“During the 18th and 19th centuries a popular prank in London involved inviting unsuspecting victims to come view the annual ceremony of washing the lions at the Tower of London. Early versions of the prank promised the curious that the lions were going to be washed in the moat. Later versions told the gullible to seek entrance to the Tower at the “White Gate” (there being no such gate). Whatever the details were, the hopeful sightseers would make the journey to the Tower in vain, because there was no annual lion-washing ceremony. This prank is best known as an April Fool’s Day joke. In fact, a report of it being perpetrated in 1698 is the earliest recorded example of an April Fool’s Day prank. The April 2, 1698 edition of Dawks’s News-Letter reported that “Yesterday being the first of April, several persons were sent to the Tower Ditch to see the Lions washed” (Notes and Queries, 1913, 357). In 1887, a correspondent to the journal Notes and Queries speculated that the prank “originated from a custom of the warders formerly deriving perquisites from the liberality of country gobemouches, who ‘tipped’ them to ‘see the white bears fed.’” The washing-the-lions prank falls into the broad category of “sleeveless errand” pranks—more commonly referred to today as “wild-goose chases.” A sleeveless errand involves sending a victim on a fruitless quest in search of an item, or event, that does not exist.”
Where Does April Fools’ Day Originate?
by Talal Al-Khatib / April 1, 2013
Figuring out the origins of the holiday can be as tricky as getting to the source of a joke. The most common theory about the earliest April Fools’ celebrations goes like this: In 1582, Pope Gregory XIII issued a papal bull decreeing a new standard calendar for Christian Europe that would take his name and centuries later become the standard internationally in the 21st century. Prior to the 15th century, Europe’s nations and city states operated using the Julian calendar. The Gregorian calendar moved the date of the new year from April 1 to January 1, among other changes. Catholic monarchies were naturally its earliest adopters, though Protestant nations later followed suit. Given the nature of the reform, both in terms of communicating such a fundamental change to a large population and dealing with critics of the new calendar, some Europeans continued to celebrate the new year between March 25 and April 1. April fools were those who still celebrated the holiday in the spring, and were the subject of pranks and ridicule by those who observed the new year months ago.
That’s just one theory for the origin of the holiday, however. Other occasions resembling April Fools’ Day preceded the more contemporary incarnation by centuries. Ancient Romans held a festival known as Hilaria. The occasion was used to celebrate the resurrection of the god Attis. Hilaria, of course, resembles the word hilarity in English. The modern equivalent of Hilaria is called Roman Laughing Day. Other non-Western cultures have their own traditions similar to April Fools’ Day as well. In India, Holi, a colorful Hindi festival that frequently entices non-Hindi participants to join in, often is celebrated by people playing jokes and throwing colorful dyes on each other. Persian culture also has a holiday with a similar theme, known as Sizdahbedar. On this day, which typically coincides with April Fools’ Day itself, Iranians play pranks on one another.
GLOBAL SOLAR CALENDAR vs LOCAL LUNAR CALENDAR
April Fools’ Day: The uncertain origins of a foolish day
by David Johnson and Shmuel Ross
April Fools’ Day, sometimes called All Fools’ Day, is one of the most light-hearted days of the year. Its origins are uncertain. Some see it as a celebration related to the turn of the seasons, while others believe it stems from the adoption of a new calendar. Ancient cultures, including those of the Romans and Hindus, celebrated New Year’s Day on or around April 1. It closely follows the vernal equinox (March 20th or March 21st.) In medieval times, much of Europe celebrated March 25, the Feast of Annunciation, as the beginning of the new year. In 1582, Pope Gregory XIII ordered a new calendar (the Gregorian Calendar) to replace the old Julian Calendar. The new calendar called for New Year’s Day to be celebrated Jan. 1. That year, France adopted the reformed calendar and shifted New Year’s day to Jan. 1. According to a popular explanation, many people either refused to accept the new date, or did not learn about it, and continued to celebrate New Year’s Day on April 1. Other people began to make fun of these traditionalists, sending them on “fool’s errands” or trying to trick them into believing something false. Eventually, the practice spread throughout Europe.
A French “poisson d’Avril” or “April Fish” postcard.
Problems With This Explanation
There are at least two difficulties with this explanation. The first is that it doesn’t fully account for the spread of April Fools’ Day to other European countries. The Gregorian calendar was not adopted by England until 1752, for example, but April Fools’ Day was already well established there by that point. The second is that we have no direct historical evidence for this explanation, only conjecture, and that conjecture appears to have been made more recently. Another explanation of the origins of April Fools’ Day was provided by Joseph Boskin, a professor of history at Boston University. He explained that the practice began during the reign of Constantine, when a group of court jesters and fools told the Roman emperor that they could do a better job of running the empire. Constantine, amused, allowed a jester named Kugel to be king for one day. Kugel passed an edict calling for absurdity on that day, and the custom became an annual event. “In a way,” explained Prof. Boskin, “it was a very serious day. In those times fools were really wise men. It was the role of jesters to put things in perspective with humor.” This explanation was brought to the public’s attention in an Associated Press article printed by many newspapers in 1983. There was only one catch: Boskin made the whole thing up. It took a couple of weeks for the AP to realize that they’d been victims of an April Fools’ joke themselves.
It is worth noting that many different cultures have had days of foolishness around the start of April, give or take a couple of weeks. The Romans had a festival named Hilaria on March 25, rejoicing in the resurrection of Attis. The Hindu calendar has Holi, and the Jewish calendar has Purim. Perhaps there’s something about the time of year, with its turn from winter to spring, that lends itself to lighthearted celebrations. April Fools’ Day is observed throughout the Western world. Practices include sending someone on a “fool’s errand,” looking for things that don’t exist; playing pranks; and trying to get people to believe ridiculous things. The French call April 1 Poisson d’Avril, or “April Fish.” French children sometimes tape a picture of a fish on the back of their schoolmates, crying “Poisson d’Avril” when the prank is discovered.
Commission for the Reform of the Calendar (Pope Gregory XIII Presiding), 1582
Curious History of the Gregorian Calendar : Eleven days that never were
by Ben Snowden
September 2, 1752, was a great day in the history of sleep. That Wednesday evening, millions of British subjects in England and the colonies went peacefully to sleep and did not wake up until twelve days later. Behind this feat of narcoleptic prowess was not some revolutionary hypnotic technique or miraculous pharmaceutical discovered in the West Indies. It was, rather, the British Calendar Act of 1751, which declared the day after Wednesday the second to be Thursday the fourteenth. Prior to that cataleptic September evening, the official British calendar differed from that of continental Europe by eleven days—that is, September 2 in London was September 13 in Paris, Lisbon, and Berlin. The discrepancy had sprung from Britain’s continued use of the Julian calendar, which had been the official calendar of Europe since its invention by Julius Caesar (after whom it was named) in 45 B.C. Caesar’s calendar, which consisted of eleven months of 30 or 31 days and a 28-day February (extended to 29 days every fourth year), was actually quite accurate: it erred from the real solar calendar by only 11½ minutes a year. After centuries, though, even a small inaccuracy like this adds up. By the sixteenth century, it had put the Julian calendar behind the solar one by 10 days.
In 1582, Pope Gregory XIII ordered the advancement of the calendar by 10 days and introduced a new corrective device to curb further error: century years such as 1700 or 1800 would no longer be counted as leap years, unless they were (like 1600 or 2000) divisible by 400. If somewhat inelegant, this system is undeniably effective, and is still in official use in the United States. The Gregorian calendar year differs from the solar year by only 26 seconds—accurate enough for most mortals, since this only adds up to one day’s difference every 3,323 years. Despite the prudence of Pope Gregory’s correction, many Protestant countries, including England, ignored the papal bull. Germany and the Netherlands agreed to adopt the Gregorian calendar in 1698; Russia only accepted it after the revolution of 1918, and Greece waited until 1923 to follow suit. And currently many Orthodox churches still follow the Julian calendar, which now lags 13 days behind the Gregorian.
Why So Difficult?
Since their invention, calendars have been used to reckon time in advance, and to fix the occurrence of events like harvests or religious festivals. Ancient peoples tied their calendars to whatever recurring natural phenomena they could most easily observe. In areas with pronounced seasons, annual weather changes usually fixed the calendar; in warmer climates such as Southern Europe, Africa, and the Middle East, the moon was used to mark time. Unfortunately, the cycles of the sun and moon do not synchronize well. A lunar year (consisting of 12 lunar cycles, or lunations, each 29½ days long) is only 354 days, 8 hours long; a solar year lasts about 365¼ days. After three years, a strict lunar calendar would have diverged from the solar calendar by 33 days, or more than one lunation. The Muslim calendar is hence the only purely lunar calendar in widespread use today. Its months have no permanent connection to the seasons— Muslim religious celebrations, such as Ramadan, may thus occur at any date of the Gregorian calendar. The phases of the moon have nonetheless remained a popular way to divide the solar year, if only because a 365¼-day year doesn’t exactly lend itself to equal subdivision (the 71¼-day month has yet to find favor among menologists). To compensate for the difference in the solar and lunar year, calendar makers introduced the practice of intercalation—the addition of extra days or months to the calendar to make it more accurate. The semilunar Hebrew calendar, consisting of twelve 29- and 30-day months, adds an intercalary month seven times every 19 years (which explains the sometimes confusing drift of Passover—and consequently Easter— through April and March).
Best of All Possible Calendars?
Despite its widespread use, the Gregorian calendar has a number of weaknesses. It cannot be divided into equal halves or quarters; the number of days per month is haphazard; and months or even years may begin on any day of the week. Holidays pegged to specific dates may also fall on any day of the week, and vanishingly few Americans can predict when Thanksgiving will occur next year. Since Gregory XIII, many other proposals for calendar reform have been made. In the 1840s, philosopher Auguste Comte suggested that the 365th day of each year be a holiday not assigned a day of the week. The generic “Year Day” would allow January 1 to fall on a Sunday every year. Needless to say, this clever solution was not widely embraced. The French Revolution also saw an attempt at the introduction of a new calendar. On October 5, 1793, the revolutionary convention decreed that the year (starting on September 22, 1792—the autumnal equinox, and the day after the proclamation of the new republic) would be divided into 12 months of 30 days, named after corresponding seasonal phenomena (e.g. seed, blossom, harvest). The remaining five days of the year, called sans-culottides, were feast days. In leap years, the extra day, Revolution Day, was to be added to the end of the year. The Revolutionary calendar had no week; each month was divided into three decades, with every tenth day to be a day of rest. This straightforward calendar, however, perished with the Republic.
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, 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. 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 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 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 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, 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, 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. 
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.
Bill Donahue http://www.hiddenmeanings.com
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 vernal equinox 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.
2015 Phases of the Moon
NEW MOON FIRST QUARTER FULL MOON LAST QUARTER d h m d h m d h m d h m JAN. 5 4 53 JAN. 13 9 46 JAN. 20 13 14 JAN. 27 4 48 FEB. 3 23 09 FEB. 12 3 50 FEB. 18 23 47 FEB. 25 17 14 MAR. 5 18 05 MAR. 13 17 48 MAR. 20 9 36 MAR. 27 7 43 APR. 4 12 06 APR. 12 3 44 APR. 18 18 57 APR. 25 23 55 MAY 4 3 42 MAY 11 10 36 MAY 18 4 13 MAY 25 17 19 JUNE 2 16 19 JUNE 9 15 42 JUNE 16 14 05 JUNE 24 11 03 JULY 2 2 20 JULY 8 20 24 JULY 16 1 24 JULY 24 4 04 JULY 31 10 43 AUG. 7 2 03 AUG. 14 14 53 AUG. 22 19 31 AUG. 29 18 35 SEPT. 5 9 54 SEPT. 13 6 41 SEPT. 21 8 59 SEPT. 28 2 50 OCT. 4 21 06 OCT. 13 0 06 OCT. 20 20 31 OCT. 27 12 05 NOV. 3 12 24 NOV. 11 17 47 NOV. 19 6 27 NOV. 25 22 44 DEC. 3 7 40 DEC. 11 10 29 DEC. 18 15 14 DEC. 25 11 11
The time of year when Sirius comes out of the rays of the Sun and is first visible on the eastern horizon at sunrise.
See Otto Neugebauer, The Exact Science in Antiquity, 2d ed. (Providence: Brown University Press, 1957), pp. 82-86.
Legendary founder and first king of Rome, ca. 750 BC.
Numa Pompilius, second legendary king of Rome, ca. 700 BC.
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.
Roman high priests.
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).
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