to find evidence as we proceed which shall
either strengthen our opinion on this point, or show it to be unsound.
We are going to make this astronomical purpose the starting-point for a
series of _a priori_ considerations, each to be tested by whatever
direct evidence may be available; and it is practically certain that if
we have thus started in an entirely wrong direction, we shall before
long find out our mistake. At least we shall do so, if we start with the
desire to find out as much of the truth as we can, and not with the
determination to see only those facts which point in the direction along
which we have set out, overlooking any which seem to point in a
different direction. We need not necessarily be in the wrong track
because of such seeming indications. If we are on the right track, we
shall see things more clearly as we proceed; and it may be that evidence
which at first seems to accord ill with the idea that we are progressing
towards the truth, may be found among the most satisfactory evidence
obtainable. But we must in any case note such evidence, even at the time
when it seems to suggest that we are on the wrong track. We may push on,
nevertheless, to see how such evidence appears a little later. But we
must by no means forget its existence. So only can we hope to reach the
truth or a portion of the truth, instead of merely making out a good
case for some particular theory.

We start, then, with the assumption that the great pyramid, called the
Pyramid of Cheops, was built for this purpose, _inter alia_, to enable
men to make certain astronomical observations with great accuracy; and
what we propose to do is to inquire what would be done by men having
this purpose in view, having, as the pyramid builders had, (1) a fine
astronomical site, (2) the command of enormous wealth, (3) practically
exhaustless stores of material, and (4) the means of compelling many
thousands of men to labour for them.

Watching the celestial bodies hour by hour, day by day, and year by
year, the observer recognizes certain regions of the heavens which
require special attention, and certain noteworthy directions both with
respect to the horizon and to elevation above the horizon.

For instance, the observer perceives that the stars, which are in many
respects the most conveniently observable bodies, are carried round, as
if they were rigidly attached to a hollow sphere, carried around an axis
passing through the station of the