tested is now placed so that the reflected image of the same object,
whatever it may be, can be observed by the same telescope. It is evident
that if the surface be a true plane, its action upon the beam of light
that comes from the object will be simply to change its direction, but not
disturb or change it any other way, hence the reflected image of the
object should be seen by the telescope, _a_, without in any way changing
the original focus. If, however, the supposed plane surface proves to be
_convex_, the image will not be sharply defined in the telescope until the
eyepiece is moved _away_ from the object glass; while if the converse is
the case, and the supposed plane is concave, the eyepiece must now be
moved _toward_ the objective in order to obtain a sharp image, and the
amount of convexity or concavity may be known by the change in the focal
plane. If the surface has periodic or irregular errors, no sharp image can
be obtained, no matter how much the eyepiece may be moved in or out.

[Illustration: FIG. 4]

This test may be made still more delicate by using the observing
telescope, _a_, at as low an angle as possible, thereby bringing out with
still greater effect any error that may exist in the surface under
examination, and is the plan generally used by Alvan Clark & Sons. Another
and very excellent method is that illustrated in Fig. 2, in which a second
telescope, _b_, is introduced. In place of the eyepiece of this second
telescope, a diaphragm is introduced in which a number of small holes are
drilled, as in Fig. 2, _x_, or a slit is cut similar to the slit used in a
spectroscope as shown at _y_, same figure. The telescope, _a_, is now
focused very accurately on a celestial or other very distant object, and
the focus marked. The object glass of the telescope, _b_, is now placed
against and "square" with the object glass of telescope _a_, and on
looking through telescope a an image of the diaphragm with its holes or