646 Transactions of the Society. 



is, in the image, represented by a more or less modified spurious 

 disk, and that the image, therefore, is built up of a continuity of 

 overlapping spurious disks, precisely as the telescopic image of the 

 sun, a star-cluster, or a nebula. 



For the Abbe theory Altmann has little but smiles and sneers ; 

 it is, however, only just to remember that he had only the exceed- 

 ingly brief and fragmentary account of it in the paper of 1873 to 

 base his opinion upon ; and when this is borne in mind, there 

 seems some excuse for Altmann' s verdict that Abbe had based very 

 broad claims on very little evidence. He raises various objections, 

 as, for instance, that even where there is diffraction by the object 

 (which in general he denies), it is only necessary to use a full cone 

 of illumination in order to smother the diffraction spectra in a 

 flood of direct light ; and tries to clinch matters by describing (on 

 page 165 of his paper) an experiment with the aerial image of a 

 grating which, he considers self-evident, cannot produce any dif- 

 fraction spectra, and which, nevertheless, forms a perfect image 

 when viewed through the Microscope. At the present time the 

 chief interest in this paper of Dr. Altmann lies in the fact that it 

 drew an immediate and characteristically vigorous reply from 

 Professor Abbe.* 



Abbe here departed from the purely experimental style of his 

 first communication, and for the first (and, unfortunately, last) 

 time insisted on the difference between self-luminous objects and 

 those illuminated from a separate source of light, and pointed out 

 how this difference was the real distinction between his theory and 

 that of Helmholtz. 



For the first time it was made clear to those acquainted with 

 the undulatory theory of light, that the " diffraction theory " was a 

 necessary and inevitable deduction from the fundamental principles 

 of the accepted theory of light. 



Only light from the same luminous point is in that condition 

 of a permanent phase-relation which must be fulfilled if any regular 

 co-operation between the several portions of light passing through 

 an objective is to be possible. Before applying the theory of 

 Helmholtz — and, still more, elaborations of it — it must therefore be 

 proved that the light emanating from any one point in the object 

 is in this condition. This proof is impossible, for an examination 

 of the conditions prevailing in the Microscope shows that an 

 entirely opposite state of affairs prevails : different points in the 

 object receive light from the same point in the necessarily more or 

 less distant source of light, whilst any one point in the object 

 receives light from different luminous points, which is therefore 

 incapable of co-operating in the manner assumed by Helmholtz, 

 and before him by Airy. 



* Uber die Grenzen der geometrischen Optik : Sitzungsberichte der Jeuaischen 

 Gesellschaft fur Medizin und Naturwissenschaft, 1880, pp. 71-109. 



