92 THE AMERICAN MONTHLY [June 



scopist, for whom there is at issue in it a very important 

 practical question not solved by any mere mathematical 

 analysis, and scarcely yet, made clear to him. This ques- 

 tion is at the bottom of the term "spectrum theory," 

 happily applied by Lord Rayleigh to Prof. Abbe's view 

 of the matter. Upon whatever general method of math- 

 ematical resolution the Abbe theory of microscopic vision 

 ultimately rested, it was itself expounded to microscop- 

 ists and discussed by them for many years as a matter of 

 fact. It was thus and then confined to the statement 

 that microscopical "resolution," or delineation of detail, 

 was due to the union and interference (in the Fresnel 

 manner) at the focal plane, of the direct dioptric beam 

 and of at least one of the beams " diffracted " by minute 

 periodic structure, in the manner of a grating illuminated 

 by light approximating to the character of plane waves : 

 such diffracted beams with white light becoming spectra. 

 The Abbe theory further affirmed that the trustworthiness 

 of the microscopical image solely depended upon, and 

 was in dire.ct proportion to, the number of orders of these 

 spectra which were grasped by the aperture of the lens ; 

 and it explained all the advantages of greater aperture 

 in greater resolution, upon this basis alone. 



This was a definite, limited, and practical theory, easily 

 grasped ; and this alone was what came to be known as 

 the Diffraction Theory or Abbe Theory. Since, there- 

 fore, that term is now applied to the wider manner of 

 regarding microscopic vision which he has set forth, in 

 order to keep things clear or even intelligible to any 

 microscopist who has followed the past discussion, there 

 is really no other course than to find a new name for the 

 more limited and already well known Abbe theory, as 

 Lord Rayleigh has so happily done. The truth or error 

 of this "spectrum" theory, or the respective measure of 

 each in it, is a matter of very great practical importance, 

 as will appear. The wider theory is largely speculative ; 



