RELATION OF APERTURE AND POWER IN THE MICROSCOPE. 257 
class. The only question which deserves consideration is therefore, 
What latitude may be properly admitted for deviations from the 
standard proportion in the direction of ducreased apertures (or 
diminished objective-powers) ? 
The case here is somewhat different from that discussed above 
in the consideration of the proper utilization of the maximum aper- 
ture of any kind of system. For the angles which come into con- 
sideration now, being more or less within the attainable maximum, 
aperture is no longer difficult to attain. A surplus being easily 
obtained, may be sacrificed without hesitation, whenever such a 
benefit may be expected therefrom as is not counterbalanced by 
greater disadvantages. The question will therefore come to merely 
practical grounds: how far a surplus of aperture may afford a real 
(not only illusory) advantage, and what is the balance between 
these advantages and disadvantages which are perhaps attendant 
’ upon the increase ? 
As has been pointed-out before (Vol. II. 1882, p. 469), there zs 
a reasonable consideration which will recommend in some cases, 
viz. for the lower angled systems, the use of somewhat wider 
apertures than can be fully utilized by the total amplifications for 
which the systems are constructed, or—what is the same thing— 
will recommend the use of dower powers with a given aperture than 
is indicated by the corresponding figures of N of Table I. The 
surplus of aperture which is thus left unemployed in regard to the 
delineating power is utilized in promoting the illuminating power 
(or the brightness of the image), at least when narrow incident 
pencils are required for proper illumination of the objects. On the 
other hand, it has been shown that the said benefit is practically 
confined within some narrow limits. 
As I have said already, I am fully aware of the uncertainty of 
the numerical data on which the above computations are based, 
which uncertainty will scarcely ever be overcome in a matter like 
that in question. Though in my opinion the figures advanced 
above will conform as nearly as possible to the present state of the 
Microscope, I should make no serious objection if any other 
observer arrived at figures which differ from mine by twenty or 
even thirty per cent., bearing in mind the interference of so many 
elements of individual judgment. I do not, therefore, lay any 
great stress upon the numerical details; the reader may try to 
improve them, or take them as a mere exemplification of general 
principles, illustrating their application to actual systems. What 
I insist upon is only that the theory of the Microscope is com- 
petent to indicate a distinct guide for the vational construction of 
objectives on the principle of proper economy of the independent 
capabilities of the systems (delineating power and amplifying 
power) ; that this principle leads necessarily to a certain propor- 
