Hi Alex,

Re your last question:

I wonder - what you think about the idea of orienting the Old Kingdom pyramids to different circumpolar stars?

Whilst we await a response from Chris, I note that you reject the idea of I.E.S. Edwards on bisecting the angle of circumpolar stars with respect to an artificial horizon, so it is appropriate to propose some other method.
(I never liked the idea of some-one standing at the centre of a circular wall. I don't think this method would be precise enough due to compression of vertebrae etc.)

There is a stone statue not far away from where I live which has a cylindrical hole through the eye to the back of the statue in order to spy what the designer had in mind on the landscape below the hill where the statue stands.

It is possible that true north was determined directly through a long tube fixed at 30 degrees to the horizontal and rotated so that a selected star traced a concentric path within the circumference of the tube.

A hole could have been drilled through a rectilinear block with the block mounted on a rectilinear platform free to rotate of a flat surface. As such the top of the platform would have needed a slope of 30 degrees to the horizontal, or a rise of 1 cubit (28 digits) for run of 48½ digits.

A set of rectilinear blocks could have had holes of different diameters so that selected stars appeared close to the edge of the holes in their circular paths around the pole of the night sky, and so that an initial viewing of a particular star could have started with a larger hole to frame the selected star easily.

The east and west sides of the rectilinear platform would then be close to the line of the north-south arc of the meridian allowing extension of either side as a straight line along the ground.

This method only yields true north, but stretching a cord across the diameter of the cylindrical hole, on the far side from the viewing point, would allow determination of the maximum elongation east or west with the cord in the traditional vertical orientation. This could have been achieved by placing a weight on the end of the cord so that the cord is indeed stretched into a vertical line.
(I don't like the notion of a horizontal cord because it is not so easy to be sure of the horizontal and there is no natural stretching.)

The platform would then need to be rotated as the star moves in such a way that the star remains just behind the vertical line. This would then give the approximate angle of maximum elongation on the ground. In subsequent determinations, night after night, the platform would get closer and closer to the angle where the star was just eclipsed by the thin cord. In this method it would have been easy to align the cord to a diameter marked on the end of the hole.

In my solar model of the Great Pyramid the pyramid should have been aligned just over 3 arc minutes west of due north as a theoretical model, but I don't disagree that other Old Kingdom pyramids might have been directed at a particular star if you can show a correlation between stars and pyramids assuming a difference of no more than say 5 arc minutes between theoretical values and observed values.

I don't think the Great Pyramid was built when Alpha Draconis was 3 arc minutes from the pole if it ever got so close because I have a solar model. It is, however, possible that the architect was also remembering a time when Alpha Draconis was so close to pole, perhaps 200 years before the pyramid was built. I don't have a model to date the pyramid as mentioned previously, but it seems unlikely that the pyramid was built at that time if a solar method could give a precise angle without needing to resort to a building a precise instrument in the manner suggested above.

The notion of holding a stretched cord at arm's length to get the azimuth seems impossible if it is claimed that the angle was determined to with a few arc minutes, but a precise instrument, as outlined above, could have been used to determine the azimuth for the more difficult task of determining the angle when two circumpolar stars became aligned vertically.

Its no use just saying the AE determined true north with enviable accuracy, or dismissing a possible method as more in keeping with the modern mind, because you will just be left with an easy and precise solar method. The hour priests may have pretended to get a sighting at night in no more than an elaborate ceremony in which the surveyors were smiling without the risk of being seen on a dark night without the moon.

Mark



Edited 2 time(s). Last edit at 02/09/2020 02:23PM by Mark Heaton.