16 



screen ten inches distant, anda l-12th objective should magnify 

 120 times. If the eye-piece is equivalent to 1-lOth single lens, 

 it again enlarges the object 100 times, and the total power 

 will be 12,000 diameters. The magnifying power of a micro- 

 scope whose objective has a focal length / and eye-piece e, 

 will be conveniently expressed by — 



10 10 100 



I have several times tested this formula against the camera 

 lucida, and have found it extremely accurate for a standard 

 of ten inches' distance of the eye-lens from the objective. 



Examples. — With a C eye-piece, Powell and Lealand's l-8th 

 objective magnifies 800 times, and its focal length is one inch. 

 The l-12th, with the same eye-piece, gives 1200 diameters, 

 and the l-50th 5000 diameters. The formula produces iden- 

 tical results, precisely expressing their printed tables : 



(1) ith. e = I, f = ^. 



M .= _M_ = 800. 

 1 X i 



(2) ^th. e = \, f = ^\. 



M = , ''\ = 1200. 



1 X yV 



(3) J^th objective, e = I, / = -^. 



M = , ^^^ , = 5000. 

 1 X Jo 



If the draw-tube be used to increase the distance by the 

 l-5th or l-6th the magnifying power will, for high objectives, 

 increase proportionately. Thus, if the draw-tube give twelve 

 inches instead of ten, and an eye-piece similar to Browning's 

 G achromatic of "1000 focal length, and a l-12th objective — 



100 12 100x12x12x10 ,,,^^ 



^ = -loooirx X 10 = 10 = ^^'^^^' 



By the formvilae the focal length of double D eye-piece 

 would, if the l-12th gives 12,000 diameters with twelve inches 

 of tubing instead of ten, be given by the equation — 



M = 12,000 = ^^^ , X ^; 



HM (• -nn • 100 X 12 3 



Iherefore, e or DD cyc-piece = 120OO x ^ X 10 = 25' 



or rather less than the 8th of an inch, or eight times deeper 



