9 
with a one-eighth, and studs the same object with black points 
(in addition to the bulbs). 
This is a fair example of deeply shaded, sharply cut defini- 
tion. All microscopic observation is a question of light and 
shadow, and the facility of changing at will the shading of 
spherical and cylindrical forms is a new avenue to truth. 
From these effects of aperture it may now be assumed that 
with a small aperture a spherical refractive particle exhibits a 
dark, even jet black, terminal annulus. Ifa body be studded 
with such beading it will necessarily appear dark from an 
assemblage of shadows; when the definition is exalted these 
beads, considered as lenses, exhibit in general too small a 
point of central illumination to be detected with ordinary 
glasses. Even if perfectly refracting and unembarrassed 
with other substrata, beads so small as ;,},,th form an 
image of a radiant source of light inconceivably minute.’ In 
some cases, therefore, they appear jet black with a small 
aperture, but most frequently invisible with an excess of 
aperture. 
Supposing the glasses free from annular aberration, greater 
depth of vision with black outlines is given by a reduced 
aperture with direct light. But if the central pencils aber- 
rate incorrigibly, then the outline will be blurred and ill- 
defined, thick and dark. 
On the other hand, enlarged aperture appears to illumi- 
nate a dark object, if transparent ; it converts, apparently, 
in many cases, opacity into translucence, transforms a 
reddish-brown scale into a brilliant object, reveals inter- 
stitial sparkling, and developes new, but often delusive, 
appearances in eidolic forms. 
It may now be stated more generally, and geometrically 
explained :—If the aperture of the objective of a microscope 
be reduced below a certain angle (83° 48’ for ordinary glass) 
spherical particles of a refractive character assume black 
annular shadows, the breadth of which is increased as the 
aperture is diminished. Assuming for a sphere f= — ie(ase a) cam 1 
(fig. 1), let BC be a refracting particle of radius 7, 
4 3 
F the principal focus for parallel rays; then, if u = 5; HF 
1 we 
= 97. Draw FN a tangent to the spherule touching it at 
N. Then it is manifest— 
1 The minute image of a brilliant flame is, in all such cases, swelled out 
by the imperfection of the glasses into an exaggerated spurious disc. 
