192 



THE amekica:n' monthly 



[October, 



sin. u. It expresses the resolving 

 power of an objective, of whatever 

 kind it may be, dry or immersion. 

 A table of numerical apertures, with 

 the theoretical power of I'esolution 

 corresponding to them, is pviblished 

 in the microscopical journals. From 

 such a table I have selected some 

 figures to illustrate the subject. 



Resolving 



Air Water Oil Power. 



■ Angle. Angle. Angle. (Line e.) 



1.52 180° 146,528 



1.33 180° 122° 6' 128,212 



1. 00 180° 97° 31' 82° 1/ 96,400 



.94 140° 6' 89° 56' 76° 24' 90,616 



It ^vill be seen that a numerical 

 aperture of 0.94 gives a resolving 

 power equivalent to a dry objective 

 of 140° 6', angular aperture, a water 

 immersion of 89° ^6', and a homoge- 

 neous immersion of 76° 24'. The 

 highest possible numerical aperttu'e 

 in air is i, in water 1.33. but in a 

 homogeneous medium 1.52. 



The resolving power of an objec- 

 tive is calculated by the formula 



o = ^- in which / = the wave-length 



2a "^ 



of the light, and a ^= aperture. Ac- 

 cording to this formula, the number 

 of lines that can be resolved by an 

 objective of the highest possible nu- 

 merical aperture is with white light 

 (/. = 0.5269) 146.543 in an inch, 

 with blue light (/ = 0.486) 158.S45, 

 and with the actinic ravs which may 

 be used in photograph}- (0/ 0.4000//) 

 193,037. Practically the limit is con- 

 siderably lower. The homogeneous 

 immersion lenses made by Mr. Zeiss 

 do not generally have a numerical 

 aperture above i .30. 



The greatest resolution vet made, 

 so far as I am aware, with any lens 

 is the 19th band of Xobert's plate, 

 having about 1 1 2,000 lines to an inch. 

 It is probable, indeed, almost certain, 

 that this limit can be exceeded with 

 the fine objectives now made, but 

 authentic records that it has been 

 done are as yet wanting. Ambitious 

 amateurs have reported resolutions 

 of 120,000 and more, but the resvdts 

 cannot be accepted without question, 

 particularly when they are in excess 



of the theoretical limit. As an indi- 

 cation of how easily observers are 

 sometimes deceived in such work, I 

 have a photograph of A. pelhicida 

 showing spurious lines which \vere 

 supposed to be an indication of lon- 

 gitudinal markings. 



It may be incidentally remarked 

 that the resolving power is a function 

 of angular aperture, independent of 

 magnification. Sufficient magnifica- 

 tion is required to cause the mark- 

 ings resolved to subtend an angle 

 such as will enable the eye to distin- 

 guish them. Beyond this point no 

 possible increase of magnification 

 can disclose additional structural de- 

 tails. 



The question of resolution of close 

 lines or particles is entirely distinct 

 from that of the visibility of isolated 

 lines or particles. A line one mil- 

 lionth of an inch in diameter may be 

 seen, but a space of i -175000 of an 

 inch between such lines will probably 

 never be seen. 



A subject closely connected with 

 the discussion of the aperture of mi- 

 croscope objectives is the considera- 

 tion of mounting media. The op- 

 tical character of the substance in 

 which an object is examined is of 

 great importance as regards the visi- 

 bility of the object. The visibility 

 of an object is proportional to the 

 diftei'ence between the index of re- 

 fraction of the object and that of the 

 medium in which it is mounted. 

 Canada balsam has been universally 

 used, and is certainly a very useful 

 and convenient medium, but more 

 highly refracting media are now de- 

 manded, and quite recently Prof. H. 

 L. Smith, of Hobart College, has 

 published* several formulas for pi^e- 

 paring compounds with refractive 

 indices of 1.7 to 2.4. The best of 

 these is probably a solution of anti- 

 mony bromide in boro-glyceride dis- 

 solved in glycei-in. This medium 

 was first described in January of this 

 year, and is but little known. The 

 very highly refractive medium men- 



* Amer. Micr. yourn., vi, i6i, and vii, 3. 



