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The Gregorian Calendar

How do we keep track of time? When do we plant our crops, how do we know when to observe religious holidays? Societies need some way to keep track of time, and complex calendars (the word comes from the Roman term for the beginning of the month) were developed early in human history. In agricultural societies the seasonal cycle of the Sun is crucial, but for shorter periods the lunar cycle suggests itself as well. Historically the problem was that the year does not contain a whole number of days or months. The mean interval between successive vernal equinoxes (365.2424 days), is about 11 minutes less than 365 1/4 days; the synodic period of the Moon (the time between successive full moons or new moons) is about 29 1/2 days, and thus 12 months add up to about 354 days. Constructing a calendar that incorporates both the movements of the Sun and Moon is therefore not a simple business. Various solutions have been tried.

The Egyptian calendar was perhaps the simplest solution. The year was made up of twelve months of thirty days each, and five days were added at the end. Since this meant an error of about 1/4 day per year, the starting date of the year slowly drifted forward with respect to the seasons until after 1460 years it had returned to where it started. The rising of the Nile, the crucial event in the Egyptian agricultural cycle, was predicted by the heliacal rising of Sirius,[1] the brightest star in the heavens. No attention was paid to the Moon.

Most cultures in the ancient Near East relied on a calendar in which months had alternating lengths of 29 and 30 days and added a month about every third year. Thus, in ancient Israel the elders added an extra month of 29 days every third year after the sixth month (Adar). But these 29 days would not make up entirely for the entire deficit of 3 x 11 1/4 days, and therefore in some years two extra months had to be added. In the Greek city states months were added haphazardly as needed and no consistent system of intercalation was ever developed.

The most sophisticated system of keeping the motions of both the Sun and Moon harnessed in a single calendar was developed in Mesopotamia. By the Persian period, ca. 500, the system incorporated the so-called Metonic cycle (we name it after the Greek Meton, ca. 425 BCE) in which the following relationship is used: 19 solar years contain 6939 3/4 days; 110 months of 29 days plus 125 months of 30 days add up to 6940 days. 19 years, then, contained 235 months, and starting in (on our calendar) 499 BC, the calendar in that part of the world was regulated on a cycle of intercalating 7 extra months in 19 years, as shown in the following scheme (in which a dash indicates a year of 12 months and a VI or XII indicated a year in which a month was added after the sixth or twelfth month):

- - XII - - XII - XII - - XII - - XII - - VI - XII

After a few irregularities, starting in 384 BCE, this scheme was rigorously adhered to, through the Greek and Roman conquests, until 75 CE, when cuneiform texts ceased.

For convenience, the month was usually subdivided into smaller time periods. The Greeks divided the month into three periods of ten days, but a division of seven days was older and more common in the Near East. We find the seven-day week already in Genesis. The names that we assign to the days have their origin in the division of the day into 24 hours, which originated in Egypt. In the Hellenistic period (300 BCE - 100 BCE) it became common to assign a ruling planet (including the Sun and Moon) to each hour of the day. The common order of the wandering heavenly bodies was Saturn-Jupiter-Mars-Sun-Venus-Mercury-Moon. The first hour of the first day was assigned to the Sun, the second to Venus, the third to Mercury, etc., repeating the cycle in the order given above. The 24th hour was thus assigned to Mercury and the first hour of the second day to the Moon. Naming the days after the planets that rule their first hours, we thus arrive at the sequence Sun's day-Moon's day-Mars's day-Mercury's day-Jupiter's day-Venus's day-Saturn's day.[2] The modern English variations on these names are due to substituting Nordic or Saxon gods for some of the Roman names: Tiw for Mars, Wotan for Mercury, Thor for Jupiter, Frigg for Venus.

Our civil method for reckoning time, then has a mixed origin. Our division of the hour into minutes and seconds is derived from the sexagesimal system of the Mesopotamians; the division of the day into 24 hours originated with the Egyptians; the seven-day week originated in the ancient Near East, while the names are derived from a Greek convention developed during the Hellenistic period. Our calendar is based on the motion of the Sun alone, but our various religious calendars are based on a combination of the motions of the Sun and Moon. Our civil calendar derives from the Romans with some alterations. Its origin is described nicely in the "Calendar" article in the 11th edition of the Encyclopedia Britannica (1910), which reads in part:

The civil calendar of all European [and American] countries has been borrowed from that of the Romans. Romulus[3] is said to have divided the year into ten months only, including in all 304 days, and it is not very well known how the remaining days were disposed of. The ancient Roman year commenced with March, as is indicated by the names September, October, November, December, which the last four months still retain. July and August, likewise, were anciently denominated Quintillis and Sextillis, their present appellations having been bestowed in compliment to Julius Caesar and Augustus. In the reign of Numa[4] two months were added to the year, January at the beginning and February at the end; and this arrangement continued till the year 452 BC., when the Decemvirs[5] changed the order of the months, and placed February after January. The months now consisted of twenty-nine and thirty days alternately, to correspond with the synodic revolution of the moon [full moon to full moon], so that the year contained 354 days; but a day was added to make the number odd, which was considered more fortunate, and the year therefore consisted of 355 days. This differed from the solar year by ten whole days and a fraction; but to restore the coincidence, Numa ordered an additional or intercalary month to be inserted every second year between the 23d and 24th of February, consisting of twenty-two and twenty-three days alternately, so that four years constituted 1465 days, and the mean length of the year was consequently 366 1/4 days. The additional month was called Mercedinus or Mercedonius, from merces, wages, probably because the wages of workmen and domestics were usually paid at this season of the year. According to the above arrangement, the year was too long by one day, which rendered another correction necessary. As the error amounted to twenty-four days in as many years, it was ordered that every third period of eight years, instead of containing four intercalary months, amounting in all to ninety days, should contain only three of those months, consisting of twenty-two days each. The mean length of the year was thus reduced to 365 1/4 days; but it is not certain at what time the octennial periods, borrowed from the Greeks, were introduced into the Roman calendar, or whether they were at any time strictly followed. It does not even appear that the length of the intercalary month was regulated by any certain principle, for a discretionary power was left with the pontiffs,[6] to whom the care of the calendar was committed, to intercalate more or fewer days according as the year was found to differ more or less from the celestial motions. This power was quickly abused to serve political objects, and the calendar consequently thrown into confusion. By giving a greater of less number of days to the intercalary month, the pontiffs were enabled to prolong the term of a magistracy or hasten the annual elections; and so little care had been taken to regulate the year, that, at the time of Julius Caesar, the civil equinox differed from the astronomical by three months, so that the winter months were carried back into autumn and the autumnal into summer. In order to put an end to the disorders arising from the negligence or ignorance of the pontiffs, [Julius] Caesar abolished the use of the lunar year and the intercalary month, and regulated the civil year entirely by the sun. With the advice and assistance of Sosigenes,[7] he fixed the mean length of the year at 365 1/4 days, and decreed that every fourth year should have 366 days, the other years having each 365. In order to restore the vernal equinox to the 25th of March, the place it occupied in the time of Numa, he ordered two extraordinary months to be inserted between November and December in the current year, the first to consist of thirty three, and the second of thirty-four days. The intercalary month of twenty-three days fell into the year of course, so that the ancient year of 355 days received an augmentation of ninety days; and the year on that occasion contained in all 445 days. This was called the last year of confusion. The first Julian year commenced with the 1st of January of the 46th before the birth of Christ, and the 708th from the foundation of the city.

In the distribution of the days through the several months, Caesar adopted a simpler and more commodious arrangement than that which has since prevailed. He had ordered that the first, third, fifth, seventh, ninth, and eleventh months, that is January, March, May, July, September and November, should have each thirty-one days, and the other months thirty, excepting February, which in common years should have only twenty-nine day, but every fourth year thirty days. This order was interrupted to gratify the vanity of Augustus, by giving the month bearing his name as many days as July, which was named after the first Caesar. A day was accordingly taken from February and given to August; and in order that three months of thirty-one days might not come together, September and November were reduced to thirty days, and thirty-one given to October and December. For so frivolous a reason was the regulation of Caesar abandoned, and a capricious arrangement introduced, which it requires some attention to remember. [8]

The additional day which occurred every fourth year was given to February, as being the shortest month, and was inserted in the calendar between the 24th and 25th day. February having then twenty-nine days, the 25th was the 6th of the calends of March, sexto calendas; the preceding, which was the additional or intercalary day, was called bis-sexto calendas,--hence the term bissextile, which is still employed to distinguish the year of 366 days. The English denomination of leap year would have been more appropriate if that year had differed from common years in defect, and contained only 364 days. In the modern calendar the intercalary day is still added to February, not, however, between the 24th and 25th, but as the 29th.

. . .

Although the Julian method of intercalation is perhaps the most convenient that could be adopted, yet, as it supposes the year too long by 11 minutes 14 seconds, it could not without correction very long answer the purpose for which it was devised, namely, that of preserving always the same interval of time between the commencement of the year and the equinox. Sosigenes could scarcely fail to know that this year was too long; for it had been shown long before, by the observations of Hipparchus [ca. 125 BCE], that the excess of 3651/4 days above a true solar year would amount to a day in 300 years. The real error is indeed more than double of this, and amounts to a day in 128 years; but in the time of Caesar the length of the year was an astronomical element not very well determined. In the course of a few centuries, however, the equinox sensibly retrograded towards the beginning of the year. When the Julian calendar was introduced, the equinox fell on the 25th of March. At the time of the Council of Nicea, which was held in 325, it fell on the 21st . . . .

The Julian Calendar was naturally adopted by the successor of the Roman Empire, Christian Europe with the Papacy at its head. By about 700 CE it had become customary to count years from the starting point of the birth of Christ (later corrected by Johannes Kepler to 4 BCE). But the equinox kept slipping backwards on the calendar one full day every 130 years. By 1500 the vernal equinox fell on the 10th or 11th of March and the autumnal equinox on the 13th or 14th of September, and the situation was increasingly seen as a scandal. The most important feast day on the Christian calendar is Easter, when the suffering, death, and resurrection of Christ are celebrated. In the New Testament we find that Christ's crucifixion occurred in the week of Passover. On the Jewish calendar, Passover was celebrated at the full moon of the first month (Nissan) of spring. In developing their own calendar (4th century CE), Christians put Easter on the first Sunday after the first full moon after the spring equinox. If the equinox was wrong, then Easter was celebrated on the wrong day. Most other Christian observances (e.g., the beginning of Lent, Pentecost) are reckoned backward or forward from the date of Easter. An error in the equinox thus introduced numerous errors in the entire religious calendar. Something had to be done. After the unification of the Papacy in Rome, in the fifteenth century, Popes began to consider calendar reform. After several false starts, a commission under the leadership of the Jesuit mathematician and astronomer Christoph Clavius (1537-1612) succeeded. Several technical changes were instituted having to do with the calculation of Easter, but the main change was simple. In 1582 Pope Gregory XIII (hence the name Gregorian Calendar) ordered ten days to be dropped from October, thus restoring the vernalequinox at least to an average of the 20th of March, close to what it had been at the time of the Council of Nicea. In order to correct for the loss of one day every 130 years, the new calendar dropped three leap years every 400 years. Henceforth century years were leap years only if divisible by 400. 1600 and 2000 are leap years; 1700, 1800 and 1900 are not.

The new calendar, although controversial among technical astronomers, was promulgated from Rome and adopted immediately in Catholic countries. Protestant countries followed suit more slowly. Protestant regions in Germany, and the northern Netherlands adopted the calendar within decades. The English, always suspicious of Rome during this period, retained the Julian Calendar. Further, while others now began the new year uniformly on 1 January, the English began it on 25 March (an older custom). Now, for example, the date 11 February 1672 in England was 21 February 1673 on the Continent. After 1700 in which the Julian Calendar had a leap year but the Gregorian did not, the difference was eleven days. The English and their American colonies finally adopted the Gregorian Calendar in the middle of the eighteenth century. George Washington was born on 11 February on the Julian Calendar; we celebrate his birthday on 22 February.

Note, finally, that the Gregorian Calendar is useless for astronomy because it has a ten-day hiatus in it. For the purpose of calculating positions backward in time, astronomers use the Julian Date.

[1]The time of year when Sirius comes out of the rays of the Sun and is first visible on the eastern horizon at sunrise.
[2]See Otto Neugebauer, The Exact Science in Antiquity, 2d ed. (Providence: Brown University Press, 1957), pp. 82-86.
[3]Legendary founder and first king of Rome, ca. 750 BC.
[4]Numa Pompilius, second legendary king of Rome, ca. 700 BC.
[5]Decemviri: any college of ten magistrates in ancient Rome. The most famous college was the decemviri legibus scribendis, or the "composers of the Twelve Tables," who ruled Rome absolutely for a few years around 450 BC.
[6]Roman high priests.
[7]A Greek astronomer and mathematician who flourished in the first century BC None of his writings have survived and we know about him only through the writings of Pliny (d. 79 AD). Pliny tells us that Sosigenes was consulted by Julius Caesar about the calendar (Natural Histories, xviii, 25).
[8]Thirty days has September, April, June, and November . . .

Gregorian Reform of the Calendar: Proceedings of the Vatican Conference to Commemorate its 400th Anniversary, 1582-1992, ed. G. V. Coyne, M. A. Hoskin, and O. Pedersen (Vatican City: Pontifical Academy of Sciences, Specolo Vaticano, 1983). Jean Meeus and Denis Savoie, "The history of the tropical year," Journal of the British Astronomical Association, 102 #1 (1992): 40-42

1995 Al Van Helden
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