84 BROOKES, ON MICROSCOPES AT THE EXHIBITION. 
who appears to have inherited his late father’s well-known apti- 
tude in adapting mechanical contrivance to optical requirement. 
In available angle of aperture considerable advances have been 
made by several of the leading artists; but as it is palpable that 
much misconception exists with regard to available angle of aper- 
ture, the reporter abstains from quoting stated angles. This fact 
may easily be shown; supposing the focal point to be at a dis- 
tance of 0°01 inch from the surface of the objective (which for most 
glasses is a very moderate assumption), a reference to a table of 
natural tangents will show that an angular aperture of 17° will ne- 
cessitate a linear aperture of 0°22 inch; an aperture of 172° will 
require 0°28 inch, and one of 174°, 0°38 inch, in order to admit the 
extreme rays, which for objectives of 4th inch focus is manifestly 
impossible, and @ fortiori for those of still shorter focus. It may 
here be remarked that an admirable method of determining the 
availbleangle of aperture of an objective was suggested to the jury by 
Professor Govin, of Turin, which consisted in placing the microscope 
perpendicular to any plane dark non-reflecting surface (as a table 
covered with green cloth), and haying converted the instrument 
into a telescope, by placing above the eye-piece a suitable combi- 
nation of two lenses (such as the “ examining-glass” of Mr. Ross), 
and then examining and marking the greatest lateral distance on 
either side at which a clear image of some distinct object, such as 
a narrow strip of white card-board or paper laid on the table, can 
be perceived. Half the distance between these two points, 
divided by the vertical distance of the focal point of the objective 
from the surface of the table, will, by reference to a table of 
natural tangents, give half the required angle of aperture. ‘This 
will in many cases be found to be considerably less than what may 
be termed the angle of admission of diffused light. 
In regard to angle of aperture, it may be desirable here to state 
that large angle of aperture is necessarily incompatible with that 
far more generally useful quality of a good objective, penetration. 
Penetrating power is synonymous with depth of focus; that is, 
extreme distance of two planes, the points of which are at the same 
time sufficiently in focus for the purpose of distinct vision. This 
distance will manifestly increase as the angle of aperture 
diminishes, just as in a landscape camera the fore and back grounds 
can be brought into sensible focus simultaneously only by the use 
of a small diaphragm, which greatly diminishes the angular aper- 
ture of the incident pencils. But at the same time it must be 
borne in mind that illumination, ceteris paribus, increases or 
diminishes with angle of aperture, and the best working glass will 
be that in which the best compromise is effected between these 
two conflicting requisites. For all practical purposes, except de- 
veloping the markings of diatoms, an objective of moderate aper- 
ture will be found most available. It may reasonably be doubted 
whether the development of the dottings of difficult diatoms is not 
an object rather of curiosity than of utility, and whether it is 
worth the labour that has been bestowed upon the production of 
