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Published by the Applied Probability Trust © Applied Probability Trust 2008 11 Henges, Heel Stones, and Analemmas JOHN D. MAHONY Introduction There are various henges in existence around the world, some old – for example Stonehenge, UK – and some new – for example Stonehenge Aotearoa, New Zealand. An understanding of heel stones and their positions around a henge may be appreciated from figure 1. In figure 1, six heel stones are shown distributed around a henge centre to mark the apparent positions of sunrise/sunset (as seen from the centre of the henge) at the equinoxes and the solstices. The solstice positions mark the extremes of the Sun’s apparent motion during a year and they are usually established by measurement with reference to distant star sets. The heel stone axis thus appears to swing through an angle 2max during the course of one year. It is a simple matter to measure the magnitude of the swing but, since the phenomenon involves primarily only the Sun and the Earth, it should be possible to obtain a simple formula that will determine an approximate value for at any point of the Earth’s orbit, not just at the solstices where it is a maximum. Results from the formula should be in reasonable agreement with known facts. 1. At Stonehenge (UK, Northerly latitude circa 51.2◦ ) the apparent magnitude of the swing at the solstices is about 80◦ (see reference 1, pp. 109–110). N Winter solstice sunset − SH Summer solstice sunset − NH Equinox sunset Winter solstice sunrise − SH Summer solstice sunrise − NH max W Summer solstice sunset − SH Winter solstice sunset − NH E Equinox sunrise Summer solstice sunrise − SH Winter solstice sunrise − NH S Figure 1 Henge showing six heel stones on Earth that mark the apparent position of sunrise/sunset at the solstices and equinoxes with reference to an east/west axis. The stars denote heel stones; ‘NH’ and ‘SH’ denote ‘northern hemisphere’ and ‘southern hemisphere’ respectively.