PROCEEDINGS OF THE SOCIETy. 157 



that will only admit such a pencil is a lens of only that angular 

 aperture. 



" If a dry lens be employed on a balsam-mounted object, a portion 

 of the radiant pencil is turned back by total reflection at the air- 

 surface of the covering-glass, when the incidence of the rays exceeds 

 the ' critical angle,' so that only a pencil of not exceeding 81^ 58' 

 can escape from out of the mounting of the object to fall upon the 

 front of the dry lens ; but that does not affect the capacity of the 

 lens, which is merely placed in circumstances wherein its full powers 

 cannot have play. 



" It may be, and is, a very good reason for using an immersion lens 

 instead of a dry one, but it is monstrous to assert that the latter has 

 an ' aperture ' exceeding that of 180° in air. The object is the thing 

 at fault, and not the lens ; the object has been placed in a condition 

 which prevents more than a pencil of 81° 58' emanating from it. 



" It follows also that the ' numerical aperturists,' if I may coin 

 such a phrase, have fallen into another error about this matter. It 

 has been assumed by them that the diiference between the pencils of 

 light admitted respectively by the dry and immersion lenses from a 

 balsam-mounted object, bears a direct proportion between the refrac- 

 tive indices of air and the fluid used for immersion ; but this is not 

 the case, for it is evident from a consideration of the preceding facts 

 detailed, that the difference can only be that between twice the critical 

 angle and the largest immersion angular aperture of the lens in use, 

 the critical angle being a constant quantity in any given medium in 

 contact with air, so that in the case of immersion lenses having an 

 angular aperture of less than 81°^ 58' there would be no diiference 

 at all. 



" I am far from undervaluing the advantages of immersion lenses. 

 In certain cases they are invaluable ; the working distance in front of 

 the lens is greater (an important consideration with very high powers), 

 the refraction by the front lens being effected entirely or chiefly at its 

 back surface ; and Mr. Stephenson has pointed out how the immersion 

 lens can be profitably adapted so as to avoid the necessity for correc- 

 tion for the varying thicknesses of the glass covering the object. 

 The only drawback that occurs to me in their use, is the necessity of 

 interposing a film of suitable fluid; but I have yet to learn that 

 immersion lenses can be constructed to include a larger angular 

 pencil of light than can be included by a dry lens, 



" If, instead of characterizing my statement as a ' fallacy,' my critic 

 had been good enough to point out any flaws he could discover in the 

 argument of my note on this subject, which he had just heard read, 

 and which appears at pp. 1089, 1090, and 1091, vol. iii., of the 

 Journal of the Eoyal Microscopical Society, it would have been a 

 far more satisfactory mode of proceeding : but, in fact, my statement 

 is not at all opposed to what is demonstrated in Professor Stokes's 

 paper, published in the Journal of the Eoyal Microscopical Society 

 for July 1878, vol. i. p. 141 et seq" 



Mr. Shadbolt then referred (in six lines) to what he conceived 

 to be the circumstances under which Professor Stokes's paper was 



