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 observer (as through a centre) and directed towards a certain point in the dome of the heavens. That point, then, is one whose direction must not only be ascertained, but must be in some way or other indicated. Whatever the nature of an astronomer's instruments or observatory, whether he have but a few simple contrivances in a structure of insignificant proportions, or the most perfect instruments in a noble edifice of most exquisite construction and of the utmost attainable stability, he must in every case have the position of the pole of the heavens clearly indicated in some way or other. Now, the pole of the heavens is a point lying due north, at a certain definite elevation above the horizon. Thus the first consideration to be attended to by the builder of any sort of astronomical observatory, is the determination of the direction of the true north (or the laying down of a true north-and-south line), while the second is the determination, and in some way or other the indication of the angle of elevation above the north point, at which the true pole of the heavens may lie.