170 PROCEEDINGS OF THE SOCIETY. 



that case the sine was multiplied by 1-33 if for water ; or going 

 higher still, by 1 • 52 for crown glass. Had Mr. Shadbolt ever seen 

 the apertometer ? If not, would he like to see it ? There was one 

 in the room which had been brought for the purpose. 



Mr. Shadbolt said he did not desire to see it ; he had simply dis- 

 puted the idea that any aperture could possibly be greater than a whole. 



Dr. Edmunds said he thought that much of the dispute on this 

 question was a question of nomenclature. A luminous object in the 

 focus of an objective could be taken in three conditions. Firstly, 

 as in air and uncovered ; secondly, as optically connected with the 

 lens-face by a homogeneous medium, such as oil or balsam ; thirdly, 

 as set in balsam under a cover-glass with a stratum of air above. 



In the first case a plane-fronted air lens may receive a pencil of 

 rays nearly a complete hemisphere. If the distance be such that a 

 pencil of 140° strikes the lens face, and the objective be capable of 

 reducing into image the whole extent of this pencil, the objective is 

 an air lens of 140° angle of aperture. In the second case, if the back 

 surfaces be so increased in depth and power as to replace the action of 

 the lens-face (abolished by the homogeneous immersion), we shall 

 have a homogeneous-immersion objective of 140° angle of aper- 

 ture. The image now given will be much brighter than the first, 

 but why ? Not because the angle of aperture has been augmented, but 

 because the amount of light transmitted within the same angular 

 range has been vastly increased by abolishing the reflection as 

 well as the refraction of the lens-face, and therefore the whole pencil 

 of 140° has actually entered the lens front. In the third case we 

 use the lens corrected for air as at first. Here the pencil of 140° 

 is divided into five portions, of which four are mechanically diverted, 

 and one only enters the lens-face. (1) That portion of the pencil 

 outside the angle of 41° is wholly reflected backwards. (2) That 

 portion of the pencil inside the angle of 41° is split into two portions, 

 of which one is reflected backwards and the other emerges from the 

 surface of the cover-glass. (3) The 82° portion emerging into air is 

 refracted so as to be expanded into a pencil of 180°, of which only 

 the central 140° reach the lens. (4) This 140° pencil is split by the 

 lens-face, one portion of the pencil is reflected, and only the remaining 

 portion enters the lens. Thus the light emitted from an object in air, 

 uncovered, is received upon the face of an air lens and utilized to the 

 full range of its angular aperture. The same object set in balsam 

 under a cover-glass is so environed that only a small portion of its 

 pencil is allowed to reach the face of an air lens. The beauty of the 

 image given by the homogeneous lens depends upon the quality and 

 intensity of the pencil which enters the lens, and not upon its increased 

 range of angular aperture. 



Mr. Crisp said that apart from Dr. Edmunds' demonstration that 

 there could be no angle of aperture exceeding 180° (which no one had 

 ever attempted to dispute), the mistakes into which he had fallen 

 were all traceable to the same fundamental error (by no means a 

 mere question of nomenclature) as that which had misled Mr. 

 Shadbolt, though expressed in a different form. 



