122 PROCEEDINGS OF THE SOCIETY. 



about antipoints not being in the same phase over their whole area, and 

 some deductions arising therefrom. Now Mr. Gordon's "antipoints" 

 are bnt another name for the false discs, or spurious discs, or diffraction 

 discs, with their attendant rings, of other writers, and that phase 

 changes occur in connection with these has been known as long ago 

 as 1835, as may be seen from Schwerd's book, " Die Beugungser- 

 scheinungen," published in that year. Mr. Gordon, it is true, refers 

 to antipoints in connection with illuminated points, as well as self- 

 luminous points, but as the factors which determine the change of 

 phase are the same in both instances, this will not affect the question. 



The analysis of the image into antipoints which overlap, and in 

 which the overlapping parts bear a phase relationship to one another, 

 which has to be taken into account, seems a perfectly legitimate pro- 

 ceeding (provided we deal with an object of no thickness, or with the 

 plane surface of an object, and know the phase and amplitude of every 

 point on that surface). But here comes the interesting part. The 

 recognition of this matter is an admission that the image of one point 

 of an object may be modified by the light which arrives at some neigh- 

 bouring, or more or less distant point of the object, because these 

 points, to begin with, bear some phase relationship to each other — one 

 of the facts assumed ab initio by the Abbe theory, which has been 

 subject to so much debate. 



Having come to recognise this, we find some unusual deductions 

 drawn therefrom. Because Lord Rayleigh has defined the conditions 

 under which an isolated luminous point, an isolated luminous line, or 

 an isolated dark bar will be visible, showing that in the latter case there 

 would be some difference, according to whether the surface on each 

 side of the bar were in a state of phase relation or not, therefore Mr. 

 Gordon jumps at the conclusion that he can now so manipulate matters 

 as to get a greater resolving power than heretofore. The factors on 

 which the resolving power depend, viz. the minimum size of the dif- 

 fraction disc or antipoint (due to the aperture of the objective) are for- 

 gotten entirely ; the fact that Lord Kayleigh dealt with isolated, not 

 periodic structure, in the investigations to which he refers, is ignored, 

 and it is likewise overlooked that Lord Rayleigh carefully pointed out 

 that the apparent width of lines or dots seen under such conditions is 

 illusory, and bears no relation to the real width ; in short, Mr. Gordon 

 falls into the mistake of confounding the problem of resolving power 

 with results analogous to those by which Dr. H. Siedentopf rendered 

 ultra-microscopic particles visible before this Society last year. 



And from this we pass to a consideration of conical wave-fronts. 

 Now a wave-front, so all text-books tell us, must satisfy three conditions. 

 It is a surface the points of which are in the same phase, the wave- 

 motion having arrived there from the same source in the same time — 

 or, in other words, the optical path-length between the source and every 

 point of the wave-front must be the same. Perhaps Mr. Gordon 

 will kindly show how the conical wave-front and the doubly conical 

 wave-front which is suggested later on comply with these conditions. 

 The fact, of course, is that since in the Microscope we have only to 

 ■deal with spherical refracting surfaces, a conical wave-front cannot 





