Note on the Proper Definition, &c. By Prof. E. Ahhe. 349 



angle, under which a given length h is displayed by the system to 

 every eye. The numerical value of this quotient gives the tangent 

 of the visual angle, under which the unit of length (h = 1) is 

 shown through the system. This quotient, therefore — i. e. the 

 ratio of tan w* to h, or the visual angle corresponding to the unit of 

 length, measured hy the tangent — is the rational expression of the 



magnification or '^ power' of an optical system, because every observer 

 will see every object enlarged through different systems in the exact 

 proportion of the value of that quotient. 



From the fundamental definition of the "equivalent focal- 

 length " of a lens-system results the identity of the above-mentioned 

 quotient with the reciprocal value of/ (focal length) : we have 



tan u* 1 



Consequently the reciprocal of the focal length of a system is, by 

 itself, the proper expression of its amplifying power, because this 

 reciprocal expresses numerically the visual angle (measured by the 

 tangent) under which the unit of length appears through the 

 system. 



This very simple expression of the amplifying power of a lens- 

 system is a strict one, it is true, under the supposition only which 

 was mentioned above, that the place of the eye be at the posterior 

 principal focus of the system, or, what is the same thing, that the 

 principal rays from the various points of the object cross at that 

 focus. 



As far as the compound Microscope is in question, no other 



