In 2015, on the Gregorian calendar (Western Churches), Septuagesima Sunday falls on February 1st, Mardi Gras on February 17th, Ash Wednesday on February 18th, Palm Sunday on March 29th, Maundy Thursday on April 2nd, Good Friday on April 3rd, Easter on April 5th, and Pentecost on May 24th. Easter on the Julian calendar (Eastern Churches) falls on April 12th, one week after Gregorian Easter (this is March 30th on the Julian Calendar). The Golden Number for 2015 is II, the Gregorian Dominical Letter D and Epact 10, and the Julian Dominical Letter E. [note]

- Introduction
- Golden Numbers and Dominical Letters
- Determining Easter, I
- Epacts
- Determining Easter, II
- Other Movable Feasts

I know that my Redeemer liveth,
and that He shall stand at the latter day upon the earth. And though worms destroy this body, yet in my flesh shall I see God. Job 19:25-26 |

One difficulty with Easter is that it is a "movable" feast: It occurs on different calendar dates, unlike a holiday like Christmas, which is always on December 25th. Indeed, Easter is **the** movable feast, since all the other ones (Ash Wednesday, Pentecost, etc.) move **with** it so as to keep the same relative position in the calendar. Easter moves as an artifact of originally having a position in the Jewish calendar. The Christian **Last Supper**, where the Orthodox and Catholics believe Jesus introduced the miracle of the **Eucharist** (a relatively trivial moment for most Protestants, though not for Martin Luther himself), was a **Passover Seder** (or at least on the day of the Passover -- some evidence tells against it being an actual Seder). Passover begins on the 15th day of the month of Nîsân, which, like its namesake the Babylonian month of Nisannu, appears to move around relative to solar calendars because it follows the moon. The month begins at the time of the New Moon or shortly thereafter. Since 12 lunar months come to only about 354 days, an extra month must be added every two or three years to keep the calendar from running ahead of the sun and the seasons. This means that Jewish calendar dates move up steadily against solar dates and then abruptly jump back. This is what Passover does, and what Easter does also.

The Jewish calendar was originally constructed so that the Full Moon of Nîsân would be the first Full Moon after, or on, the Vernal Equinox, the day when day and night are of equal length, taken by the Babylonians to mark the beginning of Spring. This practice was slightly different from the original Babylonian practice, where Nisannu was supposed to contain the first *New Moon* after the Vernal Equinox. The Jewish practice, of course, not the Babylonian, was inherited by Easter.

By the time Christianity became tolerated in the Roman Empire, and then the actual State Religion, to which citizens were expected to conform under civil or criminal penalties, some considerable tension had arisen between Jews and Christians (to say the least). One source of irritation was Christian use of the Jewish calendar, which at the time was governed by annual announcements from the Palestinian Patriarchs about whether an intercalary month would be inserted that year, and so Passover delayed until the next moon. Christians began to chafe at dependency on the Jewish authorities, and Jews were irritated that Christians should depend on such ritual announcements but afford no other particular respect for the Jews.

The solution came from both sides. The Jewish authorities (Patriarch Rabbi Hillel II) ceased making their announcements in 358/9 AD and instituted the 19 year Babylonian calendar cycle. The month of Passover could henceforth be determined by anyone who could count. At the same time, Christians decided to independently define and calculate Easter. Since The Last Supper was on a Thursday, the day before the Crucifixion, followed by Easter that Sunday, it was decided that Easter would be the first Sunday after the first Full Moon on or after the Vernal Equinox. Since Passover was the first **day** after the Full Moon, this preserved that feature of the Jewish Calendar. The Full Moon was similarly defined as the 14th day of the month, or, in more modern parlance, the day on which the "age" of the moon (which starts at zero at the New Moon) is 13 days. This 13 day old moon must then occur on or later than the Vernal Equinox, which was defined at the Council of Nicaea in 325 as March 21st.

The Golden Number simply places the year in the 19 year lunar cycle discovered by the Babylonians and still used by the Jewish Calendar. The cycle, which adds 7 months every 19 years, is accurate to a day in 220 years. The Golden Number for a given year in the Annô Domini Era can be simply determined by, first, dividing the year by 19. The **remainder** of that division **plus one** is then the Golden Number. Thus, 1998 divided by 19 is 105 with a remainder of 3. The Golden Number of 1998 is therefore 4 (often stated as a Roman Numeral--IV). When it is noticed that this makes the Golden Number of the year 1 AD come out as 2 (II), one might think it rather odd. Why not start the Era with Golden Number 1? However, it may be noted that adding 1 to the remainder solves the problem of what to do when the year is **evenly divisible** by 19. When there was no number zero, as in late antiquity, using Roman Numerals, there could be no Golden Number 0. With the provision for adding 1, however, even division simply results in a Golden Number of 1 (I).

The Golden Number will be the same regardless of whether one is using the Julian or Gregorian calendar.

The Dominical Letter tells us what days are Sundays. The letters simply run A through G, and the days of the year are given those letters starting with January 1st. A year with a Dominical Letter A means that January 1st was a Sunday, and each subsequent day lettered A will also be a Sunday. A year that starts on a Monday, will not have a Sunday until we get the to the letter G, the Dominical Letter for that year. Since the length of the year, 365 days, is exactly 52 weeks and 1 day, we have the basic simple rule that if a Sunday falls on a certain calendar date one year, it falls on the date of the previous day the next year. Or, if a certain calendar date is a Sunday one year, it will be a Monday the next year. If one year has the Dominical Letter A, the following year will have the Dominical Letter G. The chart at right enables us to determine the features of each following year. To go from one year to the next, you simply count over to the right. Given a year with a Dominical Letter F (e.g. 1991), which begins on a Tuesday, the following year (1992) will have a Dominical Letter E and will begin on a Wednesday.

This simplicity is complicated by the occurrence of **Leap Years**, which add an extra day, February 29th. The extra day means that if a Sunday falls on a certain calendar date one year, it will occur **two days** earlier the next year after the Leap Day; or, if a certain calendar date is a Sunday one year, it will be a Tuesday the next year, after the Leap Day. Thus, in Leap Years we "leap" over the expected day to the next. Leap Days are not lettered with Dominical Letters, so a leap year has **two** Dominical Letters (1992 is **E & D**), one for January 1st through Febuary 28th, and another for March 1st through the rest of the year. Leap Days are not given Dominical Letters because the only days that matter for the purposes of determining Easter are those in the "**Pascal Term**," i.e. the lunar month and week that follows March 21st, i.e. down to April 25th. This also means that the First Dominical Letter for a Leap Year can also be disregarded. This simplifies matters. The only Dominical Letter we need for a Leap Year is the second one (i.e. **D** for 1992). Since Leap Years are the anomaly, but it would be easy to count down to the Dominical Letters for the following non-Leap Years, all we really need is a convenient method to determine the Dominical Letters for all Leap Years. The following chart does this by showing the Dominical Letter indexed for every Leap Year in a Century.

There is a complication, however, given the historic use of two different calendars by Christians: (1) The **Julian Calendar**, introduced by Julius Caesar in 46 BC, and (2) the **Gregorian Calendar**, introduced by Pope Gregory XIII in 1582 AD. The Gregorian calendar was not immediately adopted by all Protestant or Orthodox churches. Some Orthodox churches still observe Easter according to the Julian Calendar. The Century index thus has two parts, one for the Julian Calendar in all the centuries of its use (back to the 1st century AD = century 00), the other for the Gregorian Calendar in all the centuries in which it has been in use (since 1582). To use the chart, one choses the appropriate calendar and century. For 1998, using the Gregorian calendar, we pick century "19" and the closest previous leap year, "96." Reading over to the right from 19 and down the column from 96, we find "F." The Dominical Letter for 1996 was F. 1998 is 2 years later, so we count over 2 on the key at the bottom, which gets us to D. The Dominical Letter for 1998 is D, which, since 1998 is not a Leap Year, means that 1998 did start on a Thursday. 1998 on the Julian Calendar, on the other hand, gives us a different Dominical Letter. Reading over to the right from the **Julian** 19 and down the column from 96, we find "G." Counting 2 years over arrives at "E."

Equipped with the Golden Number (4 for 1998) and the Dominical Letter (Gregorian D or Julian E for 1998), all we need is a table for the Paschal Term, the Dominical Letters for the days in it, and what days are Full Moons for each Golden Number.

The actual identification of the astronomical Full Moons and the full development of the Easter tables is traditionally ascribed to **Dionysius Exiguus** (Denis the Little), who is supposed to have lived in Rome in the early 6th century. Dionysius assigned dates for the years of the 19 year cycles. This may be seen at right. Given a Golden Number of 4 (for 1998), we look for 4 (04) in the left hand column. This may be seen to correspond to a date of April 3rd in the right hand column. This means that April 3rd is the first day after the Paschal Full Moon, i.e. the first Full Moon on or after March 21st. Given a Julian Dominical Letter of E (for 1998), we then see if April 3rd is lettered E. It is not. So we look for the first E after that, which is April 6th. April 6th is therefore Easter for the Julian Calendar. In the 20th century, a Julian date corresponds to a Gregorian date 13 days later, so Julian (Eastern or Orthodox) Easter is April 19th on the Gregorian Calendar.

One consequence of Dionysius's work was a new Chistian Era. The astronomical data Dionysius used for the moon was from Alexandria, where it had been dated in the years of the Era of Diocletian. Dionysius was offended that the Era of an infamous pagan and persecutor of Christians should continue to be used by Christians, so he introduced an Era based on the birth of Christ, the "Year of the Lord" (*Dominus*), **Annô Domini** (AD), Era. He didn't get this quite right, since, if Jesus lived in the days of "Herod the King," as the Bible says, he cannot have been born later than 4 BC, when Herod died. Nevertheless, Dionysius's Era was popularized by the English Church historian, the **Venerable Bede** (673-735), and has come into general use since, even by people who are not practitioners of, and want nothing to do with, Christianity.

Dionysius reckoned the year 532, in his own lifetime, to mark the beginning of a complete new Great Paschal Period. This put the beginning of the previous Period in 1 BC (0 AD), which, of course, is consistent with the system of Golden Numbers, which also begin in 1 BC. Curiously, the Era of Diocletian is still used by the Christians of Egypt, the **Copts**. They, however, call it the **Era of Martyrs**, commemorating Diocletian's victims rather than the Emperor himself.

For Gregorian Easter, we must deal with the Gregorian reform of the Julian calendar. This reform had a solar side and, for Easter, a lunar side. Since the true **Tropical Year** (the average time from one Vernal Equinox to another, as of 1900) is 365.24219878 days (cf. *The Astronomical Almanac for the Year 1998*, U.S. Government printing Office, 1997, p. K5, which states it in terms of "ephemeris seconds"), the Julian year (365.25) runs slow by a day every 128.2 years. By the Council of Trent (1545-1563), an error of 9.5 days would have built up since the Council of Nicaea, when the Vernal Equinox was defined. This meant that the actual Vernal Equinox was occuring on March 11th, instead of the 21st. The Julian year using the 19 year cycle also runs slow by a day every 307.3 years against the moon. The means that by the Council of Trent, an error of 3.3 days would have built up since Dionyius in 532. Not so bad, but in some years, Easter was wrong for the moon as well as for the sun, and something would have to be done about it.

The Gregorian Reform for the sun was to leave out three 3 Leap Days every 400 years. **Which** 3 is reckoned in a clever way: *century years*, which means years evenly divisible by 100, would ordinary be Leap Years (evenly divisible by 4), but in the Gregorian Calendar they are not, **except** for century years evenly divisible by 400. Thus, in the period in which the Gregorian calendar has been in use, 1700, 1800, and 1900, which are Leap Years on the Julian Calendar, have not been Leap Years on the Gregorian Calendar. When the Gregorian Calendar was instituted in October 1582, 10 days were dropped: On the Julian date 5 October, the Gregorian Calendar was started as 15 October. This 10 day difference increased to 11 in 1700, 12 in 1800, and 13 in 1900. 1600 **was** a Leap Year, and so will be 2000. The Gregorian correction of the Julian year (365 +1/4 -3/400) results in a year of 365.2425 days, which is off day in 3,320 years. The correction, however, was a little off. Three years out of four, the Vernal Equinox actually occurs on March 20, not March 21. An extra day should have been added in 1582, or 1600 skipped as a leap year.

The Gregorian reform for the moon was more complicated. It was also stated as a modification of the Julian calendar, subtracting 8 days in 2500 years. This ordinarily means a 1 day correction every 300 years, but with one interval of 400 years every 2500 years. That 400 year interval was regarded as having occured between 1400 and 1800 AD. What the Gregorian correction does is to approximate the **Metonic** year, which means the year produced by the 19 year lunar cycle (named after the Greek astronomer Meton). 235 lunar months (12 x 19 + 7) divided by 19 years gives 365.24675 days. Approximating this value corrects a calendar for the moon. Correcting this year for the **sun** must be done by adding or subtracting months rather than days, or the relation of the calendar to the moon is lost. The Gregorian correction of the Julian year for the moon (**365 +1/4 -8/2500**) results in a year of 365.2468 days, which is off a day in 23,810 years--quite accurate enough for anyone's purposes. But if the Julian calendar runs **slow** against both the sun and the moon, the effect of the combined corrections is that the Gregorian solar calendar runs **fast** against the moon, which means that the Metonic year is appoximating by adding rather than substracthing the correction to the Gregorian solar year: **365.2425 +43/10000 = 365.2468**. Note that +43/10000 -3/400 = -8/2500 (which is +43/10000 -75/10000 = -32/10000).

While the precise method of Gregorian lunar calculation will be explained below, we can already use a table to determine Gregorian (as well as Julian) Easter. This is a table like the previous Julian one, but with the Gregorian corrections for sun and moon. While there is one column for Julian dates (the entire previous table), there are six columns for Gregorians dates, one for each Gregorian century, 1500, 1600, 1700, 1800, 1900, and 2000. During that period, three further solar corrections were made against the Julian year (in 1700, 1800, and 1900), which means that the column of Gregorian dates is visibly moved up one each time. During that same period, one further lunar correction has been made, in 1800, which has moved up the the set of Golden Numbers and enabled the entire table to be broken in two--the left side using one set of Golden Numbers, the right side another.

Equipped with the approrpiate Golden Number and Dominical Letter, both Julian and Gregorian Easter can be read off the table. A Golden Number **4** and Julian Dominical Letter **E** for 1998 gives us **April 6** for Julian Easter, but now all we have to do is look across the table to the appropriate Gregorian century to read off the Gregorian date of Julian April 6: In the 20th and 21st centuries, the Gregorian date of Julian April 6 is **April 19**. A Golden Number **4** and Gregorian Dominical Letter **D** for 1998 means, first, we look for the Golden Number in the column of Golden Numbers that goes with Gregorian century 19 (i.e. 1900). This will be seen to be opposite April 12 in the 1900 and 2000 columns. April 12 itself bears Dominical Letter **D**, so we do not have to go further down the table: **April 12** is Gregorian Easter for 1998. It may be noted that the Gregorian Easter occurs exactly one week earlier than Julian Easter. Indeed, the identity of **Sundays** must be the same for both calendars: The Dominical Letter in the Julian column **will** correspond to the right Dominical Letter in the Gregorian column (in this case E and D).

An anomaly in this table concerns the Golden Numbers 17 and 6 for Gregorian centuries 19 and 20. They have been moved up a day (see them indexed at far right) even though no further lunar correction is called for. This provision evidently results from a desire to keep the Paschal Term the same length. Otherwise, a Golden Number 6 and a Dominical Letter D would put Easter on April 26. The entire Paschal Term might have been moved down one day, since March 22 cannot be Easter in these centuries. Instead the Golden Numbers were tightened up a day, with Number 17 moved up a day also, so as to avoid the numbers overlapping. Golden Number 6 might also have been reassigned to March 21, but March 21 cannot itself be Easter. This device will be further noted below, in the discussion of the **Epacts**.

This table now prepares one for all practical purposes to determine both Julian and Gregorian Easter, and to know why the dates are what they however. However, the lunar part of the Gregorian Easter calculation is more elaborate and elegant than this, and the table actually needed for Gregorian Easter calculation really is much simpler. This will be examined next.

The device for lunar calculation introduced for the Gregorian calendar was the "**Epact**." This was defined as the **age of the moon** on January 1. The number *zero* now being available for calculation, the age of the New Moon is 0 days, and the age of the Full Moon, as in the definition above, is 13 days. The Epacts for each year of the 19 year cycle (the Golden Numbers) are generated by a simple and convenient device: If we start with a year where a New Moon actually occurs on January 1 (Epact 0), we simply add **11** (the approximate difference between 12 lunars months and the solar year) to get the Epact of the following year. The next year, add 11 again, resulting in 22. Adding 11 again, however, gets us 33, which is longer than a lunar month. So we subtract **30**, resulting in an Epact of 3.
This calculation may be done for the Julian calendar, as seen at right. The Julian Epacts start with 0 at Golden Number 3. It may be noted that the table falls short of coming out even by just **1**: The last Epact (26) is equal to the first one (8) if we add 11, subtract 30, and then add 1.

The Julian Epacts, however, must be corrected over time. But, rather than moving a column of Golden Numbers up in a table against dates, this may now be simply done by adding or subtracting numbers from the row of Epacts. A full table, ranging from an addition of 6 to a subtraction of 11, from the 0 row of Julian Epacts, follows**:**

The numbers 24* and 25* with asterisks in the table are called "Second Epacts." When used, they count as 25 and 26, respectively, rather than as 24 and 25. This is the device discussed above, whereby the length of the Paschal Term is kept constant.

The "CX" index is a number that may be called the "Clavian Differential." This is named after the the Jesuit mathematician and astronomer **Christopher Clavius** (1537-1612), who was responsible for recommending the calendar changes to Pope Gregory. Clavius also has another considerable claim to fame: In 1610 Pope Paul V asked him to determine whether the strange things that **Galileo** claimed to be seeing through his new telescope were really there. Some people thought that the telescope was generating illusions. Clavius checked it out and, although he was not sympathetic with Galileo's Copernican astronomy, he honestly reported to the Pope that the telescope was **not** generating illusions. Later, the largest crater visible on the Moon was named "Clavius." The logician Benson Mates also credits Clavius with an important theorem in logic, **((P -> ~P) -> ~P)**, which means that if a proposition implies its own contradition, then the proposition is false. This is the basis of **reductio ad absurdum** arguments. Returning to our problem, the "Clavian Differential" is the correction to make for the moon in the Julian and Gregorian calendars, i.e. it is which row of Epacts to use for a particular calendar in a particular century. Thus, "CJ" is the correction to make for the Julian calendar and "CG" is the correction to make for the Gregorian calendar. The "GJ" value is then the **solar** Gregorian correction made against the Julian calendar.

At right is a table giving the values of the Clavian and Gregorian corrections, and how they add together into the Clavian differential for the Gregorian calendar. The asterisks show the Clavian correction for the Julian calendar (*CJ) and the centuries in which the values are changed. The table covers the entire 2500 year lunar cycle, from the 1st century to the 26th. The lone 400 year interval between 1400 and 1800 is evident. The underlined numbers (__GJ__) show the exceptions to the century years where solar corrections are made, at one out of every four centuries. It may be noted that the Clavian corrections for the Julian year increase positively, while those for the Gregorian year increase negatively. There is also one very peculiar effect: The Gregorian corrections do not increase constantly but display a couple of retrogressions, at 800 and 2400. This is improper, but as a practical matter, no one is liable to be complaining about it any time soon. One desired effect of the system was to have the Clavian-Gregorian correction equal **zero** for century 000, while the other zeroes correspond, roughly, to the solar benchmark at Nicaea and the lunar benchmark with Dionysius Exiguus.

The CJ and CG values are to be used, of course, to determine which row to use in the table of Epacts. No one would actually be using the CJ correction alone for the Julian calendar, but that is how the system was conceived, so it is included. Without using the table, Epacts may be calculated directly using the formula at right with the Golden Number and the Clavian index value (CX = CJ or CG). For the entire 20th and 21st centuries, CG = -9. The year 1998, with a Golden Number of 4, has an Epact of **2** on the Gregorian calendar but, of course, **11** on the Julian calendar (CX = 0)

The Epact and the Dominical Letter can now be used to determine Easter, as follows.

With the Dominical Letter and the Epact, Easter can be read off a simple chart of the Paschal Term. The Dominical Letter for each date is indicated as on the previous charts, but each date is also marked with an Epact. Since each Epact is the age of the Moon on January 1, the Epacts for the Paschal Term show the date immediately after the Full Moon that would occur with that Epact. Two Epacts are given, depending on whether we want to read right left or left to right. Given the definition of Easter, left to right is more natural, but both ways are equivalent.

For 1998, the Julian Dominical Letter is **E** and the Julian Epact **11**. We find the left to right Epact 11 at April 3, and we go to the right to find E at **April 6**, which is Julian Easter for 1998, as we have already seen. Reading right to left, Epact 11 is at April 9; and we read left to E at April 6 again. What we cannot determine from this chart is the corresponding Gregorian date. We must know independently the Gregorian correction, which can be found in the __GJ__ column in the chart above. The way the system is arranged, the Gregorian correction must be **substracted** from the Julian date; but since the __GJ__ number is negative (-13), the effect is to **add**. Julian April 6 - (-13) = Gregorian April 19, as we have previously seen.

Gregorian Easter can be determined without, of course, the complication of converting the date. The Gregorian Dominical Letter of 1998 is D, and the Gregorian Epact 2. Going left to right, 2 occurs at **April 12**, which is already a D, giving us our Easter. Going right to left, 2 occurs at April 18. This is not a D, so we have to go left to the D, again at April 12. Remember that in the case of a "Second Epact," 24* or 25*, these are treated like 25 and 26, respectively. Going left to right, it is clear that 24/D would require that April 26 be in the Paschal Term, so the first D before the end, April 19, is used instead.

The date of other movable feasts is determined by Easter, and all one really needs to do is count whole weeks backwards and forwards from Easter itself.

- 9 weeks before Easter is Septuagesima Sunday.
- 8 weeks before Easter is Sexagesima Sunday.
- 7 weeks before Easter is Quinquagesima Sunday, the last Sunday before Lent, 49 days before Easter.
- The Tuesday after Quinquagesima Sunday is
**Shrove Tuesday**, better known as**Mardi Gras**("Fat Tuesday" in French). Since Catholics traditionally abstained from meat, and other indulgences, during Lent, Shrove Tuesday was the last chance for a bit of indulging. This has now become, it seems, the principal holiday of the year in New Orleans, Louisiana, and in Brazil, attracting people who couldn't care less about Lent, and whose behavior is probably rather more outlandish than what the Church would like. A few years ago, Brazil officially prohibited nudity in Mardi Gras parades, but then it was ruled that body paint counted as clothes. In New Orleans, police have ceased citing or arresting women flashing their breasts, as long as no public disturbance results. - The Wednesday after Quinquagesima Sunday is
**Ash Wednesday**, which begins Lent, the period that commemorates the actual period of teaching in Jesus's life. Lent is traditionally considered 40 days long, and it is if you don't count the six Sundays. - There are then six Sundays of Lent.
- 1 Week before Easter is
**Palm Sunday**, which commemorates Jesus's entry into Jerusalem to celebrate the Passover. - The Thursday after Palm Sunday is
**Maundy Thursday**, which commemorates the Passover Seder celebrated by Jesus and the Apostles, which came to be called the "Last Supper," where Jesus is supposed (by the Catholic and Orthodox) to have instituted the miracle of the Eucharist by telling the Apostles that the bread and the wine were his "body" and his "blood". (Some now question whether the Last Supper was their Seder, since the blessing of the wine and bread is in the wrong sequence in most Gospel accounts.) Since Jesus washed the feet of the Apostles before the meal, it was a common Mediaeval ritual, still performed by the Pope, for the powerful to wash the feet of the poor. At some point the Kings of England tired of this and decided to pass out money instead. Today, Queen Elizabeth still passes out special silver pennies, called "Maundy Money," but to people in homes for the aged rather than to the poor in general. - The Friday after Palm Sunday is
**Good Friday**, which commemorates the trial and Crucifixion of Jesus. This becomes symbolic of Christianity itself, as the Cross is the principal symbol of Jesus and the Faith. - The Saturday after Palm Sunday is
**Holy Saturday**, the day the body of Jesus lay in his tomb, and the day when his spirit is supposed to have descended into Hell. Previously, all the dead, righteous and wicked, had gone to Hell (**Sheol**in Hebrew). Now Jesus carried out the**Harrowing of Hell**, releasing from confinment all the righteous who had been saved under the Old Convent, i.e. all the Patriarchs and Children of Israel. They then proceeded to Heaven. - There are then five Sundays after Easter commemorating the Period after the Resurection when Jesus walked among the living again.
- The Thursday after the 5th Sunday after Easter is
**Ascension Thursday**, commemorating the day that Jesus ascended to Heaven himself. This left the Apostles without guidance, but Jesus promised that help would come. - 7 weeks after Easter is
**Pentecost**, or**Whitsunday**, which commemorates the descent of the**Holy Spirit**on the Apostles, enabling them to speak in Tongues and perform other miracles. - The movable part of the liturgical year ends with
**Advent**, the fourth Sunday before Christmas. That Christmas has a fixed calendar date when Easter and all its attendant holy days do not is curious, but it appears that December 25 was originally observed by the Romans as the birthday of**Sol Invictus**, the "Unconquered Sun," and by Roman Mithraism as the birthday of the Iranian solar god**Mithras**(who we see at right in the central ritual sacrifice of a bull). Since many people think that Christmas has basically reverted to being a pagan holiday, perhaps the historic contest for the date continues. Otherwise, some Armenian churches still celebrate Christmas on January 6, which is comemorated by other Christians as**Epiphany**, the day that the Magi arrived to venerate the infant Jesus. Since Christmas scenes usually show the Magi already there, the story has not been gotten quite straight. Other Armenians celebrate Christmas on January 6 according to the*Julian calendar*, which is now Gregorian January 19. That would certainly be a good way to preserve its religious character, since drunken Christmas office parties are by then a fading memory. Armenia is usually credited with being the first country to officially become Christian, in**301 AD**(eleven years before Constantine's vision of the Cross at the Milvian Bridge), but there is really a rival on the opposite side of the Middle East: Ethiopia received a bishop from the Patriarch of Alexandria around 305, but the dating of this is uncertain and it does not signify exactly when the Ethiopian Emperor accepted Christianity himself. Since the Bishop, Frumentius, had already been at the Ethiopian court in the previous century, the roots of Ethiopian Christianity were already in place. There is also some question now about the early date traditionally claimed for Armenia.

Philosophy of Science, Calendars

In 2014, on the Gregorian calendar (Western Churches), Septuagesima Sunday fell on February 16th, Mardi Gras on March 4th, Ash Wednesday on March 5th, Palm Sunday on April 13th, Maundy Thursday on April 17th, Good Friday on April 18th, Easter on April 20th, and Pentecost on June 8th. Easter on the Julian calendar (Eastern Churches) coincided with Gregorian Easter. The Golden Number for 2014 was I, the Gregorian Dominical Letter E and Epact 29, and the Julian Dominical Letter F.

In 2013, on the Gregorian calendar (Western Churches), Septuagesima Sunday fell on January 27th, Mardi Gras on February 12th, Ash Wednesday on February 13th, Palm Sunday on March 24th, Maundy Thursday on March 28th, Good Friday on March 29th, Easter on March 31st, and Pentecost on May 19th. Easter on the Julian calendar (Eastern Churches), occurred on May 5th, five weeks after Gregorian Easter.

In 2012, on the Gregorian calendar (Western Churches), Septuagesima Sunday fell on February 5th, Mardi Gras on February 21st, Ash Wednesday on February 22nd, Palm Sunday on April 1st, Maundy Thursday on April 5th, Good Friday on April 6th, Easter on April 8th, and Pentecost on May 27th. Easter on the Julian calendar (Eastern Churches), occurred on April 15th, one week after Gregorian Easter.

In 2011, on both the Gregorian calendar (Western Churches) and Julian calendar (Eastern Churches), Septuagesima Sunday fell on February 20th, Mardi Gras on March 8th, Ash Wednesday on March 9th, Palm Sunday on April 17th, Maundy Thursday on April 21st, Good Friday on April 22nd, Easter on April 24th, and Pentecost on June 12th.

In 2010, on both the Gregorian calendar (Western Churches) and Julian calendar (Eastern Churches), Septuagesima Sunday fell on January 31st, Mardi Gras on February 16th, Ash Wednesday on February 17th, Palm Sunday on March 28th, Maundy Thursday on April 1st, Good Friday on April 2nd, Easter on April 4th, and Pentecost on May 23rd.

In 2009, on the Gregorian calendar (Western Churches), Septuagesima Sunday fell on February 8th, Mardi Gras on February 24th, Ash Wednesday on February 25th, Palm Sunday on April 5th, Maundy Thursday on April 9th, Good Friday on April 10th, Easter on April 12th, and Pentecost on May 31st. Easter on the Julian calendar (Eastern Churches), occurred on April 19th, one week after Gregorian Easter.

In 2008, on the Gregorian calendar (Western Churches), Septuagesima Sunday fell on January 20th, Mardi Gras on February 5th, Ash Wednesday on February 6th, Palm Sunday on March 16th, Maundy Thursday on March 20th, Good Friday on March 21st, Easter on March 23rd, and Pentecost on May 11th. Easter on the Julian calendar (Eastern Churches), occurred on April 27th, five weeks after Gregorian Easter.

In 2007, on the Gregorian calendar (Western Churches), Septuagesima Sunday fell on February 4th, Mardi Gras on February 20th, Ash Wednesday on February 21st, Palm Sunday on April 1st, Maundy Thursday on April 5th, Good Friday on April 6th, Easter on April 8th, and Pentecost on May 27th. Easter on the Julian calendar (Eastern Churches) coincided with Easter on the Gregorian calendar.