270 DR. ROYSTON-PTGOTT. 



If, however, a small central aperture be formed by a stop, 

 and any convenient distance be taken between the object and 

 image (micrometric lines are the best to measure), the focal 

 length can be easily found by the formula above quoted. 



Example. — I have a Pritchard doublet, magnifying 180 

 times at 8 inches : what is the focal length ? 



•^ — ffi + 2 ~ ]80 + 2 ~ 182 ~ 91- 



Having illustrated the use of this formvila in as simple a 

 manner as practicable, it is now requisite to settle upon what 

 principle nominal focal lengths are to be ascertained. Evi- 

 dently the first thing to be done is to agree upon the standard 

 of reference. No better, I take it, can be adopted than a 

 uniform distance between the object and magnified image of 

 ten inches. This image may be viewed by using the micro- 

 scrope as a miniature-enlarging camera, be received on ground 

 glass, or it may be viewed as a virtual image formed within 

 the stop of the eye-piece, the field glass being removed, 

 either received there upon a glass micrometer or upon thin 

 oiled paper graduated finely or carefully measured by the 

 camera lucida. 



Let us take the example of an ordinary one-inch objective 

 as now made. If the tables be examined printed by different 

 opticians, it will be found that with a C eye-piece in general 

 this power is given as 100 diameters. Now, the C eye-piece 

 magnifies ten times, and if all the glasses be removed from 

 it there will be found a certain length of tube for the body 

 of the microscope, where, Avithin the stop, an image will be 

 found to be exactly magnified ten times. This point should 

 be exactly ten inches' distance from the object. In different 

 glasses this distance will be found to vary slightly, but in 

 the main it is ten inches, neither more nor less. If now, an 

 eye-lens of exactly one inch focal length, i. e. magnifying ten 

 times, be inserted within the empty eye -piece, so that the 

 stop shall be precisely in focus, then the magnifying power 

 at this standard distance will be 100. 



Now, let us calculate what the focal length (/) of an 

 equivalent lens would be to magnify an object ten times upon 

 a screen placed ten inches from the object. 



Now, ifm be large, — may be neglected ; but m the case of 

 the inch m only equals 10. 



y* really then = r- = r- 



m-\-2 + ~ 10 + 2 + -^ 

 m 10 



