478 PROCEEDINGS OF THE SOCIETY. 



and by then showing how the antipoints vary according to the form and 

 size of the lens aperture or diaphragms above it, the way is led to 

 showing how the whole image of an object is built up of these anti- 

 points. This seems both a sound and a simple way of looking at the 

 matter, and has the advantage of a general theory, that it includes 

 images by other optical instruments, e.g. the telescope, where the star 

 discs and rings are the antipoints of the stars. 



Though, until I had read Mr. Gordon's paper (of which, by courtesy, 

 I have had the advantage of seeing an advance proof), I should certainly 

 not have known how to express the matter in so simple a way, it is one 

 of the general results I have independently arrived at, that all false 

 diffraction lines, intercostal markings, etc., no matter whether produced 

 in viewing a diatom, a grating, a slide of bacteria, or any other object, 

 are but a portion of the " antipoints " of points in the object, and, in 

 part at least, my conclusion has been drawn from the self-same observa- 

 tion of the appearances produced by rotating the three-slit diaphragm 

 of the Abbe diffraction apparatus above the objective (fig. 86), which 

 Mr. Gordon has so ably described. The disengagement of the phantom 

 lines, the trebling of the lines at a particular moment, and the cha- 

 racteristic serrated appearance formed by the tops of the lines, cannot 

 fail to strike anyone who has made this experiment. 



It may seem strange that, whilst being able to so fully concur with 

 Mr. Gordon's views with regard to the synthesis of the microscopic 

 image being a collection of antipoints, I do not hesitate to offer the 

 opinion that the deduction which he draws as to the possibility of 

 improving Microscope objectives as described is an erroneous one, and 

 that he has partially misunderstood the Abbe diffraction theory, which 

 theory is quite compatible with his own views. Two factors seem to 

 have been overlooked which fundamentally affect the whole question. 



In company with Lord Eayleigh,* Dr. Clifford Mercer, | and Mr. 

 Lewis Wright,| Mr. Gordon has apparently not sufficiently appreciated 

 the fact that light proceeding from an illuminated point does not 

 spread equally in all directions. This, in the case of the Microscope, is 

 important. § 



To fix our ideas : — think of a single pin-hole pricked in a piece of 

 tinfoil in the focus of an objective of wide-angled aperture, and let the 

 slit be illuminated by a light source some distance behind. Then the 

 light reaching the central portion of the objective will be intense com- 

 pared to that reaching other zones of the objective, and the marginal 

 zones will probably receive practically no light whatsoever. The exact 

 distribution of the light will depend on the size of the pin-hole. 



Obviously the antipoint becomes different in this case from what it 

 would be if light of equal intensity reached all parts of the objective, 

 as is practically the case with telescopes, the angular aperture of which 



* ' The Theory of Optical Instruments, with Special Reference to the Micro- 

 scope,' by Lord Rayleigh. Published in the 'Philosophical Magazine,' August 1896. 



f ' An Experimental Study of Aperture as a Factor in Microscopic Visiou,' by 

 Dr. Clifford Mercer. 



% 'Microscopic Images and Vision,' by Mr. Lewis Wright. Published in the 

 ' Philosophical Magazine,' June 1898. 



§ Special attention has been drawn to this matter by Dr. G. J. Stoney in his 

 masterly monograph on ' Microscopic Vision,' published in the ' Philosophical 

 Magazine,' October, November, and December 1896. 



