The Relation of Aperture and Power. By Prof. E. Ahbe. 303 



events more than sufficient for showing every detail which can 

 possibly be recognized by the eye under these amplifications, and 

 therefore wider apertures are useless. In point of fact, no observer 

 will see anything more or anything better with similar objectives 

 of say 0-40 (48^) and 0-75 (96') respectively, than with the 

 narrower angles indicated above, as long as the low and medium 

 oculars are in question only. These latter apertures would require 

 for their full utilization, i. e. for convenient observation of the 

 minuter details which are within their reach, amplifications of 

 much more than 150 and 300 diameters. With well-made objectives 

 of those apertures, such figures may be realized indeed, and details 

 may be shown by means of deeper eye-pieces, which remain quite 

 invisible with the lower angled systems ; but no microscopist can 

 deny the inferior quality of the images obtained in this way if 

 compared to those of equal amplification, which are obtained with 

 these same apertures when the objectives have double the j)ower 

 and the oculars the half only. Structures of so simple a com- 

 position as diatom strias may perhaps be tolerably displayed under 

 such forced amplifications of low-power objectives, but with objects 

 of somewhat irregular and complicated structure the deterioration 

 of the image attendant upon a considerable enlargement of the 

 residuary spherical and chromatic aberrations by deep eye-jjieces, 

 becomes at once obvious even with the most finished objectives. In 

 point of fact, no experienced histologist will ever use in ordinary 

 work even an ocular amplification of the amount necessary for 

 obtaining 100 diameters from a 1-inch objective or 200 from a 

 ^-inch. He would be unwise if he troubled himself with inferior 

 images whilst good images of the amplifications required could be 

 obtained with equal, or even greater, convenience with objectives of 

 the same apertures but half the focal length. 



The above is an example of waste of aperture, or lack of useful 

 power ; waste of power and lack of aperture are exemplified by every 

 objective of excessively short focal length, e. g. J^ inch. Such a 

 lens, even if immersion, cannot be made with an aperture of much 

 greater numerical value than 1 • 0, in consequence of the technical 

 obstacles arising with such very short focal lengths. Now the limit 

 of an aperture of that amount is entirely exhausted, at all events 

 with a power of lOUO to 1200 diameters, inasmuch as nothing of 

 the real attributes of an object can be seen with that aperture under 

 a higher amplification, which could not be as well recognized under 

 the lower. A -^\j, however, will yield 1500-2000 diameters with 

 the lowest eye-pieces which are usually employed. The lowest 

 attainable power is therefore an empty power already, and every 

 useful amplification available with the aperture in question could be 

 obtained under favourable conditions and with much less inconve- 

 nience by an objective of half the power, or even less. 



