The Relation of Aperture and Power. By Prof. E. Abbe. 795 



At the same time we obtain the linear dissipation of the light at 

 the ultimate (virtual) image, owing to the simple enlargement of 

 the circles e through the ocular, 



or 



E = N" € = e - , 

 4> 



E = — ?M. 



4> 



The angular diameter of the same dissipation-circles in the 

 visual image is therefore 



T, E A 

 ^ = 7 = -^"' 



which shows that the enlargement, by the action of an ocular, of 

 the dissipation-circles which are inherent in a given objective, is 

 numerically expressed by the quotient of the optical length of the 

 microscope-tube by the focal length of the ocular. 



If, for example, an objective of any kind be used with an ocular 

 of say 1 inch, the length of the tube being such that the anterior 

 principal focus of the ocular is 10 inches above the posterior 

 principal focus of the objective, we shall have the optical length of 

 the tube A = 10, ^ = 1, and the quotient will yield the number 

 10 ; and this will express the fact, that under these conditions the 

 dissipation of the light in the ultimate image of the entire Micro- 

 scope has a visual angle ten times as large as any image which is 

 projected by the same objective without an eye-piece. This result, 

 obviously, does not depend on the supposition of any definite 

 distance of projection (l). The same will hold good for every 

 position of the image, be it a virtual image (as in the ordinary use 

 of the Microscope) or a real one, as is the case when the image is 

 projected by objective and ocular conjointly on a screen or photo- 

 graphic plate. 



The foregoing proposition admits, however, of a simpler and 

 more expressive enunciation still, which is shown by the above 

 formula for the amplification of the entire Microscope : 



which may be written 



f<p 



f <P 



In this equation the quotient — (which may be denoted by the 



letter v) is one factor of the total amplification N ; and the other 



factor -J. indicates that amplification which the objective alone will 

 •^ 3 H 2 



