36 G. WEST ROYSTON-PIGOTT ON OBJECT GLASSES. 



exj^erienced in finding their exact focal length by measurement of 

 their curves. In this case, the focal length can be obtained most 

 readily by the following artifice. If the magnifying power be 

 great, a stage micrometer is to be placed exactly at ten inches dis- 

 tance from the ground glass screen. If a microscope be used, by 

 taking out the field and eye-glasses of the eye -pieces, an ordinary 

 circular 1-lOOth micrometer may be inserted ; then replacing the 

 eye-lens only, the image of the stage micrometer must be accurately 

 observed, and the magnitude of a 1-lOOth nicely determined in the 

 divisions of the eye-piece micrometer. Suppose this to be (??2), 

 the actual focal length of the lens in question will be found for 

 small lenses as follows : — 



Divide ten by this number (m), increased by two.* Larger 

 lenses will require a correction to be hereafter explained. 



Exarnple. — A small lens is found to magnify a hundredth of an 

 inch upon the stage to measure 35 hundredths at 10 inches distance 

 from the stage, within the field of an eye-piece, deprived of its field 

 lens. Find the focal length ; also for a piano convex find the curva- 

 ture of the tool to grind the lens. 



N = 2>b. /=10 -i-(ii + 2) = 10^37 

 == 0"-27027 nearly. 



In a piano convex lens radius of curvature for flint — 

 = i focal length = 0''- 135 13 inches.-f 



Example 2. — A compound lens forming an object glass of great 

 power enlarges the thousandth of an inch to 158 divisions in 

 lOOOths, as before at 10 inches. Find the approximate focal 

 length. Here 



/= 10 -r- (158 -h 2)= 10 -^ 160 = At 



* In a paper contributed to the " Philosophical Transactions," March, 1870, I 

 showed that this number (m), or the number of times the image is magnified by 

 the lens, is equal to i? — 2, for small lenses, or ?/i = ^ — 2 ; whence f = —^ 



f If perfect accuracy is required the number m (35) should be increased by the 

 reciprocal of m, namely, gU ; and the distance to be then divided not by 35 -I- 2, but 

 by 35 -i- 2 + -3I5, or 37-028571, which gives 



0"-270062, instead of 0"-27027 inches. 

 X Most pei'sons will find a difficulty in reading 158 thousandths, or 15"8 

 hundredths, on the eye micrometer ; indeed, they would more nearly read 160. 



The decimal change for the omission of the reciprocal i.^g in the divisor, which 

 ought accurately to be 158 •\-2-\- -jl^, is very slight. Performing the operation, 

 158 + 2-1- il^, for a new divisor = 1600063291. 



/= 10 H- (160-0063291) = 0062497 nearly 

 Now ,'e =0-062500 



DifPerence = "000003 

 Wliich is less than the 10,000th of an each. So that when Powell and Lealands 

 fg magnifies 1600 times with a C eye-piece of one inch focal length, it is accurately 

 Veth focal length within an almost inappreciable quantity. 



