The Relation of Aperture and Power. By Prof. Albe. 467 



latum, and other diatoms, taken with the best wide-angled lenses 

 under amplifications of about 3000 and more diameters. Now 

 the Amphipleura of these photographs, taken with apertures of 

 1*2-1*3, is the true equivalent of the PI. angulatum of 1000 

 diameters with only ' 6 aperture. It shows the same determinate 

 and energetic striation with equaUij broad ribs and interspaces, 

 which are always seen when the closeness of the structural elements 

 is not far from the limit of separation for the aperture in use. 

 Theory and experiment show that these details of the image 

 have no relation to the real composition of the object, that 

 they exhibit nothing more than typical pictures of rows of 

 elements of any shape and magnitude whatever, when their 

 closeness approaches the value of S corresponding to the aper- 

 ture. It would be contrary to all analogy to expect that in 

 Amphipleura alone we should have real bands or ridges, and 

 not, as in other diatoms, distinct elements of double periodic 

 arrangement with different closeness in different directions. This 

 admitted, the enhanced expressiveness and determinateness of the 

 image with the higher power is just the opposite of enhanced 

 recognition, because the eye is caught by features which are 

 entirely foreign to the object. If I wanted to show to any one 

 what the Microscope has really revealed of the structure of 

 diatoms, I should request him to inspect the said photographs at a 

 distance of three or four feet, in order to restore the smaller visual 

 angle corresponding to an amplification of about 1000 diameters. 

 What he is able to recognize under these circumstances are the 

 vestiges of true structure — indefinite, perhaps, but not falsified; 

 what he sees more under greater visual angle is nothing but the 

 display of dissimilarity of object and image arising from the lack 

 of aperture. The 3000 or 4000 diameters could improve the 

 recognition of the real structure, only if they were obtained by 

 apertures of 3 * or 4 • 0.* 



It is by no means otherwise with the very minute objects of 

 entirely different lines of research. If the image of a bacterium 

 or a very delicate flagellum is exhibited under a power of 3000 

 diameters with more distinctness, as regards shape and magnitude, 

 than is possible with one of 1000, the surplus will always be a 

 surplus of mere optical dissimilarity. 



The effects of excess of power in the Microscope may be illus- 

 trated by similar facts of astronomical experience. Astronomers 



* The figures of the tables should not, however, be applied directly to 

 photographic performance, but the powers indicated for each aperture should be 

 increased in the proportion of 0*41 : 0-55 (3 : 4 approximately), and the aperture 

 corresponding to a given power diminished in the same proportion. Owing to the 

 shorter wave-length of the rays of maximum chemical intensity, the value of 8 

 for every aperture is proportionately smaller in photographic than in ocular 

 observation. 



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