72 VISION WITH THE COMPOUND MICROSCOPE 



are as present to the observer as they are capable of being demon- 

 strated by calculation to the mathematician. 



Clearly, then, on these assumptions and with all other considera- 

 tions put aside, our finest homogeneous objectives of greatest aper- 

 ture inevitably fail to reveal to us the real structure of the finer 

 kinds of diatom valves. We learn that dissimilar structures will 

 give identical microscopical images when the difference of their 

 diffractive effect is removed, and conversely similar structures may 

 give dissimilar images when their diffractive images are made 

 dissimilar. A purely dioptric image answers point for point to the 

 object on the stage, and therefore enables a safe inference to be 

 drawn as to the true nature of that object ; but the diffraction or 

 interference images of minute structure stand in no direct relation 

 to the nature of the object, and are not of necessity conformable to 

 it. As Dr. Abbe has already insisted, minute structural details arc 

 not imaged by the microscope geometrically or dioptrically and can- 

 not be interpreted as images of material forms, but only 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 specific diffraction pheno- 

 mena on which the images depend. 1 



It follows, therefore, that the larger the number of diffracted rays 

 admitted into the objective the greater is the similarity between the 

 image and the object. But carefully observe 



(1) Perfect similarity between these depends always on the ad- 

 mission to, and utilisation by, the optical combination of the ivhole of 

 the diffracted rays which the structure is competent to emit. 



For the same reason the diffraction fan of isolated corpuscles or 

 Jlagella in a clear field must be exactly identical to that of equal - 

 sized holes or slits of equal shape in a dark background, and theory 

 shows that there must be a continuous and nearly uniform dissipa- 

 tion of diffracted light over the whole hemisphere, provided the 

 diameter of the object is a small fraction of the wave-length of light ; 

 and this would be so even in a medium of highest known refractive 

 index. Stick isolated objects can be seen, however minute they may 

 bz ; it is merely a question of contrast in the distribution of light, of 

 good definition in the objective, and of sensibility of the retina. 

 The diffraction theory does not put a limit to visibility with micro- 

 scopic objectives ; it simply proves, in theory and practice, what is 

 the limit of visible separation in fine striation and structure. 



In the visible flagellum of Bacterium termo only a fraction of a 

 wave-length in diameter appears as of considerably increased dia- 

 meter, even with a very wide aperture. The image seen is that of 

 another thread, the composition of which theory can be employed to 



1 See Abbe's note, p. 65. But we cannot pass over in this connection the 

 remarkable paper in the Journ. Quekett Club, ser ii. vol. iv. on the ' Sub-stage 

 Condenser,' by Mr. Nelson. His photo-micrographs illustrating the mutable diffrac- 

 tion effects of the ' small cone ' of oblique illumination, as distinct from a ' solid central 

 cone,' and the curious ' ghostly ' diffraction images of the former, as distinct from the 

 immutable diffraction images of the latter, deserve careful consideration. From 

 p. 125 of the paper this matter is carefully discussed. 



