258 Transactions of the Society. 



This is approximately the same angular magnitude as can be 

 attained without any great difficulty within the film of water in the 

 usual immersion lenses, or within the stratum of air in dry objec- 

 tives. But since the " numerical " equivalent of the angle of aperture 

 (the measure which determines the number of rays taken in by the 

 objective) is proportional not only to the sine of half the angle of 

 aperture, but also to the refractive indices of the respective media 

 employed, and since all the functions of the angle of aperture, and 

 especially the resolving power of the Microscope, are regulated by 

 this numerical equivalent, it follows that, according to theory, the 

 capacity of the new objective, compared with that of ordinary im- 

 mersion lenses, is increased in the proportion of 1 • 50 to 1 • 33, and 

 as compared with the highest dry objectives, as 1 '50 to 1. 



The product of the sine of half the angle of aperture into the 

 refractive index of the medium — the '• numerical aperture," as I 

 call it — reaches 1 • 25 to 1 • 27 in these objectives. The ratio of 

 these figures to unity expresses how much greater is the number 

 of rays admitted by the new objectives, over that number which in 

 air would fill a complete hemisphere, or which would be admitted 

 by an imaginary dry objective of 180° aperture. 



This unusually large aperture is accompanied with a notable 

 increase of resolving power. This is at once evident by the facility 

 with which very fine striae and similar markings become visible on 

 the more difficult test objects ; by the plainness with which the 

 characteristic markings stand out on the more complicated forms, 

 such as Frustiilia saxonica, Surirella gemma, &c. ; and lastly, by 

 several unusual features which appear when certain methods of 

 illumination are employed on the coarser tests of this kind, e. g. 

 P. angidatum. 



Histological preparations also furnish instances of very small 

 elements closely clustered together, granulations and such like, 

 in which clearer and more definite resolution is obtained in critical 

 cases. 



At the same time, in all these objects, especially in those last 

 named, the decidedly more perfect definition which homogeneous 

 immersion renders possible, is obtained, provided that the precision 

 of the technical execution is adequate to the reduction efi'ected in 

 the residual aberration as indicated in theory. Therefore, when 

 comparatively strong eye-pieces are used the image retains great 

 sharpness, so that in regular work higher amplification can be use- 

 fully employed than is usually the case with other objectives of 

 equal focal length. They also often enable more exact observations 

 to be made of very delicate objects, such as fine cilia, than good 

 immersion objectives of the ordinary kind would permit. 



Lastly, as a proof of excellence of definition which, though 

 indirect, is of special weight, may be mentioned the favourable 



