PROCEEDINGS OF THE SOCIETY, 169 



" If Mr. Shadbolt had been as right in his views as he has turned 

 out to be wrong, I venture to think it will be agreed that raillery 

 (even if good-natured) was a mistaken course to adopt, and in fact 

 revives the objectionable features of the old aperture controversy 

 which we hoped we had at last got rid of. I don't complain of being 

 called a ' harmless eccentric,' nor of being told that I am trying to 

 persuade the readers of the Journal of what I know (or ought to 

 know) instinctively is not true ; and so far from desiring to be above 

 criticism, I should be glad to have more criticism than I at present 

 get, that I might be better able to meet the wishes of the Fellows at 

 large ; but I think it may be fairly required that censui-e shall not be 

 persistently pressed, except as following, and not preceding, the under- 

 standing of the subject in respect of which the censure is bestowed. 

 Nelson applying his blind eye to the telescope directed upon his 

 admiral's signal, and declaring that he ' could not make it out,' may 

 have been an excellent action at its proper time and place, but cannot 

 usefully be transferred to so very different a field as we have to deal 

 with." * 



The Discussion, of which the following is a summary, subse- 

 quently took place : — 



Mr. T. Powell said that, speaking simply as an optician, he was 

 bound to say Mr. Shadbolt's Fig. 33 did not represent a practical 

 construction. 



Mr. Ingpen said that he entirely agreed with Mr. Crisp upon the 

 general question. As he had originally introduced the apertometer 

 to the Society, on the occasion when he read Mr. Zeiss's paper, 

 he should mention that that paper showed what was meant by 

 " numerical aperture," as well as the way in which the apertometer 

 was applied. All, however, that he was concerned about in the 

 present instance was to point out the explicit way in which the 

 principle of the apertometer had been explained to the Fellows. 

 The table to which Mr. Shadbolt objected was simply a table of sines. 

 If it was carried out beyond 180° it was still a table of sines, but in 



* We were asked subsequently to the meeting whether we had taken 

 Mr. Shadbolt's view to be that radiation in air and in oil were the same thing. 

 We could only reply that that was assuredly so (see ante, pp. 150 and 155). 

 Hence alone the necessity of demonstrating the " unequal equivalent of equal 

 angles in different media." We find it, nevertheless, difficult to understand how 

 this fact can seem to be paradoxical, when no one thinks it strange that a bell 

 with the same stroke will yet give out an increased sound in different media. 



This fundamental fact is, moreover, not only the answer to Mr. Shadbolt, but 

 is the key to the whole of that puzzle vihich luas knovm as the " aperture question." 

 Not being recognized, certain of the disputants wandered up and down for years 

 in the most extraordinary maze that a scientific subject was ever entangled in. 

 One of the most amusing incidents of the controversy was the way in which 

 one side puzzled not merely the opposite side, but themselves also, by such a 

 " difficulty " as the application of a small hemisphere of glass to the object. 

 This, of course, increased the amplification in the proportion of 3 : 2, so that 

 there was a higher power with the same back-combination and the same dia- 

 meter of the emergent pencil as before, and therefore increase of the aperture, 

 but the discussion went on as if there was no such amplification, or that if it 

 existed it had no influence on the problem under discussion ! 



Ser. 2.— Vol. I. N 



