


RELATION OF APERTURE AND POWER IN THE MICROSCOPE. 207 

The above is an example of waste of aperture, or lack of useful power; waste 
of power and lack of aperture are exemplified by every objective of excessively 
short focal length, ¢.g. 1-50 inch. Such a lens, even if immersion, cannot be 
made with an aperture of much greater numerical value than 1.0, in consequence 
of the technical obstacles arising with such very short focal lengths. Now the 
limit of an aperture of that amount is entirely exhausted, at all events with a 
power of 1000 to 1200 diameters, inasmuch as nothing of the real attributes of 
an object can be seen with that aperture under a higher amplification, which 
could not be as well recognized under the lower. A I- 50, however, will yield 
1500-2000 diameters with the lowest eye-pieces which are usually employed. 
The lowest attainable power is therefore an empty power already, and every 
useful amplification available with the aperture in question could be obtained 
under favourable conditions and’ with much less inconvenience by an objective 
of half the power, or even less. 
3. The preceding shows that wide apertures can only be utilized in the obser- 
vation of minute details, under high amplifications obtained with objectives of 
short focal length. Wide apertures are therefore useless when those conditions 
are not fulfilled, because in this case the same result could be obtained as well 
' with low-angled systems. But as abundance, primé facie, is no detriment, the 
foregoing considerations do not enforce any positive objection to the use of wide 
apertures for every kind of work. There are however other points of view from 
which it becomes obvious that the application of wider apertures than can be 
utilized is not merely superfluous but is a decided disadvantage, inasmuch as they 
prevent the utilization of some really valuable benefits which are the privilege of 
low and moderate apertures. 
The first disadvantage results from the reduction of the depth of vision (or 
the “ penetration ” of the Microscope) which is connected with wide apertures. 
I have given in another place * a discussion of the circumstances on which pene- 
tration depends, and the formule which afford an approximate numerical 
estimation of the depth of vision in microscopic observation. ‘These theoretical 
suggestions show (in accordance with the experience of practical microscopists) 
the reduction of penetration with increasing aperture under one and the same 
amplification, and especially when the amplification is not restricted to very 
small figures. Now there are many objects of microscopical research which do 
not require, and, indeed, do not even admit of high powers, but demand for 
effective investigation as much penetration as possible. This is always the case 
where the recognition of solid forms is of importance, and therefore a distinct 
(at least, a tolerably distinct) vision of different planes at once must be possible, 
whether the observation is assisted by stereoscopic devices or not. The greater 
part of all morphological work is of such a kind, and in this line of observation 
therefore a proper economy of aperture is of equal importance with economy of 
power. 
Whenever the depth of the object under observation is not very restricted, and 
it is essential that the depth dimension shall be within the reach of direct obser- 
vation, low and moderate powers cannot be overstepped, and no greater 
aperture should therefore be used than is required for the effectiveness of these 
powers—an excess in such a case isa real damage: High powers and corre- 
spondingly wide apertures are restricted to those observations which do not 
require any perceptible depth of vision, 2.2. to two different cases (1) when the 
objects are quite flat or exceedingly thin; (2) when preparations of greater depth 
are sufficiently transparent to admit of an indirect recognition of their solid 
structure by means of successive optical sections through successive focussing of 
different planes. For the latter method of observation the loss of penetration 
with increasing power and aperture is no drawback, but rather an advantage, 
because it enhances the distinct separation of the sectional images at successive 

* See this Journal, i. (1881) p. 689. 
