There is no less diversity in the external aspects of the pyramids. We are most familiar with the shapes of the great pyramids at Gizeh (Fig. 130 and Pl. 1, 2); their images have been multiplied to infinity by engraving and photography, but we make a great mistake when we imagine all the royal tombs at Memphis to be built upon this one model. They do not all present the same simplicity of form, the same regular slope from summit to base, or the smooth and polished casing which distinguished those great monuments when they were in complete preservation. The southern pyramid of Dashour offers us one of the most curious variations upon the original theme (Fig. 133). Its angle-ridges are not unbroken straight lines from base to summit. The slope of its faces becomes less steep at about half their height. The lower part of its sides make angles of 54° 41' with the horizon, while above they suddenly fall back to an angle of 42° 59'. This latter slope does not greatly differ from the 43° 36' of the other pyramid in the same neighbourhood. No indication has yet been discovered as to the builder of this pyramid. A second variation, still more unlike the Gizeh type, is to be found in the great pyramid of Sakkarah, the Stepped Pyramid, which was considered by Mariette as the oldest of them all. Taking a passage from Manetho as his authority, he thought himself justified in attributing it to the fourth king of the first dynasty, Ouenephes or Ata, and he was inclined to see in it the Serapeum, or Apis tomb, of the Ancient Empire. Its present elevation is about 190 feet. Each of its sides is divided horizontally into six large steps with inclined faces. The height of these steps decreases progressively, from the base to the summit, from 38 feet 2 inches to 29 feet 6 inches. The width of each step is nearly 7 feet. It will be seen, therefore, that this building rather tends to the pyramidal form than achieves it; it is a rough sketch for a pyramid. [Illustration: FIG. 133.--The southern pyramid of Dashour; from the measurements of Perring.] [Illustration: FIG. 134.--Section of the Stepped Pyramid; from Perring.] Does this want of completion result from accidental causes, or must it be referred to ignorance of the full beauties of the pyramidal form on the part of its builders? If the conjecture of Mariette is well founded, the Stepped Pyramid is not only the most ancient building in Egypt but in the whole world; and in the remote century which witnessed its construction men may not yet have learnt to fill up the angles left in their masonry, they may have been quite satisfied to leave their work in a condition which to us seems imperfect. [Illustration: FIG. 135.--The Stepped Pyramid; restored from the measurements of Perring.]