281. If the Earth had no annual motion, the Sun would never appear to
shift his place in the Ecliptic. And then every New Moon would fall in
the same Sign and degree of the Ecliptic, and every Full Moon in the
opposite: for the Moon would go precisely round the Ecliptic from Change
to Change. So that if the Moon was once Full in Pisces, or Aries, she
would always be Full when she came round to the same Sign and Degree
again. And as the Full Moon rises at Sun-set (because when any point of
the Ecliptic sets the opposite point rises) she would constantly rise
within two hours of Sun-set during the week in which she were Full. But
in the time that the Moon goes round the Ecliptic from any conjunction
or opposition, the Earth goes almost a Sign forward; and therefore the
Sun will seem to go as far forward in that time, namely 27-1/2 degrees:
so that the Moon must go 27-1/2 degrees more than round; and as much
farther as the Sun advances in that interval, which is 2-1/15 degrees,
before she can be in conjunction with, or opposite to the Sun again.
Hence it is evident, that there can be but one conjunction or opposition
of the Sun and Moon in a year in any particular part of the Ecliptic.
This may be familiarly exemplified by the hour and minute hands of a
watch, which are never in conjunction or opposition in that part of the
dial-plate where they were so last before. And indeed if we compare the
twelve hours on the dial-plate to the twelve Signs of the Ecliptic, the
hour-hand to the Sun and the minute-hand to the Moon, we shall have a
tolerably near resemblance in miniature to the motions of our great
celestial Luminaries. The only difference is, that whilst the Sun goes
once round the Ecliptic the Moon makes 12-1/3 conjunctions with him: but
whilst the hour-hand goes round the dial-plate the minute-hand makes
only 11 conjunctions with it; because the minute hand moves slower in
respect of the hour-hand than the Moon does with regard to the Sun.
[Sidenote: The Harvest and Hunter’s Moon.]
282. As the Moon can never be full but when she is opposite to the Sun,
and the Sun is never in Virgo and Libra but in our autumnal months, ’tis
plain that the Moon is never full in the opposite Signs, Pisces and
Aries, but in these two months. And therefore we can have only two Full
Moons in the year, which rise so near the time of Sun-set for a week
together as above-mentioned. The former of these is called the _Harvest
Moon_, and the latter the _Hunter’s Moon_.
[Sidenote: Why the Moon’s regular rising is never perceived but in
Harvest.]
283. Here it will probably be asked, why we never observe this
remarkable rising of the Moon but in harvest, since she is in Pisces and
Aries at least twelve times in the year besides; and must then rise with
as little difference of time as in harvest? The answer is plain: for in
winter these Signs rise at noon; and being then only a Quarter of a
Circle distant from the Sun, the Moon in them is in her first Quarter:
but when the Sun is above the Horizon the Moon’s rising is neither
regarded nor perceived. In spring these Signs rise with the Sun because
he is then in them; and as the Moon changeth in them at that time of the
year, she is quite invisible. In summer they rise about mid-night, and
the Sun being then three Signs, or a Quarter of a Circle before them,
the Moon is in them about her third Quarter; when rising so late, and
giving but very little light, her rising passes unobserved. And in
autumn, these Signs being opposite to the Sun, rise when he sets, with
the Moon in opposition, or at the Full, which makes her rising very
conspicuous.
284. At the Equator, the North and South Poles lie in the Horizon; and
therefore the Ecliptic makes the same Angle southward with the Horizon
when Aries rises as it does northward when Libra rises. Consequently, as
the Moon at all the fore-mentioned patches rises and sets nearly at
equal Angles with the Horizon all the year round; and about 48 minutes
later every day or night than on the preceding, there can be no
particular Harvest Moon at the Equator.
285. The farther that any place is from the Equator, if it be not beyond
the Polar Circle, the Angle gradually diminishes which the Ecliptic and
Horizon make when Pisces and Aries rise; and therefore when the Moon is
in these Signs she rises with a nearly proportionable difference later
every day than on the former; and is for that reason the more remarkable
about the Full, until we come to the Polar Circles, or 66 degrees from
the Equator; in which Latitude the Ecliptic and Horizon become
coincident, every day for a moment, at the same sidereal hour (or 3
minutes 56 seconds sooner every day than the former) and the very next
moment one half of the Ecliptic containing Capricorn, Aquarius, Pisces,
Aries, Taurus, and Gemini rises, and the opposite half sets. Therefore,
whilst the Moon is going from the beginning of Capricorn to the
beginning of Cancer, which is almost 14 days, she rises at the same
sidereal hour; and in autumn just at Sun-set, because all that half of
the Ecliptic in which the Sun is at that time sets at the same sidereal
hour, and the opposite half rises: that is, 3 minutes 56 seconds, of
mean solar time, sooner every day than on the day before. So whilst the
Moon is going from Capricorn to Cancer she rises earlier every day than
on the preceding; contrary to what she does at all places between the
polar Circles. But during the above fourteen days, the Moon is 24
sidereal hours later in setting; for the six Signs which rise all at
once on the eastern side of the Horizon are 24 hours in setting on the
western side of it: as any one may see by making chalk-marks at the
beginning of Capricorn and of Cancer, and then, having elevated the Pole
66-1/2 degrees, turn the Globe slowly round it’s Axis, and observe the
rising and setting of the Ecliptic. As the beginning of Aries is equally
distant from the beginning of Cancer and of Capricorn, it is in the
middle of that half of the Ecliptic which rises all at once. And when
the Sun is at the beginning of Libra, he is in the middle of the other
half. Therefore, when the Sun is in Libra and the Moon in Capricorn, the
Moon is a Quarter of a Circle before the Sun; opposite to him, and
consequently full in Aries, and a Quarter of a Circle behind him when in
Cancer. But when Libra rises Aries sets, and all that half of the
Ecliptic of which Aries is the middle. And therefore, at that time of
the year the Moon rises at Sun-set from her first to her third Quarter.
[Sidenote: The Harvest Moons regular on both sides of the Equator.]
286. In northern Latitudes, the autumnal Full Moons are in Pisces and
Aries; and the vernal Full Moons in Virgo and Libra: in southern
Latitudes just the reverse because the seasons are contrary. But Virgo
and Libra rise at as small Angles with the Horizon in southern Latitudes
as Pisces and Aries do in the northern; and therefore the Harvest Moons
are just as regular on one side of the Equator as on the other.
287. As these Signs which rise with the least Angles set with the
greatest, the vernal Full Moons differ as much in their times of rising
every night as the autumnal Full Moons differ in their times of setting;
and set with as little difference as the autumnal Full Moons rise: the
one being in all cases the reverse of the other.
[Sidenote: The Moon’s Nodes.]
288. Hitherto, for the sake of plainness, we have supposed the Moon to
move in the Ecliptic, from which the Sun never deviates. But the orbit
in which the Moon really moves is different from the Ecliptic: one half
being elevated 5-1/3 degrees above it, and the other half as much
depressed below it. The Moon’s orbit therefore intersects the Ecliptic
in two points diametrically opposite to each other: and these
intersections are called the _Moon’s Nodes_. So the Moon can never be in
the Ecliptic but when she is in either of her Nodes, which is at least
twice in every course from Change to Change, and sometimes thrice. For,
as the Moon goes almost a whole Sign more than round her Orbit from
Change to Change; if she passes by either Node about the time of Change,
she will pass by the other in about fourteen days after, and come round
to the former Node two days again before the next Change. That Node from
which the Moon begins to ascend northward, or above the Ecliptic, in
northern Latitudes, is called the _Ascending Node_; and the other the
_Descending Node_, because the Moon, when she passes by it, descends
below the Ecliptic southward.
289. The Moon’s oblique motion with regard to the Ecliptic causes some
difference in the times of her rising and setting from what is already
mentioned. For whilst she is northward of the Ecliptic, she rises sooner
and sets later than if she moved in the Ecliptic: and when she is
southward of the Ecliptic she rises later and sets sooner. This
difference is variable even in the same Signs, because the Nodes shift
backward about 19-2/3 degrees in the Ecliptic every year; and so go
round it contrary to the order of Signs in 18 years 225 days.
290. When the Ascending Node is in Aries, the southern half of the
Moon’s Orbit makes an Angle of 5-1/3 degrees less with the Horizon than
the Ecliptic does, when Aries rises in northern Latitudes: for which
reason the Moon rises with less difference of time whilst she is in
Pisces and Aries than there would be if she kept in the Ecliptic. But in
9 years and 112 days afterward, the Descending Node comes to Aries; and
then the Moon’s Orbit makes an Angle 5-1/3 degrees greater with the
Horizon when Aries rises, than the Ecliptic does at that time; which
causes the Moon to rise with greater difference of time in Pisces and
Aries than if she moved in the Ecliptic.
291. To be a little more particular, when the Ascending Node is in
Aries, the Angle is only 9-2/3 degrees on the parallel of _London_ when
Aries rises. But when the Descending Node comes to Aries, the Angle is
20-1/3 degrees; this occasions as great a difference of the Moon’s
rising in the same Signs every 9 years, on the parallel of _London_, as
there would be on two parallels 10-2/3 degrees from one another, if the
Moon’s course were in the Ecliptic. The following Table shews how much
the obliquity of the Moon’s Orbit affects her rising and setting on the
parallel of _London_ from the 12th to the 18th day of her age; supposing
her to be Full at the autumnal Equinox; and then, either in the
Ascending Node, highest part of her Orbit, Descending Node, or lowest
part of her Orbit. _M_ signifies morning, _A_ afternoon; and the line at
the foot of the Table shews a week’s difference in rising and setting.
+--------+---------------+---------------+---------------+---------------+
| | Full in her | In the | Full in her | In the lowest |
| | Ascending | highest part | Descending | part of her |
| | node. | of her Orbit. | node. | Orbit. |
| Moon’s +---------------+-------+-------+-------+-------+-------+-------+
| Age | Rises | Sets | Rises | Sets | Rises | Sets | Rises | Sets |
| | at | at | at | at | at | at | at | at |
| | H. M. | H. M. | H. M. | H. M. | H. M. | H. M. | H. M. | H. M. |
+--------+-------+-------+-------+-------+-------+-------+-------+-------+
| | _A_ | _M_ | _A_ | _M_ | _A_ | _M_ | _A_ | _M_ |
| 12 | 5 15 | 3 20 | 4 30 | 3 15 | 4 32 | 3 40 | 5 16 | 3 0 |
| 13 | 5 32 | 4 25 | 4 50 | 4 45 | 5 15 | 4 20 | 6 0 | 4 15 |
| 14 | 5 48 | 5 30 | 5 15 | 6 0 | 5 45 | 5 40 | 6 20 | 5 28 |
| 15 | 6 5 | 7 0 | 5 42 | 7 20 | 6 15 | 6 56 | 6 45 | 6 32 |
| 16 | 6 20 | 8 15 | 6 2 | 8 35 | 6 46 | 8 0 | 7 8 | 7 45 |
| 17 | 6 36 | 9 12 | 6 26 | 9 45 | 7 18 | 9 15 | 7 30 | 9 15 |
| 18 | 6 54 | 10 30 | 7 0 | 10 40 | 8 0 | 10 20 | 7 52 | 10 0 |
+--------+-------+-------+-------+-------+-------+-------+-------+-------+
| Dif. | 1 39 | 7 10 | 2 30 | 7 25 | 3 28 | 6 40 | 2 36 | 7 0 |
+--------+-------+-------+-------+-------+-------+-------+-------+-------+
This Table was not computed, but only estimated as near as could be done
from a common Globe, on which the Moon’s Orbit was delineated with a
black lead pencil. It may at first sight appear erroneous; since as we
have supposed the Moon to be full in either Node at the autumnal
Equinox, she ought by the Table to rise just at six o’clock, or at
Sun-set, on the 15th day of her age; being in the Ecliptic at that time.
But it must be considered, that the Moon is only 14-1/4 days old when
she is Full; and therefore in both cases she is a little past the Node
on the 15th day, being above it at one time, and below it at the other.
[Sidenote: The period of the Harvest Moons.]
292. As there is a compleat revolution of the Nodes in 18-2/3 years,
there must be a regular period of all the Varieties which can happen in
the rising and setting of the Moon during that time. But this shifting
of the Nodes never affects the Moon’s rising so much, even in her
quickest descending Latitude, as not to allow us still the benefit of
her rising nearer the time of Sun-set for a few days together about the
Full in Harvest, than when she is Full at any other time of the year.
The following Table shews in what years the Harvest-Moons are least
beneficial as to the times of their rising, and in what years most, from
1751 to 1861. The column of years under the letter _L_ are those in
which the Harvest-Moons are least of all beneficial, because they fall
about the Descending Node: and those under _M_ are the most of all
beneficial, because they fall about the Ascending Node. In all the
columns from _N_ to _S_ the Harvest-Moons descend gradually in the Lunar
Orbit, and rise to less heights above the Horizon. From _S_ to _N_ they
ascend in the same proportion, and rise to greater heights above the
Horizon. In both the columns under _S_ the Harvest-Moons are in the
lowest part of the Moon’s Orbit, that is, farthest South of the
Ecliptic; and therefore stay shortest of all above the Horizon: in the
columns under _N_ just the reverse. And in both cases, their rising,
though not at the same times, are nearly the same with regard to
difference of time, as if the Moon’s Orbit were coincident with the
Ecliptic.
+------------------------------------------------------------+
| |
| _Years in which the Harvest-Moons are least beneficial._ |
| |
| N L S |
| 1751 1752 1753 1754 1755 1756 1757 1758 1759 |
| 1770 1771 1772 1773 1774 1775 1776 1777 1778 |
| 1788 1789 1790 1791 1792 1793 1794 1795 1796 1797 |
| 1807 1808 1809 1810 1811 1812 1813 1814 1815 |
| 1826 1827 1828 1829 1830 1831 1832 1833 1834 |
| 1844 1845 1846 1847 1848 1849 1850 1851 1852 |
| |
| _Years in which they are most beneficial._ |
| |
| S M N |
| 1760 1761 1762 1763 1764 1765 1766 1767 1768 1769 |
| 1779 1780 1781 1782 1783 1784 1785 1786 1787 |
| 1798 1799 1800 1801 1802 1803 1804 1805 1806 |
| 1816 1817 1818 1819 1820 1821 1822 1823 1824 1825 |
| 1835 1836 1837 1838 1839 1840 1841 1842 1843 |
| 1853 1854 1855 1856 1857 1858 1859 1860 1861 |
+------------------------------------------------------------+
[Sidenote: PL. VIII.]
293. At the Polar Circles, when the Sun touches the Summer Tropic, he
continues 24 hours above the Horizon; and 24 hours below it when he
touches the Winter Tropic. For the same reason the Full Moon neither
rises in Summer, nor sets in Winter, considering her as moving in the
Ecliptic. For the Winter Full Moon being as high in the Ecliptic as the
Summer Sun, must therefore continue as long above the Horizon; and the
Summer Full Moon being as low in the Ecliptic as the Winter Sun, can no
more rise than he does. But these are only the two Full Moons which
happen about the Tropics, for all the others rise and set. In Summer the
Full Moons are low, and their stay is short above the Horizon, when the
nights are short, and we have least occasion for Moon-light: in Winter
they go high, and stay long, above the Horizon when the nights are long,
and we want the greatest quantity of Moon-light.
[Sidenote: The long continuance of Moon-light at the Poles.