158 J. RHEINBERG ON THE COLLECTED PAPERS OF 



be arranged that they issue from a surface which subtends at the 

 -object a very large angle, because then all the surfaces of light, 

 differently situated and of various sizes, which are necessary 

 for successively illuminating the object in different ways, are 

 available. So, if we have a lens-system, the aperture of which 

 for the emergent rays is 180°, it is only necessary to provide a 

 ->top which will allow of pencils of any desired degree of incidence 

 and any desired width to be used out of the whole hemisphere. 

 It is this stopping apparatus, the so-called diaphragm carrier, 

 which is the essential part of the illuminator, and its arrangement, 

 together with its connection with the lens-system, is that which 

 ■constitutes the novelty in Abbe's construction. 



The most important treatises of the whole collection are 

 undoubtedly the contributions to the theory of the microscope. 

 Although in this paper reference is made almost exclusively to 

 the microscope, the result has become of no less importance for 

 all optical instruments which produce images of non-self-luminous 

 objects. The immediate object of Abbe was to provide a sound 

 theoretical basis for the construction of microscopes, which till 

 then had been almost wholly based on a system of trials, in like 

 manner as Fraunhofer had created a basis for the construction 

 of telescopes. The difficulties were incomparably greater than in 

 the case of the telescope, and practical experts on the micro- 

 scope doubted altogether the possibility of creating such a 

 theoretical basis. Thanks to the connection of Abbe with Carl 

 Zeiss, who for a number of years placed the excellent assistance 

 of his workshops at Abbe's disposal, the end strived for was, after 

 much work, attained. In the course of these studies it was found, 

 however, that it was necessary practically to give up the old 

 theory of the microscope altogether, if it is possible to speak of 

 the existence of the latter. In the first place, the then prevalent 

 conceptions as to defects in the image-aberration were not applic- 

 able to lenses of so wide an angle of aperture as high-power 

 microscope-objectives ; and secondly, it was found out that the 

 microscopic image was bound up with physical matters whose 

 seat was in the object itself, and which hitherto had been 

 neglected. 



Whereas the extension of the theory so far as it concerned the 

 aberrations of the lens-system was purely a matter of mathe- 

 matics, which could be completely solved by application of the 



