towards noon, and receding from it afterwards. (The curve
is a conic section--an hyperbola in these regions.) At the moment when
it crosses the arc AB, mark the point A; AP is then the direction of
the sun, and, as AH is horizontal, the angle PAH is the altitude of
the sun. In the afternoon mark the point B where it crosses the same
arc; then the angle PBH is the altitude. But the right-angled
triangles PHA, PHB are obviously equal; and the sun has therefore the
same altitudes at those two instants, the one before, the other after
noon. It follows that, _if the sun has not changed its declination_
during the interval, the two positions will be symmetrically placed
one on each side of the meridian. Therefore, drawing the chord AB, and
bisecting it in M, HM will be the meridian line.

Each of the other concentric arcs, CD, EF, &c., will furnish its
meridian line. Of course these should all coincide, but if not, the
mean of the positions thus found must be taken.

The proviso mentioned above, that the sun has not changed its
declination, is scarcely ever realized; but the change is slight, and
may be neglected, except perhaps about the time of the equinoxes, at
the end of March and at the end of September. Throughout the remainder
of the year the change of declination is so slow that we may safely
neglect it. The most favourable times are at the end of June and at
the end of December, when the sun's declination is almost stationary.
If the line HM be produced both ways to the edges of the table, then
the two points on the ground vertically below those on the edges may
be found by a plummet, and, if permanent marks be made there, the
meridian plane, which is the vertical plane passing through these two
points, will have its position perfectly secured.

_To place the Style of a Dial in its True Position._--Before giving
any other method of finding the meridian plane, we shall complete the
construction of the dial, by showing how the style may now be
accurately placed in its true position. The angle which the style
makes with a hanging plumb-line, being the co-latitude of the place,
is known, and the north and south direction is also roughly given by
the mariner's compass. The style may therefore be already adjusted
approximately--correctly, indeed, as to its inclination--but probably
requiring a little horizontal motion east or west. Suspend a fine
pl