[Illustration: Fig. 8.--Section and Plan of the Northernmost Rock-cut Tomb at Beni-hassan.] Rock-cut tombs of the twelfth dynasty (2380-2167 B.C., according to Lepsius) situated at Beni-hassan, and part of the necropolis of the ancient Nus, a city early destroyed, show the polygonal pier in the two phases of eight and sixteen sided plan. The most northern of these has the octagonal unchannelled pier in the vestibule, and the sixteen-sided channelled column within. Only fifteen channels are executed on the latter, the sixteenth side being left plane for the reception of a painted row of hieroglyphics. Both exterior and interior shafts have a base like a large flat millstone, which projects far beyond the lower diameter of the column, its edge being bevelled inward. A square abacus plinth is the only medium between shaft and ceiling, the two columns of the vestibule lacking even this. A full entablature did not exist in the interior, as a representative of the outer edge of roof and ceiling there would naturally have been out of place. The northernmost tomb has no distinct entablature carved upon the exterior; but its neighbor (_Fig._ 9.) shows, cut from the solid rock, a massive horizontal epistyle above the columns, and upon this the projecting edge of the ceiling, which appears to consist of squarely hewn joists. Lattice-work was found represented upon the stone sarcophagus of Mykerinos. Here the model of a wooden ceiling is truthfully imitated upon the rock. As, in the flat coverings of rainless Egypt, roof and ceiling appear one and the same, this entablature has but two members--epistyle and cornice; while the frieze, in Greek architecture the representative of a horizontal ceiling beneath the inclined roof, does not here exist. This order of architecture, called, because of the similarity of the shaft, the Proto-Doric, was predominant in the ancient kingdom. But at least as early as the twelfth dynasty another class of columns was in use which had been developed in an entirely different manner. The Proto-Doric columns originated from the mathematical duplication of the prismatic sides and angles of the square pier; these second made the same pier their model, but followed its painted ornament, not its architectural form. The primitive designer enriched his work with flowers, striving to preserve the quickly fading natural decoration by an imperishable imitation. Many of the bands of ornament customary in antiquity may be considered as rows or wreaths of leaves and flowers, although often they do not betray their derivation at first sight, because of the original imperfect representation of nature, the subsequent strict conventionalization, and final degeneracy into formalism. [Illustration: Fig. 9.--Second Rock-cut Tomb at Beni-hassan.]