Easter is the central point of the Christian calendar, with most other feast days and holidays (the moveable feasts) being based around it. As a result, it has a major role in the civil calendar as well. So it seems curious to the unaware that it appears to jump around the calendar so randomly. This page attempts to explain what is behind this random motion.
The Bible tells us that the crucifixion took place at the time of the Passover feast, with the resurrection on the following Sunday. Since the Passover is basically on the first full moon of Spring, we get a potential definition for Easter:
Easter Sunday is the Sunday after the first full moon of Spring. The full moon may be on the first day of Spring (March 21st), but Easter will never be, and if the full moon is on a Sunday, Easter is on the following Sunday.
While other possibilities have been proposed (e.g. always having Easter on the day after the full moon), this is the one that was adopted by the mainstream church.
The rule seems fairly simple, but it has some nasty catches. Firstly, predicting the movements of the moon is far from simple, and determining the exact moment of the full moon even less so. If the moment is not got exactly right, the date of Easter could be wrong by a month (if the full moon is on the March 20th/21st boundary), or by a week (if it is on a Saturday/Sunday boundary), or both! Then there is the question of where the full moon should be observed. The moment of full moon will be on one day in parts of the world, but a different day on the other side of the International Date Line. When the rule went wrong, it could be spectacularly wrong: one extreme case had an eclipse of the (full) moon on Easter Monday!
Over time the various authorities settled on a set of compromises; the most important of these were hammered out at the Council of Niceae in 325. The basic rules that were established are:
Astronomers right back to Babylonian times have noticed that the cycles of the moon obey an interesting rule: 235 lunar months are almost exactly 19 years of 365.25 days. Therefore, if the dates of the full moons are recorded in 19 columns, we soon discover that each column will only ever contain two adjacent dates - two because the presence or absence of February 29th causes the moment of full moon to happen at 4 different times with 18 hours between the earliest and latest. For the sake of simplicity, it was tempting to ignore this detail and assign one date to each column, and this was soon done.
Full moons are slightly more than 29.5 days apart, so a reasonable approximation is to say they are alternately 29 or 30 days apart. If we ignore February 29th when counting days and always start each year with a 30 day gap, each Paschal full moon will be either 354 days after the previous one and so 11 days earlier in the calendary, or 384 days after it and so 19 days later. This allows us to compute a simple table of dates for the 19 Paschal full moons.
The result was that in the Julian Calendar, which had leap years every four years, the rules for determing Easter were very simple:
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This rule is quite simple, and also has some nice properties: Easter Sunday recurs on the same date every 532 (4 * 7 * 19) years, all 19 possible dates for the Paschal full moon are equally likely, and there is a fixed and known range of dates for Easter Sunday. Therefore it is not surprising that it lasted about 1200 years.
As is well known, the Julian Calendar has a major problem which became evident over the centuries: the year is not quite 365.25 days long, and so the dates of the year slowly drift relative to the seasons. The date of Easter also drifts, but the problem is less obvious. By the 16th century, however, it was getting to be embarassing, and so Pope Gregory XIII employed the astronomer Clavius to design a new calendar.
There are two major sources of error in the Julian Calendar.
These two discrepancies apply in opposite directions but, because they are of different magnitudes, cause the real full moon to slowly drift relative to the Paschal one, at an average rate of 0.0043 days per year or one day every 233 years.
As is well known, the Gregorian Calendar was introduced to handle these problems, and a number of days were omitted to bring the dates back into line with the seasons. In those countries obeying the Papal Bull completely (notably Italy, Poland, Portugal, and Spain), October 4th 1582 was followed by October 15th, while in most other Roman Catholic dominated parts of the world the change was made later that year or in 1583 or 1584. (The Protestant parts were suspicious of the innovation and delayed; in the British Empire September 2nd 1752 was followed by September 14th, and most other Protestant countries in Europe changed in the 18th century.) A new rule for leap years was introduced, stating that century years (1600, 1700, and so on) were only to be leap years when divisible by 400.
However, a much more important (to the church, at least) change made at the same time was to introduce a new set of rules for Easter. These new rules are based on the same principles of the old, but at the start of each century the 19 dates of the 19 Paschal full moons may be shifted to compensate for the above problems:
Neither correction happened in 2000, but both will happen - cancelling each other out - in 2100. Thus the Paschal full moons, having shifted in 1900, do not shift again until 2200.
Clavius had to deal with one complication. The 354/384 rule described above would allow the Paschal full moon to be as early as March 21st or as late as April 19th. As can be seen, while the former date appeared in the old system, the latter did not - April 18th is the latest. Rather than contradict existing descriptions of the Easter rules, Clavius looked for a way to address this. Simply omitting this date, using a 29 day range instead of a 30 day one, wouldn't work. So instead, Clavius decided that, if the Paschal full moon would have fallen on April 19th, it should be "adjusted" to occur on April 18th instead. However, doing this meant that sometimes two golden numbers would both correspond to April 18th; again this would contradict existing descriptions. But on further study Clavius noticed that, when two Paschal full moons fall on adjacent dates, the later has a golden number of 1 to 8 and the latter a golden number of 12 to 19; an implication of this is that three consecutive dates can't all have Paschal full moons. Therefore he decided that, whenever a Paschal full moon would fall on April 18th and correspond to a golden number of 12 or more, it would also be adjusted, to April 17th.
The end result was a system whereby the dates of the 19 Paschal full moons vary from century to century, with 30 different patterns being possible. Nevertheless, in any century the 19 moon are still all on different dates in the range March 22nd to April 18th inclusive.
In those countries that used to be part of the British Empire, the above rules were brought into law as part of the Calendar (New Style) Act 1750 (24 Geo.2 c.23, also available here and here). This amended the tables at the front of the Book of Common Prayer (of the Church of England) to correspond to the new rules. Two tables are important. Firstly, Table II encodes the shifts that happen each century:
T A B L E II. |
To find the Month and Days of the Month, to which the Golden Numbers ought to be prefixed in the Calendar in any given Year of our Lord, consisting of entire hundred Years, and in all the intermediate Years, betwixt that and the next hundredth Year following, look in the second Column of Table II. for the given Year, consisting of entire Hundreds, and Note the Number or Cypher which stands against it in the third Column; then, in table III. look for the same number in the Column under any given Golden Number, which when you have found, guide your Eye side-ways to the Left Hand, and in the first Column you will find the Month and Day, to which that Golden Number ought to be prefixed in the Calendar during that Period of one hundred Years. The Letter B prefixed to certain hundredth Years in Table II. denotes those Years which are still to be accounted Bissextile or Leap Years in the new Calendar; whereas all the other hundredth Years are to be accounted only common Years. | ||||||
---|---|---|---|---|---|---|---|
1 | 2 | 3 | 1 | 2 | 3 | ||
Years of our Lord |
Years of our Lord |
||||||
B B B B B B B B B |
1600 1700 1800 1900 2000 2100 2200 2300 2400 2500 2600 2700 2800 2900 3000 3100 3200 3300 3400 3500 3600 3700 3800 3900 4000 4100 4200 4300 4400 4500 4600 4700 4800 4900 5000 5100 |
0 1 1 2 2 2 3 4 3 4 5 5 5 6 6 7 7 7 8 9 8 9 10 10 10 11 12 12 12 13 13 14 14 14 15 16 |
B B B B B B B B B |
5200 5300 5400 5500 5600 5700 5800 5900 6000 6100 6200 6300 6400 6500 6600 6700 6800 6900 7000 7100 7200 7300 7400 7500 7600 7700 7800 7900 8000 8100 8200 8300 8400 8500 &c. |
15 16 17 17 17 18 18 19 19 19 20 21 20 21 22 23 22 23 24 24 24 25 25 26 26 26 27 28 27 28 29 29 29 0 |
and then Table III gives the dates of the Paschal full moons for each possible shift pattern (the adjustments introduced by Clavius are clearly visible at the bottom):
T A B L E III. | ||||||||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Pascal Full Moon |
S | The G O L D E N N U M B E R S. | ||||||||||||||||||
i | ii | iii | iv | v | vi | vii | viii | ix | x | xi | xii | xiii | xiv | xv | xvi | xvii | xviii | xix | ||
March 21 March 22 March 23 March 24 March 25 |
C D E F G |
8 9 10 11 12 |
19 20 21 22 23 |
0 1 2 3 4 |
11 12 13 14 15 |
22 23 24 25 26 |
3 4 5 6 7 |
14 15 16 17 18 |
25 26 27 28 29 |
6 7 8 9 10 |
17 18 19 20 21 |
28 29 0 1 2 |
9 10 11 12 13 |
20 21 22 23 24 |
1 2 3 4 5 |
12 13 14 15 16 |
23 24 25 26 27 |
4 5 6 7 8 |
15 16 17 18 19 |
26 27 28 29 0 |
March 26 March 27 March 28 March 29 March 30 |
A B C D E |
13 14 15 16 17 |
24 25 26 27 28 |
5 6 7 8 9 |
16 17 18 19 20 |
27 28 29 0 1 |
8 9 10 11 12 |
19 20 21 22 23 |
0 1 2 3 4 |
11 12 13 14 15 |
22 23 24 25 26 |
3 4 5 6 7 |
14 15 16 17 18 |
25 26 27 28 29 |
6 7 8 9 10 |
17 18 19 20 21 |
28 29 0 1 2 |
9 10 11 12 13 |
20 21 22 23 24 |
1 2 3 4 5 |
March 31 April 1 April 2 April 3 April 4 |
F G A B C |
18 19 20 21 22 |
29 0 1 2 3 |
10 11 12 13 14 |
21 22 23 24 25 |
2 3 4 5 6 |
13 14 15 16 17 |
24 25 26 27 28 |
5 6 7 8 9 |
16 17 18 19 20 |
27 28 29 0 1 |
8 9 10 11 12 |
19 20 21 22 23 |
0 1 2 3 4 |
11 12 13 14 15 |
22 23 24 25 26 |
3 4 5 6 7 |
14 15 16 17 18 |
25 26 27 28 29 |
6 7 8 9 10 |
April 5 April 6 April 7 April 8 April 9 |
D E F G A |
23 24 25 26 27 |
4 5 6 7 8 |
15 16 17 18 19 |
26 27 28 29 0 |
7 8 9 10 11 |
18 19 20 21 22 |
29 0 1 2 3 |
10 11 12 13 14 |
21 22 23 24 25 |
2 3 4 5 6 |
13 14 15 16 17 |
24 25 26 27 28 |
5 6 7 8 9 |
16 17 18 19 20 |
27 28 29 0 1 |
8 9 10 11 12 |
19 20 21 22 23 |
0 1 2 3 4 |
11 12 13 14 15 |
April 10 April 11 April 12 April 13 April 14 |
B C D E F |
28 29 0 1 2 |
9 10 11 12 13 |
20 21 22 23 24 |
1 2 3 4 5 |
12 13 14 15 16 |
23 24 25 26 27 |
4 5 6 7 8 |
15 16 17 18 19 |
26 27 28 29 0 |
7 8 9 10 11 |
18 19 20 21 22 |
29 0 1 2 3 |
10 11 12 13 14 |
21 22 23 24 25 |
2 3 4 5 6 |
13 14 15 16 17 |
24 25 26 27 28 |
5 6 7 8 9 |
16 17 18 19 20 |
April 15 April 16 April 17 April 17 April 18 |
G A B B C |
3 4 5 6 |
14 15 16 17 |
25 26 27 28 |
6 7 8 9 |
17 18 19 20 |
28 29 0 1 |
9 10 11 12 |
20 21 22 23 |
1 2 3 4 |
12 13 14 15 |
23 24 25 26 |
4 5 6 7 |
15 16 17 18 |
26 27 28 29 |
7 8 9 10 |
18 19 20 21 |
29 0 1 2 |
10 11 12 13 |
21 22 23 24 |
April 18 | C | 7 | 18 | 29 | 10 | 21 | 12 | 13 | 24 | 5 | 16 | 27 | 8 | 19 | 0 | 11 | 22 | 3 | 14 | 25 |
The heading S is actually Sunday Letter written sideways.
Note that the old Easter can be calculated using code 23, provided it is remembered that these are Julian, not Gregorian, dates.
Tables have their uses, particularly for making it easy for the average person to determine the date of Easter, but there are many circumstances where an algorithm is more convenient. A number of such have been published, and rather fewer have turned out to be correct - even Gauss managed to make a mistake (forgetting that the lunar correction happens on a 2500 year cycle, not a 2400 year one). The following algorithm is simple to implement and gives the correct date in all circumstances; it is also quite easy to explain.
Divide | to get | Explanation | ||
---|---|---|---|---|
this | by | quot. | rem. | |
year | 19 | a | a + 1 is the golden number. | |
year | 100 | b | c | Split the year into century and remnant. |
b | 4 | d | e | Find the place in, and the number of, 400 year cycles. 400 years is an exact number of weeks. |
c | 4 | f | g | Find the number of leap years so far this century (ignoring the century year if it was one), and the number of ordinary years since. |
8 * b + 13 | 25 | h | Determine the number of days to shift the full moons because of the lunar correction. The 8 ensures that we get a total of 8 days every 2500 years, and the 13 ensures that we start at the right point. | |
19 * a + b - d - h + 15 | 30 | j | j encodes the unadjusted date of the Paschal full moon. b - d is the number of century years that are not leap years, and so b - d - h is 7 more than the number found from Table II. Meanwhile 19 * a gives the position of a specific number (8) in the appropriate column of Table III, and the constant 15 corrects for the two offsets 7 and 8. | |
a + 11 * j | 319 | m | m will be 1 if Clavius's adjustment moves the full moon back one day, and 0 otherwise. | |
2 * e + 2 * f - g - j + m + 32 | 7 | k | k + 1 is the number of days from the Paschal full moon to
Easter Sunday. The best way to see how it is derived is to first note that the
days of the week repeat exactly every 400 years, and then to rewrite it as: 4 - [124 * e + 5 * f + g] - (j - m) + 7 * 92 The term in square brackets represents the day of the week for March 21st, the third term advances this to the Paschal full moon, the constant 4 represents Saturday, and the last term makes the result positive. Then reduce as much as possible modulo 7. | |
j - m + k + 90 | 25 | month | We now have j - m + k representing the date of Easter Sunday, with 0 being March 22nd; the constant 90 derives from 10 representing April 1st. | |
j - m + k + 19 + month | 32 | date | And finally we get the date in a similar way; adding in the month allows us to skip April 0th seamlessly. |
Sorry, but the form to try it yourself is broken at present.
Pope Gregory noted in his papal Bull that, although he had decided to keep it aligned (approximately) with the Passover, there was no reason why Easter should not lie on a fixed date. And in 1928 the UK Parliament passed the Easter Act. This states that, after due consultation with appropriate authorities, the Crown may issue an Order In Council making Easter Sunday always be the day after the second Saturday in April (as if the Paschal full moon were always on April 8th). Should this ever come to pass, these rules would become a thing of the past.