The Relation of Ajperture and Power. By Prof . E. Able. 807 



of the delineating capacity of any ajperture, the focal lengths of the 

 ohjectives must he sufficient to yield those powers which are necessary 

 for distinct vision of the least details, with no greater super-ampli- 

 fication than is indicated hy the critical values of v defined ahove. 



We shall therefore arrive at the point which is the aim of the 

 whole discussion — the determination of the proper focal lengths 

 for the various apertures — hy tracing the practical inferences from 

 this principle. 



(i) The maximum apertures of the various systems — dry, water- 

 immersion, homogeneous-immersion (for crown glass) — which are 

 fit for ordinary use, may be approximately assigned by the numbers 



a = 0-90 0=1-20 a = 1-35 



because apertures which approach the ultimate limit of any system 

 by less than about 10 per cent, cannot at all events be satisfactorily 

 used for regular scientific work. The critical values of v for these 

 apertures may be put, as has been pointed out, 



p = i V = i v = 6 



The total powers which are necessary for the proper utilization 

 of the same apertures are shown by the fourth column of the first 

 table (Vol. II. 1882, p. 463), inasmuch as no observer of normal 

 eyesight will be able to recognize distinctly details under a smaller 

 visual angle than 2' of arc. Adopting the figures of the table in 

 round numbers, we obtain therefore the normal amplification [Nl 

 which is required for the wide-angled objectives of the various 

 systems — 



480 640 720 



— = 120 - = 160 i^-^ = 120 



and consequently the focal length ( / = f^-, ) 



2-linm. = l-12th in. 1 • 56 mm. = l-16th in. 2-1 mm. = l-12th in. 



According to the views developed above, objectives of these 

 short focal lengths cannot be dispensed with, under the present 

 conditions of microscopical optics, for those lines of scientific work 

 in which it is of importance to obtain the best possible quality 

 of the image (sharpness, definition), viz. such a degree of dioptrical 

 perfection of the image as is not perceptibly inferior to the naked- 

 eye vision of real objects, even on sensitive preparations. 



As has been previously observed, higher powers than are strictly 

 necessary for exhausting the attainable apertures, are desirable, and 

 even indispensable, for many particular purposes. These may be 

 obtained satisfactorily by using higher super-amplifications with 

 the same objectives. Inasmuch as in that case the aim is merely 



