The Solution of the Pyramid Problem Part 5

And I shall show how by the aid of a simple instrument angles could be exactly observed from any point.

This Survey theory does not stand or fall on the merits of my theory of the Gzeh plan. Let it be proved that this group is not built on the exact system of triangulation set forth by me, it is still a fact that its plan is in a similar shape, and any such shape would enable a surveyor acquainted with the plan to lay down accurate surveys by observations of the group even should it not occupy the precise lines a.s.sumed by me.

And here I must state that although the lines of the plan as laid down herein agree nearly with the lines as laid down in Piazzi Smyth's book, in the Penny Cyclopaedia, and in an essay of Proctor's in the _Gentleman's Magazine_, still I find that they do not agree at all satisfactorily with a map of the Pyramids in Sharp's "Egypt," said to be copied from Wilkinson's map.

We will, however, for the time, and to explain my survey theory, suppose the plan theory to be correct, as I firmly believe it is.

And then, supposing it may be proved that the respective positions of the pyramids are slightly different to those that I have allotted to them on my plan, it will only make a similar slight difference to the lines and angles which I shall here show could be laid out by their aid.

Let us in the first place comprehend clearly the shape of the land of Egypt.

A sector or fan, with a long handle--the fan or sector, the delta; and the handle of the fan, the Nile Valley, running nearly due south.

The Pyramids of Gzeh are situate at the angle of the sector, on a rocky eminence whence they can all be seen for many miles. The summits of the two high ones can be seen from the delta, and from the Nile Valley to a very great distance; how far, I am unable to say; but I should think that while the group could be made general use of for a radius of fifteen miles, the summits of Cephren and Cheops could be made use of for a distance of thirty miles; taking into consideration the general fall of the country.

It must be admitted that if meridian observations of the star Alpha of the Dragon could be made with accuracy by peeping up a small hole in one of the pyramids, then surely might the surveyors have carried true north and south lines up the Nile Valley as far as the summit of Cheops was visible, by "_plumbing in_" the star and the apex of the pyramid by the aid of a string and a stone.

True east and west lines could have been made to intersect such north and south lines from the various groups of pyramids along the river banks, by whose aid also such lines would be prolonged.

Next, supposing that their astronomers had been aware of the lat.i.tude of Cheops, and the annual northing and southing of the sun, straight lines could have been laid out in various sectoral directions to the north-eastward and north-westward of Cheops, across the delta, as far as the extreme apex of the pyramid was visible, by observations of the sun, rising or setting over his summit. (That the Dog-star was observed in this manner from the north-west, I have little doubt.)

Fig. 37. Sun above Pyramid and sinking behind Pyramid

For this purpose, surveyors would be stationed at suitable distances apart with their strings and their stones, ready to catch the sun simultaneously, and at the very moment he became transfixed upon the apex of the pyramid, and was, as it were, "swallowed by it." (_See Figure 37_.) The knowledge of the pyramid slope angle from different points of view would enable the surveyor to place himself in readiness nearly on the line.

Surely such lines as these would be as true and as perfect as we could lay out nowadays with all our modern instrumental appliances. A string and a stone here, a clean-cut point of stone twenty miles away, and a great ball of fire behind that point at a distance of ninety odd million miles. The error in such a line would be very trifling.

Such observations as last mentioned would have been probably extended from Cephren for long lines, as being the higher pyramid above the earth's surface, and may have been made from the moon or stars.

In those days was the sun the intimate friend of man. The moon and stars were his hand-maidens.

How many of us can point to the spot of the sun's rising or setting? We, with our clocks, and our watches, and our compa.s.ses, rarely observe the sun or stars. But in a land and an age when the sun was the only clock, and the pyramid the only compa.s.s, the movements and positions of the heavenly bodies were known to all. These people were _familiar_ with the stars, and kept a watch upon their movements.

How many of our vaunted educated population could point out the Dog-star in the heavens?--but the whole Egyptian nation hailed his rising as the beginning of their year, and as the harbinger of their annual blessing, the rising of the waters of the Nile.

Fig. 38. From the North West Bearing 315 Sun in the West.

Fig. 39. From the South East Bearing 135 Sun in the West.

Fig. 40. From the North East Bearing 45 Sun in the East.

Fig. 41. From the South West Bearing 225 Sun in the East.

It is possible therefore that the land surveyors of Egypt made full use of the heavenly bodies in their surveys of the land; and while we are pitifully laying out our new countries by the circ.u.mferenter and the compa.s.s, we presume to speak slightingly of the supposed dark heathen days, when the land of Egypt was surveyed by means of the sun and the stars, and the theodolites were built of stone, with vertical limbs five hundred feet in height, and horizontal limbs three thousand feet in diameter.

Imagine half a dozen such instruments as this in a distance of about sixty miles (for each group of pyramids was effectually such an instrument), and we can form some conception of the perfection of the surveys of an almost prehistoric nation.

The centre of Lake Moeris, in which Herodotus tells us two pyramids stood 300 feet above the level of the lake, appears from the maps to be about S. 28 W., or S. 29 W. from Gzeh, distant about 57 miles, and the Meidan group of pyramids appears to be about 33 miles due south of Gzeh.

Figures 38, 39, 40 and 41, show that north-west, south-east, north-east, and south-west lines from the pyramids could be extended by simply plumbing the angles. These lines would be run in sets of two's and three's, according to the number of pyramids in the group; and their known distances apart at that angle would check the correctness of the work.

A splendid line was the line bearing 43 36' 1015?, or 223 36'

1015? from Cheops and Cephren, the pyramids covering each other, the line of hypotenuse of the great 20, 21, 29 triangle of the plan. This I call the 20, 21 line. _(See Figure_ 42.)

Figure 43 represents the 3, 4, 5 triangle line from the summits of Mycerinus and Cheops in true line bearing 216 52' 1165". This I call the south 4, west 3 line.

The next line is what I call the 2, 1 line, and is ill.u.s.trated by figure 44. It is one of the most perfect of the series, and bears S. 26 33'

549" W. from the apex of Cephren. This line demonstrates clearly why Mycerinus was cased with red granite.

Not in memory of the beautiful and rosy-cheeked Nitocris, as some of the tomb theory people say, but for a less romantic but more useful object; simply because, from this quarter, and round about, the lines of the pyramids would have been confused if Mycerinus had not been of a different color. The 2, 1 line is a line in which Mycerinus would have been absolutely lost in the slopes of Cephren but for his red color.

There is not a fact that more clearly establishes my theory, and the wisdom and forethought of those who planned the Gzeh pyramids, than this red pyramid Mycerinus, and the 2, 1 line.

Hekeyan Bey, speaks of this pyramid as of a "_ruddy complexion_;" John Greaves quotes from the Arabic book, Morat Alzeman, "_and the lesser which is coloured_;" and an Arabic writer who dates the Pyramids three hundred years before the Flood, and cannot find among the learned men of Egypt "_any certain relation concerning them_" nor any "_memory of them amongst men_," also expatiates upon the beauties of the "_coloured satin_" covering of this one particular pyramid.

Fig. 42. South 21. West 20. Bearing 223.36'.1015".

Fig. 43. South 4. West 3. Bearing 216.52'.1165".

Fig. 44. South 2. West 1. Bearing 206.33'.5418".

Fig. 45. South 96. West 55. Bearing 209.48'.3281".

Fig. 46. South 3. West 1. Bearing 198.26'.582".

Fig. 47. South 5. West 2. Bearing 201.48'.5".

Fig. 48. South 7. West 3. Bearing 203.11'.55".

Figure 45 represents the line south 96, west 55, from Cephren, bearing 209 48' 3281"; the apex of Cephren is immediately above the apex of Mycerinus.

Figure 46 is the S. 3 W. 1 line, bearing 198 26' 5.82"; here the dark slope angle of the pyramids with the sun to the eastward occupies half of the apparent half base.

Figure 47 is the S. 5, W. 2 line, bearing 201 48' 5"; here Cephren and Mycerinus are in outside slope line.

Figure 48 is the S. 7 W. 3 line, bearing 203 11' 55"; here the inside slope of Cephren springs from the centre of the apparent base of Mycerinus.

I must content myself with the preceding examples of a few pyramid lines, but must have said enough to show that from every point of the compa.s.s their appearance was distinctly marked and definitely to be determined by surveyors acquainted with the plan.

-- 11. DESCRIPTION OF THE ANCIENT PORTABLE SURVEY INSTRUMENT.

I must now commence with a single pyramid, show how approximate observations could be made from it, and then extend the theory to a group with the observations thereby rendered more perfect and delicate.

We will suppose the surveyor to be standing looking at the pyramid Cephren; he knows that its base is 420 cubits, and its apothem 346 cubits. He has provided himself with a model in wood, or stone, or metal, and one thousandth of its size--therefore his model will be O.42 cubit base, and O.3465 cubit apothem--or, in round numbers, eight and half inches base, and seven inches apothem.

This model is fixed on the centre of a card or disc, graduated from the centre to the circ.u.mference, like a compa.s.s card, to the various points of the compa.s.s, or divisions of a circle.

The model pyramid is fastened due north and south on the lines of this card or disc, so that when the north point of the card points north, the north face of the model pyramid faces to the north.