CHAPTER VI._Our Calendar The Julian calendar and its errors. How corrected by the Gregorian. Rules for finding the dominical letter, and the day of the week of any event from the days of Julius Caesar 46 B.C. to the year of our Lord four thousand; a new and easy method of fixing the date of Easter. Hebrew calendar; showing the correspondence in the date of events recorded in the Bible with our present Gregorian calendar. Illustrated by valuable tables and charts.

A NEW AND EASY METHOD OF FIXING THE DATE OF EASTER.

In determining the date of Easter, we make use of the numbers called

epacts; and, as these numbers have already been explained in the preceding

chapter, (q. v.) it will be necessary to give them only a brief notice

here. Epact, as has already been defined, is the excess of the solar year

beyond the lunar, employed in the calendar to signify the moon's age at

the beginning of the year; that is, if a new moon fall on the first day

of January in any year, it will be eleven days old on the first day of

the following year, and twenty-two days old on the first day of the third

year, and so on.

Now, in this work, in fixing the date of Easter, we abandon the use of the

new moons altogether, and make calculations wholly from the paschal full

moons, which cannot happen earlier than the 21st of March, nor later than

the 19th of April. Appendix J. The epacts are here used to show the day of

the month on which the paschal full moons fall; that is, if the paschal

moon fall on a given day of the month in any year, it will happen eleven

days earlier the following year, and twenty-two days earlier the third

year, and so on. To illustrate, suppose the paschal moon fall on the 18th

of April in any given year, on the following year it would fall on the

7th, in the third year on the 27th of March; and in the fourth year the

moon would full on the 16th of March, but that would not be the paschal

moon, which cannot happen earlier than the 21st; so the following moon

would be the paschal moon, which happens thirty days later, or the 15th of

April; then the fifth year it would fall on the 4th of April, and so on.

The solar and lunar equations or corrections are not made by change of

epacts, for only one line of epacts is used in this work, but these

corrections are made by a change of the day of the month on which the

cycle commences. This change is made at the beginning of a century, and,

of course, does not occur but once in a hundred years, and frequently no

change is made for two, and even three hundred years. The reason for

making these changes has been given in the preceding chapter, (q. v.),

and will again be noticed in the proper place. The line of epacts used are

thus represented, commencing with a cipher as the point of departure: 0,

11, 22, 3, 14, 25, 6, 17, 28, 9, 20, 1, 12, 23, 4, 15, 26, 7, 18. It

should be borne in mind that the epacts are obtained by successively

adding eleven to the epact of the former year, and rejecting thirty as

often as the sum exceeds or equals that number. But, as the intercalary

month inserted at the end of the cycle contains only 29 days, add twelve

instead of eleven, to eighteen, the last of the cycle, and then reject

thirty as before; thus, 18 + 12 = 30; then 30 - 30 = 0. The cycle being

completed, we again commence with the cipher as the point of departure.

After having found the paschal full moons for one lunar cycle, a period of

nineteen years, then the paschal moons again occur in the same order, on

the same days of the month, as they did nineteen years before. Now, as has

also been shown in the preceding chapter, this cycle might have been

continued indefinitely had the Julian intercalation been followed without

correction, and the cycle been perfectly exact; but neither of these being

true, two equations or corrections must be made, one depending on the

error of the Julian calendar, which is called the solar-equation; the

other on the error of the lunar cycle, which is called the lunar equation.

Every omission of the intercalary day, which occurs three times in 400

years, will cause the full moons to fall one day later; for example, on

the 13th of the month instead of the 12th. On the other hand, as has also

been shown in the preceding chapter, the error of the lunar cycle is one

day in 300 years; so that at the end of every 300 years the full moons

will fall one day earlier, for example, on the 11th of the month instead

of the 12th. Now, when both equations occur together, they compensate each

other; that is, while the solar equation would cause the full moon to fall

on the 13th, the lunar equation would make it fall on the 11th; therefore,

no correction is to be made--there is nothing to correct. Had they

occurred singly, the full moon, at the beginning of the cycle, would have

fallen either on the 13th or the 11th; but as they occur together, no

change is made; and the full moons of the calendar will remain as they are

for the next one hundred years.

Hence, the date of Easter may very easily be determined, as indicated in

the following tables (q. v.). It is known by actual calculation that the

paschal full moon fell on the 12th of April in the year 1596, which moon

was the first of a cycle after the reformation of the calendar by Gregory.

Now, by taking the epact of the following years of the cycle, which are

11, 22, 3, 14, 25, etc., from 12, the date of the first paschal moon, and

you will have all the moons of the cycle. Of course, the epacts 22, 25,

etc., cannot be taken from 12, but being carried back from the 12th of

April, they will show on what day in March the full moons fall. When the

epacts are greater than 12, it would be more convenient to take them from

43, as the number of days in March being 31, so 12 + 31 = 43.

To find the paschal moons of the cycle, we have then this rule: If the

epact is less than 12, take it from 12; if greater, take it from 43, and

the remainder will be the date of the paschal moon; unless the full moon

fall before the 21st of March, in which case the following moon will be

the paschal moon, which happens thirty days later. But when the solar

equation occurs in 1710, causing the cycle to commence with the 13th of

April, then the epacts must be taken from 13, or 13 + 31 = 44. And again

in 1900, the correction makes the cycle commence on the 14th of April; so

the number from which the epacts are taken is 14, or 14 + 31 = 45, and so

on. Whenever there is a change of date of the paschal moon in the

beginning of the cycle, as there is again in 2204, 2318 and 2413, etc., as

may be seen in the following tables, then the epacts must be taken from

that date, or that date plus 31, the number of days in March.

Or the date of the paschal moons may very easily be determined by taking

eleven successively from the date of every preceding full moon, and that

will give the date of the paschal moons; only it should be borne in mind

that, whenever the full moon falls before the 21st of March, the following

moon is the paschal moon, which happens thirty days later.

As Easter Sunday is the first Sunday after the paschal full moon, so all

that remains to be done in fixing the date of Easter, is to find the day

of the month on which that Sunday falls; and as this can easily be done by

the use of the dominical letter, which letter and its use in fixing dates

having been fully explained in Part Second, Chapters IV and V, (q. v.), a

repetition seems to be unnecessary here.

-----------+-------+----------+---------+--------+---------

-----------+-------+----------+---------+--------+---------

gf | 1596 | April 12 | 14 | 0 | 1

e | 1597 | " 1 | 6 | 11 | 2

d | 1598 | March 21 | 22 | 22 | 3

c | 1599 | April 9 | 11 | 3 | 4

ba | 1600 | March 29 | 2 | 14 | 5

g | 1601 | April 17 | 22 | 25 | 6

f | 1602 | " 6 | 7 | 6 | 7

e | 1603 | March 26 | 30 | 17 | 8

dc | 1604 | April 14 | 18 | 28 | 9

b | 1605 | " 3 | 10 | 9 | 10

a | 1606 | March 23 | 26 | 20 | 11

g | 1607 | April 11 | 15 | 1 | 12

fe | 1608 | March 31 | 6 | 12 | 13

d | 1609 | April 19 | 26 | 23 | 14

c | 1610 | " 8 | 11 | 4 | 15

b | 1611 | March 28 | 3 | 15 | 16

ag | 1612 | April 16 | 22 | 26 | 17

f | 1613 | " 5 | 7 | 7 | 18

e | 1614 | March 25 | 30 | 18 | 19

d | 1615 | April 12 | 19 | 0 | 1

cb | 1616 | " 1 | 3 | 11 | 2

a | 1617 | March 21 | 26 | 22 | 3

g | 1618 | April 9 | 15 | 3 | 4

f | 1619 | March 29 | 31 | 14 | 5

ed | 1620 | April 17 | 19 | 25 | 6

c | 1621 | " 6 | 11 | 6 | 7

b | 1622 | March 26 | 27 | 17 | 8

a | 1623 | April 14 | 16 | 28 | 9

gf | 1624 | " 3 | 7 | 9 | 10

e | 1625 | March 23 | 30 | 20 | 11

d | 1626 | April 11 | 12 | 1 | 12

c | 1627 | March 31 | 4 | 12 | 13

ba | 1628 | April 19 | 23 | 23 | 14

g | 1629 | " 8 | 15 | 4 | 15

f | 1630 | March 28 | 31 | 15 | 16

e | 1631 | April 16 | 20 | 26 | 17

dc | 1632 | " 5 | 11 | 7 | 18

b | 1633 | March 25 | 27 | 18 | 19

-----------+-------+----------+---------+--------+---------

By close examination of the above tables, it will be seen that there is

just eleven days difference in the date of these paschal moons, from year

to year, through the whole lunar cycle, and through all lunar cycles. In

determining the date of Easter, it will also be seen, that whenever the

full moon falls before the 21st of March, then the following moon, which

happens thirty days later, is the paschal moon, as the 21st of March is

its earliest possible date. Also when the cycle is

-----------+-------+----------+---------+--------+---------

-----------+-------+----------+---------+--------+---------

a | 1634 | April 12 | 16 | 0 | 1

g | 1635 | " 1 | 8 | 11 | 2

fe | 1636 | March 21 | 23 | 22 | 3

d | 1637 | April 9 | 12 | 3 | 4

c | 1638 | March 29 | 4 | 14 | 5

b | 1639 | April 17 | 24 | 25 | 6

ag | 1640 | " 6 | 8 | 6 | 7

f | 1641 | March 26 | 31 | 17 | 8

e | 1642 | April 24 | 20 | 28 | 9

d | 1643 | " 3 | 5 | 9 | 10

cb | 1644 | March 23 | 27 | 20 | 11

a | 1645 | April 11 | 16 | 1 | 12

g | 1646 | March 31 | 1 | 12 | 13

f | 1647 | April 19 | 21 | 23 | 14

ed | 1648 | " 8 | 12 | 4 | 15

c | 1649 | March 28 | 4 | 15 | 16

b | 1650 | April 16 | 17 | 26 | 17

a | 1651 | " 5 | 9 | 7 | 18

gf | 1652 | March 25 | 31 | 18 | 19

e | 1653 | April 12 | 13 | 0 | 1

d | 1654 | " 1 | 5 | 11 | 2

c | 1655 | March 21 | 28 | 22 | 3

ba | 1656 | April 9 | 16 | 3 | 4

g | 1657 | March 29 | 1 | 14 | 5

f | 1658 | April 17 | 21 | 25 | 6

e | 1659 | " 6 | 13 | 6 | 7

dc | 1660 | March 26 | 28 | 17 | 8

b | 1661 | April 14 | 17 | 28 | 9

a | 1662 | " 3 | 9 | 9 | 10

g | 1663 | March 23 | 25 | 20 | 11

fe | 1664 | April 11 | 13 | 1 | 12

d | 1665 | March 31 | 5 | 12 | 13

c | 1666 | April 19 | 25 | 23 | 14

b | 1667 | " 8 | 10 | 4 | 15

ag | 1668 | March 28 | 1 | 15 | 16

f | 1669 | April 16 | 21 | 26 | 17

e | 1670 | " 5 | 6 | 7 | 18

d | 1671 | March 25 | 29 | 18 | 19

-----------+-------+----------+---------+--------+---------

completed, then the paschal moons again occur in the same order, on the

same day of the month as they did nineteen years before. Now this cycle is

six times repeated in a period of 114 years, when the intercalary day

being suppressed in 1700, causes the first paschal moon of the cycle to

fall on the 13th of April instead of the 12th, and all the moons of the

cycle to fall one day later than they would had the correction not been

made. The cycle is now repeated ten times without

-----------+-------+----------+---------+--------+---------

-----------+-------+----------+---------+--------+---------

cb | 1672 | April 12 | 17 | 0 | 1

a | 1673 | " 1 | 2 | 11 | 2

g | 1674 | March 21 | 25 | 22 | 3

f | 1675 | April 9 | 14 | 3 | 4

ed | 1676 | March 29 | 5 | 14 | 5

c | 1677 | April 17 | 18 | 25 | 6

b | 1678 | " 6 | 10 | 6 | 7

a | 1679 | March 26 | 2 | 17 | 8

gf | 1680 | April 24 | 21 | 28 | 9

e | 1681 | " 3 | 6 | 9 | 10

d | 1682 | March 23 | 29 | 20 | 11

c | 1683 | April 11 | 18 | 1 | 12

ba | 1684 | March 31 | 2 | 12 | 13

g | 1685 | April 19 | 22 | 23 | 14

f | 1686 | " 8 | 14 | 4 | 15

e | 1687 | March 28 | 30 | 15 | 16

dc | 1688 | April 16 | 18 | 26 | 17

b | 1689 | " 5 | 10 | 7 | 18

a | 1690 | March 25 | 26 | 18 | 19

g | 1691 | April 12 | 15 | 0 | 1

fe | 1692 | " 1 | 6 | 11 | 2

d | 1693 | March 21 | 22 | 22 | 3

c | 1694 | April 9 | 11 | 3 | 4

b | 1695 | March 29 | 3 | 14 | 5

ag | 1696 | April 17 | 22 | 25 | 6

f | 1697 | " 6 | 7 | 6 | 7

e | 1698 | March 26 | 30 | 17 | 8

d | 1699 | April 14 | 19 | 28 | 9

c | 1700 | " 3 | 4 | 9 | 10

b | 1701 | March 23 | 27 | 20 | 11

a | 1702 | April 11 | 16 | 1 | 12

g | 1703 | March 31 | 1 | 12 | 13

fe | 1704 | April 19 | 20 | 23 | 14

d | 1705 | " 8 | 12 | 4 | 15

c | 1706 | March 28 | 4 | 15 | 16

b | 1707 | April 16 | 17 | 26 | 17

ag | 1708 | " 5 | 8 | 7 | 18

f | 1709 | March 25 | 31 | 18 | 19

-----------+-------+----------+---------+--------+---------

correction, that is, till the year 1900, a period of 190 years, when the

intercalation being again suppressed, causes the first paschal moon of the

cycle to fall on the 14th of April, and, of course, all the other moons of

the cycle to fall one day later. The reason the correction is not made the

first year of the century is, the lunar cycle must first be completed, and

that did not occur until 1710. As 100 is not a multiple of 19, the number

of years in the cycle, and, as the corrections

-----------+-------+----------+---------+--------+---------

-----------+-------+----------+---------+--------+---------

e | 1710 | April 13 | 20 | 0 | 1

d | 1711 | " 2 | 5 | 11 | 2

cb | 1712 | March 22 | 27 | 22 | 3

a | 1713 | April 10 | 16 | 3 | 4

g | 1714 | March 30 | 1 | 14 | 5

f | 1715 | April 18 | 21 | 25 | 6

ed | 1716 | " 7 | 12 | 6 | 7

c | 1717 | March 27 | 28 | 17 | 8

b | 1718 | April 15 | 17 | 28 | 9

a | 1719 | " 4 | 9 | 9 | 10

gf | 1720 | March 24 | 31 | 20 | 11

e | 1721 | April 12 | 13 | 1 | 12

d | 1722 | " 1 | 5 | 12 | 13

c | 1723 | March 21 | 28 | 23 | 14

ba | 1724 | April 9 | 16 | 4 | 15

g | 1725 | March 29 | 1 | 15 | 16

f | 1726 | April 17 | 21 | 26 | 17

e | 1727 | " 6 | 13 | 7 | 18

dc | 1728 | March 26 | 28 | 18 | 19

b | 1729 | April 13 | 17 | 0 | 1

a | 1730 | " 2 | 9 | 11 | 2

g | 1731 | March 22 | 25 | 22 | 3

fe | 1732 | April 10 | 13 | 3 | 4

d | 1733 | March 30 | 5 | 14 | 5

c | 1734 | April 18 | 25 | 25 | 6

b | 1735 | " 7 | 10 | 6 | 7

ag | 1736 | March 27 | 1 | 17 | 8

f | 1737 | April 15 | 21 | 28 | 9

e | 1738 | " 4 | 6 | 9 | 10

d | 1739 | March 24 | 29 | 20 | 11

cb | 1740 | April 12 | 17 | 1 | 12

a | 1741 | " 1 | 2 | 12 | 13

g | 1742 | March 21 | 25 | 23 | 14

f | 1743 | April 9 | 14 | 4 | 15

ed | 1744 | March 29 | 5 | 15 | 16

c | 1745 | April 17 | 18 | 26 | 17

b | 1746 | " 6 | 10 | 7 | 18

a | 1747 | March 26 | 2 | 18 | 19

-----------+-------+----------+---------+--------+---------

cannot be made only at the beginning of the cycle, so they cannot be made

the first year of the century only once in 1900 years. It may be seen from

one of the above tables that the correction is made in the year 1900, for

the reason that that is the first century which is a multiple of 19. The

next centurial year that is exactly divisible by 19, is 3800. Therefore,

none of the corrections for the next 1900 years, will occur on the first

year of the century. It may also be seen from

-----------+-------+----------+---------+--------+---------

-----------+-------+----------+---------+--------+---------

gf | 1748 | April 13 | 14 | 0 | 1

e | 1749 | " 2 | 6 | 11 | 2

d | 1750 | March 22 | 29 | 22 | 3

c | 1751 | April 10 | 11 | 3 | 4

ba | 1752 | March 30 | 2 | 14 | 5

g | 1753 | April 18 | 22 | 25 | 6

f | 1754 | " 7 | 14 | 6 | 7

e | 1755 | March 27 | 30 | 17 | 8

dc | 1756 | April 15 | 18 | 28 | 9

b | 1757 | " 4 | 10 | 9 | 10

a | 1758 | March 24 | 26 | 20 | 11

g | 1759 | April 12 | 15 | 1 | 12

fe | 1760 | " 1 | 6 | 12 | 13

d | 1761 | March 21 | 22 | 23 | 14

c | 1762 | April 9 | 11 | 4 | 15

b | 1763 | March 29 | 3 | 15 | 16

ag | 1764 | April 17 | 22 | 26 | 17

f | 1765 | " 6 | 7 | 7 | 18

e | 1766 | March 26 | 30 | 18 | 19

d | 1767 | April 13 | 19 | 0 | 1

cb | 1768 | " 2 | 3 | 11 | 2

a | 1769 | March 22 | 26 | 22 | 3

g | 1770 | April 10 | 15 | 3 | 4

f | 1771 | March 30 | 31 | 14 | 5

ed | 1772 | April 18 | 19 | 25 | 6

c | 1773 | " 7 | 11 | 6 | 7

b | 1774 | March 27 | 3 | 17 | 8

a | 1775 | April 15 | 16 | 28 | 9

gf | 1776 | " 4 | 7 | 9 | 10

e | 1777 | March 24 | 30 | 20 | 11

d | 1778 | April 12 | 19 | 1 | 12

c | 1779 | " 1 | 4 | 12 | 13

ba | 1780 | March 21 | 26 | 23 | 14

g | 1781 | April 9 | 15 | 4 | 15

f | 1782 | March 29 | 31 | 15 | 16

e | 1783 | April 17 | 20 | 26 | 17

dc | 1784 | " 6 | 11 | 7 | 18

b | 1785 | March 26 | 27 | 18 | 19

----------+-------+----------+---------+--------+----------

the above tables, that, though the intercalary day was suppressed in the

year 1800, no change is made in the date of the paschal moon. The reason

is, the lunar equation also occurred; while the former correction would

cause the paschal moon to fall one day later, that is on the 14th day of

April, the latter would make it fall one day earlier, that is on the 12th;

so they compensate each other, and there is no correction to be made until

the year 1900, when the solar equation

-----------+-------+----------+---------+--------+---------

-----------+-------+----------+---------+--------+---------

a | 1786 | April 13 | 16 | 0 | 1

g | 1787 | " 2 | 8 | 11 | 2

fe | 1788 | March 22 | 23 | 22 | 3

d | 1789 | April 10 | 12 | 3 | 4

c | 1790 | March 30 | 4 | 14 | 5

b | 1791 | April 18 | 24 | 25 | 6

ag | 1792 | " 7 | 8 | 6 | 7

f | 1793 | March 27 | 31 | 17 | 8

e | 1794 | April 15 | 20 | 28 | 9

d | 1795 | " 4 | 5 | 9 | 10

cb | 1796 | March 24 | 27 | 20 | 11

a | 1797 | April 12 | 16 | 1 | 12

g | 1798 | " 1 | 8 | 12 | 13

f | 1799 | March 21 | 24 | 23 | 14

e | 1800 | April 9 | 13 | 4 | 15

d | 1801 | March 29 | 5 | 15 | 16

c | 1802 | April 17 | 18 | 26 | 17

b | 1803 | " 6 | 10 | 7 | 18

ag | 1804 | March 26 | 1 | 18 | 19

f | 1805 | April 13 | 14 | 0 | 1

e | 1806 | " 2 | 6 | 11 | 2

d | 1807 | March 22 | 29 | 22 | 3

cb | 1808 | April 10 | 17 | 3 | 4

a | 1809 | March 30 | 2 | 14 | 5

g | 1810 | April 18 | 22 | 25 | 6

f | 1811 | " 7 | 14 | 6 | 7

ed | 1812 | March 27 | 29 | 17 | 8

c | 1813 | April 15 | 18 | 28 | 9

b | 1814 | " 4 | 10 | 9 | 10

a | 1815 | March 24 | 26 | 20 | 11

gf | 1816 | April 12 | 14 | 1 | 12

e | 1817 | " 1 | 6 | 12 | 13

d | 1818 | March 21 | 22 | 23 | 14

c | 1819 | April 9 | 11 | 4 | 15

ba | 1820 | March 29 | 2 | 15 | 16

g | 1821 | April 17 | 22 | 26 | 17

f | 1822 | " 6 | 7 | 7 | 18

e | 1823 | March 26 | 30 | 18 | 19

----------+-------+----------+---------+--------+----------

again occurs, and the first paschal moon of the cycle falls on the 14th;

which cycle is repeated sixteen times in a period of 304 years, after

which, in 2204, the date of the first paschal moon is the 15th of April.

The reason there is no correction to make in this long period is, first,

the year 2000 is a common year in the Gregorian calendar; second, in the

year 2100 both the solar and the lunar equations again occur, and

occurring together, they compensate each other; consequently

-----------+-------+----------+---------+--------+---------

-----------+-------+----------+---------+--------+---------

dc | 1824 | April 13 | 17 | 0 | 1

b | 1825 | " 2 | 2 | 11 | 2

a | 1826 | March 22 | 25 | 22 | 3

g | 1827 | April 10 | 14 | 3 | 4

fe | 1828 | March 30 | 5 | 14 | 5

d | 1829 | April 18 | 18 | 25 | 6

c | 1830 | " 7 | 10 | 6 | 7

b | 1831 | March 27 | 2 | 17 | 8

ag | 1832 | April 15 | 21 | 28 | 9

f | 1833 | " 4 | 6 | 9 | 10

e | 1834 | March 24 | 29 | 20 | 11

d | 1835 | April 12 | 18 | 1 | 12

cb | 1836 | " 1 | 2 | 12 | 13

a | 1837 | March 21 | 22 | 23 | 14

g | 1838 | " 9 | 14 | 4 | 15

f | 1839 | March 29 | 30 | 15 | 16

ed | 1840 | April 17 | 18 | 26 | 17

c | 1841 | " 6 | 10 | 7 | 18

b | 1842 | March 26 | 26 | 18 | 19

a | 1843 | April 13 | 15 | 0 | 1

gf | 1844 | " 2 | 6 | 11 | 2

e | 1845 | March 22 | 22 | 22 | 3

d | 1846 | April 10 | 11 | 3 | 4

c | 1847 | March 30 | 3 | 14 | 5

ba | 1848 | April 18 | 22 | 25 | 6

g | 1849 | " 7 | 7 | 6 | 7

f | 1850 | March 27 | 30 | 17 | 8

e | 1851 | April 15 | 19 | 28 | 9

dc | 1852 | " 4 | 4 | 9 | 10

b | 1853 | March 24 | 27 | 20 | 11

a | 1854 | April 12 | 16 | 1 | 12

g | 1855 | " 1 | 1 | 12 | 13

fe | 1856 | March 21 | 20 | 23 | 14

d | 1857 | " 9 | 12 | 4 | 15

c | 1858 | March 29 | 4 | 15 | 16

b | 1859 | April 17 | 17 | 26 | 17

ag | 1860 | " 6 | 8 | 7 | 18

f | 1861 | March 26 | 31 | 18 | 19

----------+-------+----------+---------+--------+----------

the cycle is continued until 2204, after which, as has already been

stated, the date of the first paschal moon is the 15th of April. This

cycle is repeated six times in a period of 114 years, when in 2318, for

reasons already given, the date of the first paschal moon of the next

cycle falls on the 16th, and is repeated five times in a period of 95

years, when, in 2413, the lunar equation occurs alone, and the date of the

first paschal moon for the next 95 years, that is till the year 2508,

-----------+-------+----------+---------+--------+---------

-----------+-------+----------+---------+--------+---------

e | 1862 | April 13 | 20 | 0 | 1

d | 1863 | " 2 | 5 | 11 | 2

cb | 1864 | March 22 | 27 | 22 | 3

a | 1865 | April 10 | 16 | 3 | 4

g | 1866 | March 30 | 1 | 14 | 5

f | 1867 | April 18 | 21 | 25 | 6

ed | 1868 | " 7 | 12 | 6 | 7

c | 1869 | March 27 | 28 | 17 | 8

b | 1870 | April 15 | 17 | 28 | 9

a | 1871 | " 4 | 9 | 9 | 10

gf | 1872 | March 24 | 31 | 20 | 11

e | 1873 | April 12 | 13 | 1 | 12

d | 1874 | " 1 | 5 | 12 | 13

c | 1875 | March 21 | 28 | 23 | 14

ba | 1876 | April 9 | 16 | 4 | 15

g | 1877 | March 29 | 1 | 15 | 16

f | 1878 | April 17 | 21 | 26 | 17

e | 1879 | " 6 | 13 | 7 | 18

dc | 1880 | March 26 | 28 | 18 | 19

b | 1881 | April 13 | 17 | 0 | 1

a | 1882 | " 2 | 9 | 11 | 2

g | 1883 | March 22 | 25 | 22 | 3

fe | 1884 | April 10 | 13 | 3 | 4

d | 1885 | March 30 | 5 | 14 | 5

c | 1886 | April 18 | 25 | 25 | 6

b | 1887 | " 7 | 10 | 6 | 7

ag | 1888 | March 27 | 1 | 17 | 8

f | 1889 | April 15 | 21 | 28 | 9

e | 1890 | " 4 | 6 | 9 | 10

d | 1891 | March 24 | 29 | 20 | 11

cb | 1892 | April 12 | 17 | 1 | 12

a | 1893 | " 1 | 2 | 12 | 13

g | 1894 | March 21 | 25 | 23 | 14

f | 1895 | April 9 | 14 | 4 | 15

ed | 1896 | March 29 | 5 | 15 | 16

c | 1897 | April 17 | 18 | 26 | 17

b | 1898 | " 6 | 10 | 7 | 18

a | 1899 | March 26 | 2 | 18 | 19

----------+-------+----------+---------+--------+----------

falls back to the 15th of April. After which the 16th, on account of the

solar equation, is again the date of the first paschal moon of the cycle

for another period of 95 years; that is till the year 2603, when the solar

equation causes the first paschal moon to fall on the 17th, which cycle is

repeated sixteen times during another period of 304 years, after which, in

2907, the correction makes the date of the first paschal moon of the

-----------+-------+----------+---------+--------+---------

-----------+-------+----------+---------+--------+---------

g | 1900 | April 14 | 15 | 0 | 1

f | 1901 | " 3 | 7 | 11 | 2

e | 1902 | March 23 | 30 | 22 | 3

d | 1903 | April 11 | 12 | 3 | 4

cb | 1904 | March 31 | 3 | 14 | 5

a | 1905 | April 19 | 23 | 25 | 6

g | 1906 | " 8 | 15 | 6 | 7

f | 1907 | March 28 | 31 | 17 | 8

ed | 1908 | April 16 | 19 | 28 | 9

c | 1909 | " 5 | 11 | 9 | 10

b | 1910 | March 25 | 27 | 20 | 11

a | 1911 | April 13 | 16 | 1 | 12

gf | 1912 | " 2 | 7 | 12 | 13

e | 1913 | March 22 | 23 | 23 | 14

d | 1914 | April 10 | 12 | 4 | 15

c | 1915 | March 30 | 4 | 15 | 16

ba | 1916 | April 18 | 23 | 26 | 17

g | 1917 | " 7 | 8 | 7 | 18

f | 1918 | March 27 | 31 | 18 | 19

e | 1919 | April 14 | 20 | 0 | 1

dc | 1920 | " 3 | 4 | 11 | 2

b | 1921 | March 23 | 27 | 22 | 3

a | 1922 | April 11 | 16 | 3 | 4

g | 1923 | March 31 | 1 | 14 | 5

fe | 1924 | April 19 | 20 | 25 | 6

d | 1925 | " 8 | 12 | 6 | 7

c | 1926 | March 28 | 4 | 17 | 8

b | 1927 | April 16 | 17 | 28 | 9

ag | 1928 | " 5 | 8 | 9 | 10

f | 1929 | March 25 | 31 | 20 | 11

e | 1930 | April 13 | 20 | 1 | 12

d | 1931 | " 2 | 5 | 12 | 13

cb | 1932 | March 22 | 27 | 23 | 14

a | 1933 | April 10 | 16 | 4 | 15

g | 1934 | March 30 | 1 | 15 | 16

f | 1935 | April 18 | 21 | 26 | 17

ed | 1936 | " 7 | 12 | 7 | 18

c | 1937 | March 27 | 28 | 18 | 19

-----------+-------+----------+---------+--------+---------

cycle, the 18th of April, which cycle is continued without correction till

the year 3116, a period of 209 years. By reference to the above tables, it

will be seen that the solar and lunar equations occur together in the year

2700 and compensate each other; also, that the year 2800 is a common year

in the Gregorian calendar; consequently there is no correction to make

from 2603 to 2907; also the two equations occur together

-----------+-------+----------+---------+--------+---------

-----------+-------+----------+---------+--------+---------

b | 1938 | April 14 | 17 | 0 | 1

a | 1939 | " 3 | 9 | 11 | 2

gf | 1940 | March 23 | 24 | 22 | 3

e | 1941 | April 11 | 13 | 3 | 4

d | 1942 | March 31 | 5 | 14 | 5

c | 1943 | April 19 | 25 | 25 | 6

ba | 1944 | " 8 | 9 | 6 | 7

g | 1945 | March 28 | 1 | 17 | 8

f | 1946 | April 16 | 21 | 28 | 9

e | 1947 | " 5 | 6 | 9 | 10

dc | 1948 | March 25 | 28 | 20 | 11

b | 1949 | April 13 | 17 | 1 | 12

a | 1950 | " 2 | 9 | 12 | 13

g | 1951 | March 22 | 25 | 23 | 14

fe | 1952 | April 10 | 13 | 4 | 15

d | 1953 | March 30 | 5 | 15 | 16

c | 1954 | April 18 | 25 | 26 | 17

b | 1955 | " 7 | 10 | 7 | 18

ag | 1956 | March 27 | 1 | 18 | 19

f | 1957 | April 14 | 21 | 0 | 1

e | 1958 | " 3 | 6 | 11 | 2

d | 1959 | March 23 | 29 | 22 | 3

cb | 1960 | April 11 | 17 | 3 | 4

a | 1961 | March 31 | 2 | 14 | 5

g | 1962 | April 19 | 22 | 25 | 6

f | 1963 | " 8 | 14 | 6 | 7

ed | 1964 | March 28 | 29 | 17 | 8

c | 1965 | April 16 | 18 | 28 | 9

b | 1966 | " 5 | 10 | 9 | 10

a | 1967 | March 25 | 26 | 20 | 11

gf | 1968 | April 13 | 14 | 1 | 12

e | 1969 | " 2 | 6 | 12 | 13

d | 1970 | March 22 | 29 | 23 | 14

c | 1971 | April 10 | 11 | 4 | 15

ba | 1972 | March 30 | 2 | 15 | 16

g | 1973 | April 18 | 22 | 26 | 17

f | 1974 | " 7 | 14 | 7 | 18

e | 1975 | March 27 | 30 | 18 | 19

-----------+-------+----------+---------+--------+---------

again in the year 3000 and compensate each other, is the reason there is

no correction to make from 2907 to 3116, after which the first paschal

moon falls on the 19th, and is repeated fifteen times in a period of 285

years, that is till the year 3401, when the correction makes the 20th of

April, the date of the full moon, but that cannot be the paschal moon,

which cannot happen later than the 19th; consequently the

-----------+-------+----------+---------+--------+---------

-----------+-------+----------+---------+--------+---------

dc | 1976 | April 14 | 18 | 0 | 1

b | 1977 | " 3 | 10 | 11 | 2

a | 1978 | March 23 | 26 | 22 | 3

g | 1979 | April 11 | 15 | 3 | 4

fe | 1980 | March 31 | 6 | 14 | 5

d | 1981 | April 19 | 26 | 25 | 6

c | 1982 | " 8 | 11 | 6 | 7

b | 1983 | March 28 | 3 | 17 | 8

ag | 1984 | April 16 | 22 | 28 | 9

f | 1985 | " 5 | 7 | 9 | 10

e | 1986 | March 25 | 30 | 20 | 11

d | 1987 | April 13 | 19 | 1 | 12

cb | 1988 | " 2 | 3 | 12 | 13

a | 1989 | March 22 | 26 | 23 | 14

g | 1990 | April 10 | 15 | 4 | 15

f | 1991 | March 30 | 31 | 15 | 16

ed | 1992 | April 18 | 19 | 26 | 17

c | 1993 | " 7 | 11 | 7 | 18

b | 1994 | March 27 | 3 | 18 | 19

a | 1995 | April 14 | 16 | 0 | 1

gf | 1996 | " 3 | 7 | 11 | 2

e | 1997 | March 23 | 30 | 22 | 3

d | 1998 | April 11 | 12 | 3 | 4

c | 1999 | March 31 | 4 | 14 | 5

ba | 2000 | April 19 | 23 | 25 | 6

g | 2001 | " 8 | 15 | 6 | 7

f | 2002 | March 28 | 31 | 17 | 8

e | 2003 | April 16 | 20 | 28 | 9

dc | 2004 | " 5 | 11 | 9 | 10

b | 2005 | March 25 | 27 | 20 | 11

a | 2006 | April 13 | 16 | 1 | 12

g | 2007 | " 2 | 8 | 12 | 13

fe | 2008 | March 22 | 23 | 23 | 14

d | 2009 | April 10 | 12 | 4 | 15

c | 2010 | March 30 | 4 | 15 | 16

b | 2011 | April 18 | 24 | 26 | 17

ag | 2012 | " 7 | 8 | 7 | 18

f | 2013 | March 27 | 31 | 18 | 19

-----------+-------+----------+---------+--------+---------

moon that precedes it by thirty days, and which falls on the 21st of

March, is the date of the first paschal moon of the cycle which commences

with the year 3401. The day of the month on which Easter Sunday has fallen

or will fall, from the year 1596 to 2013, is already determined, and may

be seen by reference to the above tables. From 2013 to 3401, the date of

Easter is determined for one lunar cycle only, at the

-----------+-------+----------+---------+--------+---------

-----------+-------+----------+---------+--------+---------

ag | 2204 | April 15 | 22 | 0 | 1

f | 2205 | " 4 | 7 | 11 | 2

e | 2206 | March 24 | 30 | 22 | 3

d | 2207 | April 12 | 19 | 3 | 4

cb | 2208 | " 1 | 3 | 14 | 5

a | 2209 | March 21 | 26 | 25 | 6

g | 2210 | April 9 | 15 | 6 | 7

f | 2211 | March 29 | 31 | 17 | 8

ed | 2212 | April 17 | 19 | 28 | 9

c | 2213 | " 6 | 11 | 9 | 10

b | 2214 | March 26 | 27 | 20 | 11

a | 2215 | April 14 | 16 | 1 | 12

gf | 2216 | " 3 | 7 | 12 | 13

e | 2217 | March 23 | 30 | 23 | 14

d | 2218 | April 11 | 12 | 4 | 15

c | 2219 | March 31 | 4 | 15 | 16

ba | 2220 | April 19 | 23 | 26 | 17

g | 2221 | " 8 | 15 | 7 | 18

f | 2222 | March 28 | 31 | 18 | 19

f | 2318 | April 16 | 21 | 0 | 1

e | 2319 | " 5 | 6 | 11 | 2

dc | 2320 | March 25 | 28 | 22 | 3

b | 2321 | April 13 | 17 | 3 | 4

a | 2322 | " 2 | 9 | 14 | 5

g | 2323 | March 22 | 25 | 25 | 6

fe | 2324 | April 10 | 13 | 6 | 7

d | 2325 | March 30 | 5 | 17 | 8

c | 2326 | April 18 | 25 | 28 | 9

b | 2327 | " 7 | 10 | 9 | 10

ag | 2328 | March 27 | 1 | 20 | 11

f | 2329 | April 15 | 21 | 1 | 12

e | 2330 | " 4 | 6 | 12 | 13

d | 2331 | March 24 | 29 | 23 | 14

cb | 2332 | April 12 | 17 | 4 | 15

a | 2333 | " 1 | 2 | 15 | 16

g | 2334 | March 21 | 25 | 26 | 17

f | 2335 | April 9 | 14 | 7 | 18

ed | 2336 | March 29 | 5 | 18 | 19

-----------+-------+----------+---------+--------+---------

beginning of each period; for the reason that it was deemed unnecessary,

because the paschal moons, the epacts, and the Golden Numbers are the same

for every cycle in the period. Therefore, all that remains to be done is

to find the day of the month on which the first Sunday, after the paschal

moon, falls. The dominical letters for any period may very easily be found

by counting backwards one letter each year for every common

-----------+-------+----------+---------+--------+---------

-----------+-------+----------+---------+--------+---------

f | 2413 | April 15 | 21 | 0 | 1

e | 2414 | " 4 | 6 | 11 | 2

d | 2415 | March 24 | 29 | 22 | 3

cb | 2416 | April 12 | 17 | 3 | 4

a | 2417 | " 1 | 2 | 14 | 5

g | 2418 | March 21 | 25 | 25 | 6

f | 2419 | April 9 | 14 | 6 | 7

ed | 2420 | March 29 | 5 | 17 | 8

c | 2421 | April 17 | 18 | 28 | 9

b | 2422 | " 6 | 10 | 9 | 10

a | 2423 | March 26 | 2 | 20 | 11

gf | 2424 | April 14 | 21 | 1 | 12

e | 2425 | " 3 | 6 | 12 | 13

d | 2426 | March 23 | 29 | 23 | 14

c | 2427 | April 11 | 18 | 4 | 15

ba | 2428 | March 31 | 2 | 15 | 16

g | 2429 | April 19 | 22 | 26 | 17

f | 2430 | " 8 | 14 | 7 | 18

e | 2431 | March 28 | 30 | 18 | 19

ag | 2508 | April 16 | 22 | 0 | 1

f | 2509 | " 5 | 7 | 11 | 2

e | 2510 | March 25 | 30 | 22 | 3

d | 2511 | April 13 | 19 | 3 | 4

cb | 2512 | " 2 | 3 | 14 | 5

a | 2513 | March 22 | 26 | 25 | 6

g | 2514 | April 10 | 15 | 6 | 7

f | 2515 | March 30 | 31 | 17 | 8

ed | 2516 | April 18 | 19 | 28 | 9

c | 2617 | " 7 | 11 | 9 | 10

b | 2518 | March 27 | 3 | 20 | 11

a | 2519 | April 15 | 16 | 1 | 12

gf | 2520 | " 4 | 7 | 12 | 13

e | 2521 | March 24 | 30 | 23 | 14

d | 2522 | April 12 | 19 | 4 | 15

c | 2523 | " 1 | 4 | 15 | 16

ba | 2524 | March 21 | 26 | 26 | 17

g | 2525 | April 9 | 15 | 7 | 18

f | 2526 | March 29 | 31 | 18 | 19

-----------+-------+----------+---------+--------+---------

year, and two for leap-year, the fourth letter being dominical letter for

January and February and the fifth for the rest of the year; thus, if G be

dominical letter for any given year, we would have then, G, F, E, DC; B,

A, G, FE; D, C, B, AG; F, E, D, CB, etc. By counting these letters

backwards, or in the tables, from the bottom of the column upwards, they

will occur in alphabetical order. Again it may be seen by reference

-----------+-------+----------+---------+--------+---------

-----------+-------+----------+---------+--------+---------

b | 2603 | April 17 | 24 | 0 | 1

ag | 2604 | " 6 | 8 | 11 | 2

f | 2605 | March 26 | 31 | 22 | 3

e | 2606 | April 14 | 20 | 3 | 4

d | 2607 | " 3 | 5 | 14 | 5

cb | 2608 | March 23 | 27 | 25 | 6

a | 2609 | April 11 | 16 | 6 | 7

g | 2610 | March 31 | 1 | 17 | 8

f | 2611 | April 19 | 21 | 28 | 9

ed | 2612 | " 8 | 12 | 9 | 10

c | 2613 | March 28 | 4 | 20 | 11

b | 2614 | April 16 | 17 | 1 | 12

a | 2615 | " 5 | 9 | 12 | 13

gf | 2616 | March 25 | 31 | 23 | 14

e | 2617 | April 13 | 20 | 4 | 15

d | 2618 | " 2 | 5 | 15 | 16

c | 2619 | March 22 | 28 | 26 | 17

ba | 2620 | April 10 | 16 | 7 | 18

g | 2621 | March 30 | 1 | 18 | 19

b | 2907 | April 18 | 24 | 0 | 1

ag | 2908 | " 7 | 8 | 11 | 2

f | 2909 | March 27 | 31 | 22 | 3

e | 2910 | April 15 | 20 | 3 | 4

d | 2911 | " 4 | 5 | 14 | 5

cb | 2912 | March 24 | 27 | 25 | 6

a | 2913 | April 12 | 16 | 6 | 7

g | 2914 | " 1 | 8 | 17 | 8

f | 2915 | March 21 | 24 | 28 | 9

ed | 2916 | April 9 | 12 | 9 | 10

c | 2917 | March 29 | 4 | 20 | 11

b | 2918 | April 17 | 24 | 1 | 12

a | 2919 | " 6 | 9 | 12 | 13

gf | 2920 | March 26 | 31 | 23 | 14

e | 2921 | April 14 | 20 | 4 | 15

d | 2922 | " 3 | 5 | 15 | 16

c | 2923 | March 23 | 28 | 26 | 17

ba | 2924 | April 11 | 16 | 7 | 18

g | 2925 | March 31 | 1 | 18 | 19

-----------+-------+----------+---------+--------+---------

to these tables, that Easter occurs less frequently on the 22d of March,

its earliest possible date, and the 25th of April, which has hitherto been

considered its latest possible date, than any of the days intervening. It

cannot happen on the 22d, only when the paschal moon falls on the 21st,

and that day must be Saturday. It fell on the 22d, first, after the

reformation of the calendar by Gregory in 1598; again in 1693, 1761,

-----------+-------+----------+---------+--------+---------

-----------+-------+----------+---------+--------+---------

ba | 3116 | April 19 | 23 | 0 | 1

g | 3117 | " 8 | 15 | 11 | 2

f | 3118 | March 28 | 31 | 22 | 3

e | 3119 | April 16 | 20 | 3 | 4

dc | 3120 | " 5 | 11 | 14 | 5

b | 3121 | March 25 | 27 | 25 | 6

a | 3122 | April 13 | 16 | 6 | 7

g | 3123 | " 2 | 8 | 17 | 8

fe | 3124 | March 22 | 23 | 28 | 9

d | 3125 | April 10 | 12 | 9 | 10

c | 3126 | March 30 | 4 | 20 | 11

b | 3127 | April 18 | 24 | 1 | 12

ag | 3128 | " 7 | 8 | 12 | 13

f | 3129 | March 27 | 31 | 23 | 14

e | 3130 | April 15 | 20 | 4 | 15

d | 3131 | " 4 | 5 | 15 | 16

cb | 3132 | March 24 | 27 | 26 | 17

a | 3133 | April 12 | 16 | 7 | 18

g | 3134 | " 1 | 8 | 18 | 19

d | 3401 | March 21 | 22 | 0 | 1

c | 3402 | April 9 | 11 | 11 | 2

b | 3403 | March 29 | 3 | 22 | 3

ag | 3404 | April 17 | 22 | 3 | 4

f | 3405 | " 6 | 7 | 14 | 5

e | 3406 | March 26 | 30 | 25 | 6

d | 3407 | April 14 | 19 | 6 | 7

cb | 3408 | " 3 | 10 | 17 | 8

a | 3409 | March 23 | 26 | 28 | 9

g | 3410 | April 11 | 15 | 9 | 10

f | 3411 | March 31 | 7 | 20 | 11

ed | 3412 | April 19 | 26 | 1 | 12

c | 3413 | " 8 | 11 | 12 | 13

b | 3414 | March 28 | 3 | 23 | 14

a | 3415 | April 16 | 23 | 4 | 15

gf | 3416 | " 5 | 7 | 15 | 16

e | 3417 | March 25 | 30 | 26 | 17

d | 3418 | April 13 | 19 | 7 | 18

c | 3419 | " 2 | 4 | 18 | 19

-----------+-------+----------+---------+--------+---------

and in 1818. It has not occurred since, nor will not again till 2285, a

period of 467 years. The reason that it does not occur on the 22d of March

in this long period is, the paschal moon does not fall on the 21st, from

the year 1900 to 2204, a period of 304 years. We refer to the tabular

moon, not to the true or astronomical moon, which may occur on the 21st

more than once in this long period.

Our Calendar The Julian calendar and its errors. How corrected by the Gregorian. Rules for finding the dominical letter, and the day of the week of any event from the days of Julius Caesar 46 B.C. to the year of our Lord four thousand; a new and easy method of fixing the date of Easter. Hebrew calendar; showing the correspondence in the date of events recorded in the Bible with our present Gregorian calendar. Illustrated by valuable tables and charts. · 第 6 / 8 章