the shadow of a pointed upright. For being carried
around an inclined axis directed northwards, the sun is, of course,
brought to his greatest elevation on any given day when due south. So
that if we note when the shadow of an upright is shortest on any day, we
know that at that moment the sun is at his highest or due south; and the
line joining the centre of the upright's base with the end of the shadow
at that instant lies due north-and-south.

But though theoretically this method is sufficient, it is open, in
practice, to a serious objection. The sun's elevation, when he is nearly
at his highest, changes very slowly; so that it is difficult to
determine the precise moment when the shadow is shortest. But the
direction of the shadow is steadily changing all the time that we thus
remain in doubt whether the sun's elevation has reached its maximum or
not. We are apt, then, to make an error as to time, which will result in
a noteworthy error as to the direction of the north-and-south line.

For this reason, it would be better for any one employing this shadow
method to take two epochs on either side of solar noon, when the sun was
at exactly the same elevation, or the shadow of exactly the same
length,--determining this by striking out a circle around the foot of
the upright, and observing where the shadow's point crossed this circle
before noon in drawing nearer to the base, and after noon in passing
away from the base. These two intersections with the circle necessarily
lie at equal distances from the north-and-south line, which can thus be
more exactly determined than by the other method, simply because the end
of the shadow crosses the circle traced on the ground at moments which
can be more exactly determined than the moment when the shadow is
shortest.

Now, we notice in this description of methods which unquestionably were
followed by the very earliest astronomers, one circumstance which
clearly points to a feature as absolutely essential in every
astronomical observing station. (I do not say "observatory," for I am
speaking just now of observations so elementary that the word would be
out of place.) The observer must have a perfectly flat floor on which to
receive the shadow of the upright pointer. And not only must the floor
be flat, but it must also be perfectly horizontal. At any rate, it must
not slope down either towards the east or towards the west, for then the
shadows on either side of the north-and-sou