A short time ago, I made a trip, in company with Abeken and Bonomi, to the more distant pyramids of Lisht and Meidûm. The latter interested me particularly, as it has solved for me the riddle of pyramidal construction, on which I had long been employed.[19] It lies almost in the valley of the plain, close by the Bahr Jussuf, and is only just removed from the level of inundation, but it towers so loftily and grandly from the low neighbourhood that it attracts attention from a great distance. From a casing of rubbish that surrounds almost the half of it, to the height of 120 feet, a square, sharp-edged centre rises after the manner of a tower, which lessens but little at the top, _i. e._ in an angle of 74°. At the elevation of another 100 feet there is a platform on which, in the same angle, stands a slenderer tower of moderate height, which again supports the remains of a third elevation in the middle of its flat upper side. The walls of the principal tower are mostly polished, flat, but are interrupted by rough bands, the reason of which seems hardly comprehensible. On a closer examination, however, I found also within the half-ruined building, round the foot, smoothened walls rising at the same angle as the tower, before which there lay other walls, following each other like shells. At last I discovered that the whole structure had proceeded from a little pyramid, which had been built in steps to about the height of 40 feet, and had then been enlarged and raised in all directions by a stone casing of 15 to 20 feet in breadth, till at last the great steps were filled out to a surface, and the whole received the usual pyramidal form. This gradual accumulation explains the monstrous size of single pyramids among so many smaller ones. Each king commenced the construction of his pyramid at his accession; he made it but small at first, in order to secure himself a perfect grave even if his reign should be but short. With the passing years of his government, however, he enlarged it by adding outer casings, until he thought himself near the end of his days. If he died during the erection of it, the outermost casing only was finished, and thus the size of the pyramid stood ever in proportion to the length of the king’s reign. Had the other determinative relations remained the same in the lapse of ages, one might have told off the number of years of each monarch’s reign by the casings of the pyramids, like the annual rings of trees.