PROCEEDINGS OF THE SOCIETY. 567 



speaker) supposed that in the supplementary paper read that evening- 

 Lord Rayleigh had carried the investigation somewhat further, and had 

 dealt with the light from small radiant surfaces. In the 189G paper 

 they had a demonstration of what an antipoint was, but not of what an 

 image built up of antipoints would be like. 



Except for Helmholtz' paper, so far as he knew, the formation of the 

 images by means of antipoints had not been investigated. Working side 

 by side with Lord Rayleigh there had been Dr. Johnstone Stoney, who 

 had laboured to produce a comprehensive theory in which the diffraction 

 arising from the aperture of the instrument and that arising from the 

 structure of the object on the stage should both be taken into account. 

 Such a scheme presented great difficulties, for the amount of the diffrac- 

 tion arising on the stage depended upon the curvature of the wave-fronts 

 at that point. 



If they used plane wave-fronts to illuminate the object they got 

 maximum diffraction, but if they used curved fronts they got more or 

 less diffraction according to the radius of curvature of the incident wave- 

 fronts, and it would follow that they could get rid of this diffraction 

 altogether by focussing the source of light upon the object. Dr. 

 Johnstone Stoney met this objection by contending that they could always 

 resolve.the incident light, whatever its origin, into plane wave-fronts, and 

 his very elaborate theory rests upon that postulate. 



It was therefore quite true to say that all these investigators deal 

 with the phenomena of diffraction, but it must be remembered when that 

 was said that there are two entirely distinct and independent sources of 

 diffracted light in the Microscope, — the structure of the object, and the 

 aperture of the objective — and that the investigation of the phenomena 

 arising from the one source throws no light upon the phenomena arising 

 from the other source. It is therefore of capital importance to keep the 

 two classes of phenomena distinct in our minds and in our discussions. 



Mr. Rheinberg said he had listened to Mr. Gordon's remarks with 

 great interest ; he had given them a record of what different writers had 

 done, but he appeared to think that each had done certain things which 

 did not altogether accord with the results obtained by the others. If, 

 however, they were looked at in a certain way he thought there would 

 be no difficulty in seeing that they came into agreement. They all 

 started with the diffraction by the instrument itself, and this would 

 necessarily be the very smallest amount it was possible to obtain. 

 Diffractive effects in the image, which might occur when an ordinary 

 object was viewed, might exceed but could not he less in amount than that 

 produced by the instrument pure and simple. What that minimum 

 was, was excellently shown in the case of the ultra-microscopic particles 

 as exhibited in Dr. Siedentopfs demonstration. Mr. Gordon had, he 

 thought, mentioned that Prof. Abbe had neglected the diffraction by 

 the instrument altogether, but this was certainly not the case, for it was 

 dealt with first of all in the book on the Microscope published by Dr. A. 

 Zimmermann, to which reference had formerly been made. It had been 

 most interesting to hear the various papers that evening, and to find 

 that though all had been worked out on different lines, yet they all 

 worked to the same conclusion, and that in this there appeared to be 



