RELATION OF APERTURE AND POWER IN THE MICROSCOPE, 205 

1. Every given degree of minuteness of microscopic detail requires a given 
aperture in order to obtain a complete (or perfect) image, z.e. an image which 
is a true enlarged projection of the structure, exhibiting all elements in their 
true form and arrangement. The minuter the dimensions of the elements the 
wider an aperture is necessary—the larger these dimensions the narrower an 
aperture is sufficient. Structures whose smallest elements are measured by con- 
siderable multiples of the wave-lengths of light are perfectly delineated with 
low or very moderate apertures, and their examination with wide apertures does 
not improve their recognition. On the other hand, if we are dealing with 
objects whose dimensions (or structural elements) are equal to a few wave- 
lengths only, even the widest apertures hitherto obtained will not afford com- 
plete or strictly true images, but will show these objects more or less incomplete 
or modified. This general principle holds good in regard to objects of every 
kind, regular or irregular, isolated particles or composite structures, because the 
physical conditions of microscopical delineation are always the same. 
The obvious inference from this principle is that the widest possible apertures 
must beused for the observation of objects or structures of very minute 
dimensions, low and moderate apertures for relatively large objects. 
It may perhaps be said that the objects of microscopical research do not 
justify such a distinction of large and minute, since the works of nature are 
always elaborated to the minutest details, all coarse objects being composed of 
smaller elements, and these of still smaller ores, &c. This is quite true in 
regard to the objects considered as natural things, but not as objects of scientific 
research. The interest of research is not always directed to the ultimate 
elements, but is as often confined to the consideration of the coarser parts, and 
in such cases the observer is not only allowed but sometimes compelled, to dis- 
regard everything which is not connected with the scientific aim of his investi- 
gation. To observe every object in nature throughout, from Alpha to Omega, is 
the privilege of dz/e/tante microscopy only, which has no distinct aim. There 
are many lines of the most valuable scientific research (¢.g., the greatest part of 
all morphological investigations) which have not to deal with very minute things. 
This kind of work can be completely done with low or moderate apertures. 
To recommend the application of wide-angled objectives for every branch of 
microscopy, as has been, in fact, done by excited wide-aperturists, is no more to 
be supported than it would be to recommend the use of a magnifier to a painter 
for inspecting the tree which he proposes to delineate, 
According to what has just been said, the only benefit of greater aperture is 
that it is capable of delineating minuter things. Now minute dimensions re- 
quire high amplifications in order that they may be enlarged to a visual angle 
sufficient for distinct vision.. Low figures of amplification cannot render visible 
(at least not distinctly visible) details which are beyond a certain limit of 
minuteness. Even if they are delineated by the Microscope they would remain 
hidden to the eye for want of sufficient visual angle. It follows therefore that 
wide apertures will not be utilized unless at the same time there is a linear am- 
plification of the image, at least sufficient for exhibiting to the eye the smallest 
dimensions which are within the reach of such an aperture. On the other 
hand, a high amplification will be useless if we have small apertures which 
delineate details of dimensions only capable of being distinctly seen in an image 
of much lower amplification. We have here an empty amplification, because 
there is nothing in the image which requires so much power for distinct recog- 
nition, In the first case (deficiency of power) the large aperture cannot show 
more than a smaller one; in the other case (deficiency of aperture), the high 
amplification shows no more than a lower would do. Consequently :— 
Wide apertures when high amplification is required; low or moderate 
apertures when low or moderate amplifications are sufficient or cannot be 
overstepped. 
