RELATION OF APERTURE AND POWER IN THE MICROSCOPE. 229 
— 
3. In the face of the many intricate circumstances hinted at in 
the foregoing discussions, a zwmerical estimation of the super- 
amplification which is favourable or even admissible with various 
kinds of objectives, must be a very difficult if not impossible task. 
It would rarely be possible to assign any measure which would 
receive the general assent of microscopists, because so many 
elements are concerned in the question which cannot be estimated 
apart from the individual opinions of the observers. 
One particular difficulty in observations for this purpose is to 
decide whether a given objective is really up to date or is afflicted 
with accidental defects, which might be avoided by more 
accomplished workmanship, and must therefore be disregarded. 
Another drawback to an accurate estimation arises from the before- 
mentioned very different sensibility of the image to difference of 
structure ; and not the least of all is the large amount of personal 
equation which is always met with, when a judgment as to dif- 
ference of quality has to be formed in regard to microscopic images. 
Moreover, every one who estimates the value of the element in 
question must be conscious of its provisional character. For 
whilst the amount of super-amplification which a system is able 
to bear with a certain degree of perfection of the image is the true 
standard of the progress of microscopical optics, the determination 
of the said element cannot claim anything more than a temporary 
value: those figures of v which may very well conform to the 
present conditions will not be true for the microscopes of a former 
period, and will perhaps be upset within a few years by the further 
progress of optical science and art. 
I have now made observations for the purpose in question 
during many years—studying the performance of a large number 
of objectives of various kinds and various origins, upon very dif- 
ferent objects (artificial preparations and natural: objects), and 
checking my own observations by the judgments of some ex- 
perienced working microscopists in the department of Biology. 
What I consider as the outcome of that systematic trial will be 
briefly indicated here, with all that reserve which is necessitated 
by the nature of the problem. The principal points are :— 
(1) With the best wzde-aperture objectives which have been made 
anywhere up to the present time (1882), dry or water-immersion, of 
apertures not less than 0 ‘80 and 1. ro respectively, the deterioration 
of the image by the manifestation of aberration-effects becomes 
visible as soon as the super-amplification (v) in use is greater than 
about 4 times ;* that is to say, that any trained observer would 
* I leave out of consideration here some particular objectives (recorded in this 
Journal, vol. ii. (1879) p. 815) which were made some years ago by C. Zeiss, for 
experimental purposes, on a system of construction which is not applicable to, 
and was not intended for, regular use, 
