254 THE MICROSCOPICAL NEWS, 
application, and 24 (ze. 10, 10, 15 respectively) the utmost ad- 
missible figure in regard to lenses for diatom work (the minimum 
amplifications, 480, 640, 720, being regarded); because if still 
higher ocular-powers should be required even for these minimum 
amplifications the deterioration of the image, attendant upon the 
enlargement of the aberration-circles, will become so perceptible, 
even with the least sensitive objects, that satisfactory recognition of 
the minutest details must be ungestionably lost. Though the 
details which are within the reach of the aperture may still be seen, 
the quality of the image will be so much inferior to that obtained 
by higher objective-powers and lower ocular-powers that it is 
obviously unwise to obtain under unfavourable conditions what 
may as easily be otherwise obtained. I must therefore consider as 
irrational constructions all those wide-angled lenses which do not 
yield even the lowest total power required for proper utilization of 
the aperture, except by a still greater amount of eye-piecing than 
is assigned above. 
With these various concessions to personal customs and to par- 
ticular purposes, the principles established here appear to be recon-. 
cilable with a rather wide latitude in their practical application. 
The zormal focal lengths for the wide-angled objectives of the three 
systems being taken as above, we have the admissible maximum 
values of / (or minimum powers) : 
Dry. Water- Homogeneous- 
immersion. immersion. 
‘ Bite ‘ a ape : co ae 
ee a Tina, ie 3°@ 1am, =).7. In: 5°2 mm. = _*' in. 
4°8 6°4 4°8 
And the minimum values of / (or maximum powers) : 
2°*rmm. = in, o'°78mm.= in. 1°05 min — ee 
12 32 24 
(2) As to those objectives which do not aim at the attainable 
maximum of delineating power, the discussion may be confined to 
the dry lenses, because in practice the other systems are not in use 
with much lower apertures (which is of course very prudent). In 
order to determine now the proper gradation of the focal length 
for the lower apertures of the dry system, the figures of v must be 
determined which correspond to the different apertures. These 
values, as has been pointed out above, depend on many circum- 
stances besides the aperture—particularly on the type of construc- 
tion and (in the higher and medium apertures) the ratio of the 
working distance to the focal length. It will be impossible, there- 
fore to assign values of v which could claim a general acceptance, 
even for one standard of estimation. Any definite aperture (with 
