towards the object, the aberration is 44 times 
the thickness of the lens. Hence, when a plano- 
convex lens is employed, its convex surface 
should be turned towards a distant object, 
when it is used to form an image by bringing 
toa focus parallel or slightly-diverging rays ; 
but it should be turned towards the eye, when 
it is used to render parallel the rays which are 
diverging from a very near object. The single 
lens having the least spherical aberration is 
a double convex, whose radii are as 1 to 6. 
When the flattest face is turned toward parallel 
rays, the aberration is nearly 34 times its thick- 
ness; but when the most convex side receives 
or transmits them, the aberration is only ;i,ths 
of its thickness. The spherical aberration may 
be still further diminished, however, or even 
got rid of altogether, by making use of com- 
binations of lenses so disposed that their op- 
_ posite aberrations shall correct each other, 
whilst magnifying power is still gained. For 
_ it is easily seen that, as the aberration of a con- 
cave lens is just the opposite of that of a con- 
_ vex lens, the aberration of a convex lens placed 
in its most favourable position may be cor- 
rected by a concave lens of much less power 
in its most unfavourable position; so that, 
although the power of the convex lens is weak- 
_ ened, all the rays which pass through this com- 
bination will be brought to one focus. This is 
the pencil of the aplanatic doublet proposed 
by Sir J. F.W. Herschel, consist- 
_ ing of a double-convex lens of 
the most favourable form, and a 
meniscus with the concave of 
_ longer focus than the convex.* 
_A doublet of this kind may be 
made of great use in the mi- 
_eroscope, as we shall hereafter 
_ show. Herschel’s 
_ Butthesphericalaberration is not doublet. 
the only imperfection with which the optician 
has to contend in the construction of micro- 
_seopes. A difficulty equally serious arises from 
the unequal refrangibility of the different coloured 
rays, which together make up white or colour- 
_ Tess light,t so that they are not all brought to 
_ the same focus, even by a lens free from sphe- 
rical aberration. It is this difference in their 
tefrangibility which causes their complete sepa- 
ration by the prism into a spectrum; and it 
manifests itself, though in a less degree, in the 
image formed by a convex lens. For if pa- 
rallel rays of white light fall upon a convex 
surface, the most refrangible of its component 
Tays, namely, the violet, will be brought toa 
focus at a point somewhat nearer to the lens 
than the principal focus, which is the mean 
of the whole; and the converse will be true of 
_ the red rays, which are the least refrangible, 
_ and whose focus will therefore be more distant. 
* The exact curvatures to be given to these sur- 
faces will be found in the original memoir, Pbil. 
Trans. 1821. 
+ It has been deemed better to adhere to the 
ordinary phraseology, when speaking of this fact, 
as more generally intelligible than the language in 
which it might be more scientifically described, 
and at the same time leading to no practical error. 
4 
| 
MICROSCOPE. 
335 
Fig. 158. 
Diagram illustrative of ehromatic aberration, 
A B, rays of white light refracted by a convex 
lens; C, the focus of the violet rays, which then 
cross and diverge towards E F; D, the focus 
of the red rays which are crossed at the points 
E E, by the violet; the middle point of this 
line is the mean focus, or focus of least aber- 
ration. 
This is easily proved experimentally. Ifa 
lens be so fixed as to receive the solar rays, 
and to illuminate a white screen at any dis- 
tance between the lens and the mean focus, the 
luminous circle will have a red border, because 
the red rays will there form the exterior of the 
cone; but if it be removed beyond the mean 
focus, the circle will have a violet border, be- 
cause the violet rays will then be outermost. 
As the spherical aberration would be mixed up 
with the chromatic in such an experiment, the 
undisguised effect of the latter will be better 
seen by taking a large convex lens, and co- 
vering up its central part, so as to allow the 
light to pass only through a peripheral ring ; 
and since the greater the alteration in the course 
of the rays, the greater will be the separation 
of the colours, (or dispersion, as it is techni- 
cally called,) this ring will exhibit the pheno- 
menon much better than would be done by the 
central portion of the lens. Hence, in prac- 
tice, the chromatic aberration is partly obviated 
by the same means used to diminish the sphe- 
rical aberration,—the contraction of the aper- 
ture of the lens, so that a very small portion 
of the whole sphere is really employed. But 
this contraction is attended with so much in- 
jury to the performance of the microscope in 
other respects, that it becomes extremely de- 
sirable to avoid it. In no single lens can any 
correction for chromatic aberration be effected ; 
and it requires a very nice adjustment of two, 
three, or even more, to accomplish this with 
perfection. 
The correction is accomplished by bringing 
into use the different dispersive powers of va- . 
rious materials, which bear no relation to their 
simple refracting power. As the effects of con- 
cave lenses are in all respects the converse of 
convex, it is obvious that, if a concave lens of 
the same curvature be placed in apposition 
with the convex, in such an experiment as 
that just alluded to, the dispersion of the rays 
will be entirely prevented, but neither wi!l any 
change in the course of the rays take place. 
If, however, we can obtain a substance of 
higher dispersive power in proportion to its 
power of refraction, it is obvious that a con- 
cave lens of less curvature formed of it will - 
correct the dispersion occasioned by the convex 
lens, without altogether antagonising the re- 
fraction of the latter. This is accomplished 
