354 NUMMARY or CURRENT RESEARCHES RELATING TO 



By varying the combinations of the spectra, therefore, different 

 figures of varying size and positions are produced, all of which 

 cannot of coiu'se represent the true structure. 



Not only, however, may the appearance of particular structure 

 be obliterated or created, but it may even be predicted before it has 

 been actually seen under the Microscope. If the position and relative 

 intensity of the spectra in any particular case is given, the character 

 of the resultant image can be worked out by mathematical 

 calculations solely. 



A remarkable instance of such a " jirediction " (as we may call it), 



is to be found in the case recorded by Mr. Stephenson,* where a 



mathematical student, who had never seen a diatom, worked out the 



purely mathematical result of the interference of the six spectra b-g of 



Fig. 105 (identical with angidatum) giving 



Fig. 107. the drawing copied in Fig. 107. The spe- 



^ — -„,^,.- ,, - ,_ ^--.^-,- ^ — ^ cial feature was the small markings between 



^ 1^ the hexagons, which had never been seen on 



angidatum. 



On Mr. Stephenson, however, re-examin- 

 ing a valve — stopping out the central beam, 

 I and allowing the six spectra only to pass 

 — the small markings were found actually 

 to exist, though they were so faint that they 

 had escaped observation until the result of 

 tlie mathematical deduction had shown that 

 they ought to be seen.* 

 It is therefore shown that dissimilar structures give identical 

 microscopical images when the difference of their diftractive effect is 

 removed, and conversely similar structures may give dissimilar images 

 when their diffractive images are made dissimilar. A purely dioptric 

 image produced by homofocal rays answers point for point to the 

 object on the stage, and therefore would enable a safe inference to 

 be drawn as to the actual nature of that object : the interference images 

 of minute structure, however, stand in no direct relation to the 

 nature of the object, so that the visible indications of structure in a 

 microscopical image are not always or necessarily conformable to 

 the actual nature of the object examined. 



Or as Professor Abbe puts it, minute structural details are not 

 as a rule imaged by the Microscope geometrically or dioptrically, in 

 accordance with the real nature of the object, and cannot be interpreted 

 as morphological but only as physical characters, not as images of 

 material forms, but as signs of material differences of composition of 

 the particles composing the object, so that nothing more can safely 

 be inferred from the image as presented to the eye than the presence 

 in the object of such structural peculiarities as will produce the 

 particular diffraction phenomena on which the images depend. 



The larger the number of diffracted rays admitted, the greater 

 the similarity beticeen the image and the object, a true image of the 

 real structure being produced only when all the diffracted rays from 



* f?ce this JonrnHl, i. (1878), p. 186. 



