254 Translation of Professor Ahhes Fajper on the Microscope. 
right proportion between focal distance and angular aperture, 
which are opposed in many points to the hitherto prevalent 
practice. 
Since theory demands a limitation of angular aperture of 110° 
for all dry combinations, the calculation of minutest detail accessible 
to such objective is readily made ; and it may be shown that 
if " resolving " power be not unfairly exalted at the cost of the 
general excellence of the lens, there can be no question of detail 
which a practised eye would not recognize with a good amplifica- 
tion of from 4 to 500. Now according to the present standard of 
technical constructive means, such an amplification may be gained 
with an objective of 3 mm. English inch), even if the attribute 
good be interpreted a little more strictly than is often done. With 
immersion lenses, the physical limit of "resolution," even where 
the angular aperture is the highest attainable, does not extend so 
far that an amplification of from 7 to 800 will not be fully equal 
to it ; and this amplification would be gained with ease with a weJl- 
constructed objective of xV iiich focal length. It may be admitted 
that an amplification exceeding the minimum here given as theoreti- 
cally necessary, might greatly facilitate observation and render it 
more certain if the additional amplification be as correct as can be 
possibly made, although it would not occasion any new facts to be 
seen. Yet one can scarcely estimate the significance of this empty 
amplification far beyond the limits stated, and I therefore come to 
the conclusion that the scientific value of an objective whose focal 
length (if a dry system) is much shorter than yV inch, or if an 
immersion system, than 2V i^ich, is altogether problematical. 
The actual powers of the microscope (in the strict sense of 
correct and useful power) are, in my opinion, exhausted at these 
limits, so long, that is, as no circumstances of moment are brought 
forward which change the bearing of present theory. There exists 
no microscope in which there has been seen, or will be seen, any 
structure which really exists in the object, and is inherent in its 
nature, that a normal eye cannot recognize with a sharply defining 
immersion lens magnifying 800 times. Eeports of extraordinary 
performances (especially from England) of unusually high power 
(«V inch ?) are not of such a character as to induce me to change 
my opinion and lead me into similar error, for the superiority of 
such lenses is said to have been proved upon objects to which the 
results of my observations unreservedly apply, and which are said 
to appear under such amplification as everyone who can understand 
and give an account to himself of the optical conditions of such 
performances must know to be wholly illusory. — From Proceedings 
of the Bristol Naturalists' Society, New Series, vol. i., part 2. 
