PEOCEEDINGS OF THE SOCIETY. 165 



" With a pencil in balsam of 82°, the dry lens takes up all that 

 it is capable of taking up — that pencil is the equivalent of the 180° 

 in air, — for the dry lens, that is its whole ; for it, there can be no 

 more than that whole. But the immersion lens of wide angle (i. e. 

 exceeding 82° ' balsam angle ') takes up a pencil largely in excess of 

 the 82° which was the ' whole ' of the di-y lens, — and its superior 

 performance is seen to be wholly inadequately accounted for by the 

 explanation given by Mr. Shadbolt. 



" To take a second quotation from Mr, Shadbolt {supra, p. 157) : — 

 " 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° 68' can escape from out of the mounting 

 " of the object to fall upon the front of the dry lens ; hut 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 immer- 

 " sion 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." 

 " The same figures as I have used before illustrate this case also. 

 So far from the dry lens being ' placed in circumstances wherein its 

 full powers cannot have play,' its powers have the fullest play, and in 

 the second case, quite as much as in the first, it receives its ivhole — the 

 whole 180° of the radiation in air. As a dry lens it cannot utilize more. 

 (" It will be seen that I have passed over two things : Mr. Shad- 

 bolt's omission to notice that the angle received by the front of the 

 dry lens in Fig. 35 is 170° instead of being only 80°, and also that 

 according to his demonstration an immersion lens shows exceptional 

 superiority as regards aperture over a dry lens only in the case of 

 the latter being used on objects mounted in balsam.* I do so because 

 I wish to confine the discussion to the one point on which the whole 

 matter turns.) 



" If the erroneous assumption of the optical equivalence of equal 

 angles in difierent media be granted, it is almost impossible for Mr. 

 Shadbolt, or any one else, to avoid falling into the train of reasoning 

 which appears in his paper, any more than it was possible for the 

 old astronomers to avoid the erroneous explanations of the movements 

 of the planets which were rendered necessary by the assumption that 

 the earth was the centre of the system. When it is recognized that 

 the equality or inequality depends, not on the angle only, but on 

 the refractive index of the medium also — that the sun, and not the 

 earth, is the centre — any such ' explanations ' become unnecessary. 



" So far, therefore, from Mr. Shadbolt having demonstrated 

 beyond dispute, the incorrectness of the modern doctrine of aperture, 

 he has given no demonstration that touches the question. 

 * See also the original note at pp. 1090-1 of vol. iii. 



