The Relation of Aperture and Power. By Prof. Abbe. 471 



Moreover, in microscopical observation — except under very faint 

 illumination — the iris of a sound eye always contracts to a rela- 

 tively narrow diameter, generally not more than 2 to 2-5 mm. 

 Whilst, therefore, so far as delineating power alone is concerned, 

 the largest useful aperture (for v = 2' as in Tables I. and II.) is 



— = — — -— — - or a = ■=7zt; , the maximum aperture for every am- 

 N 2(264*5) 529 



plification of the Microscope will be given by the general formula 



7 N 

 above, if d is taken = 2 • 5. We then obtain, from a = a — , 



N _ N 

 a ~ 2 * 5 ' 500" 200'" 



and conversely N = 200.a as the minimum power required to 

 enable the eye to admit all rays which emerge from the ocular. An 

 aperture of • 5 (60°) will therefore be useless in every respect (in 

 regard to light as well as delineating power) as long as it is applied 

 with powers of less than 100 diameters, and the same will be the case 

 with an aperture of 0*25 (29°) for all powers below 50 diameters. 

 Moreover, proper utilization of the rays which are admitted through 

 a given aperture, will require still further restriction. For if 

 the diameter of the pencils at their emergence from the ocular 

 should closely approach the pupils' diameter the least motion of the 

 eye will cause a stopping-off of this or that portion of the aper- 

 ture. The observer will therefore seldom utilize the full pencil, 

 and will have the awkward sensation of a continual change of the 

 illumination of the image. 



All this considered, it must be concluded that the utmost 

 amount of aperture which can be really useful under the general 

 circumstances of microscopical work, will be, for every power, 

 about twice the figures indicated by the second table. This 

 corresponds to an increase of the emergent pencils to a diameter 

 of nearly 2 mm. (1 ■ 9 mm). Every larger proportion between aper- 

 ture and power must be considered as decidedly irrational, because 

 it is not only waste of aperture in every respect, but at the same 

 time a positive disadvantage for convenient and proper observation. 



Up to the limit here assigned, I admit the benefit of increased 

 aperture, so far as the lower and lowest powers are in question, for 

 which the other requirements — as has been shown — do not impose 

 greater restrictions. In my opinion, the benefit of the increase is, 

 however, not so much the gain of light by itself, but rather the ad- 

 vantage, that narrower illuminating pencils, which do not fill up 

 the whole aperture of the objective, may be applied without incon- 

 venient reduction of light. The smaller apertures which are suffi- 

 cient for properly utilizing the delineating power of the objectives 

 would also be quite sufficient in regard to light, provided the inci- 



