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XIII. — Note on an Early Criticism of the Abbe Theory. 

 By A. E. Conrady, F.R.A.S., F.E.M.S. 



(Bead October 17th, 1906.) 



The study of Abbe's collected papers directed my attention to a 

 contribution on microscopical theory by Dr. E. Altmann,* then 

 Prosector at the University of Leipzig, which appeared in the 

 year 1880. 



This paper deals with the optics of the human eye, of the 

 telescope, and of the photographic camera, as well as with the 

 theory of the Microscope, and represents an attempt at bringing 

 all these under one universal rule, viz. that their images are com- 

 posed of " diffusion disks," formed according to Helmholtz's theory 

 of 1873, which latter, it may be remembered, appeared immediately 

 after Abbe's famous paper of the same year. 



Helmholtz had assumed that the Microscope objective was 

 completely filled with light, and arrived at the size of the spurious 

 disk and the consequent limit of resolution on that assumption. 

 Altmann, who, as a practical microscopist, knew that this condition 

 is hardly ever fulfilled in actual practice where only a part, and 

 often a very small part, of the objective is filled with direct light, 

 tried to extend the Helmholtz theory so as to include these cases. 

 For this purpose he pointed out that the incident light is refracted, 

 reflected, and diffused by the structural elements of the object, and 

 that the light is thus spread out sufficiently to more or less com- 

 pletely fill the otherwise dark space surrounding the direct light in 

 the aperture of the objective as seen when looking down the tube. 

 He does not attempt a rigorous solution of the problem of com- 

 puting the form of the spurious disk under these conditions, i.e. 

 when the light is of different intensity in different parts of the 

 aperture ; he assumes that it does not differ very much from the 

 size and nature found by Helmholtz for a uniformly filled objective. 

 He only states (page 164 of his paper) that when, owing to regular 

 diffraction by the object — as, for example, with Pleurodynia 

 anyulatum — the light is broken up into distinct maxima, then the 

 spurious disk will be the same as if we looked at a point of light 

 through a telescope with a correspondingly perl orated screen in 

 front of it. 



Altmann's theory thus tries to account for the image under all 

 conditions on Helmholtz's basis, viz. that each point in the object 



* Zur Theorie der Bilderzeugung. Archiv fur Anatomie u. Physiologie, 

 anatomische Abteilung, 1880, pp. 111-184. 



