The Relation of Aperture and Power. By Prof. E. Able. 809 



With these varioiis concessions to personal customs and to par- 

 ticular purposes, the principles established here appear to be recon- 

 cilable with a rather wide latitude in their practical application. 

 The normal focal lengths for the wide-angled objectives of the three 

 systems being taken as above, we have the admissible maximum 

 values of/ (or minimum powers) : 



Dry. 



Water- Homogeneoua- 



Immersion. immersion. 



5-2 mm. = — in. 3-9mm. = -— :m. 5-2mm. = -— in. 



4-8 6*4: i'o 



And the minimum values of/ (or maximum powers) : 



2-lmm. = — in. 0-78mm. = -in. l-05mm. = — in. 



(2) As to those objectives which do not aim at the attain- 

 able maximum of delineating power, the discussion may be confined 

 to the dry lenses, because in practice the other systems are not in 

 use with much lower apertures (which is of course very prudent). 

 In order to determine now the proper gradation of the focal length 

 for the lower apertures of the dry system, the figures of v must be 

 determined which correspond to the different apertures. These 

 values, as has been pointed out above, depend on many circum- 

 stances besides the aperture — particularly on the type of construc- 

 tion and (in the higher and medium apertures) the ratio of the 

 working distance to the focal length. It will be impossible, there- 

 fore to assign values of v which could claim a general acceptance, 

 even for one standard of estimation. Any definite aperture (with 

 the exception of very low ones) will admit of a higher super-ampli- 

 fication if realized in a triple system than in a system of two lenses 

 only, and at the same time (once more with that exception) of a 

 still higher one, when the system is made with relatively short 

 working distance, the best possible constructions being always sup- 

 posed. In order to obtain any numerical data at all, I must there- 

 fore confine myself to a few particular kinds of objectives, which 

 conform to those generally adopted standards of construction which 

 may be considered as typical. With this view I have submitted to 

 a careful trial two kinds of objectives : for the medium apertures, 

 triple systems of about 0'50 aperture, with single plano-convex 

 fronts and a working distance of about one-fifth of the focal length ; 

 for the small aperture, systems composed of two compound lenses with 

 an aperture of about • 15 and a working distance of about one-third 

 of the focal length. Having compared a considerable number of 

 specimens of both types of widely different origin (all being excluded 

 which exhibited any defect of correction or technical construction), 

 I found the critical super-amplification for the first type (a = " 50) 



Ser. 2.— Vol. III. 3 I 



