694 SUMMARY OF CURRENT RESEARCHES RELATING TO 



Now what is claimed is, that if the spider-line at O is l0 ^ 00 - inch 

 in breadth, and the objective S diminishes by 100 diameters, we should 

 have at Q a miniature image of ^ owo"7 inch, and that this is depicted 

 by the objective 2. 



This is, however, pure hypothesis, without a shadow of proof that 

 the observation of miniatured images is the same thing as that of real 

 minute objects.* The only fact is, that the observer sees the object O 

 as it is delineated by the composite objective S -J- 2 at P. 



For demonstrating the fallacy involved in the assumptions in 

 question it is not necessary to concern ourselves with any theory of 

 microscopical vision — it is sufficient to rely on the ordinary principles 

 of geometrical optics.f 



In the first place it is readily shown that the appearance of the 

 supposed miniature — as it is actually seen through the Microscope — 

 has no essential connection with that miniature, the image at P, which 

 is actually and only seen, not even requiring the existence of any 

 miniature, so that the conditions of visibility of things are discussed 

 which need not even exist at all. 



Suppose the objective S under-corrected and 2 over-corrected in a 

 corresponding degree — the aberrations of both systems just balancing 

 one another — the object at will be visible at P with the same distinct- 

 ness as if S and 2 were strictly corrected ; for the total system (S + 2) 

 is so corrected. Now it is obvious that under the above assumption 

 (antagonistic correction-defects in the two systems) no image of very 

 minute dimensions can be depicted at Q at all, where we should only 

 have large circles of confusion. 



It need hardly be said that it is an obvious fallacy to infer anything 

 concerning the existence or operation of a given phenomenon from 

 observations which would not be altered in the least degree if that 

 phenomenon did not exist at all. 



The true signification of the observations in question is obtained 

 by determining the optical character of the composite system (S -f- 2). 

 This can be done by the following formulae, which give respectively 

 (a) the focal length, (b) the amplification, and (c) the aperture angle, by 

 which three things the action of every optical system is perfectly 

 determined. If two systems are identical in all these respects (and 



* Whether a real (isolated) object, such as a fine line (bright or dark) of 

 "nnroooo i ncu i s visible or not visible through a given objective is only a question 

 of light, of sensitiveness of the observer's retina, and of good correction of the 

 objective, just as in telescopic vision a single star is always visible, however 

 small its visual angle, provided it is sufficiently bright, but a double star 

 requires a certain minimum aperture of the telescope depending on the angular 

 distance apart of the stars, 



t On the principles of the Abbe theory of microscopical vision the matter 

 would stand thus : — If there were at O a coarse object of say ^ inch in diameter, 

 the miniature image would in fact be approximately the y^y part in diameter, 

 i. e. lo 1 00 inch. But this is not the case with objects and images of such minute 

 dimensions as above referred to, the miniature of the spider-line, if it could for 

 instance be photographed (the system S being absolutely free from aberrations) 

 would be found to be a rather broad band not less in diameter than half the 

 wave-length of light. 



