126 Final Bemarks on Immersion Apertures. 



placed at my disposal, in a letter dated January 22nd, 1874, the 

 details of the construction of both the objectives described in my 

 jjaper in the November number of this Journal, with permission to 

 publish so much with regard to either or both of them as might 

 in my opinion be essential to the demonstration of the matter in 

 dispute. 



Of the two I have selected the Tuth belonging to the Museum,* 

 both on account of its superb definition (see, for example, the 

 photographs of Amphipleura i^ellucida sent with my November 

 paper), and because, as this lens has a simple hemispherical front, 

 it is an excellent example of the class of objectives with regard to 

 which the possibility of a balsam aperture of more than 82° has 

 been most strenuously denied. The data with regard to this objec- 

 tive I placed in the hands of my friend Professor K. Keith, of 

 Georgetown, with the request that he would trace the course of 

 the rays through the combination by the trigonometrical method, 

 which is of course more rigidly exact than Mr. Wenham's plan of 

 making an enlarged diagram, and tracing the rays through geome- 

 trically, and not so much more difficult as he seems to suppose.! 

 Mr. Keith's engagements did not permit him to undertake the task 

 at once, and after he commenced the discussion some delay was 

 caused by lack of information with regard to one or two points, 

 which could only be supplied by Mr. Tolles, who was absent from 

 home on account of sickness. But for these unavoidable circum- 

 stances the results of this discussion would have been ready some 

 time since. As it is, Mr, Keith has prepared a paper which 

 accompanies this, and which gives the elements of the objective, 

 and his results in detail, together with a figure reduced photo- 

 graphically from an enlarged diagram accurately constructed in 

 accordance with the computed results. 



It will be seen that Mr. Keith obtains in the position of the 

 screw-collar which gives the maximum aperture, a calculated 

 balsam angle of 110° 35' 10". Now, it will be remembered, that 

 in my account of this objective I stated its balsam angle at the 

 point of maximum, as measured by my method,^ to be only 87°, or 

 twenty-three degrees and a half less than the calculated angle. A 

 moment's examination of Mr. Keith's diagram will show the reason 

 of this, for it will be seen at once that very trifling encroachments 

 on the diameter of the hemispherical front by its setting, will 

 produce a considerable reduction of the angle. In fact, Mr. Keith 

 states that he has found by actual computation an encroachment 

 of "00162 of an inch (^^^th very nearly) on the periphery of the 

 front will reduce the calculated to the observed angle. 



I desire also to call attention in this place to the fact, that the 



* * This Journal, November, 1873, p. 214. 

 t Ibid., April, 1873, p. 164. 

 X Ibid., June, 1873, p. 2G8, for the method referred to. 



