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    Re: Shadow sights for longitude
    From: Geoffrey Kolbe
    Date: 2018 Jan 12, 23:26 -0800

    Some time ago I did some work trying to verify a method by which the Old Kingdom Egyptians might have aligned their pyramids. The pyramids on the Giza plateau are exceptionally well aligned to the cardinal points and the Great Pyramid in particular is aligned within 3 minutes or so. The method was proposed by Cambridge egyptologist Kate Spence and used two circumpolar stars, Mizar and Kochab, which in those days had a celestial longitude which was very nearly the same. Thus, when the two stars appeared vertically aligned in the night sky, their azimuth was true North. 

    The method proposed to determine the azimuth was to hang a plumbline using a thin line a few millimetres against the background of the two stars and then observe the stars through a movable vane situated about 3 metres from the line, having a vertical slit in it whose width was the same as the line diameter. The idea was to move the vane so that one of the stars was always blocked from view by the line and then at the moment when the two stars were vertically aligned, both stars would be blocked from view. With the vane now left in place, an assistant some 100 metres or so distant from the line would move across the field of view with a small lamp (candle) until the light from the lamp, as viewed through the vane, was occluded by the line. A peg driven into the ground at that point would be on the same azimuth to the line as the two stars at the moment they were vertically aligned - which for Mizar and Kochab around 2450 BC was due North.

    I did some experimental work to verify this method to see if the required accuracy could be obtained. Mizar and Kochab as a pair were no longer available, but Kochab and Alrai are suitable today and so experiments were done with that pair. The work (see "A Test of the "Simultaneous Transit Method", Journal for the History of Astronomy, Vol. 39, Part 4, November 2008) showed that the azimuth could be determined to +/- 1 minute of arc with care, which is remarkable with such simple apparatus.

    However - here I get to the point - the time at which the stars became vertically aligned depends on the observer's longitude. Since the period for which both stars are observed to be simultaneously occluded by the line is only a few seconds, it follows that the observers longitude could be determined with good accuracy by this method.

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