162 PROCEEDINGS OF THE SOCIETY. 



the author censured particular views as ' misleading and erroneous ' 

 (with other similar expressions), he would at least have ascertained 

 what those views were, especially as they were to be found in the 

 Journal of the Society for the current year. As it was admitted 

 that this had not been done, the Council would have been amply 

 justified in declining to receive the paper. 



" At the previous meeting, however, and in subsequent com- 

 munications, Mr. Shadbolt (who was President of the Society in 

 1856) has expressed so strong a feeling that a desire existed on 

 the part of some of the ' authorities ' to suppress his views and to 

 stifle discussion upon them, in the interest of ' numerical aperturists,' 

 that the Council felt they had no alternative but to accede to his 

 request and accept the paper, so that there could be no question as to 

 his having had the fullest oi:)portunity of recording his views. 



" Apertm-e and Angular Aperture. — There are points in Mr. Shad- 

 bolt's paper with which not only I, but every other Fellow of the 

 Society, will agree, and that is (1) that ' aperture ' is properly defined 

 as 'opening'; (2) that no lens can have an 'angular aperture' in 

 excess of 180° ; and (3) that a dry lens can have as large an ' angular 

 aperture ' as an immersion lens. If it is possible that any one has 

 expressed a contrary opinion on these propositions, I may venture to 

 say that he cannot have been a Fellow of this Society. 



" The points on which we disagree, however, are (1) that there 

 is no difference of aperture between dry and immersion lenses, — 

 that no lens can have an aperture of any kind which exceeds that of 

 180° angular in air ; and (2) that numerical aperture is ' misleading.' 



" Mr. Shadbolt considers that he has demonstrated the latter points 

 ' beyond dispute.' Now we know that an ' aperture controversy ' was 

 carried on for many years on this very question, and that those who 

 originally supported the view now taken by Mr. Shadbolt ultimately 

 admitted their error (or declared it was a mistake to suppose they 

 ever held it). How is it that the opposite result was not arrived at 

 if the whole matter can be explained in the extremely simple manner 

 in which Mr. Shadbolt supposes it to be explained ? 



" The answer is, that there is one fundamental fallacy which 

 underlies the whole of Mr. Shadbolt's paper, viz. the supposition 

 that equal angles * in different media, as air and oil, are optically 

 equivalent." 



[ Unequal equivalent of Equal Angles in different Media — Apertures 

 ' exceeding 180° in air.'— Mr. Crisp then, by diagrams drawn on the 

 black-board by Mr. Stewart, illustrated the phenomena of diffraction 

 in the Microscope, showing by reference to Figs. 34 and 35, that (1) 

 although the angle (at the object) was much larger in air than it is 

 when the object is mounted in balsam, yet that the two angles were 

 in reality optically equivalent ; (2) that in the same way the 180° 

 of a dry lens was the optical equivalent of the 82° of the immersion 

 lens ; and (3) that an angle in balsam greater than 82° exceeds 



* For convenience we have for the most part retained the use of the word 

 " angle " throughout a« applied to " pencils." 



