The examination of antient Eclipses.

390. By computing the times of New and Full Moons, together with the distance of the Sun and Moon from the Nodes; and knowing that when the Sun is within 17 Degrees of either Node at New Moon he must be eclipsed; and when the Moon is within 12 Degrees of either Node at Full she cannot escape an Eclipse; and that there can be no Eclipses without these limits; ’tis easy to examine whether the accounts of antient Eclipses recorded in history be true. I shall take the liberty to examine two of those mentioned in the foregoing catalogue, namely, that of the Moon at Babylon on the 19th of March in the 721st year before Christ; and that of the Sun at Athens, on the 20th of March, in the 424th year before Christ.

The time of Full Moon for the former of these Eclipses is already calculated, Page 198, and the time of New Moon for the latter, Page 196, both to the Old Style; so that we have nothing now to do but find the Sun’s distance from the Nodes the same way as we did the Anomalies; and if the Full Moon in March 721 years before Christ was within 12 degrees of either Node, she was then eclipsed; and if the Sun, at the time of New Moon in March 424 years before Christ was within 17 degrees of either Node, he must have been eclipsed at that time.

EXAMPLE I.
 
To find the distance of the Sun and Moon from the Nodes, at the time of Full Moon in March, the year before Christ 721, O. S.

The years 720 added to 1780 make 2500, or 25 Centuries.
  Sun from Node
  s ° ʹ
To the mean time of Full Moon in March 1780, Table III. 10 3 1
Add the distance for 1 Lunation [See N. B. Page 195, and Example III, Page 198] 1 0 40
Sum 11 3 41
From which subtract the Sun’s distance from the Node for 2500 years, Table V 5 4 11
Remains the Sun’s distance from the Node, March 19, 721 years before Christ 5 29 30
To which add 6 Signs for the Moon’s distance, because she was then in opposition to the Sun 6 0 0
The Sum is the Moon’s dist. from the Ascend. Node 11 29 30

That is, she was within half a degree of coming round to it again; and therefore, being so near, she must have been totally, and almost centrally eclipsed.

EXAMPLE II
 
To find the Suns distance from the Node at the Time of New Moon in March, the year before Christ 424, O. S.

The years 423 added to 1777 make 2200, or 22 Centuries.
  Sun from Node
  s ° ʹ
At the mean time of New Moon in March 1777, Tab. I. 8 23 33
From which subtract the Sun’s distance from the Node for 2200 years, Table V 3 6 0
Remains the Sun’s distance from the Ascending Node, March 21, 424 years before Christ 5 17 33
Which, taken from 6 Signs, the distance of the Nodes from each other 6 0 0
Leaves the Sun’s distance at that time from the Descending Node, Descending viz. 0 12 27

Which being less than 17 degrees, shews that the Sun was then eclipsed. And as from these short Calculations we find those two antient Eclipses taken at a venture, to be truly recorded; it is natural to imagine that so are all the rest in the catalogue.

Here follow Astronomical Tables, for calculating the Times of New and Full Moons and Eclipses.

Table I. The mean time of New Moon in March, the mean Anomaly of the Sun and Moon, the Sun’s mean Distance from the Ascending Node; with the mean Longitude of the Sun and Node from the beginning of the Sign Aries, at the times of all the New Moons in March for 100 years, Old Style.

Years of Christ. Mean time of New Moon in March. The Sun’s mean Anomaly. The Moon’s mean Anomaly. The Sun’s distance from the Node. The Sun’s Longitude from Aries. The Node’s Longitude from Aries.
D. H. M. s ° ʹ s ° ʹ s ° ʹ s ° ʹ s ° ʹ
1701 27 13 45 9 8 23 0 28 5 7 23 15 0 16 3 4 22 48
1702 16 22 34 8 27 39 11 7 53 8 1 17 0 5 20 4 4 3
1703 6 7 23 8 16 55 9 17 41 8 9 20 11 24 37 3 15 17
1704 24 4 55 9 4 30 8 23 18 9 18 3 0 13 0 2 24 57
1705 13 13 44 8 23 54 7 3 6 9 26 6 0 2 17 2 6 11
1706 2 22 32 8 13 48 5 12 54 10 4 9 11 21 34 1 17 25
1707 21 20 5 9 2 17 4 18 31 11 12 52 0 9 57 0 27 5
1708 10 4 54 8 21 10 2 28 19 11 20 55 11 29 14 0 8 19
1709 29 2 26 9 9 48 2 3 56 0 29 38 0 17 37 11 17 59
1710 18 11 16 8 28 32 0 13 44 1 7 40 0 6 54 10 29 14
1711 7 20 5 8 17 27 10 23 33 1 15 43 11 26 11 10 10 28
1712 25 17 36 9 5 8 9 29 10 2 24 26 0 14 34 9 20 8
1713 15 2 25 8 25 48 8 8 58 3 2 29 0 3 50 9 1 21
1714 4 11 14 8 14 52 6 16 46 3 10 32 11 23 7 8 12 35
1715 23 8 46 9 3 37 5 24 22 4 19 15 0 11 30 7 22 15
1716 11 17 35 8 21 26 4 4 11 4 27 18 0 0 47 7 3 29
1717 1 2 23 8 11 58 2 13 59 5 5 20 11 20 4 6 14 44
1718 19 23 56 9 0 31 1 19 36 6 14 3 0 8 27 5 24 24
1719 9 8 45 8 19 47 11 29 24 6 22 6 11 27 43 5 5 37
1720 27 6 17 9 8 9 11 5 1 8 0 49 0 16 6 4 15 17
1721 16 15 6 8 27 25 9 14 49 8 8 52 0 5 23 3 26 31
1722 5 23 55 8 16 41 7 24 38 8 16 55 11 24 40 3 7 45
1723 24 21 27 9 5 3 7 0 15 9 25 38 0 13 4 2 17 26
1724 13 6 16 8 24 19 5 10 3 10 3 41 0 2 22 1 28 41
1725 2 15 4 8 13 45 3 19 51 10 11 43 11 21 39 1 9 56
1726 21 12 37 9 1 57 2 25 28 11 20 26 0 10 3 0 19 37
1727 10 21 26 8 21 13 1 5 16 11 28 29 11 29 20 0 0 51
1728 28 18 58 9 9 35 0 10 53 1 7 13 0 17 43 11 10 30
1729 18 3 47 8 28 51 10 20 41 1 15 15 0 7 0 10 21 45
1730 7 12 36 8 18 7 9 0 29 1 23 18 11 26 17 10 2 59
1731 26 10 8 9 6 29 8 6 6 3 2 1 0 14 40 9 12 39
1732 14 18 57 8 25 45 6 15 54 3 10 3 0 3 57 8 23 54
1733 4 3 45 8 14 49 4 25 43 3 18 6 11 23 14 8 5 7
1734 23 1 18 9 3 25 4 1 20 4 26 49 0 11 37 7 14 48
1735 12 10 7 8 22 39 2 11 8 5 4 52 0 0 54 6 26 1
1736 30 7 39 0 11 1 1 16 45 6 13 35 0 19 17 6 5 42
1737 19 16 28 9 0 1 11 26 33 6 21 38 0 8 34 5 16 56
1738 9 1 17 8 19 33 10 6 21 6 29 42 11 27 51 4 28 9
1739 27 22 49 9 7 55 9 11 58 8 8 24 0 16 14 4 7 50
1740 16 7 38 8 27 11 7 21 46 8 16 27 0 5 30 3 19 3
1741 5 16 26 8 16 27 6 1 34 8 24 30 11 24 47 3 0 16
1742 24 13 59 9 4 49 5 7 11 10 3 12 0 13 10 2 9 58
1743 13 22 48 8 24 5 3 16 59 10 11 15 0 2 27 1 21 12
1744 2 7 36 8 13 21 1 26 48 10 19 18 11 21 44 1 2 25
1745 21 5 9 9 1 43 1 2 25 11 28 0 0 10 7 0 12 7
1746 10 13 58 8 20 59 11 12 13 0 6 3 11 29 44 11 23 20
1747 29 11 30 9 9 21 10 17 50 1 14 45 0 17 47 11 3 2
1748 17 20 19 8 28 37 8 27 38 1 22 49 0 7 4 10 14 15
1749 7 5 8 8 17 53 7 7 26 2 0 53 11 26 21 9 25 28
1750 26 2 40 9 6 15 6 13 3 3 9 35 0 14 44 9 5 9
1751 15 11 29 8 25 32 4 22 51 3 17 38 0 4 1 8 16 23
1752 3 20 17 8 14 47 3 2 39 3 25 41 11 23 18 7 27 37
1753 22 17 50 9 3 10 2 8 16 5 4 24 0 11 41 7 7 17
1754 12 2 39 8 22 26 0 18 4 5 12 27 0 0 59 6 18 32
1755 1 11 27 8 11 41 10 27 52 5 20 30 11 20 16 5 29 45
1756 19 9 0 9 0 4 10 3 30 6 29 13 0 8 39 5 9 27
1757 8 17 49 8 19 20 8 13 18 7 10 15 11 27 56 4 20 41
1758 27 15 21 9 7 42 7 18 55 8 15 58 0 16 19 4 0 21
1759 17 0 10 8 26 58 5 28 43 8 24 1 0 5 36 3 11 36
1760 5 8 58 8 16 13 4 8 31 9 2 4 11 24 53 2 22 49
1761 24 6 31 9 4 35 3 14 8 10 10 47 0 13 16 2 2 29
1762 13 15 19 8 23 52 1 23 56 10 18 51 0 2 33 1 13 44
1763 3 0 8 8 13 7 0 3 44 10 26 53 11 21 50 0 24 57
1764 20 21 41 9 1 29 11 9 21 0 5 36 0 10 13 0 4 37
1765 10 6 30 8 20 46 9 19 9 0 13 38 11 29 30 11 15 52
1766 29 4 2 9 9 8 8 24 46 1 22 21 0 17 53 10 25 32
1767 18 12 51 8 28 24 7 4 35 2 0 24 0 7 10 10 6 47
1768 6 21 39 8 17 39 5 14 23 2 8 27 11 26 27 9 18 1
1769 25 19 12 9 6 2 4 20 0 3 17 0 0 14 50 8 27 41
1770 15 4 1 8 25 17 2 29 48 3 25 12 0 4 7 8 8 56
1771 4 12 49 8 14 33 1 9 36 4 3 16 11 23 24 7 20 8
1772 22 10 22 9 2 56 0 15 13 5 11 49 0 11 47 6 29 48
1773 11 19 10 8 22 11 10 25 1 5 20 1 0 1 4 6 11 3
1774 1 3 59 8 11 27 9 4 49 5 28 4 11 20 21 5 22 17
1775 20 1 32 8 29 50 8 10 26 7 6 4 0 8 44 5 1 57
1776 8 10 20 8 19 5 6 20 14 7 14 50 11 28 1 4 13 12
1777 27 7 53 9 7 27 5 25 51 8 23 23 0 16 24 3 22 52
1778 16 16 42 8 26 43 4 5 40 9 1 36 0 5 41 3 4 6
1779 6 1 30 8 15 59 2 15 28 9 9 39 11 24 58 2 15 19
1780 23 23 3 9 4 21 1 21 5 10 18 22 0 13 21 1 24 59
1781 13 7 52 8 23 37 0 0 53 10 26 24 0 2 38 1 6 14
1782 2 16 40 8 12 53 10 10 41 11 4 27 11 21 54 0 17 27
1783 21 14 13 9 1 15 9 16 18 0 13 10 0 10 17 11 27 7
1784 9 23 2 8 20 32 7 26 6 0 21 13 11 29 34 11 8 22
1785 28 20 35 9 8 54 7 1 43 1 29 56 0 17 57 10 18 2
1786 18 5 23 8 28 9 5 11 31 2 7 59 0 7 14 9 29 16
1787 7 14 11 8 17 25 3 21 19 2 16 2 11 26 31 9 10 29
1788 25 11 44 9 5 47 2 26 56 3 24 45 0 14 54 8 20 9
1789 14 20 33 8 25 3 1 6 45 4 2 47 0 4 11 8 1 25
1790 4 5 21 8 14 19 11 16 33 4 10 50 11 23 28 7 12 38
1791 23 2 54 9 2 41 10 22 10 5 19 33 0 11 51 6 22 18
1792 11 11 43 8 21 57 9 1 58 5 27 56 0 1 7 6 3 32
1793 0 20 31 8 11 12 7 11 45 6 5 39 11 20 24 5 14 45
1794 19 18 4 8 29 35 6 17 23 7 14 22 0 8 48 4 24 27
1795 9 2 52 8 18 51 4 27 11 7 22 25 11 28 6 4 5 41
1796 27 0 25 9 7 13 4 2 48 9 1 8 0 16 29 3 15 21
1797 16 9 14 8 26 29 2 12 36 9 9 10 0 5 46 2 26 36
1798 5 18 2 8 15 44 0 22 24 9 17 13 11 25 3 2 7 50
1799 24 15 35 9 4 6 11 28 1 10 25 56 0 13 26 1 17 30
1800 13 0 24 8 23 23 10 7 49 11 3 59 0 2 43 0 28 44

Table II. The mean New Moons, &c. in March to the New Style.