in height, roofed by gradually projecting blocks, and having upon its floor a slide to facilitate the transport of the sarcophagus. Thereupon follows a horizontal vestibule, closed most securely by four blocks of granite which fell like portcullises. Only three of these had been let down; the fourth remained in its original position, the lower grooves never having been cut to allow its descent. The upper chamber, of polished granite, but otherwise not ornamented, is 10.48 m. long, 5.24 m. broad, and 5.84 m. high.[B] It is ceiled horizontally with nine colossal lintels of granite, a detail which seemed at first surprising, as other voids of far less width were more firmly covered, either by projecting and gradually approaching stones, as in the ascending corridor; or with blocks leaned together so as to form a gable, as in the other passages, and in the middle chamber, called that of the Queen. Yet it was for the security of this upper chamber that the greatest care proved to have been taken. The weight of the half-height of the pyramid remaining above it was by no means allowed to rest upon its horizontal lintels. There are above them five low relieving spaces separated by four stone ceilings similar to the first; mighty blocks are inclined over all these to a gable triangle. In case of rupture the horizontal beams would of themselves have formed new triangles and prevented direct downward pressure. Cheops certainly did not need to fear the ceiling of his chamber falling in upon him. Ventilation was provided for the room by two narrow air-channels, which, inclining upwards, took the shortest course to the outside. [Illustration: Fig. 2.--The Great Pyramid of Gizeh. Section North and South, looking West.] The perfectly geometrical form of the pyramids of Gizeh has from early times led to speculations upon their having been erected in conformity with mathematical or astronomical calculations; and endless attempts have been made to discover the fixed proportions which they are supposed to embody, and to determine their symbolical or metrical significance. Too much is often assumed upon the strength of accidental coincidences, generally only approximate; but if such proportions indeed existed, whatever may have been their intention, they are evidently beyond the true province of art.