PROCEEDINGS OF THE SOCIETY. 249 



lished prevents me from retaining my paper or from entirely withdrawing 

 it. As it contains the proofs of the theorems used by both of us, not 

 yet supplied by H. Abbe, and also a few simple experiments as illus- 

 trations of the theoretical investigations, its publication may appear 

 excusable even from a scientific standpoint." 



Mr. Conrady also tried to show that Mr. Gordon had not given 

 Helmholtz' proof of the sine-law at all, but only a theorem first found by 

 Lagrange, and applying to centred optical systems generally and limited 

 to negligibly small divergence-angles, and that Helmholtz deduced the 

 sine-law for finite divergence angles from the first theorem by integra- 

 tion, which latter Mr. Gordon had not given in his paper. He further 

 insisted that the sine-law was strictly applicable only to a surface element 

 in the optical axis and was only an approximation when applied to 

 objects of considerable size. In his opinion Abbe's rendering of the 

 sine-law was the one which should appeal most to practical microscopists ; 

 for as Abbe had shown that a lens offending against the sine-law had 

 different magnifying powers for different zones of its aperture, it must 

 be quite clear that there must be intolerable confusion in the image 

 produced by such a lens, especially as he could assure those present that 

 the difference of magnifying power might amount to 10 or even 20 p.c. 

 difference between the central and marginal zones if the sine-law was 

 not taken into consideration. 



Mr. Conrady thought that the old term " spurious disk " was a 

 far better and more expressive one than the one " antipoint " which 

 Mr. Gordon wished to have substituted, seeing that the image of a 

 luminous point was not a point at all but just the spurious disk which 

 it had hitherto been called. 



Finally Mr. Conrady expressed his most emphatic doubts that the 

 mutilation of oblique beams by successive diaphragms should or could 

 under any conceivable circumstances produce the distorted spurious 

 disks near the centre of the field which Mr. Gordon had tried to demon- 

 strate, seeing that adjoining elements of structure, such as pleurosigma 

 dots, subtended angles of only a few seconds of arc. 



Dr. Lindsay Johnson, in reply to the President, said he had no 

 intention of speaking, but perhaps he might just say a word or two in 

 connection with the subject which came more within his own province, 

 for the admirable exposition of the sine theorem, the oscillating screens, 

 and diffraction points had been so ably put by Mr. Gordon that it would 

 be absurd for him to attempt to criticise. Some time ago he was trying 

 to focus upon the screen of a camera some words on a poster which were 

 too far off for him to read the letters in question, but he found that by 

 rapidly oscillating the screen it became quite easy to read the letters. 

 He sometimes had patients brought to him who were suffering from 

 what was known as Miner's nystagmus, a disease, the chief symptom of 

 which being a peculiar trembling of the eyes, induced by constantly 

 directing the eyes obliquely in a confined situation and a dim light. 

 This was nature's way of doing what Mr. Gordon had done by means 

 of his oscillating screens. Having to work with only such faint light 

 as was given by a Davy lamp, the tendency for these afflicted people was 

 to get better vision by this tremulous movement of their eyes, which by 



