Part 36

So the mean time of New Moon in _June_ 1909 _New Style_ is the 18th day at 16 minutes past 9 in the Morning.

If 11 days be added to the time of any New Moon in this Table, it will give the time thereof according to the _New Style_ till the year 1800. And if 14 days 18 hours 22 minutes be added to the mean time of New Moon in either _Style_, it will give the mean time of the next Full Moon according to that _Style_.

+---------------------------------------------------------------------------------------------+ |_A_ TABLE _shewing the times of all the mean Changes of the Moon, to the nearest Hour, | |through four Lunar Periods, or 76 years._ M _signifies morning_, A _afternoon_. | +----+----+-------+------+-----+------+------+------+------+------+------+------+-------+-----+ |Yrs | |January| |March| | May | | July | |Sept. | |Novemb.| | |of |A.D.| |February| |April | | June | |August| |October| |Decemb.| |the +----+------+------+------+------+------+------+------+------+------+------+------+------+ |Cyc.| |D. H. |D. H. |D. H. |D. H. |D. H. |D. H. |D. H. |D. H. |D. H. |D. H. |D. H. |D. H. | +----+----+------+------+------+------+------+------+------+------+------+------+------+------+ | 1 |1724|14 5A|13 5M|13 6A|12 7M|11 8A|10 8M| 9 9A| 8 10M| 6 10A| 6 11M| 4 12A| 4 1A| | | | | | | | 1 4M| | | | | | | | | 2 |1725| 3 2M| 1 2A| 3 3M| 1 4A| |29 6M|28 7A|27 8M|25 8A|25 9M|23 10A|23 11M| | | | | | | |30 5A| | | | | | | | | 3 |1726|21 11A|20 11M|21 12A|20 1A|20 1M|18 2A|18 3M|16 4A|15 5M|14 5A|13 6M|12 7A| | | | | | | | | | | | | | | 2 4M| | 4 |1727|11 8M| 9 9A|11 9M| 9 10A| 9 11M| 7 12A| 7 0A| 6 1M| 4 1A| 4 2M| 2 3A| | | | | | | | | | | | | | | |31 5A| | 5 |1728|30 6M|28 7A|29 7M|27 8A|27 8M|25 9A|25 10M|23 11A|22 11M|21 12A|20 1A|20 2M| | 6 |1729|18 2A|17 3M|18 4A|17 4M|16 5A|15 6M|14 7A|12 7M|11 8A|11 9M| 9 0A| 9 11M| | | | | | | | | | | | 2 5M| | | | | 7 |1730| 7 11A| 6 0A| 8 1M| 6 1A| 6 2M| 4 3A| 4 3M| 2 4A| |30 7M|28 8A|28 9M| | | | | | | | | | | |30 6A| | | | | 8 |1731|26 9A|25 10M|26 10A|25 11M|24 11A|23 0A|23 1M|21 2A|20 2M|19 3A|18 4M|17 5A| | 9 |1732|16 5M|14 6A|15 7M|13 8A|13 8M|11 9A|11 10M| 9 11A| 8 11M| 7 12A| 6 1A| 6 2M| | | | | | | | | 1 6M| | | | | | | | 10 |1733| 4 2A| 3 3M| 4 4A| 3 4M| 2 5A| |30 8M|28 8A|27 9M|26 10A|25 11M|24 11A| | | | | | | | |30 7A| | | | | | | | 11 |1734|23 0A|22 1M|23 1A|22 2M|21 2A|20 3M|19 4A|18 5M|16 5A|16 6M|14 7A|14 8M| | 12 |1735|12 9A|11 9M|12 10A|11 11M|10 11A| 9 0A| 9 1M| 7 2A| 6 2M| 5 3A| 4 4M| 3 5A| | | | 2 5M| | 1 7M| | | | | | | | | | | 13 |1736| | ---- | |29 9M|28 9A|27 10M|26 11A|25 0A|23 12A|23 1A|22 2M|21 3A| | | | |31 6A| |30 8A| | | | | | | | | | | 14 |1737|20 3M|18 4A|20 4M|18 5A|18 5M|16 6A|16 7M|14 8A|13 8M|12 9A|11 10M|10 11A| | | | | | | | | | | | | 2 6M| | | | 15 |1738| 9 11M| 7 12A| 9 1A| 8 1M| 7 2A| 6 3M| 5 4A| 4 5M| 2 5A| |30 8M|29 8A| | | | | | | | | | | | |31 7A| | | | 16 |1739|28 9M|26 10A|28 11M|26 12A|26 0A|25 1M|24 2A|23 3M|21 3A|21 4M|19 5A|19 6M| | 17 |1740|17 6A|16 7M|16 8A|15 9M|14 9A|13 10M|12 11A|11 0A|9 12A| 9 1A| 8 2M| 7 3A| | | | | | | | | | 2 7M| | | | | | | 18 |1741| 6 3M| 4 4A| 6 4M| 4 5A| 4 5M| 2 6A| |30 8M|28 9A|28 10M|26 11A|26 11M| | | | | | | | | |31 7A| | | | | | | 19 |1742|24 12A|23 1A|25 2M|23 3A|23 3M|21 4A|21 5M|19 6A|18 6M|17 7A|16 8M|15 9A| | 20 |1743|14 9M|12 10A|14 11M|12 12A|12 0A|11 1M|10 2A| 9 3M| 7 3A| 7 4M| 5 5A| 5 6M| | | | | | | 1 9M| | | | | | | | | | 21 |1744| 3 6A| 2 7M| 2 8A| |30 10M|28 11A|28 0A|26 12A|25 1A|25 2M|23 3A|23 3M| | | | | | |30 9A| | | | | | | | | | 22 |1745|21 4A|20 5M|21 5A|20 6M|19 6A|18 7M|17 8A|16 8M|14 9A|14 10M|12 11A|12 0A| | | | | | | | | | | | | | | 1 9A| | 23 |1746|10 12A|9 1A|11 2M| 9 3A| 9 3M| 7 4A| 7 5M| 5 6A| 4 6M| 3 7A| 2 8M| | | | | | | | | | | | | | | |31 10M| | 24 |1747|29 10A|28 11M|29 11A|28 0A|27 12A|26 1A|26 2M|24 3A|23 3M|22 4A|21 5M|20 6A| | 25 |1748|19 6M|17 7A|18 8M|16 9A|16 9M|14 10A|14 11M|12 12A|11 0A|11 1M| 9 2A| 9 3M| | | | | | | | | | | 2 9M| | | | | | 26 |1749| 7 3A| 6 4M| 7 5A| 6 6M| 5 6A| 4 7M| 3 8A| |30 10M|29 11A|28 0A|27 12A| | | | | | | | | | |31 9A| | | | | | 27 |1750|26 1A|25 2M|26 3A|25 4M|24 4A|23 5M|22 6A|21 7M|19 7A|19 8M|17 9A|17 10M| | 28 |1751|15 10A|14 11M|15 11A|14 0A|13 12A|12 1A|12 2M|10 3A| 9 3M| 8 4A| 7 5M| 6 6A| | | | | | | | 2 9M| | | | | | | | | 29 |1752| 5 6M| 3 7A| 4 8M| 2 9A| |30 11M|29 12A|28 0A|27 1M|26 2A|25 3M|24 3A| | | | | | | |31 10A| | | | | | | | | 30 |1753|23 4M|21 5A|23 6M|21 7A|21 7M|19 8A|19 9M|17 10A|16 10M|15 11A|14 0A|14 1M| | 31 |1754|12 1A|11 2M|12 3A|11 4M|10 4A| 9 5M| 8 6A| 7 7M| 5 7A| 5 8M| 3 9A| 3 10M| | | | 1 10A| | 1 11A| | | | | | | | | | | 32 |1755| | ---- | |29 12A|29 1A|28 2M|27 3A|25 3M|24 4A|24 5M|22 6A|22 6M| | | |31 11M| |31 0A| | | | | | | | | | | 33 |1756|20 7A|19 8M|19 9A|18 9M|17 10A|16 11M|15 12A|14 1A|13 1M|12 2A|11 3M|10 4A| | | | | | | | | | | | | 1 14A| | | | 34 |1757| 9 4M| 7 5A| 9 6M| 7 7A| 7 7M| 5 8A| 5 9M| 3 10A| 2 10M| |30 1M|29 1A| | | | | | | | | | | | |31 0A| | | | 35 |1758|28 2M|26 3A|28 3M|26 4A|26 4M|24 5A|24 6M|22 7A|21 7M|20 8A|19 9M|18 10A| | 36 |1759|17 10M|15 11A|17 0A|16 1M|15 1A|14 2M|13 3A|12 2M|10 4A|10 5M| 8 6A| 8 7M| | | | | | | | | | 1 12A| | | | | | | 37 |1760| 6 7A| 5 8M| 5 9A| 4 10M| 3 10A| 2 11M| |30 1M|28 2A|28 3M|26 4A|26 4M| | | | | | | | | |31 1A| | | | | | | 38 |1761|24 5A|23 6M|24 7A|23 8M|22 9A|21 10M|20 10A|19 11M|17 11A|17 0A|16 1M|15 2A| | 39 |1762|14 2M|12 3A|14 3M|12 4A|12 4M|10 5A|10 6M|8 7A| 7 7M| 6 8A| 5 9M| 4 10A| +----+----+------+------+------+------+------+------+------+------+------+------+------+------+ | | | | | | | 1 1A| | | | | | | | | 40 |1763| 3 11M| 1 12A| 3 0A| 2 1M| |29 3A|29 4M|27 4M|26 5M|25 6A|24 7M|23 7A| | | | | | | |31 2M| | | | | | | | | 41 |1764|22 8M|20 9A|21 10M|19 11A|19 11M|17 12A|17 1A|16 2M|14 2A|14 3M|12 4A|12 5M| | | | | | | | | | | | | | | 1 1A| | 42 |1765|10 5A| 9 6M|10 6A| 9 7M| 8 7A| 7 8M| 6 9A| 5 10M| 3 10A| 3 11M| 1 12A| | | | | | | | | | | | | | | |31 1M| | 43 |1766|29 2A|28 3M|29 4A|28 5M|27 5A|26 6M|25 7A|24 8M|22 8A|22 9M|20 10A|20 11M| | 44 |1767|18 11A|17 0A|19 1M|17 2A|17 2M|15 3A|15 4M|13 5A|12 6M|11 6A|10 7M| 9 8A| | | | | | | | | | | 2 2M | | | | | | 45 |1768| 8 8M| 6 9A| 7 10M| 5 11A| 5 11M| 3 12A| 3 1A| |30 3M|29 4A|28 5M|27 5A| | | | | | | | | | |31 2A| | | | | | 46 |1769|26 6M|24 7A|26 7M|24 8A|24 8M|22 9A|22 10M|20 11A|19 11M|18 12A|17 1A|17 2M| | 47 |1770|15 2A|14 3M|15 4A|14 5M|13 5A|12 4M|11 7A|10 8M| 8 8A| 8 9M| 6 10A| 6 11M| | | | | | | | | | 1 4M| | | | | | | 48 |1771| 4 11M| 3 0A| 5 1M| 3 2A| 3 2M| 1 3A| |29 5M|27 6A|27 7M|25 8A|25 9M| | | | | | | | | |30 5A| | | | | | | 49 |1772|23 9A|22 10M|22 10A|21 11M|20 11A|19 0A|19 1M|17 2A|16 2M|15 3A|14 4M|13 5A| | 50 |1773|12 5M|10 6A|12 7M|10 8A|10 8M| 8 9A| 8 9M| 6 10A| 5 11M| 4 12A| 3 1A| 3 2M| | | | 1 2A| | 1 4A| | | | | | | | | | | 51 |1774| | ---- | |29 5A|29 6M|27 7A|27 8M|25 8A|24 9M|23 10A|22 11M|21 11A| | | |31 3M| |31 5M| | | | | | | | | | | 52 |1775|20 0A|19 1M|20 2A|19 3M|18 3A|17 4M|16 5A|15 6M|13 6A|13 7M|11 8A|11 9M| | | | | | | | | | | | | 1 3A| | | | 53 |1776| 9 9A| 8 10M| 8 10A| 7 11M| 6 12A| 5 0A| 5 1M| 3 2A| 2 2M| |29 5A|29 5M| | | | | | | | | | | | |31 4M| | | | 54 |1777|27 6A|26 7M|27 8A|26 9M|25 9A|24 10M|23 11A|22 0A|20 12A|20 1A|19 2M|18 3A| | 55 |1778|17 3M|15 4A|17 5M|15 6A|15 6M|13 7A|13 8M|11 9A|10 9M| 9 10A| 8 11M| 7 12A| | | | | | | | | | |1 6M| | | | | | 56 |1779| 6 0A| 5 1M| 6 2A| 5 3M| 4 3A| 3 4M| 2 5A| |29 7M|28 8A|27 9M|26 9A| | | | | | | | | | |30 6A| | | | | | 57 |1780|25 10M|23 11A|24 11M|22 12A|22 0A|21 1M|20 2A|19 3M|17 3A|17 4M|15 5A|15 6M| | 58 |1781|13 6A|12 7M|13 8A|12 9M|11 9A|10 10M| 9 11A| 8 0A| 6 12A| 6 1A| 5 2M| 4 3A| | | | | | | | 1 6M| | | | | | | | | 59 |1782| 3 3M| 1 4A| 3 5M| 1 6A| |29 8M|28 9A|27 9M|25 10A|25 11M|23 12A|23 0A| | | | | | | |30 7A| | | | | | | | | 60 |1783|22 1M|20 2A|22 2M|20 3A|20 3M|18 4A|18 5M|16 6A|15 6M|14 7A|13 8M|12 9A| | | | | | | | | | | | | | |1 6M| | 61 |1784|11 9M| 9 10A|10 11M| 8 12A| 8 0A| 7 1M| 6 2A| 5 3M| 3 3A| 3 4M| 1 5A| | | | | | | | | | | | | | | |30 6A| | 62 |1785|29 7M|27 8A|29 9M|27 10A|27 10M|25 11A|25 0A|24 1M|22 1A|22 2M|20 3A|20 3M| | 63 |1786|18 4A|17 5M|18 5A|17 6M|16 6A|15 7M|14 8A|13 9M|11 9A|11 10M| 9 11A| 9 0A| | | | | | | | | | | | 1 6M| | | | | 64 |1787| 7 12A| 6 1A| 8 2M| 6 3A| 6 3M| 4 4A| 4 5M| 2 6A| |30 8M|28 9A|28 9M| | | | | | | | | | | |30 7A| | | | | 65 |1788|26 10A|25 11M|25 12A|24 1A|24 1M|22 2A|22 3M|20 4M|19 4M|18 5A|17 6M|16 7A| | 66 |1789|15 7M|13 8A|15 9M|13 10A|13 10M|11 11A|11 0A|10 1M| 8 1A| 8 2M| 6 3A| 6 4M| | | | | | | | | 1 7M| | | | | | | | 67 |1790| 4 4A| 3 5M| 4 5A| 3 6M| 2 6A| |30 9M|28 9A|27 10M|26 11A|25 0A|24 12A| | | | | | | | |30 8A| | | | | | | | 68 |1791|23 1A|22 2M|23 3A|22 4M|21 4A|20 5M|19 6A|18 7M|16 7A|16 8M|14 9A|14 10M| | 69 |1792|12 10A|11 11M|11 12A|10 1A|10 1M| 8 2A| 8 3M| 6 4A| 5 4A| 4 5A| 3 6M| 2 7A| | | | 1 7M| | 1 9M| | | | | | | | | | | 70 |1793| | ---- | |29 10M|28 11A|27 0A|27 1M|25 1A|24 2M|23 3A|22 4M|21 4A| | | |30 8A| |30 10A| | | | | | | | | | | 71 |1794|20 5M|18 6A|20 6M|18 7A|18 7M|16 8A|16 9M|14 10A|13 10M|12 11A|11 0A|11 1M| | | | | | | | | | | | | 2 8M| | | | 72 |1795| 9 1A| 8 2M| 9 3A| 8 4M| 7 4A| 6 5M| 5 6A| 4 7M| 2 7A| |30 10M|29 10A| | | | | | | | | | | | |31 9A| | | | 73 |1796|28 11M|26 12A|27 0A|26 1M|25 1A|24 2M|23 3A|22 4M|20 4A|20 5M|18 6A|18 7M| | 74 |1797|16 7A|15 8M|16 9A|15 10M|14 10A|13 11M|12 12A|11 1A|10 1M| 9 2A| 8 3M| 7 4A| | | | | | | | | | 2 9M| | | | | | | 75 |1798| 6 4M| 4 5A| 6 6M| 4 7A| 4 7M| 2 8A| |30 10M|28 11A|28 0A|27 1M|26 1A| | | | | | | | | |31 10A| | | | | | | 76 |1799| 25 2M|23 3A|25 4M|23 5A|23 5M|21 6A|21 6M|19 8A|18 8M|17 9A|16 10M|15 11A| | 1 |1800|14 11A|12 12A|13 0A|12 1M|11 1A|10 2M| 9 3A| 8 4M| 6 4A| 6 5M| 4 6A| 4 7M| +----+----+------+------+------+------+------+------+------+------+------+------+------+------+

The year 1800 begins a new Cycle.

[Sidenote: _Easter_ Cycle, deficient.]

425. The _Cycle of Easter_, also called the _Dionysian Period_, is a revolution of 532 years, found by multiplying the Solar Cycle 28 by the Lunar Cycle 19. If the New Moons did not anticipate upon this Cycle, _Easter-Day_ would always be the _Sunday_ next after the first Full Moon which succeeds the 21st of _March_. But, on account of the above anticipation § 422, to which no proper regard was had before the late alteration of the _Style_, the _Ecclesiastic Easter_ has several times been a week different from the _true Easter_ within this last Century: which inconvenience is now remedied by making the Table which used to find Easter _for ever_, in the Common Prayer Book, of no longer use than the Lunar difference from the _New Style_ will admit of.

[Sidenote: Number of Direction.

To find the true _Easter_.]

426. The _earliest Easter possible_ is the 22d of _March_, the _latest_ the 25th of _April_. Within these limits are 35 days, and the number belonging to each of them is called the _Number of Direction_; because thereby the time of Easter is found for any given year. To find the Number of Direction, according to the _New Style_, enter Table V following this Chapter, with the compleat hundreds of any given year at the top, and the years thereof (if any) below an hundred at the left hand; and where the columns meet is the Dominical Letter for the given year. Then, enter Table I, with the compleat hundreds of the same year at the left hand, and the years below an hundred at the top; and where the columns meet is the Golden Number for the same year. Lastly, enter Table II with the Dominical Letter at the left hand and Golden Number at the top; and where the columns meet is the Number of Direction for that year; which number, added to the 21st day of _March_ shews on what day either of _March_ or _April_ Easter _Sunday_ falls in that year. Thus, the Dominical Letter _New Style_ for the year 1757 is _B_ (Table V) and the Golden Number is 10, (Table I) by which in Table II, the Number of Direction is found to be 20; which, reckoned from the 21st of _March_, ends on the 10th of _April_, and _that_ is _Easter Sunday_ in the year 1757. _N. B._ There are always two Dominical Letters to the leap-year, the first of which takes place to the 24th of _February_, the last for the following part of the year.

[Sidenote: Dominical Letter.]

427. _The first seven Letters of the Alphabet_ are commonly placed in the annual Almanacks to shew on what days of the week the days of the months fall throughout the year. And because one of those seven Letters must necessarily stand against _Sunday_ it is printed in a capital form, and called the _Dominical Letter_: the other six being inserted in small characters to denote the other six days of the week. Now, since a common _Julian Year_ contains 365 Days, if this number be divided by 7 (the number of days in a week) there will remain one day. If there had been no remainder, ’tis plain the year would constantly begin on the same day of the week. But since one remains, ’tis as plain that the year must begin and end on the same day of the week; and therefore the next year will begin on the day following. Hence, when _January_ begins on _Sunday_, _A_ is the Dominical or _Sunday_ Letter for that year: then, because the next year begins on _Monday_, the _Sunday_ will fall on the seventh day, to which is annexed the seventh Letter _G_, which therefore will be the Dominical Letter for all that year: and as the third year will begin on _Tuesday_, the _Sunday_ will fall on the sixth day; therefore _F_ will be the _Sunday_ Letter for that year. Whence ’tis evident that the _Sunday_ Letters will go annually in a retrograde order thus, _G_, _F_, _E_, _D_, _C_, _B_, _A_. And in the course of seven years, if they were all common ones, the same days of the week and Dominical Letters would return to the same days of the months. But because there are 366 days in a leap-year, if this number be divided by 7, there will remain two days over and above the 52 weeks of which the year consists. And therefore, if the leap-year begins on _Sunday_, it will end on _Monday_; and the next year will begin on _Tuesday_, the first _Sunday_ whereof must fall on the sixth of _January_, to which is annexed the Letter _F_, and not _G_ as in common years. By this means, the leap-year returning every fourth year, the order of the Dominical Letters is interrupted; and the Series does not return to its first state till after four times seven, or 28 years: and then the same days of the month return in order to the same days of the week.

[Sidenote: To find the Dominical Letter.]

428. _To find the Dominical Letter for any year either before or after the Christian Æra_[87]: In Table III or IV for _Old Style_, or V for _New Style_, look for the hundreds of years at the head of the Table, and for the years below an hundred (to make up the given year) at the left hand: and where the columns meet you have the Dominical Letter for the year desired. Thus, suppose the Dominical Letter be required for the year of CHRIST 1758, _New Style_, I look for 1700 at the head of Table V, and for 58 at the left hand of the same Table; and in the angle of meeting, I find _A_, which is the Dominical Letter for that year. If it was wanted for the same year _Old Style_, it would be found by Table IV to be _D_. But _to find the Dominical Letter for any given year before_ CHRIST, subtract one from _that_ year and then proceed in all respects as just now taught, to find it by Table III Thus, suppose the Dominical Letter be required for the 585th year before the first year of CHRIST, look for 500 at the head of Table III, and for 84 at the left hand; in the meeting of these columns is _FE_, which were the Dominical Letters for that year, and shews that it was a leap-year; because, leap-year has always two Dominical Letters.

[Sidenote: To find the Days of the Months.]

429. _To find the day of the month answering to any day of the week, or the day of the week answering to any day of the month; for any year past or to come:_ Having found the Dominical Letter for the given year, enter Table VI, with the Dominical Letter at the head; and under it, all the days in that column to the right hand are _Sundays_, in the divisions of the months; the next column to the right are _Mondays_; the next, _Tuesdays_; and so on to the last column under _G_, from which go back to the column under _A_, and thence proceed towards the right hand as before. Thus, in the year 1757, the Dominical Letter _New Style_ is _B_, in Table V, then in Table VI all the days under _B_ are _Sundays_ in that year, _viz._ the 2d, 9th, 16th, 23d, and 30th of _January_ and _October_; the 6th, 13th, 20th, and 27th of _February_, _March_ and _November_; the 3d, 10th, and 17th, of _April_ and _July_, together with the 31st of _July_: and so on to the foot of the column. Then, of course, all the days under _C_ on _Mondays_, namely the 3d, 10th, _&c._ of _January_ and _October_; and so of all the rest in that column. If _the day of the week answering to any day of the month_ be required, it is easily had from the same Table by the Letter that stands at the top of the column in which the given day of the month is found. Thus, the Letter that stands over the 28th of _May_ is _A_; and in the year 585 before CHRIST the Dominical Letter was found to be _FE_ § 428; which being a leap-year, and _E_ taking place from the 24th of _February_ to the end of that year, shews by the Table that the 25th of _May_ was on a _Sunday_; and therefore the 28th must have been on a _Wednesday_: for when _E_ stands for _Sunday_, _F_ must stand for _Monday_, _G_ for _Tuesday_, _A_ for _Wednesday_, _B_ for _Thursday_, _C_ for _Friday_, and _D_ for _Saturday_. Hence, as it appears that the famous Eclipse of the Sun foretold by THALES, by which a peace was brought about between the _Medes_ and _Lydians_, happened on the 28th of _May_, in the 585th year before CHRIST, it certainly fell on a _Wednesday_.

[Sidenote: _Julian Period._]

430. From the multiplication of the Solar Cycle of 28 years into the Lunar Cycle of 19 years, arises the great _Julian Period_ consisting of 7980 years; which had its beginning 764 years before the supposed year of the creation (when all the three Cycles began together) and is not yet compleated, and therefore it comprehends all other Cycles, Periods and Æras. There is but one year in the whole Period which has the same numbers for the three Cycles of which it is made up: and therefore, if historians had remarked in their writings the Cycles of each year, there had been no dispute about the time of any action recorded by them.

[Sidenote: To find the year of this Period.

And the Cycles of that year.]