ABBE, AND MICROSCOPE THEORY IN GERMANY. 159 



known laws of dioptrics, the theory of the formation of the micro- 

 scope image had to be created quite afresh. The general results 

 are stated by Abbe in the following paragraph : 



" Not only is it possible to determine a limit of smallness at 

 which a bar is opposed to observation of microscopic structures, 

 but a general factor also comes into play which may not be left 

 out of account in the scientific use of the microscope, for it has 

 come to light that the hitherto unassailed basis for the inter- 

 pretation of microscopic observations — viz. that a microscopic 

 image free from defects represents in all cases the real composition 

 of the object — is for a whole class of observations by no means 

 properly founded." 



It is not to be gainsaid that for decades after this result was 

 published, in 1873, scarcely any notice was taken of it by physic- 

 ists or by most microscopists, although, very soon after, special 

 reference was made to it by Nageli and Schwendener, and a little 

 later on, Dippel expounded Abbe's theory very fully in his Hand- 

 book on the Jlicroscope, along with important supplementary 

 additions which he had obtained through correspondence with 

 Abbe. 



It is true that experience had taught that the size of the angle 

 of aperture was of great importance in the performance of micro- 

 scopes, and that a great increase of eye-piece magnification by no 

 no means led to the recognition of fresh detail. But these facts 

 could not be brought into accordance with the laws of geometrical 

 optics, or at all events, they led to quite absurd conclusions. Only 

 a, short time previously, Listing had proposed to use a compound 

 microscope in place of the ordinary eye-piece, in order to increase the 

 magnification.* It was this very proposal which led Helmholtz 

 to examine the question as to why it was that by this plan, which 

 looked very promising from a purely dioptrical standpoint, no 

 improvement could be attained. Helmholtz, in his investigations 

 (which he carried out under a certain assumption, that in 

 general does not hold good for the microsco23e), arrived at the 

 result that the diffraction due to the aperture of the objective 

 imposed a very definite limit. Helmholtz at that time did not 



* This proposal was made again, in all earnestness, in the year 1891, by 

 A. Lendl. That such a proposal could be published in the foremost German 

 journal on microscopy is surely a sign of how little the knowledge of 

 Abbe's papers had become known generally. 



