ABBE, AND MICROSCOPE THEORY IX GERMANY. 161 



effect (so far as it can be taken up by the microscope) is 

 made dissimilar by artificial means. This really means that 

 images of structure brought about by this process of diffraction 

 do not stand in constant relationship to the real structure of 

 the object ; rather should we say that they stand only in a 

 constant relation to the diffraction phenomenon by the help of 

 which the image is brought about." 



It is not feasible in this review to go any further into the 

 valuable contents of this treatise. It may, however, be pointed 

 out that already here the sharp division between the effect of 

 the objective acting as a simple magnifier, and of the ocular 

 apparatus acting like aitelescope, is emphasised (pp. 60 and 61) ; 

 and likewise, the importance of the chromatic difference of the 

 spherical aberration and the chromatic difference of magnification 

 for the improvement of objectives are brought into prominence, 

 so that the goal attained later on by apochromats and com- 

 pensation oculars [p. 56 (f)] is already indicated. We further 

 find the theorem given for the aplanatism of optical systems, 

 which is then proved in detail in Treatise XI. The method of 

 examining objectives by means of the test-plate, employing the 

 so-called sensitive path of rays, is likewise reviewed somewhat 

 exhaustively. 



The controversial paper against R. Altmann, who attempted 

 to demonstrate that Abbe's views were entirely fallacious, con- 

 stitutes a further contribution to the theory of microscopical 

 observation. Although Altniann's attacks were the result of 

 misconceptions and altogether incorrect hypotheses, it must be 

 acknowledged that he was one of the few microscopists who had 

 occupied themselves with the Abbe theory. Abbe's reply was, 

 in places, somewhat forcible; it, however, gives an abundance 

 of information concerning the development of the theory of 

 diffraction, and, besides this, the important supplement regarding 

 the absorption image. For purposes of emphasising the per- 

 fectly general validity of his views as to the way in which images 

 of non-self-luminous objects are brought about he writes (p. 290) : 

 " Even fence-posts will be imaged in accordance with the same 

 laws of secondary delineation, no less than bacteria or the finest 

 striae of diatoms." 



The paper further contains a lucid description of the differences 

 between Helmholtz's and Abbe's researches (pp. 290-93). 



Jourx. Q. M. C, Series II.— No. 56. 11 



