696 SUMMARY OF CURRENT RESEARCHES RELATING TO 



the total system being supposed), and the same values of F, N, and u 

 will therefore indicate the same effect always. Consequently^ we 

 shall obtain exactly the same results whether we apply an |-inch 

 and T ^-inch, or instead of these any two Zow-power objectives with 

 the same ratio of the powers (2 : 3), for instance a 2-inch and a 3-inch or 

 (the simplest case) a single lens of 5 J inches, always preserving the 

 distances d = 400, 8 = 200 and the narrow diaphragm correspond- 

 ing to the linear aperture of the -^ (3 mm.). 



These considerations show the illusory character of the experi- 

 ments in question as all the observations would have had the same 

 result even if objectives had been applied not of the high powers 

 actually used but of low power or even consisting of a single lens, 

 that is under circumstances in which either no miniature at all is 

 formed, or none of the minute dimensions claimed. Nothing can be 

 inferred from such experiments in regard to high-power vision, at any 

 rate. They are in fact, experiments on low-power vision, and under 

 artificially and unnecessarily complicated conditions, a complicated 

 system, E + % composed of a number of lenses being employed for 

 obtaining no other effects than can be produced by a single lens of 

 small aperture. 



Black Annuli and Lines of Spherules and Threads. — In the same 

 Address * is a reference to the attempts made to demonstrate the 

 defective vision of objects under objectives with wide apertures, by 

 means of glass spherules and threads, the characteristic black lines 

 seen when low apertures are used nearly disappearing when the 

 aperture is increased. 



It is true that transparent spherules and threads of ■ 1 inch in 

 diameter, or many times greater than a wave-length, behave accord- 

 ing to the laws of refraction, and show annuli, &c, which are very 

 strong and black with low apertures, but are much less marked with 

 wide ones, but very minute spherules or filaments of the same shape, 

 which are only a wave-length or less in diameter, do not show the 

 black annuli and lines even with the narrowest apertures. They appear 

 either uniformly illuminated or with a gradation of light which has 

 not the least similarity to the annuli, &c, of the coarser refracting 

 spheres or cylinders, and this for the reason that such minute objects 

 do not act as refracting bodies but only by the retardation of the 

 transmitted waves. 



This shows the essential fallacy involved in the experiments in 

 question. That the black annuli of the coarse objects become in- 

 distinct with wide apertures proves only that wide apertures are not 

 the proper means for examining such coarse objects. This, however, 

 requires no proof nowadays, when it is well recognized that wide 

 apertures should not be applied for objects which are completely 

 depicted by low ones. 



The notion that minute objects which require high powers in order 

 to be seen are better seen with low apertures, is a conclusion derived 

 not from direct observation, but simply inferred from the supposed 



* pp. 158-9. 



