96 



THE AMEEICAN MONTHLY 



[May, 



index, and multiplying the refractive 

 index (/ ) by the sine of half the an- 

 gular aperture {sin. /4a); i X sin. Y^a 

 = n. a. 



All objectives having the same nu- 

 merical aperture, have also the same 

 resolving power, whether they work 

 dry, in water, oil, or in any other 

 fluid. Thus a numerical aperture of 

 0.98 corresponds to an air-angle of 

 147° 29', a water-angle of 92° 24', 

 an oil-angle of 78° 20', and to a re- 

 solving power of 92,544 lines to the 

 inch. A numerical aperture of i.oo 

 corresponds to the theoretical air 

 limit, I So'*. So far as we know, the 

 highest numerical aperture yet ob- 

 tained is 1.43 for a homogeneous- 

 immersion i-12-inch by Mr. T. 

 Powell. This corresponds to an oil- 

 angle of 140°, and, according to the- 

 ory, should resolve 137,000 lines to 

 the inch. The highest angle for a 

 water-immersion is 1.32 n. a., or 

 155° for a ^-inch by Powell & Lea- 

 land, which should resolve 125,000 

 lines to the inch. 



Next month we purpose giving a 

 table of numerical apertures with 

 their corresponding angular apertures 

 and resolving power in different 

 media. 



o 



Aperture and Resolution. — 

 Mr. Gundlach's article on page 85 is 

 worthy of consideration by those who 

 believe that the celebrated ^-inch 

 objective, recently made by Bausch 

 & Lomb, is capable of resolving a 

 band of 152,000 lines to the inch. By 

 referring to a table of theoretical re- 

 solving power for different numerical 

 apertures, it will be seen that in order 

 to resolve such a band, the numerical 

 aperture must be above 1.52, which is 

 equivalent to 1 80° in oil, and this would 

 require an immersion-condenser, ac- 

 cording to Mr. Gundlach's calcula- 

 tions, with a "back aperture " of over 

 four inches in diameter. 



While writing on this subject, it 

 may be well to call attention to the 

 fact that the appearance of lines in 

 the image is no evidence that the im- 



age is produced by lines. This fact 

 seems to have been quite overlooked 

 by some writers. The dots of P. 

 angulatum may be made to appear 

 like lines, and many other cases of 

 similar nature might be cited. Again, 

 the number of lines in an image is, 

 alone, no evidence of the number on 

 a lined object under examination. 

 Prof. Abbe and Mr. Crisp, of London, 

 have given satisfactory ocular proof 

 of this fact, and also Mr. Warnock, of 

 this city, who has a plate with a 

 known number of lines in a given 

 space, with which he occasionally en- 

 tertains his friends by so adjusting 

 the light that the number of lines in 

 the image is doubled. 



In a previous article we have de- 

 manded proof of the number of lines . 

 in Mr. Fasoldt's bands, by photo- 

 graphy. But photography will repre- 

 sent what we see, and in this connec- 

 tion is only of value in so far as it 

 enables us to readily count the lines, 

 and thus compare the number in the 

 image with the number claimed by 

 the maker of the plate. It is of no 

 other use whatever. If the image 

 shows the same number that the 

 maker claims, the presumption is that 

 the claim is correct. If it shows a 

 greater or less number, it is proof 

 that the claim is not well-founded. 

 But the fact must be always borne in 

 mind that the presence of lines in a 

 photograph does not prove that the 

 object is a lined object. We do not 

 see the fine lines in a band, but we see 

 the spectral images which that band 

 produces. 



Although we have freely expressed 

 our opinion concerning the claims 

 made for the ^-inch objective of 

 Bausch & Lomb, it should be fully 

 understood that we have not intended 

 to express any opinion against the 

 excellence of the objective. On the 

 contrary, during the short time when 

 one of the objectives was in our pos- 

 session we were much pleased with its 

 resolving qualities, as manifested on 

 A. pellucida. 



