FOCAL LENGTH OF ENGLISH OBJECT-GLASSES. 271 



_ _10l_ 

 ~ I2T 



= -826446, 



SO that the maker, in producing an " inch'' objective capable 

 of forming an image one hundred times larger with a C eye- 

 piece at 10 inches' distance, must form it of a solar focal 

 length of 



0-826446, 



or nearly -i-th of an inch less than one inch. 



But as the powers increase, and the focal length dimi- 

 nishes, the solar focal length more and more nearly ap- 

 proaches the nominal. 



Example 2. — " One half inch," magnifying 200 with C eye- 

 piece at 10 inches' distance : 



._ d _ 10 



»i + 2 + 1 20 -I- 2 + ^ 



_ _12_ 

 ~" 22-05 



= 0-453514, 

 focal length of " half inch" nominal. 



If the first approximation be taken, leaving out — 

 . d 10 5 / - 5 ] \ 



/i = ^^i = 22 = n v^^^ai-^y =IoO^TJ 

 = 0-545454 

 Error, ^Sth of an inch. 



Example 3. — "One sixteenth:" nominal power ] 600 : C 

 eye-piece ; m = 160. 



or, say, -poVVoths of an inch. 



A nearer approximation will be obtained by not neglecting 

 1 1 



— or TTTTT, when 

 m 160' 



. _ 1 10 



IbO + 2 + jgQ 



