44 VISION AVITH THE COMPOUND MICROSCOPE 



possible to discern them. In every case the greater ' angle ' was 

 shown to possess the greater ' resolving ' or delineating power ; and 

 this led to the important conclusion that power of ' resolution ' in a 

 lens was dependent upon ' angular aperture.' 



This, however, was at a time when only ' dry ' objectives were in 

 use ; the immersion and homogeneous systems, as we use them, were 

 unknown. 



But (as we shall subsequently see), even with objectives employed 

 only with air, the angle of the radiant pencil did not afford a true 

 comparison ; when immersion objectives were introduced objectives 

 in which water or cedar oil replaced the air between the objective 

 and the upper surface of the cover of the mounted object the 

 use of angles of aperture became in the utmost degree misleading ; 

 for different media with different refractive indices were employed, 

 and the angle of the radiant pencil was supposed not only to admit 

 of a comparison of two apertures in the same medium, but also to 

 be a standard of comparison when the media were different. It 

 was, in short, believed that an angle of 180 in air represented 

 a large excess of aperture in comparison with 96 in water and 

 82 in balsam or oil, denoting, in reality,' what was believed 

 to be the maximum aperture of any kind of objective, which 

 could not, it was held, be exceeded, but only equalled, by 180 

 in water or oil ; in other words, that a radiant pencil has exactly 

 the same value, when the angles are equal, no matter what the 

 refractive index of the medium through which the pencil might 

 be passing. 



But to a thorough physical and mathematical study of the ques- 

 tion such as that in which Professor Abbe engaged, it soon became 

 apparent that even in the same medium the only exact method of 

 comparison for objectives when the fundamental phenomena of 

 optics (which the older opticians had disregarded) were taken into 

 account was not a comparison by the angles of the radiant pencils 

 only, but a comparison by their sines; while, when the media arc 

 different, the indices of those media would be found to form an 

 essential factor in the problem ; for an angle of 1 80 in air is equal 

 to 96 in water or 82 in oil ; hence three angles might all have the 

 same number of degrees and yet denote different values, according 

 as they were in air, water, or oil. 



Thus there might be large divergence of aperture in tw T o or 

 more cases while the angle was identical, and from this the greatest 

 confusion was not only possible but was realised. 



A solution of the difficulty was (as we have indicated above) 

 discovered by Professor Abbe ; and it is to Mr. Frank Crisp's lucid 

 exposition of Abbe's elaborate monographs that the English student 

 is immensely indebted. 1 



The definition of ' aperture ' in its legitimate sense of ' opening ' 

 is shown by Abbe to be obtained when we compare the diameter of 



1 ' On the Estimation of Aperture in the Microscope ' (Abbe), Jo urn. R.M.S. 

 ser. ii. vol. i. 388 ; ' Notes on Aperture, Microscopical Vision, and the Value of wide- 

 angled Immersion Objectives,' ibid. 803 ; ' The Aperture of Microscope Objectives,' 

 English Mechanic. 



