460 Transactions of the Society. 



XI. — The Relation, of Aperture and Power in, the Microscope 

 {continued).* 



By Professor Abbe, Hon. F.K.M.S. 



(Read Uth June, 1882.) 

 II. — The Motional Balance of Aperture and Power. 



The discussion of Part I. relates to one and the same matter, 

 viz. that from all points of view which come under consideration 

 in the use of the Microscope, a certain proportion of aperture 

 to power is the necessary hasis of perfect performance. 



The question we have now to consider is: whether it is 

 possible to arrive at a more definite determination of that propor- 

 tion than is furnished by the preceding somewhat general dis- 

 cussion of the question of wide and narrow apertures, and in 

 particular, whether that can be done in such a way as to establish 

 a rational standard for the practical construction of the Microscope. 

 So far as I know, this matter has not yet been the subject of any 

 kind of regular discussion, though it will be admitted, I presume, 

 by every microscopist to be one of great practical importance. 

 I have now directed my attention to it for more than ten years, 

 not purely from theoretical points of view only, but by means 

 of a long series of practical trials in which I had the advantage 

 of the co-operation of Dr. C. Zeiss, of Jena, and I propose therefore 

 to point out here the principles which, in my opinion, furnish 

 an approximate standard for determining the proper balance of 

 aperture and power in the Microscope. 



For this, two distinct questions must be treated separately. 



First, the relation of aperture to power must be considered 

 in regard to the entire Microscope and we must ascertain what 

 amplification of the ultimate image of the Microscope is useful, 

 or necessary, for every given aperture, and conversely, what aper- 

 ture is required for the proper utilization of a given amplification. 

 If the subject admits of a scientific discussion at all, it must be 

 possible to indicate the proper relation of aperture and amplifica- 

 tion without having regard to the particular manner in which a 

 given amplification is obtained by the co-operation of objective and 

 eye-piece, provided, of course, that the amplification is obtained 

 with the best possible quality of the image. 



The second question is, what division of the entire power of 

 the Microscope between the objective and ocular will fulfil the 

 condition of a perfect image under a given amplification. This 

 relates essentially to the practical aim of the discussion — the 

 determination of the focal length of the objective which is required 

 for the utilization of a given aperture. 



* The paper (received 11th April) is written by Professor Abbe in English. 



