th line would be unequal. And
though a slope towards north or south would not affect the equality of
such shadows, and would therefore be admissible, yet it would clearly be
altogether undesirable; since the avoidance of a slope towards east or
west would be made much more difficult if the surface were tilted,
however slightly, towards north or south. Apart from this, several other
circumstances make it extremely desirable that the surface from which
the astronomers make their observations should be perfectly horizontal.
In particular, we shall see presently that the exact determination of
elevations above the eastern and western horizons would be very
necessary even in the earliest and simplest methods of observation, and
for this purpose it would be essential that the observing surface should
be as carefully levelled in a north-and-south as in an east-and-west
direction.

We should expect to find, then, that when the particular stage of
astronomical progress had been reached, at which men not only perceived
the necessity of well-devised buildings for astronomical observation,
but were able to devote time, labour, and expense to the construction of
such buildings, the first point to which they would direct their
attention would be the formation of a perfectly level surface, on which
eventually they might lay down a north-and-south or true meridional
line.

Now, of the extreme care with which this preliminary question of level
was considered by the builders of the great pyramid, we have singularly
clear and decisive evidence. For all around the base of the pyramid
there was a pavement, and we find the builders not only so well
acquainted with the position of the true horizontal plane at the level
of this pavement, but so careful to follow it (even as respects this
pavement, which, be it noticed, was only, in all probability, a
subsidiary and quasi-ornamental feature of the building), that the
pavement "was varied in thickness at the rate of about an inch in 100
feet to make it absolutely level, which the rock was not."[43]

But now with regard to the true north-and-south direction, although the
shadow method, carried out on a truly level surface, would be
satisfactory enough for a first rough approximation, or even for what
any but astronomers would regard as extreme accuracy, it would be open
to serious objections for really exact work. These objections would
have become known to observers long before the constructi