Highly Magnified Images. By J. W. Gordon. 19 



But Lord Rayleigh's results, although eminently suggestive and 

 ■stimulating to further investigation of this profoundly interesting 

 •subject, are by no means exhaustive. The dark bar is not the 

 essential and ultimate element of the microscopic picture. The 

 black dot is even more familiar and more profoundly important to 

 the microscopist. He would like to know how small it may lie 

 and yet remain visible, and he would like to know also how its 

 appearance is modified by the laws of antipoint structure. The 

 investigation of the case of the dark bar has yielded results so 

 striking and so full of promise that he grows naturally impatient to 

 have the case of the black dot similarly examined. The dark bar has 

 only one finite dimension, the black dot two finite dimensions, and 

 therefore it offers a problem of considerably increased complexity 

 for solution. But on the other hand the solution is of higher value 

 in at least an equal measure, for whereas the dark bar is an element 

 in certain pictures only, the black dot is an element in all, and the 

 most significant element of some of the pictures which have the 

 highest significance for microscopists and for humanity. 



The problems connected with the black dot constitute thus at 

 the present time the great terra incognita of the theory of the 

 Microscope. But exploration in this region, promising as it is of 

 results of the most profound significance and of the greatest prac- 

 tical importance, will certainly miscarry if it proceeds upon a false 

 postulate, and in this connection there is a question concerning the 

 structure of the antipoint which has apparently escaped attention 

 down to the present time, but which must needs be asked and 

 answered as a preliminary to any secure advance. 



In all these investigations, thus far discussed, it has been 

 tacitly assumed that the antipoint is itself monophasal. But this 

 has never been proved and it does not stand to reason. It is quite 

 possible that the successive zones of the antipoint differ not only 

 by a gradual change of light intensity but also by a gradual change 

 of phase, and if this be so it will have a most pronounced effect 

 upon the phenomena of overlapping antipoints. The discussion of 

 this question from the theoretical standpoint involves too much 

 detail to be incorporated here, and is therefore relegated to a note.* 

 But the experimental proof may well be noticed in this place. 



Let it be assumed, then, that the structure of a given antipoint 

 involves not only a variation of light intensity according to Airy's 

 law but also a gradual change of phase resulting in a retardation 

 equal to ^A, between the centre of the false disc and its boundary. 

 Such an antipoint may be represented diagrammatically by fig. 11, 

 where the false disc of the antipoint is arbitrarily cut up into five 

 concentric zones, and the symbol cf> by its inclination indicates the 

 corresponding change of phase. It is clear at once that two such 



* See Note on p. 25 below. 



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