DIFFRACTION IN MICROSCOPIC VISION. 83 



would be reasonable to assume, if the theory is correct, that the 

 images of the two sets of lines, as seen by the eye through the 

 microscope, would resemble each other. 



This object maybe attained by placing at the back of the object- 

 glass the diaphragm, Fig. B. It will be seen that when this is 

 placed over Fig. II, each alternate one of the spectra of the upper 

 (more widely separated) lines is cut off, so that they become identical 

 with those of the lower lines. On now replacing the eye-piece, and 

 looking at the object in the ordinary way, the appearance shown in 

 Fig. b will be presented, and it will be seen that the wider lines 

 have doubled in number, and, so far as definition is concerned, have 

 become identical with the lower lines, the only possible mode of 

 distinguishing them being by a slight decrease in light, which is 

 necessarily caused by the partly opaque silver film in reality existing 

 where the false lines appear. 



We can carry this experiment a step farther, for better illustration 

 of the effects produced, by again " tampering " with the spectra. 

 If the object had consisted of lines twice as close as those of the 

 lower set of Fig. I, the spectra would have been twice as far apart, 

 that is, at the distance of the outermost ones of Fig. II (the space 

 between them and the central beam being unoccupied). 



This state of things can be produced artificially by cutting off 

 all but the outermost spectra by the use of the diaphragm 

 (Fig. C), and when that is done, instead of the two sets of wide 

 and narrow lines, or two sets of equally distant ones (as in Figs. I 

 and b), we have the wide ones quadrupled and the others doubled 

 in number, so that the object presents the appearance of Fig. c, 

 and, as in the previous case, no one seeing them would hesitate to 

 affirm that the finer lines really existed. 



This leads us to the application of Prof. Abbe's theory in the 

 true explanation of angular aperture. 



If, in the last experiment, the lines were still closer together, the 

 spectra, now almost at the verge of the field, would have been 

 thrown outside it altogether, and we should have had nothing but 

 the central beam, with the same result as first shown, viz., the entire 

 disappearance of all lines ; in other words, the object would not be 

 " resolved" by an object-glass that would only take in the former 

 spectra. 



If, however, we had an object-glass of larger angular aperture, so 

 that the spectra thrown outside the field of view in the former case 



