566 PK0CEED1NGS OF THE SOCIETY. 



paper itself had been overlooked in his preparation. Adverting to the 

 discussion "which had already taken place, he suggested that the remarks 

 of Dr. Czapski and some others who had taken part in it would bear a 

 little further elaboration. They had been discussing the subject of 

 resolution generally, and Prof. Abbe's relation to the diffraction theory 

 had been brought up. It might be of interest, therefore, if he shortly 

 reviewed the labours of the principal workers in that field. The question 

 of diffraction and its effect upon the definition of an image, was first 

 considered by Sir George Airy, who in 1834 attacked this problem : — 

 given a flat wave-front passing through a lens, what effect would diffrac- 

 tion have upon the focussing of that wave-front by the lens ? Sir 

 George Airy went no farther. He considers only the case of a simple 

 series of repeated wave-fronts and calculated the light intensity in 

 various parts of the diffraction disc — or antipoint — produced by the 

 aperture of the object-glass. The diffraction of which he took account 

 was diffraction arising from the aperture of the instrument, and the case 

 which he dealt with was the case of light issuing from a single point in 

 the object. So the matter stood until the seventies when the question 

 of diffraction was again treated by Prof. Helmholtz. He dealt with it 

 in a more comprehensive way, for treating not of the telescope but of the 

 Microscope, he had to deal with two diffraction discs, one in the object — 

 that is to say on the stage of the instrument — and the other in the image- 

 plane of the instrument, or, as the case might be, in the observer's eye. 

 But, like Sir George Airy, he discussed the diffraction caused by the 

 aperture of the objective. 



Prof. Abbe, on the other hand, spoke of diffraction produced by the 

 structure of the object, an entirely different problem having nothing to 

 do with the discussion initiated by Airy and carried on by Helmholtz. 



Then in 1896 came Lord Rayleigh s paper in which, following and 

 carrying on the work of Airy and Helmholtz, he elaborated the mathe- 

 matical theory of the diffraction which arises from the aperture of the 

 objective, and instead of the diffraction produced by one series of wave- 

 fronts only considered the reciprocal interference of two antipoints or 

 diffraction discs. 



Three such cases were separately considered in Lord Rayleigh's paper. 

 In two of them the light was assumed to be polarised in the same plane. 

 In the first case there was supposed to be no difference of phase between 

 two radiant points, and it was shown that if they were no more than 

 half a wave-length apart they would appear to coalesce in the image. 

 In the second case the two radiant points were assumed to be synchro- 

 nised in opposite phases, and in that case it was shown that there would 

 at the half wave-length interval be complete resolution. A third case 

 was that in which the two undulations were polarised at right angles to 

 one another and there was no direct interference, but the two antipoints 

 overlapped to a certain extent so giving rise to confusion and imperfect 

 resolution in the image. Lord Rayleigh discussed these three condi- 

 tions, assuming mathematical points for his theoretical resources of 

 light, but he did not enter upon the practical question of the form of 

 the light-intensity curve of the antipoint — when small surfaces were 

 substituted for the mathematical points of his hypothesis. He (the 



