exquisite workmanship often found in the early periods, did not so much depend on a large school or widespread ability, as on a few men far above their fellows, whose every touch was a triumph. In this way we can reconcile it with the crude, and often clumsy, work in building and sculpture found in the same ages. There were no trades union rules against ‘besting one’s mates’ in those days, any more than in any business at present where real excellence is wanted. The results were decidedly destructive for the theories. The fundamental length of the base of the pyramid does not agree to any of the theoretical needs: and though no doubt some comfort has been extracted from hypothetical lengths of what the pyramid base would be if continued down to levels below the pavement (such as the different sockets), yet no such bases ever existed, nor could even be guessed at or theorised on, so long as the pyramid base was intact, as the sockets were entirely covered by casing and pavement. Various other theories fare as badly; and the only important one which is well established is that the angle of the outside was such as to make the base circuit equal to a circle struck by the height as a radius. See also the account of Medum. The second pyramid was built by Khafra. His name was first found with it on the piece of a mace-head of white stone, which I found in the temple. The form is here completed from another head of the twelfth dynasty; and drawings of maces from Medum show the head and stick entire. In accuracy Khafra’s work is inferior to that of Khufu. The errors of the pyramid length are double, and of angle quadruple that found in the earlier work, and the bulk of its masonry is far rougher. But the sarcophagus in it is of much better work, without any mistakes, and generally showing more experience and ability. The third pyramid, of Menkaura, is again inferior to the second, in both its outer form and internal work. It has moreover been most curiously altered; originally intended to be of small size, it has been greatly enlarged, not by repeated coatings, but at one operation. The original entrance passage was abandoned, and the chamber was deepened, another passage cut from the inside outwards so as to emerge lower down, and another chamber excavated below the level of the first, and lined with granite. [Illustration: 7. MACE-HEAD OF KHAFRA.] Some very usual fallacies with regard to the [Illustration: 8. PYRAMID DOORS.] [Illustration: 9. PIVOT HOLE OF DOOR AND CUTTING OF ROOF; SOUTH PYRMAID, DAHSHUR.]