de 30 deg. north, the sun at noon in spring (or, to speak
precisely, on the day of the vernal equinox) is just twice as far from
the horizon as he is from the point vertically overhead; and if a
pointed post were set exactly upright at true noon (supposed to occur at
the moment of the vernal or autumnal equinox), the shadow of the post
would be exactly half as long as a line drawn from the top of the pole
to the end of the shadow. But observations based on this principle would
have presented many difficulties to the architects of the pyramid. The
sun not being a point of light, but a globe, the shadow of a pointed rod
does not end in a well-defined point. The moment of true noon, which is
not the same as ordinary or civil noon, never does agree exactly with
the time of the vernal or autumnal equinox, and may be removed from it
by any interval of time not exceeding twelve hours. And there are many
other circumstances which would lead astronomers, like those who
doubtless presided over the scientific preparations for building the
great pyramid, to prefer a means of determining the latitude depending
on another principle. The stellar heavens would afford practically
unchanging indications for their purpose. The stars being all carried
round the pole of the heavens, as if they were fixed points in the
interior of a hollow revolving sphere, it becomes possible to determine
the position of the pole of the star sphere, even though no bright
conspicuous star actually occupies that point. Any bright star close by
the pole is seen to revolve in a very small circle, whose centre is the
pole itself. Such a star is our present so-called pole-star; and, though
in the days when the great pyramid was built, that star was not near the
pole, another, and probably a brighter star lay near enough to the
pole[17] to serve as a pole-star, and to indicate by its circling motion
the position of the actual pole of the heavens. This was at that time,
and for many subsequent centuries, the leading star of the great
constellation called the Dragon.

The pole of the heavens, we know, varies in position according to the
latitude of the observer. At the north pole it is exactly overhead; at
the equator the poles of the heavens are both on the horizon; and, as
the observer travels from the equator towards the north or south pole of
the earth, the corresponding pole of the heavens rises higher and higher
above the horizon. In latitude 30 deg. north, or