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# Happy Easter!

On the first page of this section on calendars, which shows a perpetual calendar on which the day of the week might be found, I mentioned the Dominical Letter, which is used as one way of naming the day of the week on which a year starts. And, on a later page, in discussing the three cycles, the solar cycle of the Julian calendar, the Metonic cycle, and the cycle of the Indictions, which formed the basis for the Julian era on which Julian Day Numbers were based, I noted that the version of the Metonic cycle used was that which corresponded to the Golden Number.

Well, if I have discussed Dominical Letters and Golden Numbers, it seems reasonable that I should also discuss the calculation of the date of Easter, in which these things are used.

The table for the Dominical Letter is similar to that used for the perpetual calendar on the first page:

00 01 02 03    04 05
06 07    08 09 10 11
12 13 14 15    16
17 18 19    20 21 22
23    24 25 26 27
28 29 30 31    32 33
34 35    36 37 38 39
40 41 42 43    44
45 46 47    48 49 50
51    52 53 54 55
56 57 58 59    60 61
62 63    64 65 66 67
68 69 70 71    72
73 74 75    76 77 78
79    80 81 82 83
84 85 86 87    88 89
90 91    92 93 94 95
96 97 98 99

Gregorian
A  G  F  E  D  C  B       1600 2000 2400 2800 3200 3600
C  B  A  G  F  E  D       1700 2100 2500 2900 3300 3700
E  D  C  B  A  G  F       1800 2200 2600 3000 3400
G  F  E  D  C  B  A  1500 1900 2300 2700 3100 3500

Julian
F  E  D  C  B  A  G        400 1100
G  F  E  D  C  B  A        500 1200
A  G  F  E  D  C  B        600 1300
B  A  G  F  E  D  C     0  700 1400
C  B  A  G  F  E  D   100  800 1500
D  C  B  A  G  F  E   200  900 1600
E  D  C  B  A  G  F   300 1000 1700

In the case of a leap year, look under the space preceding the number for the year for the Dominical Letter applicable to the months of January and February. These letters apply to calendar years from January to December, rather than to a year beginning in March, as used for the perpetual calendar on the first page.

And the following table is used to determine the Golden Number of a year, whether for the Julian or the Gregorian calendar:

00 01 02 03 04 05 06 07 08 09 10 11 12 13 14 15 16 17 18
19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37
38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56
57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75
76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94
95 96 97 98 99

1  2  3  4  5  6  7  8  9 10 11 12 13 14 15 16 17 18 19      0 1900
6  7  8  9 10 11 12 13 14 15 16 17 18 19  1  2  3  4  5    100 2000
11 12 13 14 15 16 17 18 19  1  2  3  4  5  6  7  8  9 10    200 2100
16 17 18 19  1  2  3  4  5  6  7  8  9 10 11 12 13 14 15    300 2200
2  3  4  5  6  7  8  9 10 11 12 13 14 15 16 17 18 19  1    400 2300
7  8  9 10 11 12 13 14 15 16 17 18 19  1  2  3  4  5  6    500 2400
12 13 14 15 16 17 18 19  1  2  3  4  5  6  7  8  9 10 11    600 2500
17 18 19  1  2  3  4  5  6  7  8  9 10 11 12 13 14 15 16    700 2600
3  4  5  6  7  8  9 10 11 12 13 14 15 16 17 18 19  1  2    800 2700
8  9 10 11 12 13 14 15 16 17 18 19  1  2  3  4  5  6  7    900 2800
13 14 15 16 17 18 19  1  2  3  4  5  6  7  8  9 10 11 12   1000 2900
18 19  1  2  3  4  5  6  7  8  9 10 11 12 13 14 15 16 17   1100 3000
4  5  6  7  8  9 10 11 12 13 14 15 16 17 18 19  1  2  3   1200 3100
9 10 11 12 13 14 15 16 17 18 19  1  2  3  4  5  6  7  8   1300 3200
14 15 16 17 18 19  1  2  3  4  5  6  7  8  9 10 11 12 13   1400 3300
19  1  2  3  4  5  6  7  8  9 10 11 12 13 14 15 16 17 18   1500 3400
5  6  7  8  9 10 11 12 13 14 15 16 17 18 19  1  2  3  4   1600 3500
10 11 12 13 14 15 16 17 18 19  1  2  3  4  5  6  7  8  9   1700 3600
15 16 17 18 19  1  2  3  4  5  6  7  8  9 10 11 12 13 14   1800 3700

Easter, of course, falls on a Sunday.

March 21st of the Gregorian calendar is taken as the approximation to the vernal equinox to use.

The Metonic cycle of 19 years is corrected by a Lunar Equation and a Solar Equation to indicate the age of the Moon (given by the Epact) more accurately.

This table gives the Epact from the Golden Number and the displacement resulting from the Lunar and Solar equations:

Golden Number:  1  2  3  4  5  6  7  8  9 10 11 12 13 14 15 16 17 18 19
Displacement:
1          1 12 23  4 15 26  7 18 29 10 21  2 13 24  5 16 27  8 19
0          * 11 22  3 14 25  6 17 28  9 20  1 12 23  4 15 26  7 18
-1         29 10 21  2 13 24  5 16 27  8 19  * 11 22  3 14 25  6 17
-2         28  9 20  1 12 23  4 15 26  7 18 29 10 21  2 13 24  5 16
-3         27  8 19  * 11 22  3 14 25  6 17 28  9 20  1 12 23  4 15
-4         26  7 18 29 10 21  2 13 24  5 16 27  8 19  * 11 22  3 14

and the changes in the displacement in years ending with two zeroes and the resulting displacement is shown in the table below:

Year     Lunar Solar  Displacement
1700           -1        0
1800     +1    -1        0
1900           -1       -1
2000                    -1
2100     +1    -1       -1
2200           -1       -2
2300           -1       -3
2400     +1             -2
2500           -1       -3
2600           -1       -4
2700     +1    -1       -4
2800                    -4

the shifts to the displacement repeating in the 1200 year cycle shown.

The solar displacement reflects the difference between the Gregorian calendar and the Julian calendar, and compensates for the fact that in the Gregorian calendar, not all centuries are equal in length. So, when a new century is preceded by a year that is not a leap year, events happen a day later by the calendar, and so the Moon's age on a given day, which is what the Epact signifies, is one day less.

The lunar displacement reflects the difference between the Metonic cycle and the Julian calendar, which is taken as one day every 300 years.

The mean length of the lunar synodic month is 29.530588853 days, as we have noted. A Metonic cycle is composed of 235 lunar months, and is therefore about 6939.68838 days, while 19 Julian years are 6939.75 days, and 19 Gregorian years, on the other hand, are 6939.6075 days.

A difference of 0.06162 days every 19 years works out to a difference of 1 day about every 308.34 years, which makes the Lunar Equation a very close approximation.

Based on the Dominical Letter, the Sundays following March 21st are:

March April
A    26  2  9 16 23
B    27  3 10 17
C    28  4 11 18
D 22 29  5 12 19
E 23 30  6 13 20
F 24 31  7 14 21
G 25  1  8 15 22

and based on the Epact, the day on which the approximated Full Moon falls is:

Epact Date        Epact Date        Epact Date
22    March 22    12    April  1     2    April 11
21    March 23    11    April  2     1    April 12
20    March 24    10    April  3     *    April 13
19    March 25     9    April  4    29    April 14
18    March 26     8    April  5    28    April 15
17    March 27     7    April  6    27    April 16
16    March 28     6    April  7    26,25 April 17
15    March 29     5    April  8
14    March 30     4    April  9
13    March 31     3    April 10

Epacts 26 or 25 give a Full Moon date of April 17 because the lunar month is about 29 and a half days long, not 30 days long, and so the year is taken as being composed of 30 day lunar months alternating with 29 day lunar months, and Easter is affected by that in this case.

Thus, starting with the date found from the Epact in the table above, in the row given by the year's Dominical Letter, look for the earliest date that agrees with it or is after it, and that will be the date of Easter.

As previously noted, the current cycle in which the Golden Number goes from 1 through 19 consists of the years from 1995 to 2013.

### The Alternative is Already in Place

Keeping track of when Easter will fall is, as can be seen from the foregoing, complicated. It would be more convenient in our industrialized society, where few people are concerned with the phase of the moon, if the date of Easter were determined in a more conventional fashion.

To prevent conflict and inconsistency in attempts for reform, it should be noted that a specific scheme for such a change has already been proposed.

In 1928, Great Britain passed a law establishing the date of Easter as the Sunday following the second Saturday in April. However, the law included a provision that it would not take effect until the agreement of the churches to such a change was obtained.

The Anglican Church had, at the time this act was adopted, expressed interest in making such a change. The Roman Catholic Church itself has been reported as being favorably disposed to the change, but not willing to proceed unless this took place in the context of a unification of the date of Easter between theirs and that that of the Orthodox Church.

### If You Think Friday the 13th Is Unlucky

then you're probably using the wrong calendar.

Since this unlucky day is held to fall on a Friday, it is quite reasonable to suspect that this superstition has some connection with Good Friday, on which the Crucifixion is commemorated.

The number 13 may be considered unlucky as a number for a number of reasons.

When one considers those odd, strange, and peculiar numbers known as prime numbers, one might think of them this way:

• 2 and 3 are very useful numbers, good for dividing dozens up into halves and thirds;
• 5 is the number of fingers we have on each hand, if you call the thumb a finger; and, if you follow Abraham Lincoln, it's still the number of digits we have on each hand. So, it, too, plays an important role in counting things.
• 7 is awkward, but it is the number of visible planets plus the Sun and the Moon, it is the number of notes in the musical scale, it is the number of distinctive colors in the spectrum, if one wishes to distinguish Indigo and Violet from Blue, and, being the approximate number of days between the four quarters of the Moon, it ended up as the number of days of the week; so, rather than a threatening number, it is considered beautiful and glorious.
• 11 is one more than ten, on which we base our counting, so it is taken for granted that things don't go evenly into it.
• Finally, 13 comes along, the first prime number that has no good excuse for being awkward. So we heap our calumny upon it, while 17, 19, 23, and so on are just left ignored.

Or, it is also held that, given Jesus and the 12 Apostles, Judas was the 13th person at the table at the Last Supper.

However, there is another association between the number 13 and the Crucifixion which is more definitely calendrical in nature.

Before the Gregorian calendar was adopted, the calculation of Easter for the Julian calendar was accomplished in a manner similar to the one above, but somewhat simpler.

But this practice was one instituted by the Roman Church. The preceding practice of the early Christian church was to celebrate Easter on Nisan 14th each year, regardless of the day of the week on which it fell. Since the Jewish months begin on the New Moon, the 14th of the month would be a representation of the Full Moon.

And, when Nisan 14th, Passover, falls on the Sabbath, and by this I mean Saturday, the Jewish Sabbath, not Sunday, the Day of the Lord as followed in Christian worship, as it is recorded by the Gospels as having taken place subsequent to the Crucifixion, then Nisan 13th would be a Friday.

However, if this is the case, it is based on a popular misconception. The Biblical account of the Crucifixion notes that the Last Supper took place on Passover. Christ was arrested the day after that, and handed over to Pontius Pilate one day later. This was the day of the Crucifixion, and the Bible also notes that Christ lay dead for three days and three nights. And then it notes that Christ was found to be risen early on Sunday morning.

This would seem to mean that Christ appeared before Pontius Pilate on Wednesday, so that while He was placed on the Cross on Wednesday, His death took place at some time on the night between Wednesday and Thursday, and then, three days later, His resurrection took place on the night between Saturday and Sunday. In that case, the arrest of Jesus took place on Tuesday, and Passover was on Monday.

This is not entirely certain; the arrest of Jesus could have taken place in the evening following Passover, on what we would regard as the same day. And many Christian denominations take the position that the statement concerning Christ being in the grave for three days and three nights is not to be taken literally.

Thus, the Crucifixion may have taken place on Wednesday or Thursday, and Passover of that year, the day of the Last Supper, would have been either Monday, Tuesday, or Wednesday.

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