on of the
pyramid was commenced, and would have been associated with the
difficulties which suggested, I think, the idea itself of constructing
such an edifice.

Supposing an upright pointed post is set up, and the position of the end
of the shadow upon a perfectly level surface is noted; then whatever use
we intend to make of this observation, it is essential that we should
know the precise position of the centre of the upright's base, and also
that the upright should be truly vertical. Otherwise we have only
exactly obtained the position of one end of the line we want, and to
draw the line properly we ought as exactly to know the position of the
other end. If we want _also_ to know the true position of a line joining
the point of the upright and the shadow of this point, we require to
know the true height of the upright. And even if we have these points
determined, we still have not a _material_ line from the point of the
upright to the place of its shadow. A cord or chain from one point to
the other would be curved, even if tightly stretched, and it would not
be tightly stretched, if long, without either breaking or pulling over
the upright. A straight bar of the required length could not be readily
made or used: if stout enough to lie straight from point to point it
would be unwieldy, if not stout enough so that it bent under its own
weight it would be useless.

Thus the shadow method, while difficult of application to give a true
north-and-south horizontal line, would fail utterly to give material
indications of the sun's elevation on particular days, without which it
would be impossible to obtain in this manner any material indications of
the position of the celestial pole.

A natural resource, under these circumstances--at least a natural
resource for astronomers who could afford to adopt the plan--would be to
build up masses of masonry, in which there should be tubular holes or
tunnellings pointing in certain required directions. In one sense the
contrivance would be clumsy, for a tunnelling once constructed, would
not admit of any change of position, nor even allow of any save very
limited changes in the direction of the line of view through them. In
fact, the more effective a tunnelling would be in determining any
particular direction, the less scope, of course, would it afford for any
change in the direction of a line of sight along it. So that the
astronomical architect would have to limit the use of this