52 IT. LeConte Stevens — Microscope Magnification. 



the upper surface of the field lens to that of the topmost lens 

 of the objective. 



The present writer had occasion, some time since, to pur- 

 chase a binocular microscope, with several objectives and eye- 

 pieces, for which a table of magnification was furnished. 

 Examination of this table showed that the magnification was 

 calculated by dividing 100 by the product of what were called 

 the focal lengths of objective and eye-piece, expressed in 

 inches. On inquiry of the dealer this rule was found to be 

 the one he had employed, and it was said- to be in common 

 use. Its results were admitted to be only approximate, but it 

 was supposed to be near enough to the truth for most prac- 

 tical purposes. 



It has seemed desirable, therefore, to test this rule, and in 

 so doing to search out a few points that may possibly be of 

 interest to those who use the microscope as a physical instru- 

 ment. Its deduction is very simple. Let the object, ab, be 



focalized by the objective, O, at a'b'. Oc is taken as the 

 focal length of the objective, and Oc' as the tube-length, 10 

 inches. If m be the magnifying power of the objective alone, 

 we have, 



_ a'b' _ 10 

 m ~ ab ~ /' 



The visual angle, a, subtended at O by a'b' is the same as that 

 subtended by ab, if an eye placed at O were capable of suffi- 

 cient accommodation to secure distinct vision at so short a dis- 

 tance. The image, a'b'. is viewed with an eye-piece, which 

 increases the visual angle from a to a', producing a virtual 

 image which is assumed to be 10 inches away. If m' be the 

 magnifying power of the eye-piece whose focal length is f, 

 we have, approximately, 



,_tan|«'_10 

 "'"tanf^ - /'" 



If M be the total magnification, the result therefore is 



Ar < 10 ° n\ 



M = mm=——. . . . (1). 



In applying this formula, if previous measurements have 

 not been made upon the lenses composing the eye-piece, a 



