The Julian calendar was introduced by Julius Caesar in 46 BC, taking force in 45 BC or 709 ab urbe condita. It was chosen after consultation with the Alexandrian astronomer Sosigenes and was probably designed to approximate the tropical year, known since Hipparchus. It has a regular year of 365 days divided into 12 months, and a leap day is added every 4 years. The calendar remained in use into the 20th century in some countries and is still used by many national Orthodox churches. However with this scheme too many leap days are added with respect to the astronomical seasons, which on average occur earlier in the calendar by about 11 minutes per year. It is said that Caesar was aware of the discrepancy, but felt it was of little importance. In the 16th century the Gregorian calendar reform was introduced to improve its accuracy with respect to the time of the vernal equinox and the synodic month (for Easter). Sometimes the reference Old Style or O.S., as opposed to 'New Style' for the Gregorian Calendar, is used when there is a confusion about which date is found in a text.
From Roman to Julian
The previous Roman calendar consisted of 12 months with a total of 355 days. In addition, an intercalary month Intercalaris was inserted between February and March, usually in every second or third year. Intercalaris was formed by adding 22 days to the last five days of February, creating a 27-day month. Since it began after a truncated February having 23 or 24 days, it had the effect of adding only 22 or 23 days, forming an intercalary year of 377 or 378 days.
If managed correctly, this system allowed the Roman year, on average, to stay roughly aligned to a tropical year. However, at times the calendar was allowed to drift badly, and special steps had to be taken to realign it. One such period was during and after the Second Punic War. This happened again during Julius Caesar's pontificate, 63 BC to 46 BC, when there were only five intercalary months, whereas there should have been eight, and none at all between 52 BC and 46 BC. Thus by 46 BC a calendar date was occurring three months earlier than it should have against the tropical year.
The Julian reform was intended to correct this problem permanently. Before it took effect, the deficit was corrected by inserting 67 days (22+23+22) between November and December of 46 BC in the form of two months, which are now sometimes referred to as Unodecember and Duodecember, in addition to 23 days which had already been added to February. Thus 90 days were added to this last year of the Roman Republican calendar, giving it 445 days. Because it was the last of a series of irregular years, this extra-long year was, and is, referred to as the last Year of Confusion. The first year of operation of the new calendar was 45 BC.
Leap years error
Despite the new calendar being much simpler than the Roman calendar, those tasked with implementing it, the Pontifices, apparently misunderstood the algorithm. They added a leap day every three years, instead of every four years. This resulted in too many leap days. Augustus Caesar remedied this discrepancy by skipping several leap days after 36 years of such mistakes.
The historic sequence of leap years (i.e. years with a leap day) in this period is not given explicitly by any ancient source, although the existence of the triennial leap year cycle is confirmed by an inscription that dates from 9 or 8 BC. The chronologist Joseph Scaliger established in 1583 that the Augustan reform was instituted in 8 BC, and inferred that the sequence of leap years was 42 BC, 39 BC, 36 BC, 33 BC, 30 BC, 27 BC, 24 BC, 21 BC, 18 BC, 15 BC, 12 BC, 9 BC, AD 8, AD 12 etc. This proposal is still the most widely accepted solution. It has also sometimes been suggested that 45 BC was a leap year.
Other solutions have been proposed from time to time. Kepler proposed in 1614 that the correct sequence of leap years was 43 BC, 40 BC, 37 BC, 34 BC, 31 BC, 28 BC, 25 BC, 22 BC, 19 BC, 16 BC, 13 BC, 10 BC, AD 8, AD 12 etc. In 1883 the German chronologist Matzat proposed 44 BC, 41 BC, 38 BC, 35 BC, 32 BC, 29 BC, 26 BC, 23 BC, 20 BC, 17 BC, 14 BC, 11 BC, AD 4, AD 8, AD 12 etc., based on a passage in Dio Cassius that mentions a leap day in 41 BC that was said to be contrary to (Caesar's) rule. In the 1960s Radke argued the reform was actually instituted when Augustus became pontifex maximus in 12 BC, suggesting the sequence 45 BC, 42 BC, 39 BC, 36 BC, 33 BC, 30 BC, 27 BC, 24 BC, 21 BC, 18 BC, 15 BC, 12 BC, AD 4, AD 8, AD 12 etc.
In 1999, an Egyptian papyrus was published which gives an ephemeris table for 24 BC with both Roman and Egyptian dates. From this it can be shown that the most likely sequence was in fact 44 BC, 41 BC, 38 BC, 35 BC, 32 BC, 29 BC, 26 BC, 23 BC, 20 BC, 17 BC, 14 BC, 11 BC, 8 BC, AD 4, AD 8, AD12 etc., very close to that proposed by Matzat. This sequence shows that one aim of the Augustan reform was to ensure that key dates of his career, notably the fall of Alexandria on 1 August 30 B.C., were unaffected by his correction.
Naming of the months
The Romans eventually named months after Caesar and Augustus, renaming Quintilis [Fifth month, with March = month 1] as Iulius (July) in 44 BC and Sextilis [Sixth month] as Augustus (August) in 8 BC. Other months were renamed by other emperors, but none of the later changes survived their deaths. Caligula renamed Septembris [Seventh month] as Germanicus; Nero renamed Aprilis as Neroneus, Maius as Claudius and Iunius as Germanicus; and Domitian renamed Septembris as Germanicus and Octobris [Eighth month] as Domitianus. Septembris was also renamed as Antoninus and Tacitus. Novembris was renamed Faustina and Romanus. Commodus was unique in renaming all twelve months after his own adopted names: Amazonius, Invictus, Felix, Pius, Lucius, Aelius, Aurelius, Commodus, Augustus, Herculeus, Romanus, and Exsuperatorius (January to December).
Length of the months
According to the 13th century scholar Sacrobosco, the original scheme for the months in the Julian Calendar was very regular, alternately long and short. From January through December, the month lengths according to Sacrobosco for the Roman Republican calendar were:
He then thought that Julius Caesar added one day to every month except February, a total of 11 more days, giving the year 365 days. A leap day could now be added to the extra short February:
He then said Augustus changed this to:
giving us the irregular month lengths which we still use today, so that the length of Augustus would not be shorter (and therefore inferior) than the length of Iulius.
Sacrobosco is almost certainly wrong on this point. First of all, a wall painting of a Roman Republican calendar has survived  (http://www.clubs.psu.edu/up/aegsa/rome/fasti4.html) which confirms the literary accounts that the months were already irregular before Julius Caesar reformed it:
Also, one thing that was not changed by the switch from the old Roman calendar to the new Julian calendar was the dates of the Nones and Ides. In particular, the Ides are late (on the 15th rather than 13th) in March, May, July and October. This suggests that these months always had 31 days in the Julian calendar. Further, Sacrobosco's theory is explicitly contradicted by the third and fifth century authors Censorinus and Macrobius, and, finally, it is inconsistent with seasonal lengths given by Varro, writing in 37 BC, before the Augustan reform, and with the 31-day Sextilis given by the new Egyptian papyrus from 24 BC.
The dominant method that the Romans used to identify a year for dating purposes was to name it after the two consuls who took office in it. Since 153 BC, they had taken office on 1 January, and Julius Caesar did not change the beginning of the year. Thus this consular year was an eponymous or named year. Roman years were named this way until the last consul was appointed in 541. Only rarely did the Romans number the year from the founding of the city (of Rome), ab urbe condita (AUC). This method was used by Roman historians to determine the number of years from one event to another, not to date a year. Different historians had several different dates for the founding. The Fasti Capitolini, an inscription caontaining an official list of the consuls which was published by Augustus, used an epoch of 752 BC. The epoch used by Varro, 753 BC, has been adopted by modern historians. Indeed, Renaissance editors often added it to the manuscripts that they published, giving the false impression that the Romans numbered their years. Most modern historians tacitly assume that it began on the day the consuls took office, and ancient documents such as the Fasti Capitolini which use other AUC systems do so in the same way. However, the Varronian AUC year did not formally begin on 1 January, but on Founder's Day, 21 April. This prevented the early Roman church from celebrating Easter after 21 April because the festivities associated with Founder's Day conflicted with the solemnity of Lent, which was observed until the Saturday before Easter Sunday.
In addition to consular years, the Romans sometimes used the regnal year of the emperor. Anno Diocletiani, named after Diocletian, was often used by the Alexandrian Christians to number their Easters during the fourth and fifth centuries. In AD 537, Justinian required that henceforth the date must include the name of the emperor, in addition to the indiction and the consul (the latter ending only four years later). The indiction caused the Byzantine year to begin on 1 September. In AD 525 Dionysius Exiguus proposed the system of anno Domini, which gradually spread through the western Christian world, once the system was adopted by Bede. Years were numbered from the supposed date of the "incarnation" or "annunciation" of Jesus Christ on 25 March, although this soon changed to Christmas, then back to Annunciation Day in Britain, and the numbered year even began on Easter in France.
From Julian to Gregorian
The Julian calendar was in general use in Europe from the times of the Roman Empire until 1582, when Pope Gregory XIII promulgated the Gregorian Calendar, which was soon adopted by most Catholic countries. The Protestant countries followed later, and the countries of Eastern Europe even later. Great Britain had Thursday 14 September 1752 follow Wednesday 2 September 1752. Sweden adopted the new style calendar in 1753, but also for a twelve-year period starting in 1700 used a modified Julian Calendar. Russia remained on the Julian calendar until after the Russian Revolution (which is thus called the 'October Revolution' but occurred in November according to the Gregorian calendar).
Although all Eastern European countries had adopted the Gregorian calendar on or before 1923, their national Eastern Orthodox churches had not. A Revised Julian calendar was proposed during a synod in Constantinople in May of 1923, consisting of a solar part which was and will be identical to the Gregorian calendar until the year 2800, and a lunar part which calculated Easter astronomically at Jerusalem. All Orthodox churches refused to accept the lunar part, so almost all Orthodox churches continue to celebrate Easter according to the Julian calendar (the Finnish Orthodox Church uses the Gregorian Easter). The solar part was only accepted by some Orthodox churches, those of Constantinople, Alexandria, Antioch, Greece, Cyprus, Romania, Poland, and Bulgaria (the last in 1963), thus they celebrate the Nativity on the same day that Western Christians do, 25 December Gregorian until 2800. The Orthodox churches of Jerusalem, Russia, and Serbia and some other groups (e.g. the Holy Synod in Resistance) continue to use the Julian calendar for their fixed dates, thus they celebrate the Nativity on 25 December Julian (7 January Gregorian until 2100).
cs:Juliánský kalendář da:Julianske kalender de:Julianischer Kalender es:Calendario juliano eo:Julia kalendaro fr:Calendrier julien [[ko:율리우스력]] it:Calendario giuliano [[he:הלוח היוליאני]] nl:Juliaanse kalender ja:ユリウス暦 no:Juliansk kalender pl:Kalendarz juliański pt:Calendário juliano ro:Calendarul iulian sl:Julijanski koledar sv:Julianska kalendern zh-cn:儒略历