RELATION OF APERTURE AND POWER IN THE MICROSCOPE, 255 
the exception of very low ones) will admit of a higher super-ampli- 
fication if realized in a triple system than in a system of two lenses 
only, and at the same time (once more with that exception) of a 
still higher one, when the system is made with relatively short 
working distance, the best possible constructions being always sup- 
posed. In order to obtain any numerical data at all, I must there- 
fore confine myself to a few particular kinds of objectives, which 
conform to those generally adopted standards of construction which 
may be considered as typical. With this view I have submitted to 
a careful trial ¢wo kinds of objectives: for the medium apertures, 
triple systems of about o*50 aperture, with single plano-convex 
fronts and a working distance of about one-fifth of the focal length; 
for the small aperture, systems composed of two compound lenses 
with an aperture of about 0‘15 anda working distance of about 
one-third of the focal length. Having compared a considerable 
number of specimens of both types of widely different origin (all 
being excluded which exhibited any defect of correction or tech- 
nical construction), I found the critical super-amplification for the 
first type (@=0'50) v=5, and for the second. type (a= 0°15) 
vy = 9 in round numbers.* 
Combining these values with the figure of v assigned above for 
PROPORTION OF APERTURE AND FocaL LENGTH IN A NORMAL SERIES 
OF Dry LENSEs. 
; Critical 
: Total Power|Value of the} Objective 
Numerical Aperture d-|s eae Pp Focal Length 
Aerts, | “Hage” ewe | nikescon, | reqdred, | "=m 
i mm. 
ae 115 53 10°0 a Be 
0°20 ne ey ae si 19-4 
; ) 2 12° 
0°25 132 7"4 17° 14°0 
0°30 35°0 159 67 23°7 10°5 
ee ilke une vie leas 
47°0 212 5 37°9 
0°45 238 5°3 45° 5°5 
0°50 60'0 265 5'0 53°0 sad, 
O53 291 4'8 60°6 ae 
j 73°7 317 4°6 68°9 : 
eel os ae eee 
‘Oo 370 A102) 86°0 
ee oe 397 4°2 94°4 268 
100° 423 Arar 1032 ; 
0°85 450 40 112'4 2°22, 
0°90 128°3 476 40 1190 2°10 
* The observations mentioned above were made several years ago, 1874-5. 
In the mean time nothing, however, has occured which can have changed the 
essential conditions in regard to the construction of dry lenses. 
