RELATION OF APERTURE AND POWER IN THE MICROSCOPE, 227 
objectives of wide than with objectives of low aperture, which 
inference is fully justified by experience.* 
(2) On the other hand, theory indicates different conditions for 
the residuary aberrations, with even the same (numerical) apertures, 
when objectives of different systems—dry and tmmersion—are com- 
pared. The uncorrectable residuals of the aberrations will always 
be greater when the total amount of aberrations requiring correc- 
,tion is greater. Now the front-aberration, which is a very pre- 
dominant part of the total amount in dry lenses of somewhat wide 
aperture, is considerably diminished with water-immersion and 
almost entirely suppressed by the homogeneous-immersion system, 
We expect therefore a higher value of admissible super-amplifica- 
tion in the case of homogeneous immersion than in that of water- 
immersion ; and a still higher for water-immersion than for dry— 
provided always that objectives of the same (numerical) aperture 
are compared ; and conversely, one and the same super-amplifica- 
tion will admit of an equal degree of perfection of image with a 
greater aperture in objectives for homogeneous-immersion than in 
water-immersion or dry lenses—which is also in accordance with 
the facts. | 
(c) Another point which deserves particular attention in every 
attempt to assign the proper relation of aperture to power, relates 
to the great influence of the 2//umination and the nature of the 
object on the visibility of the residual defects of the objectives. If 
we could determine numerically the inherent angular dissipation 
of the rays (the angle ~) for a given objective, either by computation 
or by experiment, the value of # would then indicate the visual 
angle of the circles of indistinctness in an image which is obtained 
under the normal amplification of the objective (if, for instance, 
the objective were used without an eye-piece, as a hand-magnifier) 
and U =v # the same visual angle for a super-amplification of »— 
* The-above statement does not of course imply the opinion, that an objective 
of lower aperture should, under @// circumstances, admit of a higher super- 
amplification practically than one of wider aperture. The ‘‘definition”’ of a 
lens, in the generally adopted sense, is quite another thing to the dioptrical 
precision of the image, which is in question here. There may be lack of 
“ delineating power” when a certain amplification is reached, and then every 
increase of the amplification renders the impression of the image worse and 
worse, notwithstanding the utmost perfection of the dioptrical performance of 
the lens. If, for instance, an objective of 0° 1 N.A. were made with the short 
focal length of a 1-8th, it would not bear even the lowest eye-piece, because the 
normal power of the system (80 diameters) is already an empty power for so 
narrow an aperture, whilst a well-made 1-8th of 0°8 N.A. will give a satis- 
factory image with a relatively strong ocular. If, however, an objective of 
o‘1 N.A. has a focal length of say 1 inch, it will bear a deeper eye-piece than 
a 1-8th of o°8 without any perceptible loss of sharpness. In order to compare 
microscopic images in regard to their dioptrical conditions, the strange element 
of “lack of definition of empty powers” must be excluded. 
