52 Transactions of the 



proportion of the miniature to its object at a given distance, expressed 

 by the formula given by the writer (' Phil. Tr.,' vol. ii., 1870), viz.— 



Focal length of equivalent single lens 



distance between object and image * 



'diminution of image + 2 + 1 -r- diminution 



which in our case is 



m + 2 + — 

 m 



100 



1 

 m + 2 + - 



Kemaek. — When the miniature is extremely small compared 

 with object, - may be neglected. 



JE7aj. — A Huyghenian eye-piece is placed like a condenser, and 

 forms an image of a ten-inch disk, 100 inches distant from the stage 

 micrometer ; and with a low power the miniature is found to measure 

 147 thousandths (0 ■ 147 inch) by stage micrometer, required the focal 

 length. Here the miniature is reduced in the proportion of 10 

 inches to ■ 147 or 68 times nearly ;som = 68. 



100 inches 100 



Then F = = 



68 + 2 + ¥ V 70-015 



= l^g very nearly. 



The next question arises, if such be the siderealf focal length of 

 the eye-piece, what is the magnifying power ? 



The writer has for this purpose worked out the following simple 

 problem : — 



If D be the distance at which an observer can see an object dis- 

 tinctly and the distance at which he sees really the field of view in 

 the microscope, F the focal length of a single lens, then the mag- 

 nifying power, or the proportion of the size of the image to the object 

 is one less than the distance of distinct vision divided by focal 

 length, 



or m = - - I. 



If the observer's eye adopts 10 inches, 



Then m = - — 1. 

 F 



Ex. 2. — Find the magnifying power of the eye-piece of last 

 example at 10 inches' distance for distinct vision. 

 m = — — 1 = 6i times. 



1 10 



* This formula will be found extremely useful to photographers. 

 f •' Sidereal and solar focal lengths " are terms indifferently used for expressing 

 the principal focus or focal point formed by parallel rays. 



