790 Transactions of the Society. 



XV. — The Relation of Aperture and Power in the Microscope 



{continued)* 



By Professor E. Abbe, Hon. F.R.M.S. 



{Read lith June, 1882.) 

 11. — Tlie Rational Balance of Aperture and Power {continued). 



(ii.) Division of the entire Poiver of the Microscope between 

 Ocular and Objective. 



Having determined — as definitely as the circumstances will permit 

 — what total power of the Microscope is necessary or useful for the 

 utilization of a given aperture, the next question can now be dis- 

 cussed, which is : What power of the objective is required for the 

 same purpose ? 



From the principles on which the former discussion was based, 

 this question has raised a distinct issue. If we find that with an 

 aperture of • 50 (60^) a total amplification of 2()5 diameters is 

 required, in order to display the smallest dimensions which are 

 within its reach under a visual angle of 2', it follows that for the 

 actual effectiveness of that amplification the microscope-system 

 (objective and ocular combined), must so collect the rays in the 

 ultimate image that the image-points shall have sufficient sharpness 

 for the distinct exhibition of details of that small visual angle. The 

 question will therefore be : What composition of the Microscope 

 must be used, and in particular, what power or focal length of the 

 objective is necessary and sufficient, in order to obtain these 265 

 diameters without an obvious loss of sharpness of the image ? If 

 we are able to determine that focal length, we have at the same 

 time assigned the proper focal length for the aperture of "50. 



1. The discussion of this subject is based on the following optical 

 principles : — 



(1) If we could obtain lenses or systems, of an ideal per- 

 fection, collecting all rays to mathematically sharp points without 

 any aberrations, the composition of the whole Microscope would 

 be absolutely unimportant. If the effect of the aberrations is dis- 

 regarded, all functions of the IMicroscope depend solely on the 

 aperture and the focal length of the entire system, and are quite 

 independent of the number and arrangement of its constituent 

 elements. Upon this assumption a given short focal length of the 

 whole Microscope, which means high linear amplification of the 

 ultimate image (which is the quotient of the distance of vision by 



* Tlie paper (received 14th June, 1882) is written by Professor Abbe in 

 Englisli. Tlio corrected jiroof was not received from him in time for insertion in 

 the last number of tiie Journal. 



