f the Meridian Plane._--The various methods given above
for finding the meridian plane have for ultimate object the
determination of the plane, not on its own account, but as an element
for fixing the instant of noon, whereby the style may be properly
placed.

We shall dispense, therefore, with all this preliminary work if we
determine noon by astronomical observation. For this we shall want a
good watch, or pocket chronometer, and a sextant or other instrument
for taking altitudes. The local time at any moment may be determined
in a variety of ways by observation of the celestial bodies. The
simplest and most practically useful methods will be found described
and investigated in any work on astronomy.

For our present purpose a single altitude of the sun taken in the
forenoon will be most suitable. At some time in the morning, when the
sun is high enough to be free from the mists and uncertain refractions
of the horizon--but to ensure accuracy, while the rate of increase of
the altitude is still tolerably rapid, and, therefore, not later than
10 o'clock--take an altitude of the sun, an assistant, at the same
moment, marking the time shown by the watch. The altitude so observed
being properly corrected for refraction, parallax, &c., will, together
with the latitude of the place, and the sun's declination, taken from
the _Nautical Almanac_, enable us to calculate the time. This will be
the solar or apparent time, that is, the very time we require.
Comparing the time so found with the time shown by the watch, we see
at once by how much the watch is fast or slow of solar time; we know,
therefore, exactly what time the watch must mark when solar noon
arrives, and waiting for that instant we can fix the style in its
proper position as explained before.

We can dispense with the sextant and with all calculation and
observation if, by means of the pocket chronometer, we bring the time
from some observatory where the work is done; and, allowing for the
change of longitude, and also for the equation of time, if the time we
have brought is clock time, we shall have the exact instant of solar
noon as in the previous case.

In former times the fancy of dialists seems to have run riot in
devising elaborate surfaces on which the dial was to be traced.
Sometimes the shadow was received on a cone, sometimes on a cylinder,
or on a sphere, or on a combination o