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.

Dominical Letter.	Year.	Paschal Full Moon.		Easter.	Epact.	Golden Number.
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 Letter.	Year.	Paschal Full Moon.		Easter.	Epact.	Golden Number.
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 Letter.	Year.	Paschal Full Moon.		Easter.	Epact.	Golden Number.
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 Letter.	Year.	Paschal Full Moon.		Easter.	Epact.	Golden Number.
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 Letter.	Year.	Paschal Full Moon.		Easter.	Epact.	Golden Number.
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 Letter.	Year.	Paschal Full Moon.		Easter.	Epact.	Golden Number.
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 Letter.	Year.	Paschal Full Moon.		Easter.	Epact.	Golden Number.
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 Letter.	Year.	Paschal Full Moon.		Easter.	Epact.	Golden Number.
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 Letter.	Year.	Paschal Full Moon.		Easter.	Epact.	Golden Number.
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 Letter.	Year.	Paschal Full Moon.		Easter.	Epact.	Golden Number.
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 Letter.	Year.	Paschal Full Moon.		Easter.	Epact.	Golden Number.
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 Letter.	Year.	Paschal Full Moon.		Easter.	Epact.	Golden Number.
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 Letter.	Year.	Paschal Full Moon.		Easter.	Epact.	Golden Number.
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 Letter.	Year.	Paschal Full Moon.		Easter.	Epact.	Golden Number.
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,

Dominical Letter.	Year.	Paschal Full Moon.		Easter.	Epact.	Golden Number.
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.

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