248 PROCEEDINGS OF THE SOCIETY. 



through the objective unmutilated. For the beam which emerged from 

 the radiant point in the object was, under the specified conditions, always 

 narrower than the aperture of the objective. Being such, it passed 

 through unmutilated, even when it was disposed obliquely to the axis 

 of collimation. As very clearly pointed out by Mr. Gordon, the marginal 

 zone of unoccupied objective, which Mr. Nelson has shown to be essential 

 to critical definition, allows room for the unmutilated passage of oblique 

 beams. 



Mr. G-ifford said he should like to have some further information as 

 to the oscillating screens mentioned by Mr. Gordon and exhibited in the 

 room. Mr. Gordon spoke of three oscillations per second, and he should 

 like to understand what these were and what was the amount of the 

 displacement. So far as he could judge, the effect seemed to be due not 

 only to the number of vibrations per second, but also to the distance 

 travelled by any given point on the screen at each excursion to and fro. 



Mr. C. Beck said he had the advantage of seeing this apparatus 

 working quietly a few days before, and in case there might be any diffi- 

 culty in using it to advantage in a crowded room, he should like to 

 mention that he examined a slide of angulatum with the screen in action 

 and with the screen removed, and found that the definition with the 

 screen was enormously better with a high-power eye-piece than it was 

 without the screen. It was quite possible with the oscillating screen to 

 see the hexagons clearly. He thought extreme credit was due to 

 Mr. Gordon t for thinking out such a plan, which was not obviously a 

 result of Prof. Helmholtz's paper, but was a matter upon which an 

 enormous amount of thought had been expended. He must, however, 

 protest against Mr. Gordon's elaboration of the sine condition. It 

 might be a prejudice of bis, but he had always thought it only applied 

 to images on the axis of the system, and that it was an impossibility to 

 produce an extended collinear image with wide-angled pencils as a tan- 

 gent condition was essential to this result. It had also been suggested 

 to him that it was Prof. Abbe who was responsible for the sine-law 

 before it was enunciated by Prof. Helmholtz, and if this was so it did 

 not seem quite fair to Abbe to give the whole credit to Helmholtz. 



Mr. Conrady thought this was evident from the postscript of Helm- 

 holtz' paper, of which he gave the following translation : — 



" The above paper was completely finished and ready for despatching, 

 when, at the last moment, I came across Prof. E. Abbe's ' Contributions to 

 the Theory of the Microscope and of Microscopical Vision ' as published 

 in the April number of 1874 of the ' Archiv fur mikroskopische Ana- 

 tomie.' This paper contains a preliminary collection of the results of 

 extensive investigations — partly theoretical and partly experimental — 

 which to a great extent coincide with what I have given here. The 

 theorems on the divergence of rays, on the magnitude of diffraction in 

 Microscopes, and on the brightness of their images, which form the 

 foundation of my conclusions, have been found by Prof. Abbe, but are 

 published for the present without proof. But in addition his paper 

 contains a short account of important investigations of diffraction in the 

 microscopical objects themselves with narrow illuminating pencils. The 

 special festive occasion on which this volume of the ' Annalen ' is pub- 



