A sundial with hour lines portraying the Earth

摘要

The study of sundials is an age-old discipline of science. The greatest developments were achieved in the Antiquity and in the Middle Ages, but modern physicists also contributed their part. In 1956, a former student of Wolfgang Pauli, Heinz Schilt, constructed an underwater sundial in his garden pond, using refraction to reshape the sundial's hour lines. His approach is developed further in this paper and combined with Thales' geometric concept of gnomonic projection. Together, this leads to a beautiful result: Snell's law can be used to build a sundial whose hour lines portray the Earth and its meridians. A prototype has been built to demonstrate the idea.