Luke, I've been digging at some of the history on the analemma. Otto Neugebauer in his "A History of Ancient Mathematical Astronomy" discussing the concept of true solar day vs mean solar day states that "The correction which transforms a true into a mean time interval is technically known as the "equation of time."" "It is characteristic for the high level of hellenistic astronomy that a correct determination of this correction was achieved. We do not know to whom it is due this important step in the theory of time reckoning: in the sources available to us the equation of time, or its equivalent, is first attested in the Almagest." So according to ON, Ptolemy is the first to have indicated the relationship. According to Don Edward's work on the "Peri Analemmatos", the use of the word analemma is in the sense of a projection from spherical geometry to a plane (mentioned earlier by Fred Sawyer). Of obvious use in creating dials, but not limited to that use. He discusses the term extensively use numerous sources. ON also seems to use analemma in the same way in the ref. above. It would be interesting to see how an experienced ancient observer, (or modern one) with out the aid of an accurate clock, could have determined the difference between true and mean civil noon. Water clocks seem to have been well developed by Ptolemy's time. A proto klepsydra was in use during the 15 century BC by Minoan priests to keep libations pouring onto the altars. Thales in the 6 th century, according to Cleomedes, seems to have determined the angular diameter of the sun using a klepsydra to compare the time it required for the sun to set compared to the time it took to rise then set. These water clocks were in common use in Classical Greece from the 5th century on. By about 350 BC, there was a town water clock in the Athenian Agora which was maintained in some regular fashion. About 140 BC, a large water clock was constructed in the Roman Agora in Athens called the Tower of the Winds. It has been analysed by Derek DeSolla Price. It also contains sundials on each of its 8 sides possibly to calibrate the water clock? Price has written on the operation of the clock. Also, Herman Keinast of the German archaeological society in Athens is currently working on the Tower. He tells me he is working on an alternate hypothesis.
ON also briefly discusses the "analemma" in the context of geometrical construction. He says that "as described by Vitruvius, (it) serves only for the determination of the length of the noonshadow...for a given solar longitude....at a place of know geographical latitude." Since one use of the gnomon was to determine the season of the year by observing the length of the noon shadow, I can see how (as the measurement of mean time became possible) the connection was made with the time difference between mean and true sun and its declination. mike Michael E. Mickelson Professor of Physics Planetary Atmospheres Laboratory Department of Physics and Astronomy Denison University Granville OH 43023 [EMAIL PROTECTED] Office: 614-587-6467 FAX: 614-587-6240
