by a little more than 12 hours
from the right ascension of the Pole star. The great circle which
joins the two stars passes therefore close to the pole. When the Pole
star, at a distance of about 1 deg. 14' from the pole, is crossing the
meridian above the pole, the star [eta] _Ursae Majoris_, whose polar
distance is about 40 deg., has not yet reached the meridian below the
pole.

When [eta] _Ursae Majoris_ reaches the meridian, which will be within
half an hour later, the Pole star will have left the meridian; but its
slow motion will have carried it only a very little distance away. Now
at some instant between these two times--much nearer the latter than
the former--the great circle joining the two stars will be exactly
vertical; and at this instant, which the observer determines by seeing
that the plumb-line hides the two stars simultaneously, neither of the
stars is strictly in the meridian; but the deviation from it is so
small that it may be neglected, and the plane through the eye and the
plumb-line taken for meridian plane.

In all these cases it will be convenient, instead of fixing the plane
by means of the eye and one fixed plummet, to have a second plummet at
a short distance in front of the eye; this second plummet, being
suspended so as to allow of lateral shifting, must be moved so as
always to be between the eye and the fixed plummet. The meridian plane
will be secured by placing two permanent marks on the ground, one
under each plummet.

This method, by means of the two stars, is only available for the
upper transit of _Polaris_; for, at the lower transit, the other star
[eta] _Ursae Majoris_ would pass close to or beyond the zenith, and
the observation could not be made. Also the stars will not be visible
when the upper transit takes place in the daytime, so that one-half of
the year is lost to this method.

Neither could it be employed in lower latitudes than 40 deg. N., for
there the star would be below the horizon at its lower transit;--we
may even say not lower than 45 deg. N., for the star must be at least
5 deg. above the horizon before it becomes distinctly visible.

There are other pairs of stars which could be similarly employed, but
none so convenient as these two, on account of _Polaris_ with its very
slow motion being one of the pair.

_To place the Style in its True Position without previous
Determination o