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 at least since Hipparchus. It has a regular year of 365 days divided into 12 months, and a leap day is added every 4 years, hence the average Julian year is 365.25 days. 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, causing it to gain a day about every 128 years. 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 ordinary year in the previous Roman calendar consisted of 12 months, for a total of 355 days. In addition, an intercalary month named Intercalaris was sometimes inserted between February and March. Intercalaris was formed by inserting 22 days before the last five days of February, creating a 27-day month. It began after a truncated February having 23 or 24 days, so that it had the effect of adding 22 or 23 days to the year, forming an intercalary year of 377 or 378 days.
According to the later writers Censorinus and Macrobius, the ideal intercalary cycle consisted of ordinary years of 355 days alternating with intercalary years, which were alternately 377 and 378 days long. On this system, the average Roman year would have had 366¼ days over four years, giving it an average drift of one day per year relative to any solstice or equinox. Macrobius describes a further refinement wherein, for 8 years out of 24, there were only three intercalary years each of 377 days. This refinement averages the length of the year to 365¼ days over 24 years. In practice, intercalations did not occur schematically according to these ideal systems, but were determined by the pontifices. So far as can be determined from the historical evidence, they were much less regular than these ideal schemes suggest. They usually occurred every second or third year, but were sometimes omitted for much longer, and occasionally occurred in two consecutive years.
If managed correctly this system allowed the Roman year, on average, to stay roughly aligned to a tropical year. However, if too many intercalations were omitted, as happened after the Second Punic War and during the Civil Wars, the calendar would drift rapidly out of alignment with the tropical year. Moreover, since intercalations were often determined quite late, the average Roman citizen often did not know the date, particularly if he were some distance from the city. For these reasons, the last years of the pre-Julian calendar were later known as years of confusion. The problems became particularly acute 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 during the five Roman years before 46 BC.
The Julian reform was intended to correct this problem permanently. Before it took effect, the missed intercalations during Julius Caesar's pontificate were made up by inserting 67 days (22+23+22) between November and December of 46 BC in the form of two months, 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, 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. Caesar Augustus remedied this discrepancy by restoring the correct frequency after 36 years of this mistake. He also skipped several leap days in order to realign the year.
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, 39, 36, 33, 30, 27, 24, 21, 18, 15, 12, 9 BC, AD 8, 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, 40, 37, 34, 31, 28, 25, 22, 19, 16, 13, 10 BC, AD 8, 12 etc. In 1883 the German chronologist Matzat proposed 44, 41, 38, 35, 32, 29, 26, 23, 20, 17, 14, 11 BC, AD 4, 8, 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, 42, 39, 36, 33, 30, 27, 24, 21, 18, 15, 12 BC, AD 4, 8, 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, 41, 38, 35, 32, 29, 26, 23, 20, 17, 14, 11, 8 BC, AD 4, 8, 12 etc., very close to that proposed by Matzat. This sequence shows that the standard Julian leap year sequence began in AD 4, the twelfth year of the Augustan reform. Also, under this sequence the actual Roman year coincided with the proleptic Julian year between 32 and 26 BC. This suggests that one aim of the realignment portion of the Augustan reform was to ensure that key dates of his career, notably the fall of Alexandria on 1 August 30 BC, were unaffected by his correction.
Roman dates before 32 BC were typically a day or two before the day with the same Julian date, so 1 January in the Roman calendar of the first year of the Julian reform actually fell on 31 December 46 BC (Julian date). A curious effect of this is that Caesar's assassination on the Ides (15th day) of March in 44 BC fell on 14 March 44 BC in the Julian calendar.
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 apparently none of the later changes survived their deaths. Caligula renamed September [Seventh month] as Germanicus; Nero renamed Aprilis (April) as Neroneus, Maius (May) as Claudius and Iunius (June) as Germanicus; and Domitian renamed September as Germanicus and October [Eighth month] as Domitianus. September was also renamed as Antoninus and Tacitus. November [Ninth month] was renamed Faustina and Romanus. Commodus was unique in renaming all twelve months after his own adopted names (January to December): Amazonius, Invictus, Felix, Pius, Lucius, Aelius, Aurelius, Commodus, Augustus, Herculeus, Romanus, and Exsuperatorius.
Much more lasting than the ephemeral month names of the post-Augustan Roman emperors were the names introduced by Charlemagne. He renamed all of the months agriculturally into Old High German. They were used until the 15th century, and with some modification until the 18th century in modern German (January-December): Wintarmanoth (winter month), Hornung (bastard?), Lentzinmanoth (Lent month), Ostarmanoth (Easter month), Winnemanoth (grazing month), Brachmanoth (plowing month), Heuvimanoth (hay month), Aranmanoth (harvest month), Witumanoth (wood month), Windumemanoth (vintage month), Herbistmanoth (grazing month), and Heilagmanoth (holy month).
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:
- 30, 29, 30, 29, 30, 29, 30, 29, 30, 29, 30, and 29, totaling 354 days.
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:
- 31, 29 (30), 31, 30, 31, 30, 31, 30, 31, 30, 31, and 30
He then said Augustus changed this to:
- 31, 28 (29), 31, 30, 31, 30, 31, 31, 30, 31, 30, and 31
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.
Although this theory is still widely repeated, Sacrobosco is almost certainly wrong. First of all, a wall painting of a Roman Republican calendar has survived 
which confirms the literary accounts that the months were already irregular before Julius Caesar reformed it:
- 29, 28, 31, 29, 31, 29, 31, 29, 29, 31, 29, and 29
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 containing 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 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, Serbia, Georgia and the Greek Old Calendarists continue to use the Julian calendar for their fixed dates, thus they celebrate the Nativity on 25 December Julian (7 January Gregorian until 2100).