PKOCEEDINGS OF THE SOCIETY. 161 



"Of course, if it amuses anybody to adopt the views set forth because 

 they may seem to glorify the objectives they possess by crediting them 

 with excessive apertures, I see no reason against their indulging in a 

 harmless eccentricity for their own satisfaction; but this does not 

 alter the facts ; and if they try to force others who understand perfectly 

 that no ' aperture,' call it by what name you will, can possibly admit 

 more than the whole of the emitted rays, they should not be surprised 

 to find their assertions met with some not ill-natured raillery." 



Mr, Crisp said that he should have much preferred that Mr. Shad- 

 bolt's paper were dealt with by some one from the general body of the 

 Fellows ; but, inasmuch as his censure for the dissemination of erro- 

 neous scientific views was directed both to the editorial conduct of 

 the Journal and to the " authorities " of the Society, it had been 

 thought better that he should deal with the matter. Having been 

 suffering from somewhat severe indisposition which seemed to render 

 it improbable that he should get to the meeting, he had committed 

 what he had to say to paper, and must ask the indulgence of the 

 Meeting to allow him to read from it. 



" I quite accept Mr. Shadbolt's assurance that his raillery is not ill- 

 natured, although, as will be seen in the sequel, he could not have 

 chosen a more unfortunate occasion (so far as he personally is concerned) 

 for the exercise of raillery of any kind. We have had oft-repeated 

 demonstrations of the meaning of ' numerical aperture ' ; as full an 

 explanation as could well be given has appeared in our ' Transactions,' 

 a copy being sent to every Fellow ; and yet we are presented with 

 a paper to-night in which the author describes it as ' this mysterious 

 numerical aperture of which we have no definition ' ; asserts that those 

 who employ the term ' have never, that he is aware, condescended to 

 explain in definite terms what they mean hy it ' ; treats an incidental 

 paper of Mr. Stephenson's in the second volume of the Journal, 

 which he accidentally ' stumbled over,' as a ' simple expression of Mr. 

 Stephenson^ s opinion' which enables him (Mr. Shadbolt) to see that 

 ' the mysterious numerical aperture is not an aperture at all, hut a 

 mere product of an arbitrary calculation ' ; that ' as the best of the jolce, ■ 

 it is actually based upon the much-m,aligned angular aperture,' and that 

 the ' table on the cover of the Journal is erroneous and misleading, and 

 should at once be discontinued.' 



" Incredible as it may seem, it is nevertheless a fact, admitted by 

 Mr. Shadbolt himself, that all this has been written — two months 

 after the original note of November — without his having referred 

 either to the papers of Mr. Zeiss * and Mr. Stephenson f in the first 

 volume of the Journal, or to that of Professor Abbe % in the third (not 

 yet a year old), which leaves no room for any ' mystery,' but gives 

 the exact definition which it is asserted we are without, accompanied 

 by full explanations. 



" The Council were naturally placed in a position of difficulty as 

 to this paper. Inasmuch as it was one presented to a scientific society 

 on a scientific subject, it was not unreasonable to expect that before 

 * See this Journal, i. (1878) p. 19. f lb. p. 51. % lb. iii. (1880) p. 20. 



Ser. 2.— Vol. I. M 



