Highly Magnified Images. By J. W. Gordon. 3 



The theory of the formation of the image in a Microscope as at 

 present developed is to be found, so far as I am aware, in the 

 papers above enumerated. Having regard to the great interest and 

 importance of the subject, one must consider this a singularly meagre 

 list, and it is, no doubt, incomplete, since I have depended ex- 

 clusively on my own reading, which is but fragmentary. I shall 

 no doubt be asked why I have omitted to notice the many papers 

 which have been written in recent years upon the so-called 

 Abbe theory. The answer to that question is very simple, but I 

 must preface it by protesting once more against the use in this 

 connection of Professor Abbe's name. Something of discourtesy 

 is involved in thus making a distinguished man responsible for 

 an hypothesis which he never fully formulated, and has of late 

 explicitly disavowed. Lord Eayleigh has proposed the name 

 " spectrum theory " (Journ. E.M.S., 1903, p. 450) for one of its many 

 forms, but this term has not in fact become current, and if it had 

 it could hardly express the whole confused body of mutually in- 

 compatible speculations winch go under the name of the Abbe 

 theory. For tins is a case in which quot homines tot scntcntice. It 

 seems impracticable therefore to break away from the accepted 

 nomenclature, and I employ it under protest and with a sincere 

 ■apology to Professor Abbe whose name is thus misused. 



Mention has just been made of the confused variety of theories 

 which go by this generic name. But they all have one point in 

 •common. That is to say, they all set out to explain the image of the 

 object seen in the view plane of the instrument by the image of some- 

 thing else seen in another plane, usually by the image of the source 

 of light seen wherever its image may happen to fall in the tube of the 

 instrument, or by the image of a theoretical source of light seen in 

 the principal focal plane of the objective. JSTow quite apart from 

 the obvious criticism that this image of the source of light itself 

 stands in need of explanation and of the same explanation as that 

 which the image in the view plane demands, there is another and even 

 'more fatal objection to any theory which proceeds upon these lines. 

 For the calculations necessary to connect these two disconjugate 

 images one with the other cannot be made, the reason being that 

 the conditions of aplanatism in the one plane imply a want of 

 aplanatism in the other plane. Thus, if we assume an objective to 

 be so corrected as to yield a flat and aplanatic image in the view 

 plane of a flat object on the stage, that assumption implies two 

 things about the lengths of the optical paths : (1) that all paths 

 from the aperture to a given point in the image are equal, the 

 aperture being, for this purpose, taken to coincide with a plane 

 wave-front, coming to focus in that point ; and (2) that all points 

 in the object are equidistant optically from their conjugate points 

 in the image. The first of these follows immediately from the well- 

 known theorem concerning the equality of optical paths between 



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