16 THE AMERICAN MONTHLY fJan. 



tical to the scratches ou the glass, and, when the proper 

 distance is found, it will be seen the vertical scratch will 

 not show the vertical wires, but will clearly show the 

 horizontT?! ones, whilst the horizontal scratch will only 

 show the vertical wires. The amount of light that passes 

 through each scratch is exactly the same. kSo it will be 

 seen it is the aperture diameter, which crosses the wires, 

 that determines the distance at which they can be re- 

 solved. We then see that the rays form the image, and 

 the aperture determines the resolution. This is the same 

 whether applied to a deep microscope objective, resolv- 

 ing a fine diatom, or to a telescope dividing a double 

 star. And whether the diffraction theory does or does 

 not apply to either of these cases, the very same numer- 

 ical law of relation between aperture and resolution 

 applies to all. 



Every microscopist knows the Abbe diffraction theory, 

 and how it took the microscopical world by storm ; and 

 also how the theory has been successively modified, as 

 error after error has been demonstrated. Abbe main- 

 tained that the image was not dioptically formed, but 

 was an interference image. This he demonstrated with 

 a fine diatom of about 93,000 striations to the inch, using 

 a lens of 1.26 N. A., and very oblique illumination, till 

 the narrow pencil he used appeared on the margin of the 

 back of the lens. On the opposite side of tLe lens ap- 

 peared a blue light, and when this was covered up every 

 vestige of markings disappeared, and only the shell of 

 the diatom was seen. By his excessive oblique light he 

 had increased the aperture of his lens, but directly his 

 narrow cone was interfered with all benefit was lost 

 again. Not so with a wide cone. I have many times 

 put a ring around the back of a lens, and allowing the 

 central and most marginal rays only to enter the micros- 

 cope, even when half of the few marginial rays were ob- 

 structed, the markings of the image yet remained. 



