PBOCEEDINGS OF THE SOCIETY. 171 



In the first place, lie reproduced the view which was current when 

 immersion objectives were first introduced, and explained the " vast 

 increase" of light transmitted by the homogeneous-immersion objective 

 as compared with a dry objective of 140°, as being due to the " abolition 

 of the reflection and refraction of the lens face." Now the increase of 

 light in the immersion-objective was as 1 : (1 • 5)^, or as 1 : 2j, i. e. an 

 increase of 125 per cent. But the loss by reflection in the case of the 

 dry lens was only 10 or 12 per cent., so that there was an enormous 

 surplus left unaccounted for, and the explanation now given was 

 wholly untenable. 



In the second place. Dr. Edmunds treated the object mounted in 

 balsam as being " so environed that only a small portion of its pencil 

 is allowed to reach the face of an air lens." This is the old fallacy 

 —pure and simple — that there is a reduction of aperture on balsam- 

 mounted objects. So far, however, from the " environment " of the 

 object being an impediment, the dry lens receives the whole pencil in 

 that case as much as it does when the object is in air and uncovered. 



Mr. J. Mayall, jun., wished to know from Mr. Shidbolt, whether 

 he maintained that no immersion objective could utilize rays from a 

 radiant in air that were not effective when an ordinary dry objective 

 was used ? 



Mr. Shadbolt said that was not his point — his paper was to 

 demonstrate that not only a dry lens, but that no lens of any kind 

 could have an aperture of any kind that exceeded that of 180° 

 angular in air. No angle greater than the whole of the rays emitted 

 from an object could by any possibility be got. 



Mr. Mayall said that what had been demonstrated over and over 

 again was that, under suitable conditions, an immersion lens may 

 utilize image-rays that cannot be utilized by any dry lens. When 

 the angle of aperture of the highest-angled dry lens, approaching 180° 

 air angle, was measured in the body of an ordinary crown glass semi- 

 cylinder or hemisphere, the reading was always well within 82°, that 

 is to say, twice the " critical " angle. But some of the recent homo- 

 geneous-immersion lenses gave a reading of upwards of 140°. How 

 were we to designate apertures such as this latter ? If a dry lens with 

 a plane front was limited to 82° in glass (which is the equivalent of 

 the maximum air angle of 180°), whilst an immersion lens gave 140° 

 in glass, the aperture of the latter was greater than the equivalent of 

 the maximum air aperture. Some term must be found to meet the 

 case, and Professor Abbe had accordingly suggested "numerical" 

 aperture, which enabled a comparison of apertures in all media to be 

 made by simple inspection. If Mr. Shadbolt could suggest a better 

 plan of universal notation for apertures, doubtless it would readily 

 find supporters. To take the interior angle (in the front lens) led, 

 as Professor Abbe had shown,* to the same absurd results as " angle 

 of aperture " itself. 



Mr. Shadbolt said he thought the case between Mr. Mayall and 

 himself to be that Mr. Mayall assumed that an immersion lens 



* See this Journal, iii. (1880) p. 24:. 



