The Pyramids and Temples of Gizeh by Sir Flinders Petrie - Positions and Orientation of the Pyramids

The Pyramids and Temples of Gizeh by W. M. Flinders Petrie

Chap. 13. Positions and Orientation of the Pyramids Pages 125 - 127

92 . p 125. The relative positions of the three larger Pyramids to one another were completely fixed in the triangulation, which included them all. The following are their distances apart, as measured on parallels inclined 5' to true N. i.e., at the mean azimuth of the First and Second Pyramids; and also the distances, and the angles from these parallels, of the direct lines from one Pyramid to another :




Centre of First to centre of Second Pyramid

13931.6 and

13165.8 = 19

168.4 at 43 22' 52"

Centre of First to centre of Third Pyramid

29102.0 and

22616.0 = 36

857.7 at 37 51' 6"

Centre of Second to centre of Third Pyramid

15170.4 and

9450.2 = 17

873.2 at 34 10' 11"

There does not appear to be any exact relation between their centres, or between the corners; and from the nature and appearance of the ground, and the irregularity of the penbolus walls, it would not seem likely that any connection had been planned.

93 . The orientation of the Great Pyramid is about 4' West of North; a difference very perceptible, and so much larger than the errors of setting out the form (which average 12"), that such a divergence might be wondered at. When, however, it is seen that the passage, which was probably set out by a different observation, nearly agrees in this divergence, it seems unlikely to be a mere mistake. And when, further, the Second Pyramid sides, and also its passages, all diverge similarly to the W. of North, the presumption of some change in the position of the North point itself, seems strongly indicated. The Third and lesser Pyramids are so inferior in work, that they ought not to interfere with the determination from the accurate remains ; they would, however, scarcely affect the mean deviation if included with the better data. The azimuths of the two large Pyramids are thus :

Great Pyramid, casing sides

Great Pyramid, core sides

Second Pyramid, casing sides

Second Pyramid, passage (Smyth)

Great Pyramid, passage (Smyth)

-- 3' 43" 6"

-- 5' 16" 10"

-- 5' 26" 16"

-- 5' 37" 10" ?

-- 5' 49" 7"

p 126. In considering these results, the difference of the casing and core azimuths of the Great Pyramid shows that probably a re-determination of the N. was made after the core was finished; and it must be remembered that the orientation would be far more difficult to fix after, than during, the construction; as a high face of masonry, for a plumb-line, would not be available. The passages of the Great and Second Pyramids are the most valuable elements ; as, being so nearly at the polar altitude; a very short plumb-line would transfer the observations to the fixed plane. Considering, then, that the Great Pyramid core agrees with the passages far closer than does the casing, the inference seems to be that the casing was fixed by a re-determination of N., by the men who finished the building. These men had not the facilities of the earlier workers; and are shown, by the inferiority of the later work in the Pyramid, to have been far less careful. Hence the casing may probably be left out of consideration, in view of the close agreement of the four other determinations, one of which---the passage---was laid out by the most skilful workmen of the Great Pyramid, with their utmost regularity, the mean variation of the built part being but 1/50 inch.
The simple mean of the last four data is -- 5' 32" 6"; their divergences being just what would be expected from their intrinsic probable errors. The passages are, however, probably far the most accurate lines in their execution and as the Second Pyramid is inferior in its workmanship, --5' 45" 5" might be well taken as the result from them alone. On the whole, considering the various values of the data, -- 5' 40" 10" may be taken as a safe statement of the suggested place of the pole, at the epoch of the Pyramid builders.

94 . There are, however, two checks on the supposition of such a change in the pole: the observations of any change in later times, and the existence of an a4equate cause for the change. Now, the best latitude observations at Greenwich, those on Polaris---least affected by erroneous refractions---appear to show a latitude of 51 28' 38.58" during 7 years, 1840-7; 38.30" during 10 years, 1851-61 ; 38.22" during 3 years, 1862-5; and 38.30" during 8 years, 1868-76;* or on an average a decrease of .28" latitude in 28 years, or 1.0" per century.

See diagram in Mr. Christie's paper: Mem. Ast. Soc., XlV.

But Maskelyne's discussion in the last century yielded 39.7", for mean epoch 1761. This implies a decrease of 1.38" per century, agreeing as closely as could be expected with the change in recent observations.

Hence, in 4,000 to 6,000 years---the age of the Pyramids by different chronologers---the change of Greenwich latitude would amount to just about 1'. Thus, as far as observation can lead us, it seems to show a shift of the earth's axis in longitude 0 to a fifth of the extent shown in longitude 121 by the Pyramid orientations; and therefore a change of the same order, and not improbable in its extent. p 127. As to the adequacy of a cause for such a change, it is hopeless, in our ignorance of the exact amount and velocity of the ocean currents at different depths, for us to strike a balance of them, and see how much motion is outstanding to affect the axis of rotation. But we can at least see what sort of proportion the required effective current would bear to the whole of the currents. Assuming a change of place of the axis amounting to 1' in 1,000 years, it seems that a ring of water circulating around the earth, across the Poles, at I mile per hour, and only 4 square miles in section, would suffice to cause such a change. This is an amount of unbalanced, or outstanding, current which is quite imperceptible in the balancing effects of the various ocean currents; and therefore amply accounted for by existing and known causes, even apart from atmospheric currents.

Thus the apparent change in the axis of rotation shown by the orientation of the Pyramids, is of the same order as a change actually observed. It is also far within the changes likely to be produced by known causes, and the uniform deviation is otherwise unaccountable in its origin. Hence it appears that it may legitimately be accepted as a determination of a factor which is of the highest interest, and which is most difficult to observe in any ordinary period.*

* Careful re-determinations of the meridians fixed in the beginning of the Ordnance Survey might be of value ; as (according to the Pyramids) a change of 5" might be expected in their azimuths.