than the tropical year. Using observations of the equinoxes and solstices, Hipparchus found that the length of the tropical year was 365+1/4−1/300 days, or 365.24667 days (Evans 1998, p. 209). Comparing this with the length of the sidereal year, he calculated that the rate of precession was not less than 1° in a century. From this information, it is possible to calculate that his value for the sidereal year was 365+1/4+1/144 days (Toomer 1978, p. 218). By giving a minimum rate, he may have been allowing for errors in observation. To approximate his tropical year Hipparchus created his own lunisolar calendar by modifying those of Meton and Callippus in On Intercalary Months and Days (now lost), as described by Ptolemy in the Almagest III.1 (Toomer 1984, p. 139). The Babylonian calendar used a cycle of 235 lunar months in 19 years since 499 BC (with only three exceptions before 380 BC), but it did not use a specified number of days. The Metonic cycle (432 BC) assigned 6,940 days to these 19 years producing an average year of 365+1/4+1/76 or 365.26316 days. The Callippic cycle (330 BC) dropped one day from four Metonic cycles (76 years) for an average year of 365+1/4 or 365.25 days. Hipparchus dropped one more day from four Callippic cycles (304 years), creating the Hipparchic cycle with an average year of 365+1/4−1/304 or 365.24671 days, which was close to his tropical year of 365+1/4−1/300 or 365.24667 days. Hipparchus's mathematical signatures are found in the Antikythera Mechanism, an ancient astronomical computer of the second century BC. The mechanism is based on a solar year, the Metonic Cycle, which is the period the Moon reappears in the same place in the sky with the same phase (full Moon appears at the same position in the sky approximately in 19 years), the Callipic cycle (which is four Metonic cycles and more accurate), the Saros cycle and the Exeligmos cycles (three Saros cycles for the accurate eclipse prediction). The study of the Antikythera Mechanism proves that the ancients have been using very accurate calendars based on all the aspects of solar and lunar motion in the sky. In fact, the Lunar Mechanism which is part of the Antikythera Mechanism depicts the motion of the Moon and its phase, for a given time, using a train of four gears with a pin and slot device which gives a variable lunar velocity