several inches from the eye,
when the dark lines caused by a total extinction of the light by
interference may be seen.

[Illustration: FIG. 7.]

If now you look toward the edge of a gas or lamp flame; you will see a
series of colored bands, that bring out the phenomenon of partial
interference. This experiment shows the difficulty in obtaining a perfect
focus of the holes or the slit in the diaphragm, as the interference
fringes are always more or less annoying. Notwithstanding these defects of
the two systems I have mentioned, in the hands of the practical workman
they are productive of very good results, and very many excellent surfaces
have been made by their use, and we are not justified in ignoring them,
because they are the stepping stones to lead us on to better ones. In my
early work Dr. Draper suggested a very excellent plan for testing a flat
surface, which I briefly describe. It is a well known truth that, if an
artificial star is placed in the exact center of curvature of a truly
spherical mirror, and an eyepiece be used to examine the image close
beside the source of light, the star will be sharply defined, and will
bear very high magnification. If the eyepiece is now drawn toward the
observer, the star disk begins to expand; and if the mirror be a truly
spherical one, the expanded disk will be equally illuminated, except the
outer edge, which usually shows two or more light and dark rings, due to
diffraction, as already explained.

[Illustration: FIG. 8.]

Now if we push the eyepiece toward the mirror the same distance on the
opposite side of the true focal plane, precisely the same appearance will
be noted in the expanded star disk. If we now place our plane surface any
where in the path of the rays from the great mirror, we should have
identically the same phenomena repeated. Of course it is presumed, and is
necessary, that the plane mirror shall be much less in area than the
spherical mirror, else the beam of light from the artificial star will be
shut off, yet I may here say that any one part of a truly spherical mirror
will act just as well as the whole surface, there being of course a loss
of light according to the area of the mirror shut off.

This principle is illustrated in Fig. 3, where _a_ is the spherical
mirror, _b_ the source of light, _c_ the eyepiece as used when the plane
is not interposed, _d_ the plane introduced into the path at an angle of
45 deg. to the central beam, and _e_ the