eee iy of Microscopic Objectives. 157 
of distinct vision, as well as about the length used by microscopists 
in actual work. 
An inspection of the formula f = oy shows (1) that the 
focal length of any lens is not inversely proportional to its magnify- 
ing power with a given distance J between the conjugate foci, as is 
commonly assumed, but to @ 1 the ordinary supposition ap- 
proaching absolute correctness as m increases. Hence the inaccuracy 
of any system of estimating focal lengths upon this assumption 
when applied to lenses of long focus. 
(2.) The shorter the focal length of the objective, the less will 
any error in the measurement of / affect the result. 
(3.) Any error in the measurement of n also affects the result 
less in a lens of short focus. It would therefore appear that by 
this method the most accurate results are obtained with the objec- 
tives of highest power. The following examples from the records 
of my observations will illustrate this last pomt. The numerators 
of the fractions are the readings on the paper scale, the denomi- 
nators, the number of spaces of the micrometer scale corresponding 
to these readings, the quotient being of course the value of one of 
these magnified spaces in fiftieths of an inch, 
With objective No. 16*, Smith and Beck, 1} inch— 
Scale readings 
32°8 32°7 32°7 
= = 2°982. sae 2°973. i 2°973, 
Give values of n = 5:964. 5-946. 5° 946. 
The corresponding values of f are— 
1°3362 inch. 1:°3392 inch. 1°3392 inch. 
2=276 mm. m=1°'3382in. Difference of extremes = +0030 in. 
With objective No. 8, Natchet No. 2— 
Scale readings 
4} -2 AL? 34:4, cate ae 
+ = 6866. = 6866. = = 6880. a= 6883. 
Give values of n = 
34°879. 34°879. 34 °950. 34-965. 
The corresponding values of f are— 
*25494 inch. °25494 inch. °25446 inch. ‘254385 inch. 
7=239 mm. m=‘25466in. Difference of extremes = *00059 in. 
With objective No. 1, ¢, Hartnack, No, 10— 
Poe 24°2 36°3 36°3 
Tp =2 447. liens 420. 75 =? 420. 1 aie 420. 
