102 THE AMERICAN MONTHLY [June 



analys«is led to the conclusion that a circular aperture 

 must exceed a square aperture by say 10 per cent 

 to give equal resolution. Airy in a slightly different 

 manner calculated that the circular aperture must 

 exceed by about 20 per cent. Experimental test 

 was made using a 50-to-the-inch wire grating in 

 front of a sodium flame, and two different rectangular 

 apertures (with sides parallel to the wires) on the object- 

 glass of a telescope, measuring the distance at which the 

 object-glass (with aperture) resolved the grating. Of 

 circular apertures, four were employed in the same way. 

 The two observers differed very slightly, and the mean 

 for the four circular apertures worked out in the pro- 

 portions of 1-13, 1-09, 1-09, and 1-09 to 10 of rectangular 

 aperture. Here the grating in front of the flame is 

 regarded as self-luminous, just as in the experiment with 

 the microscope above described. 



Thus far experiment confirms the analysis ; but Dr. 

 Stoney considers (in the previous dicussion with me 

 which Lord Rayleigh alludes to) that the same methods 

 cannot be applied to microscopical resolution, on account 

 of the wider angle of the cones of rays concerned, and 

 the physical consequences of that difference. At all 

 events, the agreement of experiment with analysis as 

 regards both kinds of image, in the microscope also, is 

 remarkable. 



Calculating by the E line for white light, the ultimate 

 limit of resolution for a dry objective of utmost aperture 

 (N. A. I'O) is 96,410 lines per inch, which we suppose to 

 be attainable according to the "spectrum" theory, 

 although the aperture is circular. In 1888 Mr. E. M. 

 Nelson, whose microscopic vision is phenomenally keen, 

 just " glimsed " the strisB of A. pelhicida, mounted in 

 the arsenic medium. Including the double system, or 

 all across the valve, these striae are about 1-2500 of an 

 inch in length. He used An oiUmmersian condenser of 



