APPENDIX. 329 



sine of 90,=radius or 100, we find this standard to be equalled by a 

 ' water ' immersion objective of only 96, and by an ' oil ' or * homogene- 

 ous' immersion lens of only 82; the ' numerical apertures 'of these, 

 obtained by multiplying the sines of their respective semi-angles by the 

 refractive index of water in one case and of oil in the other, being 1.00 

 in both. Each, therefore, will have as great a power of receiving and 

 utilizing divergent rays, as any ' dry ' lens can even theoretically possess, 

 an angle of nearly 70 being the limit of what is practically attainable. 

 But as the actual angle of an ( immersion ' Objective can be opened-out 

 to the same extent as that of an ' air' objective, it follows that the ( aper- 

 ture ' of the former can be augmented far beyond even the theoretical 

 maximum of the latter; the maxima of numerical aperture being 1.52 



water-immersion, and the fourth an oil-immersion, their apertures have 

 hitherto been designated, on the angular aperture notation, by (for 

 instance) 47 and 74 air-angle; 85 water-angle; and 117 oil-angle; so 

 that it is difficult witho.ut calculation to judge of their relative apertures. 

 By the numerical notation, however, the apertures of the four are seen 

 to be as .40, .60, .90 and 1.30; so that a comparison is readily made, 

 and it is seen whether the two latter have larger or smaller apertures than 

 the maximum of a dry objective. 



This important doctrine may be best made practically intelligible by 

 a comparison (Fig. 500) of the relative diameters of the back lenses of 

 ' dry' with those of ' water ' and ( oil ' immersion Objectives of the same 

 2)oiver, from an * air-angle ' of 60 to an ' oil-angle ' of 180; these diam- 

 eters expressing in each case, the opening between the extreme pencil- 

 forming rays at their issue from the posterior surface of the combination, 

 to meet in its conjugate focus for the formation of the image; the extent 

 of which opening in relation to focal length (not that of the rays entering 

 the Objective), is the real measure of the Aperture of the combination. 

 The dotted circles in the interior of 1 and 2 are of the same diameter as 

 3; and therefore show the excess in the diameters of the back lenses of 

 the ' oil ' and ' water ' immersion-objectives, over that of the ' dry ' at 

 their respective theoretical limits. 



Now this difference is capable of being practically tested by a simple 

 experiment originally suggested by Mr. Stephenson, and thus described 

 by Prof. Abbe: "Take any immersion-objective of balsam angle exceed- 

 ing the critical angle, and focus it on a balsam-mounted object, which is 

 illuminated by any kind of immersion-condenser, in such a way that the 

 whole range of the aperture-angle is filled by the incident rays. Remove 

 the eye-piece, and place the pupil of the eye at the place where the air- 

 image is projected by the objective, and look down on the lens. You see 

 a uniformly bright circle of well-defined diameter, which is the true cross 

 section of the image-forming pencil emerging from the Microscope (for 

 the eye receives now all rays which have been transmitted through a 

 small central portion of the object that portion which is conjugate to 

 the pupil and receives no other rays). After this, focus the same objec- 



1 At p. 325 of Vol. i., Ser. 2 (1881) of the " Journ. of the Roy. Microsc. Soc.," 

 will be found a Table calculated by Mr. Stephenson of the Equivalent Angles of 

 Aperture of Dry, Water-immersion, and Oil (or homogeneous) immersion Objec- 

 tives, with their respectiye Illuminating powers, and Theoretical Resolving 

 powers, for every 0.02 of Numerical Aperture, from 0.40 to 1.52. 



