The table or disc comprising the lower limb of the instrument, might have been supported upon a small stand with a circular hole in the centre, so arranged that the instrument could be either set up alone and supported by its own tripod, or rested fairly on the top of any of those curious stone boundary marks which were made use of, not only to mark the corners of the different holdings, but to show the level of the Nile inundations. (See Figure 49, copied from Sharpe's Egypt, vol. I., p. 6.) The peculiar shape of the top of these stone landmarks, or "sacred boundary stones," appears suitable for such purposes, and it would have been a great convenience to the surveyor, and conducive to accuracy, that it should be so arranged that the instrument should be fixed immediately over the mark, as appears probable from the shape of the stone.
Fig 49.
A noticeable point in this theory is, that it is not in the least essential that the apex of a pyramid should be complete. If their summits were left permanently flat, they would work in for survey purposes quite as well, and I think better, than if carried to a point, and they would be more useful with a flat top for defined shadows when used as sun dials.
In the Gïzeh group, the summit of Cheops appears to me to have been left incomplete the better to get the range with Cephren for lines down the delta.
In this system of surveying, there is always a beautiful connection between the horizontal bearings and the apparent or observed angles presented by the slopes and edges of the pyramid. Thus, in pyramids like those of Gïzeh, which stand north and south, and whose meridional sections contain less, and whose diagonal sections contain more than a right angle, the vertex being the point at which the angle is measured—this law holds:— That the smallest interior angle at the vertex, contained between the inside edge and the outside edge, will exhibit the same angle as the bearing of the observer's eye from the apex of the pyramid when the angle at the apex contained by the outside edges appears to be a right angle.
Figures 50 to 55 inclusive illustrate this beautiful law from which it will be seen that the Gïzeh surveyors possessed, in this manner alone, eight distinctly defined bearings from each pyramid.
|
| Fig. 50. | |||||||||||||||||||||||||||||
|
| Fig. 51. | |||||||||||||||||||||||||||||
|
| Fig. 52. | |||||||||||||||||||||||||||||
|
| Fig. 53. | |||||||||||||||||||||||||||||
|
| Fig. 54. | |||||||||||||||||||||||||||||
|
| Fig. 55. | |||||||||||||||||||||||||||||
