The Aperture Question. Bij J. May all, jun. 135 



could adduce on behalf of the original claim that the aperture of 

 the I exceeded 82', — the evidence being Professor Keith's com- 

 putation of the angle, and the actual measurement by means of 

 Professor Abbe's apertometer which I exhibited at the meeting in 

 June last. 



Mr. Wenham's answer to the computation amounts to this : — 

 Because the computed angle is based on the assumption that the 

 radiant is in balsam, therefore it falls to the ground. 



Now the question with regard to this lens never was to know 

 if the aperture in the body of the front lens could exceed 82° when 

 adjusted so as to have a front-focus in air. No one had ever alleged 

 such a proposition. All admit that 82^ (in glass) is the limit for 

 dry lenses, and, of course, all lenses may be regarded as dry if there 

 be a stratum of air between the object and the front lens. The 

 question was, What is the aperture when the lens is adjusted to have 

 a front-focus in balsam? To this Professor Keith's computation 

 answers by tracing the paths of different rays from the back-focus 

 to the front-focus in balsam, and the result (110°) proves that the 

 formula is designed to produce an aperture greater than corresponds 

 to 180^ in air, — which was to be demonstrated. Mr. Wenham's 

 criticism upon it is thus seen to be irrelevant. 



When the radiant is in balsam, and in immersion contact with 

 the front lens, the critical angle (between glass and air) is no longer 

 a factor in the elements, and can have nothing to do with the aper- 

 ture, because the rays do not go into air until their emergence at 

 the second surface of the front lens, which is not parallel to the 

 plane front, but deeply curved. With a dry lens, the effective angle 

 of rays from the object in balsam is limited at the object itself to 

 82^ — no greater pencil can emerge from the cover-glass. With an 

 immersion lens this limit varies with the immersion medium ; with 

 water it is about 126°, with oil the limit depends on the construc- 

 tion of the lens, and may possibly be carried as near to 180° in 

 glass as the present dry lenses approach their limit of 82°. This is 

 a matter for the ingenuity of the opticians. 



With regard to the elements furnished for the computation, it is 

 extremely improbable that Mr. ToUes arrived at the precise nume- 

 rical data by mere guessing ; but even in that case, as formerly re- 

 marked by Professor Keith, " the force of the result would have 

 been the same." 



In confutation of Mr. Wenham's position in the aperture ques- 

 tion, we have had two formulae for immersions placed before us, by 

 which an aperture in the body of the front lens exceeding the limit 

 of dry objectives has been traced to the radiant in balsam : the one 

 relating to the yV (three system) by Tolles in the collection of the 

 United States Army Medical Museum ; the other, to the \ (four 

 system) referred to above ; in each of which Professor Keith has 



