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BY PEOFESSOK HELMHOLTZ, with a Preface by 

 LE. H. PEIPP. 



rpHE last n amber of our Proceedings contained a translation of 

 •*- Professor Abbe's article on the ''Theory of the Microscope," 

 originally published in Schultze's Archives. In that article, 

 Professor Abbe stated the general conclusions at which he had 

 arrived after a prolonged investigation of the optical laws affecting 

 the transmission of light through the lenses of the microscope. 

 These laws relate to 1. — The divergence of the rays of light 

 forming a geometrical image. 2. — The brightness of that image. 

 3. — The dispersion of colored rays, and its consequences, and 4. — The 

 diffraction of light occasioned by minute particles in the ohjects 

 placed under, (or before) the microscope. In explanation of these 

 several phenomena, a theory of the microscope was stated in general 

 terms, themathematicaldemonstrationof this theory, and its various 

 applications, being reserved for a future communication. 



Simultaneously with Professor Abbe's researches, a most 

 interesting investigation of the same subject, was completed by 

 Professor Helmholtz, and appeared in Poggendorff's Annals (1874.) 



