4 
THEORY OF THE MICROSCOPE. 
turned towards parallel rays, has its spherical aberration about 
times its thickness, while in the reverse position the aberra- 
tion is only about IjJo times the thickness of the lens. 
7. Proportionate Cnrvature. It is thus seen that the 
spherical aberration of a lens may be considerably reduced, by 
giving a proper proportion to the respective curvatures of its 
two surfaces, and by turning the more convex surface towards 
parallel rays, or the rays that are nearest parallel. 
The thickness of a lens being very nearly as the square of 
its diameter, a lens of small diameter will have only about one 
fourth as much spherical aberration as a lens of the same curva- 
ture with double its diameter. 
Hence, if only the central portion of the lens is used, the 
aberration will be still further diminished. This plan is adopted 
in all the common and cheap microscopes, but the amount of 
light transmitted is very small, and other imperfections result, 
which will be understood when we treat of angular ajperture, 
(See 15, 16, 17.) 
If the refraction is performed by two lenses of shallow cur- 
vature, the aberration is less than if the same amount of refrac- 
tion takes place in a single lens of deep curvature. 
8. iVegative Aberration. A concave lens has the same 
amount of spherical aberration as a convex lens, but it takes 
place in an opposite direction, and is therefore called negative 
aberration. 
9. Aberration of Sphericity : Curvature of the linage. 
When a flat object is viewed through a single lens, so placed 
that the central portion is clearly seen, the borders of the 
object appear indistinct, and the lens must be brought still 
nearer in order to view the lateral portions clearly. This effect 
takes place chiefly because the lateral portions of the object 
are more distant from the optical centre of the lens than the 
central portions, and partly because the refractive power of the 
lens is exerted more strongly on pencils of light, passing 
obliquely through it, than on those passing so that their axes 
coincide with the axis of the lens. For the same reason an 
image formed by a lens appears curved towards the lens 
J. & W. GRUNOW & CO’S ILLUSTRATED 
