PROCEEDINGS OF THE SOCIETY. 1091 



light as the lens is constracted to admit, irrespective of the mounting 

 of the object, but in no case can it reach, far less exceed, 180^. 



It may be as well here to note, that with a dry lens, both the front 

 and back surfaces of the front lens take part in the refractions ; but 

 with an immersion lens, the refraction at the front surface is sup- 

 pressed or greatly reduced. 



Before concluding, I wish to make a remark or two upon some of 

 the statements in the article, and as it is anonymous, I trust I can do 

 so without offence ; my sole object being to resist the promulgation of 

 erroneous views, and the use of vague and incorrect expressions in 

 matters of scientific interest. What does the writer of the article 

 mean by ' radiant spaces ? ' How can ' diffraction spectra ' pass 

 through them ? How can a ' space of 6° ' become larger or smaller ? 

 It is to such expressions as these that confusion of ideas arises, far 

 more than from any inability to gi-asp the fact that a lens cannot have 

 an aperture of more than 180^." 



Mr. Wilson said that Mr. Shadbolt appeared to have altogether 

 misapprehended the note at p. 875. That did not refer to " angle " 

 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. Shad- 

 bolt's letter related in fact to two distinct matters. 



Mr. Crisp said the note referred to would certainly not have been 

 admitted into the ' Journal ' if it had been inconsistent with Mr. Shad- 

 bolt's demonstration as to an angle of 180^ On receipt of his letter, 

 he had written to Mr. Shadbolt, pointing out that the note referred to 

 aperture, and had received a further letter, in which he said : — 



" I cannot assent to the word ' aperture ' as employed. The abso- 

 lute ' aperture ' of a telescopic lens is sufficiently intelligible, so is 

 the ' angular aperture ' of a microscopical lens, but an ' apertui-e ' that 

 is neither absolute nor angular is not intelligible at all, esj^ecially if 

 you call it ' numerical aperture.' Now, if it had been called ' nuyncrical 

 resolving poicer,' it would I fancy be nearer to what is really meant. 



I am fully alive to the advantage of immersion lenses in appro- 

 priate conditions, but I altogether deny their universal apjdicability. 

 There is no difficulty in getting the largest practicable pencil of light, 

 say 170^", into a dry lens; the difficulty is, that you cannot get such a 

 pencil out of the mounting of the object when iu balsam, or similar 

 medium, and that is bounded by a stratum of air. 



Tliis is very easily demonstrable by a few lines added to the diagram 

 given by Professor Stijkes, at p. lil, V(d. i. of the present scries. 

 Witli a little, modification this observation apj)lies also to an object 

 mounted dry, but covered with a thin film of glass. 



Sliould there be any kind of discussion, kindly put forward these 

 remarks in my absence." 



Mr. Wilson said that Professor Stokes' paper was a refutation of 

 tho very fallacy on which Mr. Shadbidt's reasoning was based. Tho 

 expression " angle of apijrturo " had never in fact been a measure of 

 the relative apertures of even dry objectives, and on tho introduction of 



