614 Transactions of the Society. 



rays from different and independently vibrating points of the 

 source of light, and the corresponding undulations — being inco- 

 herent — could not possibly unite to form the regular spherical 

 wave-front demanded by the spurious disc theory. On the other 

 hand, different points in the object would receive light from the 

 same point of the source of light, and the light proceeding from 

 different parts of the object would therefore be capable of inter- 

 ference — again contrary to the requirements of the spurious disc 

 theory. 



Prof. Abbe then went on to demonstrate that the image formed 

 under these conditions of illumination could only be explained by 

 diffraction produced by the object itself, and that microscopical 

 images were thus something quite different from telescopic images. 

 The logic of Prof. Abbe's reasoning is so perfect, and his theory is 

 such an immediate and necessary consequence of the fundamental 

 properties of light according to the undulatory theory of light, 

 than which no theory, not even that of gravitation, is better 

 established, that it has only been subjected to occasional decidedly 

 futile attacks which could not but fail to impress anyone fairly 

 well acquainted with mathematical optics. But the theory was 

 put forward as an extension of theoretical optics rather than as a 

 practical explanation of the formation of ordinary microscopical 

 images, and the experiments cited in proof are subject to the same 

 reproach ; for, whilst admirably adapted to remove the slightest 

 doubt as to the accuracy of Prof. Abbe's conclusions from the 

 mind of any competent physicist, inasmuch as they show that 

 theory and experiment agree even under conditions which imply 

 the destruction of all similarity between object and image, they 

 have created no end of confusion in the minds of practical micro- 

 scop ists by the grotesque dissimilarity between object and image 

 which they proved to be possible. And thus it comes about that, 

 through the brief and purely theoretical manner in which it has 

 been put forward, the Abbe theory occupies a curious and anoma- 

 lous position. No text-book is complete without some account 

 of it, and especially of the famous experiments. Every serious 

 microscopist is, as a consequence, ever afraid of spurious images 

 comparable in dissimilarity to the original with the startling 

 nightmares included amongst those self-same experiments. And 

 yet it is peculiarly barren and forbidding ; it frightens rather than 

 guides the microscopist; it hints at mysterious possibilities of 

 deception rather than supplying definite information and well- 

 defined warnings. In other words, the Abbe theory has never 

 been presented in a form which would appeal to practical micro- 

 scopists. What the latter require to know is : — 



1. Which, if any, of the many possibilities of deception de- 

 monstrated by the experiments with the diffraction plate are likely 

 to be realised in the ordinary intelligent use of the Microscope ; 



