22C NOTES AND MEMORANDA. 



to which I particularly wish to direct attention is the limit 

 of visibility depending on the constitution of li^ht, beyond 

 which light itself is of too coarse a nature to allow of our 

 seeing objects distinctly defined. This question has been 

 treated of in an admirable manner by Helmholtz in the 

 jubilee volume of ' PoggendorfTs Annalen ' (1874, p. 573). 

 The conclusion to which he arrives is that the limit depends 

 on the confusion in the image due to the bright interference 

 fringes overlapping the dark outlines of the object. This 

 limit varies directly as the wave-length of the light, and in- 

 versely as the sine of half the angle of the aperture of the 

 object-glass when illuminated by means of a condenser of 

 equal aperture. According to this principle the limit for 

 dry object glasses of 60° aperture is, roughly speaking, 

 about equal to the wave-length of the light, and for the 

 largest possible aperture equal to ^ the wave-length. In the 

 case of immersion object glasses of the same aperture, the 

 limit is about f of that for dry. 



On comparing this theory with the results of observation, 

 the agreement is very striking. It indicates exactly the same 

 law for the increased defining powers of lenses of large 

 aperture, as has been determined by experiment, and gives 

 for the theoretical limit of distinct visibility g o-^o^h part 

 of an inch, which is exactly the same as the mean of the 

 experimental determination of a number of the most skilful 

 microscopists. It also shows why in the case of lines at 

 equal intervals, like Nobert's bands or the markings on Dia- 

 tomacese, it is possible so to manage the illumination that 

 the dark fringes of interference may coincide with the true 

 lines of structure, and give rise to good definition, even be- 

 yond the normal limit, and also agrees with the fact that lines 

 less than -ro-oV"o-oth of an inch apart can be photographed, 

 though seen with extreme difficulty, if indeed truly resolved, 

 except under very peculiar and exceptional conditions ; since 

 the waves of light at the blue end of the spectrum, which 

 are concerned in photography, are short enough to give good 

 definition of lines so near together that the interference 

 fringes due to the longer waves at the red end would give an 

 indistinct image. Taking everything into consideration, the 

 agreement between observation and the theory is so close as 

 to make it extremely probable, and to justify the conclusion 

 that the normal limit of distinct visibility with the most 

 perfect microscope is \ of the wave-length of the light. If 

 so, we must conclude that, even with the very best lenses, 

 except under special conditions, light itself is of too coarse 

 a nature to enable us to define objects less than ^^yVir th or 



