PROCEEDINGS OF THE SOCIETY. 565 



could give a visible image, but it did not exhibit the separation of two 

 objects less than half a wave-length apart. This paper of Lord Ray- 

 leigh's was supplementary to a much longer one, published in 1896, 

 containing an exhaustive discussion of the conditions on which resolu- 

 tion by an optical instrument depends. Abbe, in his great paper of 

 1873 on Microscopic Perception, had laid down, with the promise of a 

 future proof, the law that a grating of fine lines could not be resolved 

 by a Microscope, unless at least two of the spectra given by the grating 

 co-operated in the formation of the image ; and that the amount of 

 detail which could be shown in microscopic objects depended essentially 

 on the number of these spectra that co-operated. Lord Rayleigh's 

 paper of 1896 contained the first proof of these assertions ; the proof 

 being based on an application of Fourier's theorem. The paper con- 

 tained a large amount of matter, and some parts of it were very tough 

 reading ; but its value as a contribution to microscopic science could 

 hardly be overestimated. The supplementary paper dealt with a kindred 

 subject, and its contention was admirably illustrated by Mr. Siedentopf's 

 brilliant experiment. 



Dr. Czapski was also of opinion that the discussion of these three 

 papers might be taken together ; he said he would be glad if he could 

 do something to remove some misapprehensions which appeared to exist 

 about the Abbe theory. Lord Rayleigh had shown that the fundament 

 of the Abbe theory of microscopic vision was correct, but there seemed 

 to be an idea that the Abbe theory dealt with nothing else than with 

 the question of resolution. This would always be a matter of great 

 interest to the optician, but what in the majority of cases is of principal 

 interest for the practical microscopist is to know whether, and to what 

 extent, what they are seeing is a true representation of the real object ; 

 and from ivhat conditions as regards construction and use of the Micro- 

 scope the truthfulness of its working teas depending upon. It was 

 quite true that Prof. Abbe had not published his theory in a somewhat 

 detailed form in writing, but he had given it in his University lectures 

 since 1897-8, and he hoped Prof. Abbe would be able to publish these 

 lectures in good time. He felt quite sure that the new paper by Lord 

 Rayleigh would give the greatest pleasure to all who were able to follow 

 his mathematical demonstrations ; his developments were so clear that 

 they imbued one with that sense of beauty which only work of the very 

 highest class does. 



It was likewise with a sense of pleasure that he had followed Dr. 

 Johnstone Stoney's work in this connection, which he considered one of 

 the most valuable contributions to the subject. 



Mr. J. W. Gordon, being called upon by the Chairman, said he had 

 not intended to take any part in the discussion of this subject, as he 

 was unable to be present sufficient early to hear Lord Rayleigh's paper 

 read. He should, however, like to say by way of personal explanation, 

 that if Lord Rayleigh's paper of 1896 had been in his hands at the 

 time when he was preparing his paper on the Helmholtz theory, he 

 should certainly have made use of it. He explained that the fourth 

 volume of Lord Rayleigh's collected works, containing the reprint of 

 this paper, had only appeared in the present year, and for that reason the 



