Fig. 155. 
Formation of images by convex lenses. 
tance on the other side of the lens, will be of 
the same dimensions with the object: whilst, 
on the other hand, if the object be nearer the 
lens, the image will be farther from it, and of 
larger dimensions ; and if the object be farther 
from the lens, the image will be nearer to it, and 
smaller than itself. Further, it is to be re- 
marked, that the larger the image in proportion 
to the object, the less bright it will be, because 
the same amount of light has to be spread over 
a greater surface ; whilst a smaller image will 
be much more brilliant, in the same proportion. 
The knowledge of these general facts will 
enable us readily to understand the ordinary 
operation of the microscope; but the instru- 
ment is subject to imperfections of various 
kinds, the mode of remedying which cannot be 
comprehended without an acquaintance with 
their nature. One of these imperfections re- 
sults from the spherical aberration of the rays 
which have passed through lenses, whose curva- 
tures are equal over their whole surfaces. Hf 
the course of the rays be carefully laid down, it 
will be found that they do not all meet exactly 
Fig. 156. 
AB, rays falling on the periphery of the lens; F, 
focus of these; a, b, rays falling nearer the 
centre ; f, more distant focus of these. 
in the foci already stated, but that the focus of 
the rays which have passed through the peri- 
heral portion of the lens is much closer to it 
than that of the rays which are nearer the line 
of its axis; so that, if a screen be held in the 
former, the rays which have passed through the 
central portion of the lens will be orpe by 
it before they have come to a focus; and if the 
screen be carried back into the focus of these, 
the rays which were most distant from the axis 
will have previously met and crossed, so that 
they will come to it in a state of divergence. 
In either case, therefore, the image will have a 
certain degree of indistinctness ; and there is 
no one point to which all the rays can be 
brought by a lens of spherical curvature. The 
difference between the focal points of the cen- 
tral and of the peripheral rays is termed the 
spherical aberration. It is obvious that, to 
MICROSCOPE. 
produce the desired effect, the curvature is re- 
uired to be increased around the centre of 
e lens, so as to bring the rays which pass 
through it more — to a focus, and to be 
diminished towards the circumference, so as to 
throw the focus of the rays influenced by it to 
a greater distance. The requisite conditions 
may be exactly fulfilled by a lens one of whose 
surfaces, instead of being spherical, is a 
of an ellipsoid or hyperboloid of certain pro- 
portions ; but the difficulties in the way of the 
mechanical execution of lenses of this ip- 
tion are such, that, for all practical purposes, 
they have been entirely abandoned in favour of 
lenses with spherical surfaces. Various means 
have been devised for diminishing the aber- 
ration of these. In microscopes of ordi 
construction, the method employed is to dimi- 
nish the aperture or working te? te of the lens, 
so as to employ only the rays that pass 
the central part, which, if sufficiently small in 
proportion to the whole sphere, will bring them 
all to nearly the same focus. The use of this 
may be particularly noticed in the object-glasses — 
of common microscopes ; where, although the 
lens itself be large, the greater portion of its 
surface is rendered inoperative by a stop, which 
is a plate with a circular aperture interposed 
between the lens and the rest of the instrument. 
If this aperture be gradually enlarged, it will 
be seen that, although the image becomes more 
and more illuminated, it is at the same time 
becoming more and more indistinct; and that, 
in order to gain defining , the aperture 
must be reduced again. Now this reduction is 
attended with two great inconveniences ; in 
first place, the loss of ieee of light, the de- 
gree of which will depend upon the quantity 
transmitted by the toon? and will vary therefore 
with its aperture; and, secondly, the diminu- 
tion of the number or quantity of rays, which 
will prevent the surfaces of objects from bei 
properly seen. Thus, for example, we shall 
suppose the observer to be looking at the scales 
of a butterfly’s wing with a microscope fur- 
nished with two object-glasses of the same 
focal length,—one corrected, the other not so. 
If, with the same illumination of the object, he 
apply to it the uncorrected objective, the aper- 
ture of which is necessarily small, after having 
looked at it with the corrected lens, he will, in 
the first place, perceive that the whole field is 
much darker; but if, by increasing his illumi- 
nation, he give the image an equal brightness, 
and see its outline with equal distinctness, he 
will be completely unable to see with the un- 
corrected lens a series of delicate lines upon 
the surface of the scale, which the other es. 
evident. The power of exhibiting these and 
similar objects 1s termed penetration; it de- 
pends upon the size of the conical pencils of 
light admitted by the lens, and therefore upon 
its aperture. ‘ 
The spherical aberration may be considerably 
diminished by making the most advantageous 
use of single nani Thus the aberration of a 
plano-convex lens, whose convex side is turned 
towards parallel rays, is only #4ths of its 
thickness, whilst, if the plane side be turned 
