period, i.e. such that the projection of the horizontal aperture upon
this direction is one wave-length. We conclude that a _double line
cannot be fairly resolved unless its components subtend an angle
exceeding that subtended by the wave-length of light at a distance
equal to the horizontal aperture_. This rule is convenient on account
of its simplicity; and it is sufficiently accurate in view of the
necessary uncertainty as to what exactly is meant by resolution.

If the angular interval between the components of a double line be
half as great again as that supposed in the figure, the brightness
midway between is .1802 as against 1.0450 at the central lines of each
image. Such a falling off in the middle must be more than sufficient
for resolution. If the angle subtended by the components of a double
line be twice that subtended by the wave-length at a distance equal to
the horizontal aperture, the central bands are just clear of one
another, and there is a line of absolute blackness in the middle of
the combined images.

The resolving power of a telescope with circular or rectangular
aperture is easily investigated experimentally. The best object for
examination is a grating of fine wires, about fifty to the inch,
backed by a sodium flame. The object-glass is provided with diaphragms
pierced with round holes or slits. One of these, of width equal, say,
to one-tenth of an inch, is inserted in front of the object-glass, and
the telescope, carefully focused all the while, is drawn gradually
back from the grating until the lines are no longer seen. From a
measurement of the maximum distance the least angle between
consecutive lines consistent with resolution may be deduced, and a
comparison made with the rule stated above.

Merely to show the dependence of resolving power on aperture it is not
necessary to use a telescope at all. It is sufficient to look at wire
gauze backed by the sky or by a flame, through a piece of blackened
cardboard, pierced by a needle and held close to the eye. By varying
the distance the point is easily found at which resolution ceases; and
the observation is as sharp as with a telescope. The function of the
telescope is in fact to allow the use of a wider, and therefore more
easily measurable, aperture. An interesting modification of the
experiment may be made by using light of various wave-lengths.

Since the limita