The Hebrew calendar is used within Judaism to observe religious festivals. It is also the official calendar in Israel. However, the Gregorian calendar is used for all secular activities. It is based on the movements of the moon and the earth's seasons to coincide with the observance of the feasts of the Torah. Priests would originally appoint a series of eyewitnesses to watch the moon. When the witnesses announced a new moon, the Sanhedrin would decree a new month. The information was then spread to the nearby towns by means of smoke signals from hilltops to reach the Jewish people throughout the length and breadth of the area. Similarly, an intercalary month was added before the month of Nissan if the witnesses failed to spot signs of spring in the fields. Later on, as the Jewish people came increasingly under threat of exile, Rabbi Hillel, son of Yehuda Hanassi and head of the Sanhedrin, devised a rule-based calendar system in the year 358 of the common era so that it could be observed around the world. * The algorithm of the Jewish calendar is based on the Gregorian calendar (one Gregorian year = 365 days and 97/400 = 365.2425 days) which was introduced in 1582 AD. As a result, dates calculated prior to 1582 may be slightly inaccurate on account of the Julian calendar (one Julian year = 365 1/4 days ). * Calendar type: lunisolar, in other words based on lunar months but realigned with the solar year by adding additional days as necessary from year to year. * Calendar start-date: the first of Tishri of year One corresponds to Sunday, 6 September 3761 BCE. * Start of the day: in the evening (at sunset) of the day prior to the corresponding Christian date. Julian calendar Intent on putting an end to the abuse by politicians of their powers, Julius Caesar summoned a Greek astronomer by the name of Sosigenes of Alexandria to study the possibility of reforming the calendar. This gave rise to the "Julian calendar", the ancestor of our modern calendar. Caesar began by adding to the current year, 708 A.U.C. (46 BC), one month of 23 days, which had to be intercalated that year, an additional 2 months between November and December, one month of 33 days, and another month comprising 34 days, in order to correct the drift. The result was a 455-day year, which came to be known as the "year of confusion". On the advice of Sosigenes, Caesar decreed that one year, adjusted to coincide with the movement of the sun, would have 365 days, and that, as a surplus of 6 hours remained (corresponding to 24 hours over 4 years), 1 additional day would be added every fourth year. Inserted after 24 February, which was known in the Roman calendar as "sexto ante calendas martii", this day was called "bi sexto ante calendas martii", whence the expression "bis-sextile year", more commonly known as a leap year. The 10 days of the new year were distributed across the months, alternating between 30 or 31 days, apart from February with 30 days in leap years and only 29 days in ordinary years. As the reform was introduced by Julius Caesar, it was decided in the year 716 A.U.C. (38 BC), on a proposal from Anthony who had been appointed consul with Caesar, to change the month Quintilis to Julius. The reform itself was called the "Julian reform" and the resulting calendar the "Julian calendar". The reform was not properly implemented at first. The pontiffs intercalated a leap year every three years and not every four. By the end of 36 years, 12 leap years had been intercalated where only 9 were needed. Fortunately, the mistake was spotted and Augustus, who was then in power, ordered no further leap years for the next 12 years, thereby setting the Julian reform back on course. In reward for his service, the Roman Senate decreed, in the year 746 A.U.C. (8 BC) that the month Sextilis would be renamed Augustus, as had been done for Julius Caesar. Augustus was also persuaded, being no less an emperor than Caesar, that his month should have just as many days; one day was therefore removed from Februarius and added to Augustus, which therefore numbered 31 days. Then, to avoid three successive months of 31 days, the 31st day of September was given to October, and the same swap was made between November and December. Neither the number nor names of the days in each month have changed since and are the same today as they were at the end of the reign of Emperor Augustus. The months, by contrast, were not divided in the same way; the days were divided into months in three unequal parts: from the Calends to the Nones, from the Nones to the Ides, and from the Ides to the end of the month. This division goes back to ancient times when the inhabitants of Latium measured time by moons. The first day of the month, corresponding to the new moon, was called Calends. Unlike today, the days were not counted by adding one to another but were counted down from the Calends to the Nones, from the Nones to the Ides, and from the Ides to the next Calends, such as the 5th, 4th, 3rd before the Nones, or before the Ides, or before the Calends.This method of calculation lasted until the Middle Ages; public documents can be found written in Latin and dated in the Roman format up to the16th century. Similarly, the years were counted from the foundation of Rome (A.U.C. or ab urbe condita) in 753 BC.