There remain about a hundred of these in the vicinity of the ancient city of Memphis, extending over a considerable extent of country, and others are found in Thebes and at Meroë in Ethiopia. There have been many theories advanced upon the subject of their origin and purpose, and many arguments set forth seeking to prove that they were observatories, temples, granaries, meteorological monuments, or tombs. Nearly all modern authorities agree upon the last as the most probable solution of the problem, not only from the sarcophagi and mummies found within many of them, and from inscriptions relating events in the lives of important personages which adorn the walls of some of their inner chambers, but from the fact that these buildings are never found beyond the confines of cemeteries. In erecting these monuments, the Egyptians usually selected a site upon a rocky plateau, on which a space equal to the superficial area required for the base was made level, a mound being left in the centre which was bonded in with the masonry. Below this platform a sepulchral chamber and connecting passage were hollowed in the rock. The pyramid was built over this chamber and contained one or more additional apartments, reached from the outside by narrow and inclined corridors. It was generally constructed with blocks of limestone, in successive steps receding at an angle varying from forty-five to seventy degrees. The outside was afterward cased with slabs of polished syenite, upon which inscriptions were engraved or painted. The interior chambers and corridors were likewise lined with polished granite, sometimes so mathematically jointed that a needle could not be pushed between the stones. Ceilings were formed by inclined slabs resting against each other or the walls were corbelled inward until they met. The entrances to the passages were invariably closed and concealed, and portcullises of heavy granite blocks, sliding in grooves, were placed at intervals along the corridors, the more effectually to preserve the sepulchre from violation. Nearly all have, nevertheless, been entered and rifled, so that but little is left to aid the archæologist in his researches. Fragmentary inscriptions and local observations compared with the accounts given by Greek and Latin authors have, however, resulted in the piecing together of what may be presumed to be an accurate history of the pyramid-builders. The three largest pyramids are situated at Gizeh, a small village near Cairo, and are respectively those of Cheops, known also as Suphis or Shoofoo, Chephren or Shafra, and Mycerinus. The following table shows the dimensions given by two of the best authorities: SIDE OF BASE. PERPENDICULAR HEIGHT.