A. A. C. ELIOT MERLIN ON THE MINIMUM VISIBLE. 389 



In biological investigations it is frequently required to view 

 widely scattered living particles, or germs, of various sizes down 

 to the most minute dot that can just be detected. When any 

 such particle is under observation nothing is easier than to 

 measure its dimensions accurately by the anti point method. 

 There is in my cabinet a section of fluor spar, given to me by 

 Mr. Traviss, which contains numerous liquid-filled cavities of 

 various sizes. In each cavity there is a rapidly moving bubble. 

 Some of these bubbles, under a 1/1 2th apochromat of 1*4KA., 

 appear as mere trembling specks only just visible and within the 

 grip of the objective, and there are probably others too minute 

 to be seen at all. Selecting a bubble just visible under such 

 conditions when illuminated with a large axial cone and Gifford 

 screen, if we wish to ascertain its diameter we have only to refer 

 to Mr. Nelson's papers, "A Micrometric Correction for Minute 

 Objects," * and " The Influence of the Antipoint on the Micro- 

 scopic Image shown graphically." f These papers contain all 

 the necessary explanations and data, and we find from the 

 amended table in the latter paper that with a working aperture 

 of 1*4 and screen the minimum particle visible must have a 

 diameter of 0-00000265 (l/377,358th) in., or 0'0673 /x : the photo- 

 graphic limit being with similar aperture 0-00000209 (l/478,4:69th) 

 in., or 0'5031 /x. 



Thus we can measure accurately the diameter of the smallest 

 particle or bubble visible with a given aperture. The accuracy 

 of the result depends on knowing exactly the N.A. employed at 

 extinction point, and this must in each case be found with an 

 accurate apertometer. It is advisable that the working aperture 

 should nearly equal the N.A. of the objective at the extinction 

 point, but it need not necessarily be quite full cone. When the 

 critical point is reached a very slight decrease of N.A. makes all 

 the difference between easy visibility and invisibility. Mr. 

 Nelson's first table " was computed by the formula 



5-4686 \ W.A. 

 The numerical coefficient was determined from data found by the 



* Journ. R.M.S., 1903, pp. 579-82. 



t Ibid., 1904, pp. 269-71. See also " On the Measurement of Very- 

 Minute Microscopical Objects " {Journ. R.M.S., 1909, pp. 549-50). 



