The height was 472 ft., and the angle of casing 53° 10ʹ.
The Third Pyramid was never quite finished, and there is some difficulty in determining the exact level of platform. The mean length of the sides was calculated by Mr. Petrie as 346 ft. 1·6 in., its height 215 ft., and the angle of its casing 51° 10ʹ.
From this it will be seen that the area of the Great Pyramid (more than 13 acres) is more than twice the extent of that of St. Peter’s at Rome, or of any other building in the world.[[33]] Its height is equal to the highest spire of any cathedral in Europe; for, though it has been attempted to erect higher buildings, in no instance has this yet been successfully achieved. Even the Third Pyramid covers more ground than any Gothic cathedral, and the mass of materials it contains far surpasses that of any erection we possess in Europe.
All the pyramids (with one exception) face exactly north, and have their entrance on that side—a circumstance the more remarkable, as the later builders of Thebes appear to have had no notion of orientation, but to have placed their buildings and tombs so as to avoid regularity, and facing in every conceivable direction. Instead of the entrances to the pyramids being level, they all slope downwards—generally at angles of about 26° to the horizon—a circumstance which has led to an infinity of speculation, as to whether they were not observatories, and meant for the observation of the pole-star, &c.[[34]] All these theories, however, have failed, for a variety of reasons it is needless now to discuss; but among others it may be mentioned that the angles are not the same in any two pyramids, though erected within a few years of one another, and in the twenty which were measured by Colonel Vyse they vary from 22° 35ʹ to 34° 5ʹ. The angle of the inclination of the side of the pyramid to the horizon is more constant, varying only from 51° 10ʹ to 52° 32ʹ, and in the Gizeh pyramid it would appear that the angle of the passage was intended to have been about one-half of this.
Mr. Petrie gives a synopsis of the various theories connected with the Great Pyramid, which applies not only to the outside form but to the several chambers and passages in the interior. “There are three great lines of theory,” he says,[[35]] “throughout the Pyramid, each of which must stand or fall as a whole, they are scarcely contradictory, and may almost subsist together;” these are (1) the Egyptian cubit (20·62 in.) theory; (2) the π proportion or radius and circumference theory; (3) the theory of areas, squares of lengths and diagonals.
Of the two first, and applying these only to the exterior by the cubit theory, the outside form of pyramid is 280 cubits high and 440 cubits length of side, or 7 in height to 11 of width. This is confirmed by the π theory, where we get the very common proportion that the height is to the circumference as the radius is to the circumference of a circle inscribed within its base; thus taking the mean height of 481 ft. 4 in., we have 481·33 × 2 × 3·1416 = 3024, whilst the side 755·75 × 4 = 3023, so near a coincidence that it can hardly be accidental, and if it was intended, all the other external proportions follow as a matter of course.
Even if this theory should not be accepted as the true one, it has at least the merit of being nearer the truth than any other yet proposed. I confess it appears to me so likely that I would hardly care to go further, especially as all the astronomical theories have signally failed, and it seems as if it were only to some numerical fancy that we must look for a solution of the puzzle.
Be this as it may, the small residuum we get from all these pyramid discussions is, that they were built by the kings of the early dynasties of the old kingdom of Egypt as their tombs. The leading idea that governed their forms was that of durability—a quasi-eternity of duration is what they aimed at. The entrances were meant to be concealed, and the angle of the passages was the limit of rest at which heavy bodies could be moved while obtaining the necessary strength where they opened at the outside, and the necessary difficulty for protection inside, without trenching on impossibility. By concealment of the entrance, the difficulties of the passages, and the complicated but most ingenious arrangement of portcullises, these ancient kings hoped to be allowed to rest in undisturbed security for at least 3000 years. Perhaps they were successful, though their tombs have since been so shamefully profaned.
To the principal dimensions of the Great Pyramid given above, it may be added that the entrance is 55 ft. 8 in. above the base, on the 19th course, which is deeper than the 11 to 14 courses above and below; at present there remain 203 courses, to which must be added 12 to 14 missing. Their average height is nearly 2 ft. 6 in., but they diminish in height—generally speaking, but not uniformly—towards the top. The summit now consists of a platform 32 ft. 8 in. square; so that about 27 ft. is wanting, the present actual height being 454 ft. It contains two chambers above-ground, and one cut in the rock at a considerable depth below the foundations.
The passages and chambers are worthy of the mass; all are lined with polished granite; and the ingenuity and pains that have been taken to render them solid and secure, and to prevent their being crushed by the superincumbent mass, raise our idea of Egyptian science higher than even the bulk of the building itself could do.