Our Calendar Part 10

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 repet.i.tion seems to be unnecessary here.

-----------+-------+----------+---------+--------+--------- _Dominical_ _Year._ _Paschal_ _Easter._ _Epact._ _Golden_ _Letter._ _Full_ _Number._ _Moon._ -----------+-------+----------+---------+--------+--------- 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

-----------+-------+----------+---------+--------+--------- _Dominical_ _Year._ _Paschal_ _Easter._ _Epact._ _Golden_ _Letter._ _Full_ _Number._ _Moon._ -----------+-------+----------+---------+--------+--------- 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

-----------+-------+----------+---------+--------+--------- _Dominical_ _Year._ _Paschal_ _Easter._ _Epact._ _Golden_ _Letter._ _Full_ _Number._ _Moon._ -----------+-------+----------+---------+--------+--------- 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

-----------+-------+----------+---------+--------+--------- _Dominical_ _Year._ _Paschal_ _Easter._ _Epact._ _Golden_ _Letter._ _Full_ _Number._ _Moon._ -----------+-------+----------+---------+--------+--------- 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

-----------+-------+----------+---------+--------+--------- _Dominical_ _Year._ _Paschal_ _Easter._ _Epact._ _Golden_ _Letter._ _Full_ _Number._ _Moon._ -----------+-------+----------+---------+--------+--------- 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

-----------+-------+----------+---------+--------+--------- _Dominical_ _Year._ _Paschal_ _Easter._ _Epact._ _Golden_ _Letter._ _Full_ _Number._ _Moon._ -----------+-------+----------+---------+--------+--------- 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

-----------+-------+----------+---------+--------+--------- _Dominical_ _Year._ _Paschal_ _Easter._ _Epact._ _Golden_ _Letter._ _Full_ _Number._ _Moon._ -----------+-------+----------+---------+--------+--------- 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,

-----------+-------+----------+---------+--------+--------- _Dominical_ _Year._ _Paschal_ _Easter._ _Epact._ _Golden_ _Letter._ _Full_ _Number._ _Moon._ -----------+-------+----------+---------+--------+--------- 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

-----------+-------+----------+---------+--------+--------- _Dominical_ _Year._ _Paschal_ _Easter._ _Epact._ _Golden_ _Letter._ _Full_ _Number._ _Moon._ -----------+-------+----------+---------+--------+--------- 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

-----------+-------+----------+---------+--------+--------- _Dominical_ _Year._ _Paschal_ _Easter._ _Epact._ _Golden_ _Letter._ _Full_ _Number._ _Moon._ -----------+-------+----------+---------+--------+--------- 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

-----------+-------+----------+---------+--------+--------- _Dominical_ _Year._ _Paschal_ _Easter._ _Epact._ _Golden_ _Letter._ _Full_ _Number._ _Moon._ -----------+-------+----------+---------+--------+--------- 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

-----------+-------+----------+---------+--------+--------- _Dominical_ _Year._ _Paschal_ _Easter._ _Epact._ _Golden_ _Letter._ _Full_ _Number._ _Moon._ -----------+-------+----------+---------+--------+--------- 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

-----------+-------+----------+---------+--------+--------- _Dominical_ _Year._ _Paschal_ _Easter._ _Epact._ _Golden_ _Letter._ _Full_ _Number._ _Moon._ -----------+-------+----------+---------+--------+--------- 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

-----------+-------+----------+---------+--------+--------- _Dominical_ _Year._ _Paschal_ _Easter._ _Epact._ _Golden_ _Letter._ _Full_ _Number._ _Moon._ -----------+-------+----------+---------+--------+--------- 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. .h.i.therto 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 Sat.u.r.day. It fell on the 22d, first, after the reformation of the calendar by Gregory in 1598; again in 1693, 1761,

-----------+-------+----------+---------+--------+--------- _Dominical_ _Year._ _Paschal_ _Easter._ _Epact._ _Golden_ _Letter._ _Full_ _Number._ _Moon._ -----------+-------+----------+---------+--------+--------- 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.

CHAPTER VII.

CHURCH FEASTS AND FASTS WHOSE DATE DEPEND ON THE DATE OF EASTER.

Feasts, or Festivals, are days set apart by the church, either for the grateful memorial of the most remarkable events connected with the plan of redemption, or upon which to commemorate the actions and sufferings of such persons as have been most instrumental in carrying forward the designs of G.o.d for the salvation of mankind.

The ecclesiastical year is divided into eight seasons, namely: Advent-tide, Christmas-tide, Epiphany-tide, Lenten-tide, Easter-tide, Ascension-tide, Whitsun-tide, and Trinity-tide. The first day of each of these seasons has been, and is now observed by the church in commemoration of some of the most remarkable events connected with the plan of redemption. All these will be noticed in the order in which they occur in the ecclesiastical year, while many other days intervening, which are observed as feasts or fasts, will be given a pa.s.sing notice.

_a_--Advent Sunday, which is the day nearest St. Andrew's Day (Nov. 30), or the first Sunday after the 26th of November, has been recognized since the sixth century as the first day of the ecclesiastical year.

Advent (Latin _Adventus_, the coming,) signifies the coming of our Saviour, the period of the approach of the nativity. As Advent-tide lasts from Advent Sunday to Christmas, the length of the season depends upon the day of the month on which Advent Sunday falls. As it may happen as early as the 27th of November or as late as the 3d of December, so Advent-tide will contain no more than twenty-eight days nor less than twenty-two. It should be borne in mind that, though this festival is cla.s.sed among the movable feasts, it does not depend upon the date of Easter, but upon the day of the month on which Advent Sunday falls. The four Sundays before Christmas were made preparation days for the festival of Christmas, and were called the first, second, third, and fourth Sundays in Advent.

Ember days and Ember weeks are the four seasons set apart by the Western church for special prayer and fasting, and the ordination of clergy; known in the church as _quatuor tempora_, (the four seasons.) The Ember weeks are the weeks next following St. Lucy's Day (Dec. 13th), the first Sunday in Lent, Whitsun Day, and Holy Cross Day (Sept. 14th). The Wednesdays, Fridays and Sat.u.r.days of these weeks are the Ember days distinctively. The name by some is supposed to be derived from a German word signifying Abstinence; by others it is supposed to signify Ashes.

_b_--Christmas (from Christ and the Saxon _maess_, signifying the ma.s.s and a feast), is a festival held in commemoration of the nativity of our Saviour throughout nearly the whole of Christendom. It is occupied, therefore, with the event (the incarnation) which forms the center and turning point of the history of the world. Though the day of Christ's birth cannot be ascertained from the New Testament, nor from any other source, yet the whole Christian world for more than 1300 years have concurred in celebrating the nativity on the 25th of December. This is the first of the four great feasts in the ecclesiastical year; the other three are Easter, Ascension, and Whitsun Day. The length of Christmas-tide or season is twelve days, lasting from the 25th of December to Epiphany.

_c_--Epiphany (Greek _Epiphania_, _Theophania_ or _Christophania_,) is a festival in commemoration of the manifestation of Jesus Christ to the world as the Son of G.o.d, and referring to the appearance of the star which announced our Saviour's birth to the Gentiles, and the visit of the Magi, or wise Men of the East to the infant Jesus. This festival is held on the 6th of January invariably, consequently is not a movable feast, though the length of Epiphany-tide depends upon the date of Easter. As Easter may happen as early as the 22d of March or as late as the 26th of April (a variation of thirty-five days), so Epiphany-tide may consist of no less than twelve days nor more than forty-seven, as the season always ends the day before Septuagesima Sunday. (See tables at the close of this chapter.)

Septuagesima, s.e.xagesima, Quinquagesima. There being exactly fifty days between the Sunday next before Lent and Easter Day, inclusive, that Sunday was termed Quinquagesima, i. e., the fiftieth; and the two immediately preceding Sundays were called from the next round numbers s.e.xagesima, the sixtieth; and Septuagesima, the seventieth.

The Paschal Season extends from Septuagesima Sunday to Low Sunday, a period of seventy days. It takes its name from the Paschal festival or Easter, whose services end with Low Sunday, the octave, or eighth day, of Easter. It begins with Septuagesima Sunday because the church services then begin to prepare the minds of the faithful for the services of Lent, which are themselves the preparation for Easter. May not Septuagesima Sunday be so called because there are just seventy days in the Paschal Season?