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 and were used in combination with later eclipses by Hipparchus about six centuries later and by Ptolemy between two and three centuries after Hipparchus to determine the different elements in the motion of the Moon. It is probable that they had previously been used for a similar purpose by the Babylonians themselves. In modern times great use has been made of these eclipses for the determination of the Moon's acceleration, though I have preferred to ignore all the ancient lunar eclipses before the Greek period. These eclipses are referred to the years of Babylonian, and after the Babylonian series to years of Persian and Egyptian kings and of Roman emperors, and Ptolemy gives a canon showing the regnal years of these kings and emperors from B.C. 747 onwards. As modern eclipse computations verify this canon consistently, we have in it a reliable foundation for ancient chronology, and through the Babylonian and Persian dates we are able to fix Hebrew and Greek dates. This canon has been recognized from the close of the sixteenth century as our primary chronological authority. The latter part of the Assyrian eponym canon is found to be in agreement with it, and we can therefore carry dates back through the whole range of that canon into the tenth century B.C. These dates also give us a starting-point for Babylonian chronology for which we now have lists of kings extending through thousands of years, but we have few astronomical checks on the chronology before this series of eclipses.

Eclipses of the Annals of Lu.

One year later than the first of Ptolemy's eclipses falls the first of thirty-six eclipses recorded in the Annals of the Chinese state of Lu. These enable us to fix Chinese chronology with certainty for the period