness of the image). The proper function of the theoretical 

 considerations of the foregoing paragraphs cannot therefore be to 

 establish an absolute rule, but rather to afford a proper basis for 

 finding a rational balance between the various requirements of the 

 practical use of the Microscope. 



Regarding those in which the advantage is always on the side 

 of the lower aperture, it will be obvious that all of them become 

 less and less important as lower apertures and lower powers are in 

 question. As has been pointed out in the first part, restrictions 

 of the working distance and inconvenient sensibility of the systems 

 (unsteadiness of the corrections for different thicknesses of the 

 covering glass, &c.) are not met with as long as the aperture does 

 not exceed 0*25 (about 30°) and even with somewhat greater 

 apertures, up to • 5, they do not occur in any very obnoxious 

 degree. The third element, the penetration of the Microscope, 

 has been more fully discussed on another occasion,* where it was 

 shown that with decreasing amplification the actual penetration, 

 i. e. the depth which is accessible to the eye with one focussing, is 

 more and more the result of the accommodative faculty of the eye 

 and more and more independent therefore of the aperture. With 

 very low powers, not much exceeding 50 diameters, a normal eye 

 has a perceptible amount of depth of vision without any regard to 

 the aperture. The lower the power, therefore, the more liberty is 

 left for increasing the aperture in proportion to the power without 

 any perceptible disadvantage in respect to the various points above 

 mentioned. 



There is, as I have said, one element in the performance of the 

 Microscope in which a surplus of aperture will be a benefit, viz. 

 the illuminating power, or the brightness of the image. It would, 

 however, be a great mistake to expect that this should be without 

 any limits or conditions, a3 the following considerations will 

 show : — 



So far as the illumination of the objects by transmitted light 

 is effected with light of a given intensity, and the illuminating 

 pencils utilize the whole aperture of the objective, the brightness 

 * See this Journal, i. (1881) p. 689. 



