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CENTIMETRIC LOCATION OF THE ELEMENTS OF THE RAMP
As noted by Georges Goyon [3], locations are difficult to consider with such
precision if, all through the erection of the pyramid, we cannot have access
to the knowledge of its axis, materialised by a plumbline permanently pointing
to a mark on the ground. This implies, as he notes it ( [3] page 184) keeping
a shaft open pointing to this point, this fitting with the fact that the sepulchral
rooms are displaced towards the south. Picture 14 reproduces picture 67 in his
work.
Picture 23: Respective positions of the sepulchral rooms and the axis
of the pyramid.
For a plumbline to be permanently pointed at the mark on the ground ( or made on the sculpted rocky table, initially present on the Giza plateau), a man must be on site to do this checking. Then there are two solutions. Either this man gets down this shaft, which raises a problem of ventilation, or this man has access to this workplace through a narrow horizontal gallery, at the level of the ground, constituted at the very beginning of the works. Even if the only thing required from this gallery is to allow a man to creep along it, its ceiling has to be very strong, either consisting of a corbelled construction ( as in the Great Gallery)or equipped with voussoirs. Indeed this gallery will be located at a level where it will have to bear all the weight of the pyramid and where the stress on its ceiling will be maximal. The second solution eliminates the problem of ventilation. Locations done with the help of two practicables, one placed in the centre of the work platform and the other placed next to the angular set to be constituted will allow to determine the position in space of the outer corner with a centimetric precision. Let us go into the details of the method to be used. A first practicable is placed at the base of the shaft in which the plumbline goes down, materialising the axis of the pyramid. Men can move about under this practicable and another man can have access to the top of this practicable with the help of a ladder.
Picture 24: Central practicable.
Picture 25: The sighting table placed on the floor of the practicable.
The use of such a viewing table has already been mentioned by G.Goyon in his book, [3] page 185, picture 68. Its horizontality is ensured by a the use of a level. The surveyors move the table until a plumbline starting from its centre points, at the bottom of the pit, to a mark on the ground, which a man on site announces. The viewing table consists of a rotary part sliding in a circular groove (a work that the Egyptians, experts in cabinetmaking, could have easily achieved). Various sightings can be made, as suggested by Strabon [9], Moret et Maspéro [10]. Goyon ([11], [12]) thinks that the Kerkasôre site could in fact be a distant geodesic point used for locating , equipped with an obelisk topped by a convex mirror capable of giving a quasi-punctual picture of the sun at such a distance, which would make locating easier. We could also work by making a nocturnal sighting towards the polar region, or by night time, by sighting a torch lit in the distance. Under the “pointing table”, four plumblines are hanging, whose fastening points identify with the central part of picture 11. The circle with a radius a (approximately one metre) , the plumblines, starting from this circle are on the North, South, East, West positions. The planes defined by the plumblines (North and East),(South and East), (south and West) contain all the vertexes of the external angles of the “angular sets of the ramp. To achieve a precise positioning of these points in space, it is necessary to place a second practicable at this spot.
Picture 26: Angle practicable
This practicable is put on an “angular set”. The height of this practicable is superior to 4 h, which will be that of the angular set whose vertex must be located precisely. At the top of this practicable, there is a piece of wood which can revolve around an axis. A first plumbline allows to bring this axis exactly at the base of the external vertex of this angular set on which our practicable lies. A second plumbline hangs from the extremity of the pole at a distance equal to the diagonal of a square with a side 4 a. When the wooden pole revolves
Round its axis, this second plumbline makes a vertical cylinder,
materialising its generating line. When the latter fits into the plane corresponding
to the central sighting previously described, the line identifies with the vertical
edge of the angular set to be positioned. Then several additional locations
and sightings allow to position the external corner with precision. As the external
corners of the angular sets are located on straight lines parallel to the edges
of the pyramid, they must be aligned on a direction of sighting forming the
same angle with the vertical line (spotted by the plumbline). Two corners of
adjacent angular sets must be separated by a distance ?, previously determined.
The crosschecking of all these measurements allows to position all the external
corners of the angular sets within a centimetre, all through the construction.
When the work is completed, we have the object of picture 10. What now remains
to do is to locate the pyramid itself starting from this object “inner
structure plus ramp”. The finishing of the pyramid does not consist in
removing the blocks of this ramp to let the inner structure appear, and then
adding the stones making up the casing, but it consists in fitting out this
stone ramp by cutting its blocks in an appropriate way so as to finalize the
work.
CENTIMETRIC LOCATION OF THE EDGES OF THE PYRAMID
How to let “the pyramid which is inside appear”, starting from this
stone ramp?
Picture 27: Location of the edge of the pyramid within the angular sets.
To constitute the edges of the pyramid, we shall start from the straight lines constituted by the external vertexes of the “residual structure” and we shall have tem make a vertical translation h+. These straight lines “pierce” the angular sets according to two points, indicated on the corresponding faces on the picture situated at the top and on the right.
Picture 28: Top part. Location of the edges and positioning of the pyramidion.
Picture 29: Top part with the measurements.
We have, on purpose, removed the last five inclined planes allowing the setting
of the pyramidion.
On this picture, we have replaced these ramps, which show how the slope increases when reaching the top, with the setting up of a pyramidion whose base is a square with side 3 a. The base of this monolith is convex and will fit into a concave receptacle which will make sure it stays in place in case of a heavy seismic tremor.
Picture 30: Setting up the pyramidion.
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