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Julian Calendar

Julian calendar

The Julian calendar was introduced in 46 BC by Julius Caesar and took force in 45 BC (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 to February every four years. Hence the Julian year is on average 365.25 days long. The Julian calendar remained in use into the 20th century in some countries and is still used by many national Orthodox churches. However, too many leap days are added with respect to the astronomical seasons on this scheme. On average, the astronomical solstices and the equinoxes advance by about 11 minutes per year against the Julian year, causing the calendar to gain a day about every 134 years. While Hipparchus and presumably Sosigenes were aware of the discrepancy, although not of its correct value, it was evidently felt to be of little importance. However, it accumulated significantly over time, and eventually led to the reform of 1582, which replaced the Julian calendar with the more accurate Gregorian calendar. The notation "Old Style" (OS) is sometimes used to indicate a date in the Julian calendar, as opposed to "New Style", which indicates a date in the Gregorian Calendar. This notation is used when there might otherwise be 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, the Mensis Intercalaris, was sometimes inserted between February and March. This intercalary month 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. According to Macrobius, the error was the result of counting inclusively, so that the four year cycle was considered as including both the first and fourth 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

Immediately after the Julian reform, the twelve months of the Roman calendar were named Ianuarius, Februarius, Martius, Aprilis, Maius, Iunius, Quintilis, Sextilis, September, October, November, and December, just as they were before the reform. Their lengths were set to their modern values. The old intercalary month, the Mensis Intercalaris, was abolished and replaced with an single intercalary day at the same point (i.e. five days before the end of Februarius). The first month of the year continued to be Ianuarius, as it had been since 153 BC. The Romans later renamed months after Caesar and Augustus, renaming Quintilis (originally, "the Fifth month", with March = month 1) as Iulius (July) in 44 BC and Sextilis ("Sixth month") as Augustus (August) in 8 BC. (Note that the letter J was not invented until the 17th century). Quintilis was renamed to honour Caesar because it was the month of his birth. According to a senatusconsultum quoted by Macrobius, Sextilis was renamed to honour Augustus because several of the most significant events in his rise to power, culminating in the fall of Alexandria, fell in that month. 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. At other times, September was also renamed as Antoninus and Tacitus, and 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 modifications until the late 18th century in Germany and in the Netherlands (January-December): Wintarmanoth (winter month), Hornung (spring), 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 (autumn/harvest month), and Heilagmanoth (holy month). Translations of these month names are still used to this day in some Slavic languages, such as Polish.

Lengths 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 than (and therefore inferior to) the length of Iulius. Although this theory is still widely repeated, it is certainly wrong. First, a wall painting of a Roman Republican calendar has survived [http://www.personal.psu.edu/users/w/x/wxk116/RomanCalendar/Fasti4.gif] 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, the Julian reform did not change 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, showing that these months always had 31 days in the Roman calendar, whereas Sacrobosco's theory requires that the length of October was changed. 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, with the 31-day Sextilis given by the new Egyptian papyrus from 24 BC, and with the 28-day February shown in the Fasti Caeretani, which is dated before 12 BC.

Year numbering

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, which is still used in the Eastern Orthodox Church for the beginning of the liturgical year. 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), in 1917, while Greece continued to use it until 1923. 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, Bulgaria (in 1963), and the Orthodox Church in America (although some OCA parishes are permitted to use the Julian calendar). Thus, these churches celebrate the Nativity on the same day that Western Christians do, 25 December Gregorian until 2800. The Orthodox churches of Jerusalem, Russia, Serbia, Georgia, Ukraine, 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).

External links

- [http://aa.usno.navy.mil/data/docs/JulianDate.html Julian-Gregorian Converter]
- [http://webexhibits.org/calendars/index.html Calendars through the ages] on WebExhibits.
- [http://www.tyndale.cam.ac.uk/Egypt/ptolemies/chron/roman/chron_rom_cal.htm Roman Dates]
- [http://penelope.uchicago.edu/~grout/encyclopaedia_romana/calendar/romancalendar.html The Roman Calendar]
- [http://5ko.free.fr/jul-greg.php?e=en Synoptical Julian-Gregorian Calendar] - compare the Julian and Gregorian calendars for any date between 1582 and 2100 using this side-by-side reference. Category:Ancient Rome Category:Specific calendars als:Julianischer Kalender ko:율리우스력 ja:ユリウス暦 simple:Julian calendar th:ปฏิทินจูเลียน

46 BC

Events

- February 6 – Julius Caesar defeats the combined army of Pompeian followers and Numidians under Metellus Scipio and Juba at Thapsus.
- April 20 – Cicero, in Rome, writes to Varro "If our voices are no longer heard in the Senate and in the Forum, let us follow the example of the ancient sages and serve our country through our writings, concentrating on questions of ethics and constitutional law."
- November – Caesar leaves for Farther Hispania to deal with a fresh outbreak of resistance.
- Caesar is "elected" Pontifex Maximus for life, and reforms the Roman calendar to create the Julian calendar. The transitional year is extended to 445 days to synchronize the new calendar and the seasonal cycle. The Julian Calendar would remain the standard in the western world for over 1600 years, until superceeded by the Gregorian Calendar in 1582.
- Caesar gets drunk and hits a member of the Roman Senate.
- Caesar appoints his nephew Octavian his heir.

Births

Deaths

- Marcus Porcius Cato, the younger commits suicide after the battle of Thapsus
- Metellus Scipio (Quintus Caecilius Metellus Pius Cornelianus Scipio Nasica) killed at the battle of Thapsus while his forces attempt to surrender.
- Vercingetorix, Gaul leader Category:46 BC ko:기원전 46년 simple:46 BC

45 BC

Events

Rome :
- January 1 - Julian calendar goes into effect :
- March 17 - In his last victory, Julius Caesar defeats the Pompeian forces of Titus Labienus and Pompey the younger in the Battle of Munda. Pompey the younger was excuted, and Labienus died in battle, but Sextus Pompey escaped to take command of the remnants of the Pompeian fleet. :
- The veterans of Julius Caesar's Legions Legio XIII Gemina and Legio X Equestris dembobilized. The veterans of the 10th legion would be settled in Narbo, while those of the 13th would be given somewhat better lands in Italia it'self. :
- Julius Caesar is named dictator for life :
- Caesar probably writes the Commentaries in this year.
- Possible first year of the Azes I Era

Births

- Iullus Antonius - son of Mark Antony and Fulvia; consul 10 BC
- Wang Mang - "usurper" of the Han Dynasty and Emperor of the Xin Dynasty

Deaths

- February - Tullia, daughter of Cicero
- March 17 - Titus Labienus, killed in the battle of Munda
- March 17 - Gnaeus Pompeius, son of Pompey the Great, executed after the battle of Munda Category:45 BC ko:기원전 45년

Alexandria

Located on the Mediterranean Sea coast, Alexandria (in Arabic, الإسكندرية, transliterated al-ʼIskandariyyah) is the chief seaport in Egypt, and that country's second largest city, and the capital of the Al Iskandariyah governate. It is located at , 208 km (129 miles) northwest of Cairo. The Canopic mouth of the Nile (now dry) was 19 km (12 miles) east, near the ancient city of Canopus. It has a population of approximately 3,723,000. It was named after its founder, Alexander the Great, and as the seat of the Ptolemaic rulers of Egypt quickly became one of the greatest cities of the Hellenistic world — second only to Rome in size and wealth throughout much of antiquity. However, upon the founding of Cairo by Egypt's mediæval Islamic rulers its status as the country's capital was ended, and it fell into a long decline, which by the late Ottoman period had seen it reduced to little more than a small fishing village. Ottoman, was inaugurated in 2001]] 2001

History

The history of Alexandria covers four periods:
- The Ptolemaic era which starts with the founding of the city and ends with the arrival of the Romans (blue).
- The Roman era from 80 BC until the arrival of the Arabs in 641 (green).
- The Arab city from 641 until 1798 when Napoleon arrived (yellow).
- The modern city from 1798 (red).

Founding

Alexandria was founded by Alexander the Great in or around 334 BC (the exact date is disputed) as Ἀλεξάνδρεια (Aleksándreia; see also List of traditional Greek place names). Alexander's chief architect for the project was Deinocrates of Rhodes. Ancient accounts are extremely numerous and varied, and much influenced by subsequent developments. One of the more sober descriptions, given by the historian Arrian, tells how Alexander undertook to lay out the city's general plan, but lacking chalk or other means, resorted to sketching it out with grain. Alexander's seers, and in particular Aristander of Telmessus, interpreted this as an omen that the city would prosper, particularly in grain. Other authors make the omen not the grain itself, but the arrival of flocks of birds to eat it. In any case, the story explains Alexandria's role as the shipping-point for Egyptian grain, which fed the Hellenistic and Roman world. A number of the more fantastic foundation myths are found in the Alexander Romance, and were picked up by mediæval Arab historians. The 14th century Arab historian Ibn Khaldun ridiculed one where sea-monsters prevent the foundation, but are thwarted when Alexander descends in a glass box, and armed with exact knowledge of their appearance, erects metal effigies on the beach which succeed in frightening the monsters away. Alexandria was intended to supersede Naucratis as a Greek centre in Egypt, and to be the link between Greece and the rich Nile Valley. If such a city was to be on the Egyptian coast, there was only one possible site, behind the screen of the Pharos island and removed from the silt thrown out by Nile mouths. An Egyptian townlet, Rhacotis, already stood on the shore and was a resort of fishermen and pirates. Behind it there were five native villages scattered along the strip between Lake Mareotis and the sea, according to a history of Alexander attributed to the author known as pseudo-Callisthenes. A few months after the foundation, Alexander left Egypt for the East and never returned to his city. His general, Ptolemy (later Ptolemy I of Egypt) succeeded in bringing Alexander's body to Alexandria, where it became a famous tourist destination for ancient travellers. After Alexander departed, his viceroy, Cleomenes, continued the creation of Alexandria. The Heptastadion, however, and the mainland quarters seem to have been mainly Ptolemaic work. Inheriting the trade of ruined Tyre and becoming the centre of the new commerce between Europe and the Arabian and Indian East, the city grew in less than a generation to be larger than Carthage and in a century it was the largest city in the world; and for some centuries more it was second only to Rome. Nominally a free Greek city, Alexandria retained its senate to Roman times; and indeed the judicial functions of that body were restored by Septimius Severus, after temporary abolition by Augustus. It was not only a center of Hellenism, but was also the greatest Jewish city in the world. There the Septuagint was produced. The early Ptolemies kept it in order and fostered the development of its museum into the leading Greek university but they were careful to maintain the distinction of its population into three nations, "Greek", Jew and Egyptian. One of the earliest inhabitants was the geometer and number-theorist Euclid. From this division arose much of the later turbulence which began to manifest itself under Ptolemy Philopater, who reigned 221–204 BC. In ancient times, Alexandria was known for its lighthouse (one of the Seven Wonders of the World) and its library (the largest in the world). Ongoing maritime archaeology in the harbor of Alexandria, begun in 1994, is revealing details of the Alexandria of the Ptolemaic dynasty.

Roman jurisdiction

The city passed formally under Roman jurisdiction in 80 BC, according to the will of Ptolemy Alexander: but it had been under Roman influence for more than a hundred years previously. Julius Caesar dallied with Cleopatra in Alexandria in 47 BC and was mobbed by the rabble; his example was followed by Marc Antony, for whose favor the city paid dear to Octavian, who placed over it a prefect from the imperial household. Alexandria seems from this time to have regained its old prosperity, commanding, as it did, an important granary of Rome; this fact, doubtless, was one of the chief reasons which induced Augustus to place it directly under imperial power. In AD 215 the emperor Caracalla visited the city; and, for some insulting satires that the inhabitants had directed at him, he abruptly commanded his troops to put to death all youths capable of bearing arms. This brutal order seems to have been carried out even beyond the letter, for a general massacre was the result. Even as its main historical importance had formerly sprung from pagan learning, so now it acquired fresh importance as a centre of Christian theology and church government. There Arianism was formulated and there Athanasius, the great opponent of both Arianism and pagan reaction, triumphed over both, establishing the Patriarch of Alexandria as a major influence in Christianity for the next two centuries. As native influences, however, began to reassert themselves in the Nile valley, Alexandria gradually became an alien city, more and more detached from Egypt; and, losing much of its commerce as the peace of the empire broke up during the 3rd century AD, it declined fast in population and splendour. In the late 4th century, persecution of pagans by Christians had reached new levels of intensity. Temples and statues were destroyed throughout the Roman empire, pagan rituals forbidden under punishment of death, and libraries closed. In 391, Emperor Theodosius ordered the destruction of all pagan temples, and the Patriarch Theophilus, complied with this request. It is possible that the great Library of Alexandria was destroyed about this time. The Brucheum and Jewish quarters were desolate in the 5th century, and the central monuments, the Soma and Museum, fallen to ruin. On the mainland, life seems to have centred in the vicinity of the Serapeum and Caesareum; both become Christian churches. The Pharos and Heptastadium quarters remained populous and intact. In 616 it was taken by Khosrau II, king of Persia. Although the Byzantine Emperor Heraclius recovered it a few years later, in 640 the Arabians, under the general Amr ibn al-As, captured it for good after a siege that lasted fourteen months. The city received no aid from Constantinople during that time; Heraclius was dead and the new Emperor Constantine III was barely twelve years old. Notwithstanding the losses that the city had sustained, Amr was able to write to his master, the caliph Omar, that he had taken a city containing "4,000 palaces, 4,000 baths, 12,000 dealers in fresh oil, 12,000 gardeners, 40,000 Jews who pay tribute, 400 theatres or places of amusement."

After Amr

Shortly after its capture, Alexandria again fell into the hands of the Greeks, who took advantage of Amr's absence with the greater portion of his army. On hearing what had happened, however, Amr returned, and quickly regained possession of the city. About the year 646, Amr was deprived of his government by the caliph Uthman ibn Affan. Amr was greatly beloved by the Egyptians; they threatened such a revolt over this that the Greek emperor was determined to reduce Alexandria. The attempt proved successful. The caliph, perceiving his mistake, immediately restored Amr, who, on his arrival in Egypt, drove the Greeks within the walls of Alexandria, but was only able to capture the city after a most obstinate resistance by the defenders. This so exasperated him that he completely demolished its fortifications, although he seems to have spared the lives of the inhabitants as far as lay in his power. The city was for some time a center of the Mediterranean spice trade, receiving overland caravans of pepper, cinnamon, nutmeg, mace and more from India and beyond, which were bought by European traders at enormously inflated prices. The locations of the source of these spices were carefully guarded by their Indian and Arabian merchants. The building of Cairo in 969, and, above all, the discovery of the route to the East by the Cape of Good Hope in 1498, nearly ruined the commerce of Alexandria; the canal, which supplied it with Nile water, became blocked; and although it remained a principal Egyptian port, at which most European visitors in the Mamluk and Ottoman periods landed, we hear little of it until about the beginning of the 19th century. Alexandria figured prominently in the military operations of Napoléon's Egyptian expedition of 1798. The French troops stormed the city on July 2 1798, and it remained in their hands until the arrival of the British expedition of 1801. The battle of Alexandria, fought on March 21 that year between the French and the British, took place near the ruins of Nicopolis, on the narrow spit of land between the sea and Lake Abukir.

The 1800s

During the anarchy which accompanied Ottoman rule in Egypt from first to last, Alexandria sank to a small town of about 4,000 inhabitants, and it owed its modern rennaissance solely to Mehemet Ali, who wanted a deep port and naval station for his viceregal domain. He restored its water communication with the Nile by making the Mahmudiya canal, finished in 1820; and he established at Ras et-Tin his favorite residence. The old Eunostus harbour became the port, and a flourishing city arose on the Pharos island and the Heptastadion district, with outlying suburbs and villa residences along the coast eastwards and the Mareotic shore. Being the starting-point of the "overland route" to India, and the residence of the chief foreign consuls, it quickly acquired a European character and attracted not only French residents, but great numbers of Greeks, Jews and Syrians. There most of the negotiations between the powers and Mehemet Ali were conducted; from there started the Egyptian naval expeditions to Crete, the Morea and Syria; and thither sailed the betrayed Ottoman fleet in 1839. It was twice threatened by hostile fleets, the Greek in 1827 and the combined British, French and Russian squadrons in 1828. The latter withdrew on the viceroy's promise that Ibrahim should evacuate the Morea. The fortifications were strengthened in 1841, and remained in an antiquated condition until 1882, when they were renovated by Arabi Pasha. Alexandria was connected with Cairo by railway in 1856. Much favored by the earlier viceroys of Mehemet Ali's house, and removed from the Mameluke troubles, Alexandria was the real capital of Egypt until Said Pasha died there in 1863 and Ismail Pasha came into power. Though this prince continued to develop the city, giving it a municipality in 1861 and new harbour works in 1871–1878, he developed Cairo still more; and the center of gravity definitely shifted to the inland capital.

Bombardment of 1882

1882]] Fate, however, again brought Alexandria to the front. After a mutiny of soldiers there in 1881, the town was greatly excited by the arrival of an Anglo-French fleet in May 1882, and on June 11 a terrible riot and massacre took place, resulting in the death of four hundred Europeans. Since satisfaction was not given for this and the forts were being strengthened at the instigation of Arabi Pasha, the war minister, the British admiral, Sir Frederick Beauchamp Seymour (afterwards Lord Alcester), sent an ultimatum on July 10 and opened fire on the forts the next day. They were demolished, but as no troops were landed immediately a fresh riot and massacre ensued. As Arabi did not submit, a British military expedition landed at Alexandria on August 10, following which the British engaged in the occupation of the whole country.

Under British control

August 10] Alexandria has greatly expanded since then. As the British consular report for 1904 stated, "Building … for residential and other purposes proceeds with almost feverish rapidity. The cost of living has doubled and the price of land has risen enormously." More Greeks continued to settle the city, establishing financial and cultural centres. The Greek poet Constantine Cavafy was born and lived here. British occupied Alexandria developed into a major Royal Navy base, with the strategic Suez Canal to the east. During Second World War and the North Africa Campaign of 1940–1943 The decisive Battles of El Alamein were fought to its west. The Egyptian military coup of 1952 saw the destruction of the Egyptian monarchy and British protectorate status. Colonel Nasser took power and the Anglo-Egyptian Treaty of 1954 made provision for the withdrawal of British troops. The numbers of the city's foreign population have dwindled ever since. A small Greek community, however, remains to this day. The film Ice Cold in Alex would later be set here.

Geography

Ice Cold in Alex

Layout of the ancient city

The Greek Alexandria was divided into three regions: #The Jews' quarter, forming the northeast portion of the city; #Rhacotis, on the west, occupied chiefly by Egyptians; #Brucheum, the Royal or Greek quarter, forming the most magnificent portion of the city. In Roman times Brucheum was enlarged by the addition of an official quarter, making up four regions in all. The city was laid out as a grid of parallel streets, each of which had an attendant subterranean canal. Two main streets, lined with colonnades and said to have been each about 60 metres (200 feet) wide, intersected in the centre of the city, close to the point where rose the Sema (or Soma) of Alexander (his Mausoleum). This point is very near the present mosque of Nebi Daniel; and the line of the great east–west "Canopic" street only slightly diverged from that of the modern Boulevard de Rosette. Traces of its pavement and canal have been found near the Rosetta Gate, but better remains of streets and canals were exposed in 1899 by German excavators outside the east fortifications, which lie well within the area of the ancient city. Alexandria consisted originally of little more than the island of Pharos, which was joined to the mainland by a mole nearly a mile long (1240 m) and called the Heptastadion ("seven stadia" — a stadium was a Greek unit of length measuring approximately 180m). The end of this abutted on the land at the head of the present Grand Square, where rose the "Moon Gate". All that now lies between that point and the modern Ras et-Tin quarter is built on the silt which gradually widened and obliterated this mole. The Ras et-Tin quarter represents all that is left of the island of Pharos, the site of the actual lighthouse having been weathered away by the sea. On the east of the mole was the Great Harbour, now an open bay; on the west lay the port of Eunostos, with its inner basin Kibotos, now vastly enlarged to form the modern harbour. In Strabo's time, (latter half of 1st century BC) the principal buildings were as follows, enumerated as they were to be seen from a ship entering the Great Harbour. #The Royal Palaces, filling the northeast angle of the town and occupying the promontory of Lochias, which shut in the Great Harbour on the east. Lochias (the modern Pharillon) has almost entirely disappeared into the sea, together with the palaces, the "Private Port" and the island of Antirrhodus. There has been a land subsidence here, as throughout the northeast coast of Africa. #The Great Theatre, on the modern Hospital Hill near the Ramleh station. This was used by Caesar as a fortress, where he stood a siege from the city mob after the battle of Pharsalus #The Poseideion, or Temple of the Sea God, close to the Theatre #The Timonium built by Mark Antony #The Emporium (Exchange) #The Apostases (Magazines) #The Navalia (Docks), lying west of the Timonium, along the sea-front as far as the mole #Behind the Emporium rose the Great Caesareum, by which stood the two great obelisks, each later known as "Cleopatra's Needle," and now removed to New York City and London. This temple became in time the Patriarchal Church, some remains of which have been discovered; but the actual Caesareum, so far as not eroded by the waves, lies under the houses lining the new sea-wall. #The Gymnasium and the Palaestra are both inland, near the Boulevard de Rosette in the eastern half of the town; sites unknown. #The Temple of Saturn; site unknown. #The Mausolea of Alexander (Soma) and the Ptolemies in one ring-fence, near the point of intersection of the two main streets #The Musaeum with its famous Library and theatre in the same region; site unknown. #The Serapeum, the most famous of all Alexandrian temples. Strabo tells us that this stood in the west of the city; and recent discoveries go far to place it near "Pompey's Pillar" which, however, was an independent monument erected to commemorate Diocletian's siege of the city. The names of a few other public buildings on the mainland are known, but there is no information as to their position. On the eastern point of the Pharos island stood the Great Lighthouse, one of the "Seven Wonders," reputed to be 138 meters (450 feet) high. The first Ptolemy began it, and the second completed it, at a total cost of 800 talents. It took 12 years to construct. It is the prototype of all lighthouses in the world. The light was produced by a furnace at the top. It was built mostly with solid blocks of limestone. The Pharos lighthouse was destroyed by an earthquake. A temple of Hephaestus also stood on Pharos at the head of the mole. In the Augustan age the population of Alexandria was estimated at 300,000 free citizes, in addition to an immense number of women, freedmen, children and slaves. The total population has been estimated to range from 500,000 to over 1,000,000 people.

The modern city

Augustan Augustan The city is built on the strip of land which separates the Mediterranean from Lake Mareotis (Mariout), and on a T-shaped peninsula which forms harbors east and west. The stem of the T was originally a mole (breakwater) leading to the island of Pharos which formed the cross-piece. In the course of centuries this mole has been silted up and is now an isthmus half a mile wide. On it a part of the modern city is built. The cape at the western end of the peninsula is Ras et-Tin (Cape of Figs); the eastern cape is known as Pharos or Kait Bey. South of the town — between it and Lake Mareotis — runs the Mahmudiya canal, which enters the western harbour by a series of locks. isthmus The Place Mehemet Ali, usually called the Grand Square, is an oblong open space, tree-lined, in the center of which there is an equestrian statue of the ruler after whom it is named. The square is faced with handsome buildings mainly in the Italian style. The most important are the law courts, exchange, Ottoman bank, English church and the Abbas Hilmi theatre. theatre On the Ras et-Tin promontory, overlooking the harbour, is the khedivial yacht club (built 1903) and the palace, also called Ras et-Tin, built by Mehemet Ali. In the district between the Grand Square and the western harbour, one of the poorest quarters of the city, is an open space with Fort Caffareli or Napoleon in the center. A major new library and cultural complex, the Bibliotheca Alexandrina, was recently built with the help of the United Nations. The original library contained authentic books from the time of Cleopatra but they were later burned when the library was destroyed. The predominant languages spoken, besides the Arabic of the natives, are Greek, French, English and Italian. Alexandria is served by a network of trams traveling east and west roughly parallel to the Corniche, or sea wall.

Ancient remains

Corniche Very little of the ancient city has survived into the present day. Much of the royal and civic quarter has sunk beneath the harbour due to earthquake subsidence, and much of the rest has been built upon in modern times. "Pompey's Pillar" is the most well-known ancient monument still standing. It is located on Alexandria's ancient acropolis — a modest hill located adjacent to the city's Arab cemetery — and was originally part of a temple colonnade. Including its pedestal it is 30m (99 feet) high; the shaft is of polished red granite, roughly three meters in diameter at the base, tapering to two and a half meters at the top. It has, however, nothing to do with Pompey, having been erected in AD 293 for Diocletian. Beneath the acropolis itself are the subterranean remains of the Serapeum, where the mysteries of the god Serapis were enacted, and whose carved wall niches are believed to have provided overflow storage space for the ancient Library. Alexandria's catacombs, known as "Kom al Sukkfa" are a short distance southwest of the pillar, consist of a multi-level labyrinth, reached via a large spiral staircase, and featuring dozens of chambers adorned with sculpted pillars, statues, and other syncretic Romano-Egyptian religious symbols, burial niches and sarcophagi, as well as a large Roman-style banquet room, where memorial meals were conducted by relatives of the deceased. The most extensive ancient excavation currently being conducted in Alexandria is known as "Kom al Dikka", and it has revealed the ancient city's well-preserved theatre, and the remains of its Roman-era baths.

Antiquities

Persistent efforts have been made to explore the antiquities of Alexandria. Encouragement and help have been given by the local Archaeological Society, and by many individuals, notably Greeks justly proud of a city which is one of the glories of their national history. The past and present directors of the museum have been enabled from time to time to carry out systematic excavations when opportunity offered; Mr D.G.Hogarth made tentative researches on behalf of the Egypt Exploration Fund and the Society for the Promotion of Hellenic Studies in 1895; and a German expedition worked for two years (1898–1899). But two difficulties face the would-be excavator in Alexandria. First, since the great and growing modern city stands right over the ancient one, it is almost impossible to find any considerable space in which to dig, except at enormous cost. Second, the general subsidence of the coast has sunk the lower-lying parts of the ancient town under water. Unfortunately the spaces still most open are the low grounds to northeast and southwest, where it is practically impossible to get below the Roman strata. The most important results were those achieved by Dr G Botti, late director of the museum, in the neighbourhood of "Pompey's Pillar," where there is a good deal of open ground. Here substructures of a large building or group of buildings have been exposed, which are perhaps part of the Serapeum. Hard by immense catacombs and columbaria have been opened which may have been appendages of the temple. These contain one very remarkable vault with curious painted reliefs, now lighted by electricity and shown to visitors. The objects found in these researches are in the museum, the most notable being a great basalt bull, probably once an object of cult in the Serapeum. Other catacombs and tombs have been opened in Kore es-Shugafa Hadra (Roman) and Ras et-Tin (painted). The Germans found remains of a Ptolemaic colonnade and streets in the north-east of the city, but little else. Mr Hogarth explored part of an immense brick structure under the mound of Kom ed-Dik, which may have been part of the Paneum, the Mausolea or a Roman fortress. The making of the new foreshore led to the dredging up of remains of the Patriarchal Church; and the foundations of modern buildings are seldom laid without some objects of antiquity being discovered. The wealth underground is doubtless immense; but, despite all efforts, there is not much for antiquarians to see in Alexandria outside the museum and the neighbourhood of "Pompey's Pillar." The native tomb-robbers, well-sinkers, dredgers and the like, however, come upon valuable objects from time to time, which find their way into private collections.

External links

- [http://www.alex4all.com/english/cat.php Alex4All]
- [http://wikitravel.org/en/article/Alexandria Wikitravel: Alexandria]
- http://ce.eng.usf.edu/pharos/Alexandria/index.html
- [http://www.sevenwondersworld.com/wonders_of_world_lighthouse_alexandria.html Seven Wonders of the world: Lighthouse of Alexandria]
- [http://www.unesco.org/csi/pub/source/alex5.htm Mostafa el-Abbadi on the pivotal place of Alexandria in Greek and Roman era trade networks]
- [http://st-takla.org/Alexandria-1.html More about Alexandria.. past and present at St Takla Church - Alex. website] Category:Cities in Egypt Category:Roman legions camps Category:World Book Capital Category:Hellenistic colonies ja:アレクサンドリア

Tropical year

A tropical year is the length of time that the Sun, as viewed from the Earth, takes to return to the same position along the ecliptic (its path among the stars on the celestial sphere). The precise length of time depends on which point of the ecliptic one chooses: starting from the (northern) vernal equinox, one of the four cardinal points along the ecliptic, yields the vernal equinox year; averaging over all starting points on the ecliptic yields the mean tropical year. At J 2000.0 it was 365.242190517 days or 365 d., 5 h., 48 min. and about 45.26 s. On Earth, we notice the progress of the tropical year from the slow motion of the Sun from south to north and back; the word "tropical" is derived from Greek tropos meaning "turn". The tropics of Cancer and Capricorn mark the extreme north and south latitudes the Sun reaches during this cycle. The position of the Sun can be measured by the variation from day to day of the length of the shadow at noon of a gnomon (a vertical pillar or stick). This is the most "natural" way of measuring the year in the sense that the variations of insolation drive the seasons. Because the vernal equinox moves back along the ecliptic due to precession, a tropical year is shorter than a sidereal year (in 2000, the difference was 20.409 minutes; it was 20.400 min in 1900).

Subtleties

The motion of the Earth in its orbit (and therefore the apparent motion of the Sun among the stars) is not completely regular due to gravitational perturbations by the Moon and planets. Therefore the time between successive passages of a specific point on the ecliptic will vary. Moreover, the speed of the Earth in its orbit varies (because the orbit is elliptic rather than circular). Furthermore, the position of the equinox on the orbit changes due to precession. As a consequence (explained below) the length of a tropical year depends on the specific point that you select on the ecliptic (as measured from, and moving together with, the equinox) that the Sun should return to. Therefore astronomers defined a mean tropical year, that is an average over all points on the ecliptic; it has a length of about 365.2422 SI days. Besides this, tropical years have been defined for specific points on the ecliptic: in particular the vernal equinox year, that start and ends when the Sun is at the vernal equinox. Its length is about 365.2424 days. An additional complication: We can measure time either in "days of fixed length": SI days of 86,400 SI seconds, defined by atomic clocks, or dynamical days defined by the motion of the Moon and planets; or in mean "natural" days, defined by the rotation of the Earth with respect to the Sun. The duration of the mean natural day is steadily getting longer as measured by clocks (or conversely, clock days are steadily getting shorter, as measured by a sundial). One must use the mean natural day because the "instantaneous" natural day varies regularly over time, as the equation of time shows. As explained at [http://www.hermetic.ch/cal_stud/cassidy/err_trop.htm Error in Statement of Tropical Year], using the value of the "mean tropical year" to refer to the vernal equinox year defined above, is strictly speaking an error. The words "tropical year" in astronomical jargon refer only to the mean tropical year Newcomb-style of 365.2422 SI days. The vernal equinox year of 365.2424 natural days is also important, because it is the basis of most solar calendars, but it is not the "tropical year" of modern astronomers. The number of natural days in a vernal equinox year has been oscillating between 365.2424 and 365.2423 for several millennia and will likely remain near 365.2424 for a few more. This long-term stability is pure chance, because in our era the slowdown of the rotation, the acceleration of the mean orbital motion, and the effect at the vernal point of shape changes in the Earth's orbit's happen to almost cancel out. In contrast, the mean tropical year, measured in SI days, is getting shorter. It was 365.2423 SI days at about AD 200, and is currently near 365.2421875 SI days (cf. J.H. von Mädler).

Current mean value

At the epoch J2000 (1 January 2000, 12h TT), the mean tropical year was: : 365.242 189 670 SI days. Due to changes in the precession rate and in the orbit of the Earth, there exists a steady change in the length of the tropical year. This can be expressed with a polynomial in time; the linear term is: : −0.000 000 061 62×a days (a in Julian years from 2000), or about 5 ms/year, which means that 2000 years ago the tropical year was 10 seconds longer. Note: these and following formulae use days of exactly 86400 SI seconds. a is measured in Julian years (365.25 days) from the epoch (2000). The time scale is Terrestrial Time which is based on atomic clocks (formerly, Ephemeris Time was used instead); this is different from Universal Time, which follows the somewhat unpredictable rotation of the Earth. The (small but accumulating) difference (called ΔT) is relevant for applications that refer to time and days as observed from Earth, like calendars and the study of historical astronomical observations such as eclipses.

Different lengths

As already mentioned, there is some choice in the length of the tropical year depending on the point of reference that one selects. The reason is that, while the precession of the equinoxes is fairly steady, the apparent speed of the Sun during the year is not. When the Earth is near the perihelion of its orbit (presently, around January 3–4), it (and therefore the Sun as seen from Earth) moves faster than average; hence the time gained when reaching the approaching point on the ecliptic is comparatively small, and the "tropical year" as measured for this point will be longer than average. This is the case if one measures the time for the Sun to come back to the southern solstice point (around December 21–22), which is close to the perihelion. Conversely, the northern solstice point presently is near the aphelion, where the Sun moves slower than average. Hence the time gained because this point has approached the Sun (by the same angular arc distance as happens at the southern solstice point) is notably greater: so the tropical year as measured for this point is shorter than average. The equinoctial points are in between, and at present the tropical years measured for these are closer to the value of the mean tropical year as quoted above. As the equinox completes a full circle with respect to the perihelion (in about 21,000 years), the length of the tropical year as defined with reference to a specific point on the ecliptic oscillates around the mean tropical year. Current values and their annual change of the time of return to the cardinal ecliptic points are:
- vernal equinox: 365.24237404 + 0.00000010338×a days
- northern solstice: 365.24162603 + 0.00000000650×a days
- autumn equinox: 365.24201767 − 0.00000023150×a days
- southern solstice: 365.24274049 − 0.00000012446×a days Notice that the average of these four is 365.2422 SI days (the mean tropical year). This figure is currently getting smaller, which means years get shorter, when measured in seconds. Now, actual days get slowly and steadily longer, as measured in seconds. So the number of actual days in a year is decreasing too. The differences between the various types of year are relatively minor for the present configuration of Earth's orbit. On Mars, however, the differences between the different types of years are an order of magnitude greater: vernal equinox year = 668.5907 Martian days (sols), summer solstice year = 668.5880 sols, autumn equinox year = 668.5940 sols, winter solstice year = 668.5958 sols, with the tropical year being 668.5921 sols [http://pweb.jps.net/~tgangale/mars/facts/factsi.htm]. This is due to Mars' considerably greater orbital eccentricity. It should be noted that Earth's orbit goes through cycles of increasing and decreasing eccentricity over a timescale of about 100,000 years (Milankovitch cycles), and its eccentricity can reach as high as about 0.06, so in the distant future, Earth will also have much more divergent values of the various equinox and solstice years.

Calendar year

This distinction is relevant for calendar studies. The main Christian moving feast has been Easter. Several different ways of computing the date of Easter were used in early christian times, but eventually the unified rule was accepted that Easter would be celebrated on the Sunday after the first full moon on or after the day of the vernal equinox, which was established to fall on 21 March. The church therefore made it an objective to keep the day of the vernal (spring) equinox on or near 21 March, and the calendar year has to be synchronized with the tropical year as measured by the mean interval between vernal equinoxes. From about AD 1000 the mean tropical year (measured in SI days) has become increasingly shorter than this mean interval between vernal equinoxes (measured in actual days), though the interval between successive vernal equinoxes measured in SI days has become increasingly longer. Now our current Gregorian calendar has an average year of: :365 + 97/400 = 365.2425 days. Although it is close to the vernal equinox year (in line with the intention of the Gregorian calendar reform of 1582), it is slightly too long, and not an optimal approximation when considering the continued fractions listed below. Note that the approximation of 365 + 8/33 used in the Iranian calendar is even better, and 365 + 8/33 was considered in Rome and England as an alternative for the Catholic Gregorian calendar reform of 1582. Moreover, modern calculations show that the vernal equinox year has remained between 365.2423 and 365.2424 calendar days (i.e. mean solar days as measured in Universal Time) for the last four millennia and should remain 365.2424 days (to the nearest ten-thousandth of a calendar day) for some millennia to come. This is due to the fortuitous mutual cancellation of most of the factors affecting the length of this particular measure of the tropical year during the current era.

Approximations

Continued fractions of the decimal value for the vernal equinox year quoted above give successive approaches to the average interval between vernal equinoxes, in terms of fractions of a day. These can be used to intercalate years of 365 days with leap years of 366 days to keep the calendar year synchronized with the vernal equinox:
- 365 (No intercalated days)
- 365 + 1/4 (Julian intercalation cycle; 1-in-4)
- 365 + 7/29 (6 × Julian cycle + 1-in-5; 7-in-29)
- 365 + 8/33 (Khayyam cycle; 7 × 1-in-4 + 1-in-5)
- 365 + 143/590 (17 × Khayyam cycle + 7-in-29) etc. Note that 590 years hence, the year length will have changed, postponing the need for any 7-in-29 subcycle.

References

- [1] According to Jean Meeus an "improved value for the length of the tropical year at epoch 2000.0" obtained by [http://rcswww.urz.tu-dresden.de/~lohrmobs/addresses.html Pierre Bretagnon, Paris] (1942-2002) in 2000.
Source: Jean Meeus, (2002), More mathematical astronomy morsels, page 365, note 3; Willmann-Bell, Richmond, VA. ISBN 0-943396-74-3.
- [2] Derived from: Jean Meeus (1991), Astronomical Algorithms, Ch.26 p. 166; Willmann-Bell, Richmond, VA. ISBN 0-943396-35-2 ; based on the VSOP-87 planetary ephemeris.
- Also: Jean Meeus and Denis Savoie, "The history of the tropical year", Journal of the British Astronomical Association 102 (1992) 40–42.[http://adsbit.harvard.edu/cgi-bin/nph-iarticle_query?1992JBAA..102...40M] Category:Units of time Category:Timekeeping Category:Calendars ja:太陽年

Hipparchus (astronomer)

Hipparchus (Greek Ἳππαρχος) (ca. 190 BC – ca. 120 BC) was a Greek astronomer, geographer, and mathematician. Hipparchus was born in Nicaea (now Iznik, Turkey) and probably died on the island of Rhodes. He is known to have been active at least from 147 BC to 127 BC. Hipparchus is considered the greatest astronomical observer, and by some the greatest astronomer of antiquity. He was the first Greek to develop quantitative and accurate models for the motion of the Sun and Moon. For this he made use of the observations and knowledge accumulated over centuries by the Chaldeans from Babylonia. He was also the first to compile a trigonometric table, which allowed him to solve any triangle. With his solar and lunar theories and his numerical trigonometry, he was probably the first to develop a reliable method to predict solar eclipses. His other achievements include the discovery of precession, the compilation of the first star catalogue, and probably the invention of the astrolabe. Claudius Ptolemaeus, three centuries later depended much on Hipparchus. However, his synthesis of astronomy superseded Hipparchus's work: although Hipparchus wrote at least fourteen books, only his commentary on the popular astronomical poem by Aratus has been preserved by later copyists. As a consequence, we know comparatively little about Hipparchus. Aratus

Life and work

Most of what is known about Hipparchus comes from Ptolemy's (2nd century) Almagest ("the great treatise"; ed. [Toomer 1981]), with additional references to him by Pappus of Alexandria and Theon of Alexandria (4th century) in their commentaries on the Almagest; from Strabo's Geographia ("Geography"), and from Pliny the Elder's Naturalis historia ("Natural history") (1st century). There is a strong tradition that Hipparchus was born in Nicaea (Greek Νικαία), in the ancient district of Bithynia (modern-day İznik in province Bursa), in what today is Turkey. The exact dates of his life are not known, but Ptolemy attributes astronomical observations to him from 147 BC to 127 BC; earlier observations since 162 BC might also be made by him. The date of his birth (ca. 190 BC) was calculated by Delambre based on clues in his work. Hipparchus must have lived some time after 127 BC because he analyzed and published his latest observations. Hipparchus obtained information from Alexandria as well as Babylon, but it is not known if and when he visited these places. It is not known what Hipparchus' economic means were and how he supported his scientific activities. Also, his appearance is unknown: there are no contemporary portraits.In the 2nd and 3rd centuries coins were made in his honour in Bithynia that bear his name and show him with a globe; this confirms the tradition that he was born there. Hipparchus is believed to have died on the island of Rhodes, where he spent most of his later life — Ptolemy attributes observations to him from Rhodes in the period from 141 BC to 127 BC. Hipparchus's main original works are lost. His only preserved work is Toon Aratou kai Eudoxou Fainomenoon exegesis ("Commentary on the Phaenomena of Eudoxus and Aratus"). This is a critical commentary in two books on a popular poem by Aratus based on the work by Eudoxus. It was published by Karl Manitius (In Arati et Eudoxi Phaenomena, Leipzig, 1894). Hipparchus also made a list of his major works, which apparently mentioned about fourteen books, but which is only known from references by later authors. His famous star catalogue probably was incorporated into the one by Ptolemy, but cannot be reliably reconstructed. We know he made a celestial globe; a copy of a copy may have been preserved in the oldest surviving celestial globe accurately depicting the constellations: the globe carried by the Farnese Atlas [Schaefer 2005]. Hipparchus is recognized as the originator and father of scientific astronomy. He is believed to be the greatest Greek astronomical observer, and many regard him as the greatest astronomer of ancient times, although Cicero gave preferences to Aristarchus of Samos. Some put in this place also Ptolemy of Alexandria. Hipparchus' writings had been mostly superseded by those of Ptolemy, so later copyists have not preserved them for posterity. Also see the biographical articles by [Toomer 1978] and [Jones 2001].

Babylonian sources

Many of the works of Greek scientists - mathematicians, astronomers, geographers - have been preserved up to the present time, or some aspects of their work and thought are still known through later references. However, achievements in these fields by Middle Eastern civilizations, notably those in Babylonia, had been forgotten. After the discovery of the archaeological sites in the 19th century, many writings on clay tablets have been found, some of them related to astronomy. Most known astronomical tablets have been described by A. Sachs, and later published by Otto Neugebauer in "Astronomical Cuneiform Texts" (3 vol.; Princeton and London, 1955). Since the rediscovery of the Babylonian civilization, it has become apparent that Greek astronomers, and in particular Hipparchus, borrowed a lot from the Chaldeans. F.X. Kugler demonstrated in his book Die Babylonische Mondrechnung ("The Babylonian lunar computation", Freiburg im Breisgau, 1900) the following: Ptolemy had stated in his Almagest IV.2 that Hipparchus improved the values for the Moon's periods known to him from "even more ancient astronomers" by comparing eclipse observations made earlier by "the Chaldeans", and by himself. However Kugler found that the periods that Ptolemy attributes to Hipparchus had already been used in Babylonian ephemerides, specifically the collection of texts nowadays called "System B" (sometimes attributed to Kidinnu). Apparently Hipparchus only confirmed the validity of the periods he learned from the Chaldeans by his newer observations. It is clear that Hipparchus (and Ptolemy after him) had an essentially complete list of eclipse observations covering many centuries. Most likely these had been compiled from the "diary" tablets: these are clay tablets recording all relevant observations that the Chaldeans routinely made. Preserved examples date from 652 BC to AD 130, but probably the records went back as far as the reign of the Babylonian king Nabonassar: Ptolemy starts his chronology with the first day in the Egyptian calendar of the first year of Nabonassar, i.e., 26 February 747 BC. This raw material by itself must have been hard to use, and no doubt the Chaldeans themselves compiled extracts of e.g., all observed eclipses (some tablets with a list of all eclipses in a period of time covering a saros have been found). This allowed them to recognise periodic recurrences of events. Among others they used in System B (cf. Almagest IV.2):
- 223 (synodic) months = 239 returns in anomaly (anomalistic month) = 242 returns in latitude (draconic month). This is now known as the saros period which is very useful for predicting eclipses.
- 251 (synodic) months = 269 returns in anomaly
- 5458 (synodic) months = 5923 returns in latitude
- 1 synodic month = 29;31:50:08:20 days (sexagesimal; 29.53059413... days in decimals = 29 days 12 hours 44 min 3⅓ s) The Babylonians expressed all periods in synodic months, probably because they used a lunisolar calendar. Various relations with yearly phenomena led to different values for the length of the year. Similarly various relations between the periods of the planets were known. The relations that Ptolemy attributes to Hipparchus in Almagest IX.3 had all already been used in predictions found on Babylonian clay tablets. All this knowledge was transferred to the Greeks probably shortly after the conquest by Alexander the Great (331 BC). According to the late classical philosopher Simplicius (early 6th century AD), Alexander ordered the translation of the historical astronomical records under supervision of his chronicler Callisthenes of Olynthus, who sent it to his uncle Aristotle. It is worth mentioning here that although Simplicius is a very late source, his account may be reliable. He spent some time in exile at the Sassanid (Persian) court, and may have accessed sources otherwise lost in the West. It is striking that he mentions the title tèresis (Greek: guard) which is an odd name for a historical work, but is in fact an adequate translation of the Babylonian title massartu meaning "guarding" but also "observing". Anyway, Aristotle's pupil Callippus of Cyzicus introduced his 76-year cycle, which improved upon the 19-year Metonic cycle, about that time. He had the first year of his first cycle start at the summer solstice of 28 June 330 BC (Julian proleptic date), but later he seems to have counted lunar months from the first month after Alexander's decisive battle at Gaugamela in fall 331 BC. So Callippus may have obtained his data from Babylonian sources and his calendar may have been anticipated by Kidinnu. Also it is known that the Babylonian priest known as Berossus wrote around 281 BC a book in Greek on the (rather mythological) history of Babylonia, the Babyloniaca, for the new ruler Antiochus I; it is said that later he founded a school of astrology on the Greek island of Kos. Another candidate for teaching the Greeks about Babylonian astronomy/astrology was Sudines who was at the court of Attalus I Soter late in the 3rd century BC. In any case, the translation of the astronomical records required profound knowledge of the cuneiform script, the language, and the procedures, so it seems likely that it was done by some unidentified Chaldeans. Now, the Babylonians dated their observations in their lunisolar calendar, in which months and years have varying lengths (29 or 30 days; 12 or 13 months respectively). At the time they did not use a regular calendar (such as based on the Metonic cycle like they did later), but started a new month based on observations of the New Moon. This made it very tedious to compute the time interval between events. What Hipparchus may have done is transform these records to the Egyptian calendar, which uses a fixed year of always 365 days (consisting of 12 months of 30 days and 5 extra days): this makes computing time intervals much easier. Ptolemy dated all observations in this calendar. He also writes that "All that he (=Hipparchus) did was to make a compilation of the planetary observations arranged in a more useful way" (Almagest IX.2). Pliny states (Naturalis Historia II.IX(53)) on eclipse predictions: "After their time (=Thales) the courses of both stars (=Sun and Moon) for 600 years were prophecied by Hipparchus, ...". This seems to imply that Hipparchus predicted eclipses for a period of 600 years, but considering the enormous amount of computation required, this is very unlikely. Rather, Hipparchus would have made a list of all eclipses from Nabonasser's time to his own. Other traces of Babylonian practice in Hipparchus' work are:
- first Greek known to divide the circle in 360 degrees of 60 arc minutes.
- first consistent use of the sexagesimal number system.
- the use of the unit pechus ("cubit") of about 2° or 2½°.
- use of a short period of 248 days = 9 anomalistic months. Also see G.J. Toomer (1981?): Hipparchus and Babylonian Astronomy.

Geometry and trigonometry

Hipparchus is recognised as the first mathematician who compiled a trigonometry table, which he needed when computing the eccentricity of the orbits of the Moon and Sun. He tabulated values for the chord function, which gives the length of the chord for each angle. He did this for a circle with a circumference of 21,600 and a radius of (rounded) 3438 units: this has a unit length of 1 arc minute along its perimeter. He tabulated the chords for angles with increments of 7.5°. In modern terms, the chord of an angle equals twice the sine of half of the angle, i.e.: : chord(A) = 2 sin(A/2). He described it in a work (now lost), called Toon en kuklooi eutheioon (Of Lines Inside a Circle) by Theon of Alexandria (4th century) in his commentary on the Almagest I.10; his table seems to have survived in astronomical treatises in India, for instance the Surya Sidhanta. This was a significant innovation, because it allowed Greek astronomers to solve any triangle, and made it possible to make quantitative astronomical models and predictions using their preferred geometric techniques. See [Toomer 1973]. For his chord table Hipparchus must have used a better approximation for π than the one from Archimedes (between 3 + 1/7 and 3 + 10/71); maybe the one later used by Ptolemy: 3;8:30 (sexagesimal) (Almagest VI.7); but it is not known if he computed an improved value himself. Hipparchus could construct his chord table using the Pythagorean theorem and a theorem known to Archimedes. He also might have developed and used the theorem in plane geometry called Ptolemy's theorem, because it was proved by Ptolemy in his Almagest (I.10) (later elaborated on by Carnot). Hipparchus was the first to show that the stereographic projection is conformal, and that it transforms circles on the sphere that do not pass through the center of projection to circles on the plane. This was the basis for the astrolabe. Besides geometry, Hipparchus also used arithmetic techniques from the Chaldeans. He was one of the first Greek mathematicians to do this, and in this way expanded the techniques available to astronomers and geographers. There is no indication that Hipparchus knew spherical trigonometry, which was first developed by Menelaus of Alexandria in the 1st century. Ptolemy later used the new technique for computing things like the rising and setting points of the ecliptic, or to take account of the lunar parallax. Hipparchus may have used a globe for this (to read values off the coordinate grids drawn on it), as well as approximations from planar geometry, or arithmetical approximations developed by the Chaldeans.

Lunar and solar theory

Motion of the moon

Hipparchus also studied the motion of the Moon and confirmed the accurate values for some periods of its motion that Chaldean astronomers had obtained before him. The traditional value (from Babylonian System B) for the mean synodic month is 29 days;31,50,8,20 (sexagesimal) = 29.5305941... d. Expressed as 29 days + 12 hours + 793/1080 hours this value has been used later in the Hebrew calendar (possibly from Babylonian sources). The Chaldeans also knew that 251 synodic months = 269 anomalistic months. Hipparchus extended this period by a factor of 17, because after that interval the Moon also would have a similar latitude, and it is close to an integer number of years (345). Therefore, eclipses would reappear under almost identical circumstances. The period is 126007 days 1 hour (rounded). Hipparchus could confirm his computations by comparing eclipses from his own time (presumably 27 January 141 BC and 26 November 139 BC according to [Toomer 1980]), with eclipses from Babylonian records 345 years earlier (Almagest IV.2; [Jones 2001]). Already al-Biruni (Qanun VII.2.II) and Copernicus (de revolutionibus IV.4) noted that the period of 4,267 lunations is actually about 5 minutes longer than the value for the eclipse period that Ptolemy attributes to Hipparchus. However, the best clocks and timing methods of the age had an accuracy of no better than 8 minutes. Modern scholars agree that Hipparchus rounded the eclipse period to the nearest hour, and used it to confirm the validity of the traditional values, rather than try to derive an improved value from his own observations. From modern ephemerides [Chapront et al. 2002] and taking account of the change in the length of the day (see ΔT) we estimate that the error in the assumed length of the synodic month was less than 0.2 s in the 4th century BC and less than 0.1 s in Hipparchus' time.

Orbit of the Moon

It had been known for a long time that the motion of the Moon is not uniform: its speed varies. This is called its anomaly, and it repeats with its own period; the anomalistic month. The Chaldeans took account of this arithmetically, and used a table giving the daily motion of the Moon according to the date within a long period. The Greeks however preferred to think in geometrical models of the sky. Apollonius of Perga had at the end of the 3rd century BC proposed two models for lunar and planetary motion: # In the first, the Moon would move uniformly along a circle, but the Earth would be eccentric, i.e., at some distance of the center of the circle. So the apparent angular speed of the Moon (and its distance) would vary. # The Moon itself would move uniformly (with some mean motion in anomaly) on a secondary circular orbit, called an epicycle, that itself would move uniformly (with some mean motion in longitude) over the main circular orbit around the Earth, called deferent; see deferent and epicycle. Apollonius demonstrated that these two models were in fact mathematically equivalent. However, all this was theory and had not been put to practice. Hipparchus was the first to attempt to determine the relative proportions and actual sizes of these orbits. Hipparchus devised a geometrical method to find the parameters from three positions of the Moon, at particular phases of its anomaly. In fact, he did this separately for the eccentric and the epicycle model. Ptolemy describes the details in the Almagest IV.11. Hipparchus used two sets of three lunar eclipse observations, which he carefully selected to satisfy the requirements. The eccentric model he fitted to these eclipses from his Babylonian eclipse list: 22/23 December 383 BC, 18/19 June 382 BC, and 12/13 December 382 BC. The epicycle model he fitted to lunar eclipse observations made in Alexandria at 22 September 201 BC, 19 March 200 BC, and 11 September 200 BC.
- For the eccentric model, Hipparchus found for the ratio between the radius of the eccenter and the distance between the center of the eccenter and the center of the ecliptic (i.e., the observer on Earth): 3144 : 327+2/3 ;
- and for the epicycle model, the ratio between the radius of the deferent and the epicycle: 3122+1/2 : 247+1/2 . The somewhat weird numbers are due to the cumbersome unit he used in his chord table. The results are distinctly different. This is partly due to some sloppy rounding and calculation errors, for which Ptolemy criticised him (he himself made rounding errors too). Anyway, Hipparchus found inconsistent results; he later used the ratio of the epicycle model (3122+1/2 : 247+1/2), which is too small (60 : 4;45 hexadecimal): Ptolemy established a ratio of 60 : 5+1/4 . See [Toomer 1967].

Apparent motion of the Sun

Before Hipparchus, Meton, Euktemon, and their pupils at Athens had made a solstice observation (i.e., timed the moment of the summer solstice) on June 27, 432 BC (proleptic Julian calendar). Aristarchus is said to have done so in 280 BC, and Hipparchus also had an observation by Archimedes. Hipparchus himself observed the summer solstice in 135 BC, but he found observations of the moment of equinox more accurate, and he made many during his lifetime. Ptolemy gives an extensive discussion of Hipparchus' work on the length of the year in the Almagest III.1, and quotes many observations that Hipparchus made or used, spanning 162 BC to 128 BC. Ptolemy quotes an equinox timing by Hipparchus (at 24 March 146 BC at dawn) that differs from the observation made on that day in Alexandria (at 5h after sunrise): Hipparchus may have visited Alexandria but he did not make his equinox observations there; presumably he was on Rhodes (at the same geographical longitude). He may have used his own armillary sphere or an equatorial ring for these observations. Hipparchus (and Ptolemy) knew that observations with these instruments are sensitive to a precise alignment with the equator. The real problem however is that atmospheric refraction lifts the Sun significantly above the horizon: so its apparent declination is too high, which changes the observed time when the Sun crosses the equator. Worse, the refraction decreases as the Sun rises, so it may appear to move in the wrong direction with respect to the equator in the course of the day - as Ptolemy mentions; however, Ptolemy and Hipparchus apparently did not realize that refraction is the cause. At the end of his career, Hipparchus wrote a book called Peri eniausíou megéthous ("On the Length of the Year") about his results. The established value for the tropical year, introduced by Callippus in or before 330 BC (possibly from Babylonian sources, see above), was 365 + 1/4 days. Hipparchus' equinox observations gave varying results, but he himself points out (quoted in Almagest III.1(H195)) that the observation errors by himself and his predecessors may have been as large as 1/4 day. So he used the old solstice observations, and determined a difference of about one day in about 300 years. So he set the length of the tropical year to 365 + 1/4 - 1/300 days (= 365.24666... days = 365 days 5 hours 55 min, which differs from the actual value (modern estimate) of 365.24219... days = 365 days 5 hours 48 min 45 s by only about 6 min). Between the solstice observation of Meton and his own, there were 297 years spanning 108,478 days. This implies a tropical year of 365.24579... days = 365 days;14,44,51 (sexagesimal; = 365 days + 14/60 + 44/60² + 51/60³), and this value has been found on a Babylonian clay tablet [A. Jones, 2001]. This is an indication that Hipparchus' work was known to Chaldeans. Another value for the year that is attributed to Hipparchus (by the astrologer Vettius Valens in the 1st century) is 365 + 1/4 + 1/288 days (= 365.25347... days = 365 days 6 hours 5 min), but this may be a corruption of another value attributed to a Babylonian source: 365 + 1/4 + 1/144 days (= 365.25694... days = 365 days 6 hours 10 min). It is not clear if this would be a value for the sidereal year (actual value at his time (modern estimate) ca. 365.2565 days), but the difference with Hipparchus' value for the tropical year is consistent with his rate of precession (see below).

Orbit of the Sun

Before Hipparchus the Chaldean astronomers knew that the lengths of the seasons are not equal. Hipparchus made equinox and solstice observations, and according to Ptolemy (Almagest III.4) determined that spring (from spring equinox to summer solstice) lasted 94 + 1/2 days, and summer (from summer solstice to autumn equinox) 92 + 1/2 days. This is an unexpected result given a premise of the Sun moving around the Earth in a circle at uniform speed. Hipparchus' solution was to place the Earth not at the center of the Sun's motion, but at some distance from the center. This model described the apparent motion of the Sun fairly well (of course today we know that the planets like the Earth move in ellipses around the Sun, but this was not discovered until Johannes Kepler published his first two laws of planetary motion in 1609). The value for the eccentricity attributed to Hipparchus by Ptolemy is that the offset is 1/24 of the radius of the orbit (which is too large), and the direction of the apogee would be at longitude 65.5° from the vernal equinox. Hipparchus may also have used another set of observations (94 + 1/4 and 92 + 3/4 days), which would lead to different values. The question remains if Hipparchus is really the author of the values provided by Ptolemy, who found no change three centuries later, and added lengths for the autumn and winter seasons.

Calendar

"To be written"

Distance, parallax, size of the Moon and Sun

Hipparchus also undertook to find the distances and sizes of the Sun and the Moon. He published his results in a work of two books called Peri megethoon kai 'apostèmátoon ("On Sizes and Distances") by Pappus in his commentary on the Almagest V.11; Theon of Smyrna (2nd century) mentions the work with the addition "of the Sun and Moon". Hipparchus measured the apparent diameters of the Sun and Moon with his diopter. Like others before and after him, he found that the Moon's size varies as it moves on its (eccentric) orbit, but he found no perceptible variation in the apparent diameter of the Sun. He found that at the mean distance of the Moon, the Sun and Moon had the same apparent diameter; at that distance, the Moon's diameter fits 650 times into the circle, i.e., the mean apparent diameters are 360/650 = 0°33'14". Like others before and after him, he also noticed that the Moon has a noticeable parallax, i.e., that it appears displaced from its calculated position (compared to the Sun or stars), and the difference is greater when closer to the horizon. He knew that this is because the Moon circles the center of the Earth, but the observer is at the surface - Moon, Earth and observer form a triangle with a sharp angle that changes all the time. From the size of this parallax, the distance of the Moon as measured in Earth radii can be determined. For the Sun however, there was no observable parallax (we now know that it is about 8.8", more than ten times smaller than the resolution of the unaided eye). In the first book, Hipparchus assumes that the parallax of the Sun is 0, as if it is at infinite distance. He then analyzed a solar eclipse, presumably that of 14 March 190 BC. It was total in the region of the Hellespont (and in fact in his birth place Nicaea); at the time the Romans were preparing for war with Antiochus III in the area, and the eclipse is mentioned by Livy in his Ab Urbe Condita VIII.2. It was also observed in Alexandria, where the Sun was reported to be obscured for 4/5 by the Moon. Alexandria and Nicaea are on the same meridian. Alexandria is at about 31° North, and the region of the Hellespont at about 41° North; authors like Strabo and Ptolemy had fairly decent values for these geographical positions, and presumably Hipparchus knew them too. So Hipparchus could draw a triangle formed by the two places and the Moon, and from simple geometry was able to establish a distance of the Moon, expressed in Earth radii. Because the eclipse occurred in the morning, the Moon was not in the meridian, and as a consequence the distance found by Hipparchus was a lower limit. In any case, according to Pappus, Hipparchus found that the least distance is 71 (from this eclipse), and the greatest 81 Earth radii. In the second book, Hipparchus starts from the opposite extreme assumption: he assigns a (minimum) distance to the Sun of 470 Earth radii. This would correspond to a parallax of 7', which is apparently the greatest parallax that Hipparchus thought would not be noticed (for comparison: the typical resolution of the human eye is about 2'; Tycho Brahe made naked eye observation with an accuracy down to 1'). In this case, the shadow of the Earth is a cone rather than a cylinder as under the first assumption. Hipparchus observed (at lunar eclipses) that at the mean distance of the Moon, the diameter of the shadow cone is 2+½ lunar diameters. That apparent diameter is, as he had observed, 360/650 degrees. With these values and simple geometry, Hipparchus could determine the mean distance; because it was computed for a minumum distance of the Sun, it is the maximum mean distance possible for the Moon. With his value for the eccentricity of the orbit, he could compute the least and greatest distances of the Moon too. According to Pappus, he found a least distance of 62, a mean of 67+1/3, and consequently a greatest distance of 72+2/3 Earth radii. With this method, as the parallax of the Sun decre

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