128 Transactions of the Society. 



Let the initial magnifying power of an objective whose focus is 



f be N, then N = -> ; and let n represent the initial magnifying 



power of the objective calculated according to its designated focus <j>, 



then n = - - ; and let ri be the initial magnifying power of the eye- 

 9 



piece whose focus is /', then ri = ,., . 



Column A contains the power m of the objective alone, measured 

 by projection upon a screen placed 100 in. from the object upon the 

 stage, no eye-piece being used. 



B. The initial magnifying power N of the objective. This is ob- 

 tained by adding 2 to the figures in column A and dividing the sum 



by 10. 



C. The true focal length. This is found by looking up the figures 

 in column B in a reciprocal table, and moving the decimal point 

 one place to the right. 



1). The combined power of the objective and eye-piece (the 

 mechanical tube being kept at 8f in.) measured by projection at a 

 distance of 10 in.* from the posterior focal point of the eye-piece. 

 The focal length of the eye-piece used was ■ 854.7, and ri its power 



11-7. 



E. The length of the optical tube d. This is found by multiplying 

 the product of the figures in columns C and D by • 8547, the focal 

 length of the eye-piece, dividing by 10, and adding the focal lengths 

 of the objective and eye-piece to the quotient. 



F. The length of Prof. Abbe's optical tube A. This is the same 

 as E, omitting the adding of the focal lengths of the objective and 

 eye-piece. 



G. In this column, p' is the calculated combined power of the 

 objective and eye-piece, assuming that A = 10 in. The focal length of 

 the objective /is that given in column C, and that of the eye-piece/' 

 is 0-8547 as before, p' = N»', or figures in column B X 11*7. 



H. The percentage of error in the actual measured power in 

 column D, compared with the calculated power in column G. In 

 brief, it is the percentage of error due to the deficiency or excess of 

 the tube length above or below 10 in. 



K. The calculated combined power p" of objective and eye- piece, 

 assuming that A = 10 in., and that 9 the focal length of the ob- 

 jective is true to its designation, i.e. that the 4 in. is a 4 in. and not 

 a 2^ ; that the ^ is a £ and not a ^, &c. p" = 11 ri. 



L. The percentage of error in column 1) compared with that in K. 



The figures in column K show what the magnification ought to 

 be, and what we ought to expect it to be. In the first lens, the lowest 



* As a matter of fact the distance web 20 in., and the magnifying power was 

 halved. This plan ensures greater accuracy. 



