56 Tr. LeConte Stevens — Microscope Magnification. 



Let p = distance of stage micrometer from this optical center, 

 Let£>'= " eye-piece " " " 



p' 



or p = — . . . (8) 



Then, 



P 



m — — 



It is. impossible to measure either p or p' directly, but we 

 can measure the distance between the two micrometer scales, 

 which is equal to their sum. Calling this I, we have, 



l=p -\-p', or p = I — p' . . (9) 



Eliminating^ between equations (8) and (9), 



, ml 

 p = 



From the equation of lenses, 



?n -j- 1 



- + ~, = ^ we have/(p +/>') = pp[ 



(10) 



;n) 



Substituting in equation (11) from equations (9) and (10), 

 and reducing, the result is 



'=o5Tir • ' • • (12) 



Since this formula is independent of p and p', it may be 

 applied without any knowledge of the optical center of either 

 a single lens or a system of lenses. 



The ej^e-pieces of the microscope to which reference has been 

 already made are devoid of labels, although the instrument is a 

 fine one, and the maker was one of the best known in America, 

 a careful and intelligent German, now dead. They have been 

 subjected to measurement, with the result given in Table I. 

 The two eye-pieces labeled in the table A 1 and A 2 were evi- 

 dently intended to be, in ordinary nomenclature, 2-inch eye- 

 pieces ; those labeled B x and B 2 , 1-J-inch eye-pieces, and the 

 one labeled C, a f inch eye-piece. All measurements of length 

 were made in millimeters. 



Table I. 



1. 



2. 



3. 



4. 



5. 



6. 



7. 



8. 



9. 





/' 



/" 



d 



F 



If 



F' 



e% 



to' 



A, 



35-5 



58-8 



54-0 



51-8 



53-2 



2-07 



-3-4 



5-82 



A, 



34-9 



58-1 



54-0 



52-0 



52-3 



2-08 



-3-9 



5-82 



B, 



21-3 



40-0 



38-0 



36-6 



31-9 



1-46 



+ 2-7 



7-83 



Bo 



21-1 



40-9 



38-0 



36-0 



31-6 



1-44 



+ 42 



7-94 



C 



13-6 



28-7 



23-0 



20-2 



20-4 



•81 



-7-4 



13*38 



On comparison of columns 2, 3, and 4, it is seen that in no 

 case isfi // = Sf, or d=2f', as generally assumed in relation to 

 the negative eye-piece. To multiply the focal length of the 



