§ 14. A SIMPLE INSTRUMENT FOR LAYING OFF "PRIMARY TRIANGLES."
A simple instrument for laying off "primary triangles" upon the ground, might have been made with three rods divided into a number of small equal divisions, with holes through each division, which rods could be pinned together triangularly, the rods working as arms on a flat table, and the pins acting as pointers or sights.
One of the pins would be permanently fixed in the table through the first hole of two of the rods or arms, and the two other pins would be movable so as to fix the arms into the shape of the various "primary triangles."
Thus with the two main arms pinned to the cross arm in the 21st and 29th hole from the permanently pinned end, with the cross arm stretched to twenty divisions, a 20, 21, 29 triangle would be the result, and so on.
§ 14a. GENERAL OBSERVATIONS.
I must be excused by geometricians for going so much in detail into the simple truths connected with right-angled trigonometry. My object has been to make it very clear to that portion of the public not versed in geometry, that the Pyramids of Egypt must have been used for land surveying by right-angled triangles with sides having whole numbers.
A re-examination of these pyramids on the ground with the ideas suggested by the preceding pages in view, may lead to interesting discoveries.
For instance, it is just possible that the very accurately and beautifully worked stones in the walls of the King's chamber of Cheops, may be found to indicate the ratios of the rectangles formed by the bases and perpendiculars of the triangulations used by the old surveyors—that on these walls may be found, in fact, corroboration of the theory that I have set forth. I am led to believe also from the fact that Gïzeh was a central and commanding locality, and that it was the custom of those who preceded those Egyptians that history tells of, to excavate mighty caverns in the earth—that, therefore, in the limestone upon which the pyramids are built, and underneath the pyramids, may be found vast excavations, chambers and galleries, that had entrance on the face of the ridge at the level of High Nile. From this subterraneous city, occupied by the priests and the surveyors of Memphis, access may be found to every pyramid; and while to the outside world the pyramids might have appeared sealed up as mausoleums to the Kings that it may have seen publicly interred therein, this very sealing and closing of the outer galleries may have only rendered their mysterious recesses more private to the priests who entered from below, and who were, perhaps, enabled to ascend by private passages to their very summits. The recent discovery of a number of regal mummies stowed away in an out of the way cave on the banks of the Nile, points to the unceremonious manner in which the real rulers of Kings and people may have dealt with their sovereigns, the pomp and circumstance of a public burial once over. It is just possible that the chambers in the pyramids may have been used in connection with their mysteries: and the small passages called by some "ventilators" or "air passages," sealed as they were from the chamber by a thin stone (and therefore no ventilators) may have been auditory passages along which sound might have been projected from other chambers not yet opened by the moderns; sounds which were perhaps a part of the "hanky panky" of the ancient ceremonial connected with the "mysteries" or the "religion" of that period.
Down that "well" which exists in the interior of Cheops, and in the limestone foundations of the pyramid, should I be disposed to look for openings into the vast subterraneous chambers which I am convinced do exist below the Pyramids of Gïzeh.
The priests of the Pyramids of Lake Mœris had their vast subterranean residences. It appears to me more than probable that those of Gïzeh were similarly provided. And I go further:—Out of these very caverns may have been excavated the limestone of which the pyramids were built, thus killing two birds with one stone—building the instruments and finding cool quarters below for those who were to make use of them. In the bowels of that limestone ridge on which the pyramids are built will yet be found, I feel convinced, ample information as to their uses. A good diamond drill with two or three hundred feet of rods is what is what is wanted to test this, and the solidity of the pyramids at the same time.