boats to close below the hill, were raised to their required places along gently sloping causeways.  The internal arrangement of the pyramids, the lengths of the passages and their heights, were very variable; the pyramid of Khufu (Cheops) rose to 475 feet above the ground, the smallest was not 30 feet high.  The difficulty of imagining now what motives determined the Pharaohs to choose such different proportions has led some to think that the mass built was in direct proportion to the time occupied in building; that is to say, to the length of each reign.  Thus it was supposed that the king would begin by hastily erecting a pyramid large enough to contain the essential parts of a tomb; and then, year by year, would add fresh layers around the first core, until the time when his death for ever arrested the growth of the monument.  But the facts do not justify this hypothesis.  The smallest of the pyramids of Sakkarah is that of Unas, who reigned thirty years; while the two imposing pyramids of Gizeh were raised by Khufu and Khafra (Chephren), who governed Egypt, the one for twenty-four, and the other for twenty-three years.  Merenra, who died very young, had a pyramid as large as that of Pepi II., whose reign lasted more than ninety years (Note 16).  The plan of each pyramid was laid down, once for all, by the architect, according to the instructions which he had received, and the resources placed at his disposal.  He then followed it out to the end of the work, without increasing or reducing the scale (Note 17).

[Illustration:  Fig. 136.—­Section of the Great Pyramid.[30]]

The pyramids were supposed to have their four faces to the four cardinal points, like the mastabas; but, either from bad management or neglect, the greater part are not oriented exactly, and many vary distinctly from the true north (Note 18).  Without speaking of the ruins of Abu Roash or Zowyet el Aryan, which have not been studied closely enough, they naturally form six groups, distributed from north to south on the border of the Libyan plateau, from Gizeh to the Fayum, by Abusir, Sakkarah, Dahshur, and Lisht.  The Gizeh group contains nine, including those of Khufu, Khafra, and Menkara, which were anciently reckoned among the wonders of the world.  The ground on which the pyramid of Khufu stands was very irregular at the time of construction.  A small rocky height which rose above the surface was roughly cut (fig. 136) and enclosed in the masonry, the rest being smoothed and covered with large slabs, some of which still remain (Note 19).  The pyramid itself was 481 feet high and 755 feet wide, dimensions which the injuries of time have reduced to 454 feet and 750 feet respectively.  It preserved, until the Arab conquest, a casing of stones of different colours (Note 20), so skilfully joined as to appear like one block from base to summit.  The casing work was begun from the top, and the cap placed on first, the steps being covered one after the other, until they reached the bottom (Note 21).