§ 5. THE EXACT DIMENSIONS OF THE PYRAMIDS.
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Fig. 15. Cheops.
Fig. 16. Cheops.Figures 15 to 20 inclusive, show the linear dimensions of the three pyramids, also their angles. The base angles are, Cheops, 51° 51′ 20"; Cephren, 52° 41′ 41″; and Mycerinus, 51° 19′ 4″.
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Fig. 17. Cephren.
Fig. 18. Cephren.
Fig. 19. Mycerīnus.
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Fig. 20. Mycerīnus:In Cheops, my dimensions agree with Piazzi Smyth—in the base of Cephren, with Vyse and Perring—in the height of Cephren, with Sir Gardner Wilkinson, nearly—in the base of Mycerinus, they agree with the usually accepted measures, and in the height of Mycerinus, they exceed Jas. J. Wild's measure, by not quite one of my cubits.
In my angles I agree very nearly with Piazzi Smyth, for Cheops, and with Agnew, for Cephren, differing about half a degree from Agnew, for Mycerinus, who took this pyramid to represent the same relation of Π that P. Smyth ascribes to Cheops (viz.: 51° 51′ 14·″3), while he gave Cheops about the same angle which I ascribe to Mycerinus.
I shall now show how I make Cephren and Cheops of equal bases of 420 R.B. cubits at the same level, viz.—that of Cephren's base.
John James Wild made the bases of Cheops, Cephren, and Mycerinus, respectively, 80, 100, and 104·90 cubits above some point that he called Nile Level.
His cubit was, I believe, the Memphis, or Nilometric cubit—but at any rate, he made the base of Cephren 412 of them.
I therefore divided the recognized base of Cephren—viz., 707·75 British feet—by 412, and got a result of 1·7178 British feet for his cubit. Therefore, his measures multiplied by 1·7178 and divided by 1·685 will turn his cubits into R.B. cubits.
I thus make Cheops, Cephren, and Mycerinus, respectively, 81·56, 101·93, and 106·93 R.B. cubits above the datum that J. J. Wild calls Nile Level. According to Bonwick's "Facts and Fancies," p. 31, high water Nile would be 138½ ft. below base of Cheops (or 82·19 R.B. cubits).
Piazzi Smyth makes the pavement of Cheops 1752 British inches (or 86·64 R.B. cubits) above average Nile Level, but, by scaling his map, his high Nile Level appears to agree nearly with Wild.
It is the relative levels of the Pyramids, however, that I require, no matter how much above Nile Level.
Cephren's base of 420 cubits being 101·93 cubits, and Cheops' base of 452 cubits being 81·56 cubits above Wild's datum, the difference in level of their bases is, 20·37 cubits.
The ratio of base to altitude of Cheops being 330 to 210, therefore 20·37 cubits divided by 210 and multiplied by 330 equals 32 cubits; and 452 cubits minus 32 cubits, equals 420.
Similarly, the base of Mycerinus is 5 cubits above the base of Cephren, and the ratio of base to altitude 32 to 20; therefore, 5 cubits divided by 20 and multiplied by 32 equals 8 cubits to be added to the 210 cubit base of Mycerinus, making it 218 cubits in breadth at the level of Cephren's base.
Thus, a horizontal section or plan at the level of Cephren's base would meet the slopes of the Pyramids so that they would on plan appear as squares with sides equal to 218, 420, and 420 R.B. cubits, for Mycerinus, Cephren, and Cheops, respectively.
Fig. 21. Click on the image to view larger version.
| R.B. Cub. | |
| Apex of Cephren above Base Cheops | 295·98 |
| Apex of Cheops above Base Cheops | 287·77 |
| Apex of Mycerinus above Base Cheops | 156·51 |
| Base Cephren above base of Cheops | 20·37 |
| Base Mycerinus above base of Cheops | 25·37 |
Piazzi Smyth makes the top of the tenth course of Cheops 414 pyramid inches above the pavement; and 414 divided by 20·2006 equals 20·49 R.B. cubits.
But I have already proved that Cheops' 420 cubit base measure occurs at a level of 20·37 cubits above pavement; therefore is this level the level of the top of the tenth course, for the difference is only 0·12 R.B. cubits, or 2½ inches.
I wish here to note as a matter of interest, but not as affecting my theory, the following measures of Piazzi Smyth, turned into R.B. cubits, viz.:—
| PYR. INCHES. | R.B. CUBITS. | ||
| King's Chamber floor, above pavement | 1702· | = | 84·25 |
| Cheops' Base, as before stated | 9131·05 | = | 452·01 |
| King's Chamber, "True Length," | 412·132 | = | 20·40 |
| King's Chamber, "True First Height," | 230·389 | = | 11·40 |
| King's Chamber, "True Breadth," | 206·066 | = | 10·20 |
He makes the present summit platform of Cheops 5445 pyramid inches above pavement. My calculation of 269·80 R.B. cub. (See Fig. 21) is equal to 5450 pyramid inches—this is about 18 cubits below the theoretical apex.
Figure 21 represents the comparative levels and dimensions of Mycerinus, Cephren, and Cheops.
The following peculiarities are noticeable:—That Cheops and Cephren are of equal bases at the level of Cephren's base;—that, at the level of Cheops' base, the latter is only half a cubit larger;—that, from the level of Mycerinus' base, Cheops is just double the height of Mycerinus;—and that from the level of Cephren's base, Cephren is just double the height of Mycerinus; measuring in the latter case, however, only up to the level platform at the summit of Cephren, which is said to be about eight feet wide.
The present summit of Cephren is 23·07 cubits above the present summit of Cheops, and the completed apex of Cephren would be 8·21 cubits above the completed apex of Cheops.
In the summit platforms I have been guided by P. Smyth's estimate of height deficient, 363 pyr. inches, for Cheops, and I have taken 8 feet base for Cephren's summit platform.