calendar. Most sources thought he had established intercalation with the rest of his calendar. Although Livy's Numa instituted a lunar calendar, the author claimed the king had instituted a 19-year system of intercalation equivalent to the Metonic cycle centuries before its development by Babylonian and Greek astronomers. Plutarch's account claims he ended the former chaos of the calendar by employing 12months totalling 354days—the length of the lunar and Greek years—and biennial intercalary months of 22days. According to Livy's Periochae, the beginning of the consular year changed from March to January1 in 153BC to respond to a rebellion in Hispania. Plutarch believed Numa was responsible for placing January and February first in the calendar; Ovid states January began as the first month and February the last, with its present order owing to the Decemvirs. W. Warde Fowler believed the Roman priests continued to treat January and February as the last months of the calendar throughout the Republican period. According to the later writers Censorinus and Macrobius, to correct the mismatch of the correspondence between months and seasons due to the excess of one day of the Roman average year over the tropical year, the insertion of the intercalary month was modified according to the scheme: common year (355 days), leap year with 23-day February followed by 27-day Mercedonius (377 days), common year, leap year with 23-day February followed by 28-day Mercedonius (378 days), and so on for the first 16 years of a 24-year cycle. In the last 8 years, the intercalation took place with the month of Mercedonius only 27 days, except the last intercalation which did not happen. Hence, there would be a typical common year followed by a leap year of 377 days for the next 6 years and the remaining 2 years would sequentially be common years. The result of this twenty-four-year pattern was of great precision for the time: 365.25 days, as shown by the following calculation: The consuls' terms of office were not always a modern calendar year, but ordinary consuls were elected or appointed annually. The traditional list of Roman consuls used by the Romans to date their years began in 509BC. Flavian reform Gnaeus Flavius, a secretary (scriba) to censor App. Claudius Caecus, introduced a series of reforms in 304BC. Their exact nature is uncertain, although he is thought to have begun the custom of publishing the calendar in advance of the month,