PROCEEDINGS OF THE SOCIETY. 155 



" gether misappreliencled the note at p. 875. That did not refer to 

 *' ' idngle ' at all, but to ' aperture,' and it was now well established 

 " that they were not synonymous terms ; he did not therefore follow 

 " Mr. Shadbolt's demonstration as to the angle being necessarily less 

 *' than 180°, which he imagined that no one disputed. The original 

 " note and Mr. Shadbolt's letter related in fact to two distinct 

 " matters." 



B. " Mr. Wilson said that Professor Stokes' paper was a refuta- 

 *' tion of the very fallacy on which Mr. Shadbolt's reasoning was 

 " based. The expression ' angle of aperture ' had never, in fact, been 

 " a measure of the relative apertures of even dry objectives, and on 

 " the introduction of immersion objectives, it had ceased to have any 

 " definite meaning whatever." 



Mr. Shadbolt's paper then proceeded as follows : — 



" I presume no one will be found hardy enough to contend that 

 the total amount of light emitted from a radiant point under a given 

 fixed illumination would be greater if the said radiant point were 

 in oil or any other dense transparent medium, than if it were in 

 air. In point of fact, we may regard this total amount of radiant 

 light as a fixed quantity while the illumination of the object remains 

 unaltered. 



" Quotation A. — It is quite possible that I may have to some 

 extent misapprehended the note at p. 875, seeing that those who 

 employ the term ' numerical aperture ' have never, that I am aware, 

 condescended to explain in definite terms what they mean by it. In 

 point of fact, I deny its existence altogether as ' aperture,' which 

 term means ' opening,' and nothing else. The term aperture may 

 be fitly applied in two ways, viz. by quoting its actual size, or by 

 quoting the angular pencil of light which it allows to pass through 

 it : the ' angular aperture ' of a lens, whether dry or immersion, is 

 just the measure of the pencil of light which it will bring to a focus, 

 with or without the aid of other lenses behind it : it is therefore 

 evident, as shown in my previous note, that no lens can really have an 

 aperture of 180°. 



" The absolute aperture of a lens — say half an inch — one-tenth of 

 an inch — one-hundredth of an inch — gives no measure of the propor- 

 tion of a pencil of rays from a radiant point that it will allow to pass 

 through, without at the same time its focal distance is quoted ; on the 

 contrary, if its ' angular aperture ' be quoted it gives a very exact 

 idea of the proportion. The accurate measurement of that aperture 

 may be a difficult matter; but easy or difficult, that does not affect 

 the question at issue. Thus a Microscope objective, with a half-inch 

 aperture, may, and generally does, admit a smaller angular pencil of 

 rays than one of a tenth of an inch : in fact, it all depends upon the 

 distance of the said apertures from the radiant point. Now, with an 

 angular pencil of 180°, there is no question of distance of the aperture 

 from the object ; it must be absolutely in the same plane with the 

 object, and no question about its size, so that it includes the radiant 

 point. The words ' angular aperture ' therefore convey a correct 

 and definite idea of the pencil of rays admitted ; the words ' nume- 



