The Relation of Aperture and Power. By Frof. E. AUbe. 805 



my observations do not indicate a decided difference between dry 

 and water-immersion lenses may be well accounted for by the fact 

 that tbe advantage of diminished front-aberrations in the immersion 

 system is balanced by the increased aperture. With immersion- 

 lenses of not more than 1*0 or less (other circumstances being 

 equal), a somewhat higher value of v would be found. On the 

 other hand, I have always observed a perceptible lowering of the 

 critical super-amplification with objectives of greater apertures 

 than 0"90 for the dry system, and of 1'20 for the water immer- 

 sion, when preparations are used for the experiment which put the 

 utmost marginal zone of the aperture in action simultaneously with 

 the intermediate portions between the centre and the margin. 



(2) A decided advance in the performance, in regard to the 

 critical value of v, is found in well-made objectives of the homo- 

 geneous-immersion system. With the same standard of judgment, 

 and on the same principle which has been explained above, I con- 

 sider a super-amplification of about 6 as that which will just raise 

 the inherent aberrations up to the threshold of vision, for an aperture 

 of about 1'30,* It appears quite intelligible that the total (or 

 nearly total) suppression of the front-aberrations should not only 

 compensate for the increased aperture but in fact should leave a 

 surplus benefit, as is indicated in the higher value of v. 



(3) Eegarding the lower apertures of the dry system, my 

 comparisons show a relatively slotv increase of the critical v, as the 

 apertures diminish. This may be sufficiently accounted for by the 

 circumstance that these lower apertures are always made with 

 relatively greater working-distance (the clear air-space between 

 the front surface and the radiant being a greater fraction of the 

 focal length) than is adopted in the wide-aperture systems. 



The relief to the front-aberration, and the corresponding 

 reduction of the residuary aberrations, which is due to the reduction 

 of the angle of the pencil, is therefore partly compensated by the 



* If any one should wonder at the low super-amplifications assigned here, and 

 should consider the above statements to be poor evidence of the present condition 

 of microscopical optics, I would ask him to reiiect upon what it means, that 

 ohjectives even of rather short focal length should bear a super-amplification up 

 to 4 and 6, without any perceptible injury to the sharpness of the image. This 

 means nothing less than that the Microscope is capable of showing objects 

 enlarged to more than 800 diameters under the same conditions, so far as the 

 geometrical precision of the obseiTation is concerned, as if the microscopic objects 

 could be enlarged in that degree corporeally, not optically, and were then seen 

 with the naked eye at a distance of 250 mm., without the interference of any 

 optical apparatus. Up to those high figures of amplificatioii the modern Micro- 

 scope maintains therefore the undiminished sharpness of naked-eye vision, and 

 performs without any perceptible difference in the same way as if material 

 bodies, instead of mere enlarged images, were depicted upon the retina. The 

 time is not long past when no system, except very low-angled lenses, could bear 

 even its own proper power without any super-amplification, and not lOU diameters 

 could then be obtained without great inferiority when compared with direct 



