198 American Quarterly Microscopical Journal. 



with glass, we could focus the objective as a dr}'lens; in doing 

 this the plane surface of the lens will be brought nearer to e 

 than it was when used as an immersion — this distance, with 

 the i-8th inch already alluded to, is about 1-50 of an inch, so 

 that, if the base, of the little triangle whose apex is at e 

 (Fig. i) subtended an angle of 87 '^, when the objective was 

 used as an immersion, it will now subtend 144° (the true air 

 angle) when the objective is used dry; we have supposed 

 the lines touching the flat surface of the lens at the same 

 points, in each case. 



It must be borne in mind that these rays, at an angle of 144° 

 in air in front of the lens, will not enter the lens at that 

 angle, but refracted at the plane surface, will now pursue 

 paths, so that, if prolonged backwards, they will only include 

 an angle of 77 ".5; 10' less than before, when the objective was 

 used as an immersion. I believe that the immersions of 

 highest angles, like the oil-objectives of M. Zeiss, and certainly 

 those of the Spencers, do not focus at all as dry lenses. 



The apparatus which I use for measuring the true angle, 

 in all cases, and which is shown in Plate XVII., Fig. 2, may, for 

 angles in glass, or for immersions, be used precisely like Dr. 

 Abbe's apertometer, and indeed, it seems to me has some 

 advantages over that instrument, which will not give the 

 direct air angle, but deduces it from the angle in glass; a 

 separate graduation being required when it is to be read off 

 directly. The 180 degrees are compressed into an arc of 

 82', and the whole space on that arc between 60° and 80', is 

 not more than that between o' and 10'; /. e., the graduations 

 are necessarily unequal, and the instrument is only graduated 

 to ever}^ fifth degree. The cylindrical surface, though it may 

 show a sliding edge with sufficient clearness, is not so good 

 as the more easily made spherical surface which forms a part 

 of the instrument I shall describe, and by means of which one 

 may bisect a minute white circle with the greatest accuracy. 

 Moreover, few would be able to graduate the "apertometer" 

 correctly, and the process of computation, though easy enough, 

 is not necessar)'. 



a (Fig. 2) is a brass tube, say two inches long, supported on a 

 pillar, into which another tube {b) slides easily, carrying at one 

 end the objective (<r). And for this purpose it is fitted with the 

 Society screw; the other end {b) is open, except when a cap 



