length of the central rays are equal. If, when the cap is on, the
eye-piece has to be pulled out for distinct vision, the spherical
aberration has not been fully corrected; if the eye-piece has to be
pushed in, the aberration has been over-corrected. As a further test, we
may cut off the central rays, by means of a circular card covering the
middle of the object-glass, and compare the focal length for distinct
vision with the focal length when the cap is applied. The extent of the
spherical aberration may be thus determined; but if the first experiment
gives a satisfactory result, no other is required.

A star of the first magnitude should next be brought into the field of
view. If an irradiation from one side is perceived, part of the
object-glass has not the same refractive power as the rest; and the
part which is defective can be determined by applying in different
positions a cap which hides half the object-glass. If the irradiation is
double, it will probably be found that the object-glass has been too
tightly screwed, and the defect will disappear when the glass is freed
from such undue pressure.

If the object-glass is not quite at right angles to the axis of the
tube, or if the eye-tube is at all inclined, a like irradiation will
appear when a bright star is in the field. The former defect is not
easily detected or remedied; nor is it commonly met with in the work of
a careful optician. The latter defect may be detected by cutting out
three circular cards of suitable size with a small aperture at the
centre of each, and inserting one at each end of the eye-tube, and one
over the object-glass. If the tube is rightly placed the apertures will
of course lie in a right line, so that it will be possible to look
through all three at once. If not, it will be easy to determine towards
what part of the object-glass the eye-tube is directed, and to correct