Part 19

279. Having rectified the Globe, turn it until the patch at _0_, about the beginning of ♓ Pisces on the half _LUI_ of the Ecliptic, comes to the Eastern side of the Horizon; and then keeping the ball steady, set the hour Index to XII, because _that_ hour may perhaps be more easily remembred than any other. Then, turn the Globe round westward, and in that time, suppose the patch _0_ to have moved thence to _1_, 13-1/6 degrees, whilst the Earth turns once round its Axis, and you will see that _1_ rises only about 20 minutes later than _0_ did on the day before. Turn the Globe round again, and in that time suppose the same patch to have moved from _1_ to _2_; and it will rise only 20 minutes later by the hour-index than it did at _1_ on the day or turn before. At the end of the next turn, suppose the patch to have gone from _2_ to _3_ at _U_, and it will rise 20 minutes later than it did at _2_. And so on for six turns, in which time there will scarce be two hours difference: Nor would there have been so much if the 6 degrees of the Sun’s motion in that time had been allowed for. At the first Turn the patch rises south of the East, at the middle Turn due East, and at the last Turn north of the East. But these patches will be 9 hours of setting on the western side of the Horizon, which shews that the Moon will be so much later of setting in that week in which she moves through these two Signs. The cause of this difference is evident; for Pisces and Aries make only an Angle of 15 degrees with the Horizon when they rise; but they make an Angle of 62 degrees with it when they set § 275. As the Signs Taurus, Gemini, Cancer, Leo, Virgo, and Libra rise successively, the Angle increases gradually which they make with the Horizon; and decreases in the same proportion as they set. And for that reason, the Moon differs gradually more in the time of her rising every day whilst she is in these Signs, and less in her setting: After which, through the other six Signs, _viz._ Scorpio, Sagittary, Capricorn, Aquarius, Pisces, and Aries, the rising difference becomes less every day, until it be at the least of all, namely, in Pisces and Aries.

280. The Moon goes round the Ecliptic in 27 days 8 hours; but not from Change to Change in less than 29 days 12 hours: so that she is in Pisces and Aries at least once in every Lunation, and in some Lunations twice.

[Sidenote: Why the Moon is always Full in different Signs.

Her periodical and synodical Revolution exemplified.]

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.

Fig. V.]

294. At the Poles, one half of the Ecliptic never sets, and the other half never rises: and therefore, as the Sun is always half a year in describing one half of the Ecliptic, and as long in going through the other half, ’tis natural to imagine that the Sun continues half a year together above the Horizon of each Pole in it’s turn, and as long below it; rising to one Pole when he sets to the other. This would be exactly the case if there were no refraction: but by the Atmosphere’s refracting the Sun’s rays, he becomes visible some days sooner § 183, and continues some days longer in sight than he would otherwise do: so that he appears above the Horizon of either Pole before he has got below the Horizon of the other. And, as he never goes more than 23-1/2 degrees below the Horizon of the Poles, they have very little dark night: it being twilight there as well as at all other places till the Sun be 18 degrees below the Horizon, § 177. The Full Moon being always opposite to the Sun, can never be seen while the Sun is above the Horizon, except when the Moon falls in the northern half of her Orbit; for whenever any point of the Ecliptic rises the opposite point sets. Therefore, as the Sun is above the Horizon of the north Pole from the 20th of _March_ till the 23d of _September_, it is plain that the Moon, when Full, being opposite to the Sun, must be below the Horizon during that half of the year. But when the Sun is in the southern half of the Ecliptic he never rises to the north Pole, during which half of the year, every Full Moon happens in some part of the northern half of the Ecliptic, which never sets. Consequently, as the polar Inhabitants never see the Full Moon in Summer, they have her always in the Winter, before, at, and after the Full, shining for 14 of our days and nights. And when the Sun is at his greatest depression below the Horizon, being then in Capricorn, the Moon is at her First Quarter in Aries, Full in Cancer, and at her Third Quarter in Libra. And as the beginning of Aries is the rising point of the Ecliptic, Cancer the highest, and Libra the setting point, the Moon rises at her First Quarter in Aries, is most elevated above the Horizon, and Full in Cancer, and sets at the beginning of Libra in her Third Quarter, having continued visible for 14 diurnal rotations of the Earth. Thus the Poles are supplied one half of the winter time with constant Moon-light in the Sun’s absence; and only lose sight of the Moon from her Third to her First Quarter, while she gives but very little light; and could be but of little, and sometimes of no service to them. A bare view of the Figure will make this plain; in which let _S_ be the Sun, _e_ the Earth in Summer when it’s north Pole _n_ inclines toward the Sun, and _E_ the Earth in Winter, when it’s north Pole declines from him. _SEN_ and _NWS_ is the Horizon of the north Pole, which is coincident with the Equator; and, in both these positions of the Earth, ♈♋♎♑ is the Moon’s Orbit, in which she goes round the Earth, according to the order of the letters _abcd_, _ABCD_. When the Moon is at _a_ she is in her Third Quarter to the Earth at _e_, and just rising to the north Pole _n_; at _b_ she changes, and is at the greatest height above the Horizon, as the Sun likewise is; at _c_ she is in her First Quarter, setting below the Horizon; and is lowest of all under it at _d_, when opposite to the Sun, and her enlightened side toward the Earth. But then she is full in view to the south Pole _p_; which is as much turned from the Sun as the north Pole inclines towards him. Thus in our Summer, the Moon is above the Horizon of the north Pole whilst she describes the northern half of the Ecliptic ♈♋♎, or from her Third Quarter to her First; and below the Horizon during the progress through the southern half ♎♑♈; highest at the Change, most depressed at the Full. But in winter, when the Earth is at _E_, and it’s north Pole declines from the Sun, the New Moon at _D_ is at her greatest depression below the Horizon _NWS_, and the Full Moon at _B_ at her greatest height above it; rising at her First Quarter _A_, and keeping above the Horizon till she comes to her Third Quarter _C_. At a mean state she is 23-1/2 degrees above the Horizon at _B_ and _b_, and as much below it at _D_ and _d_, equal to the inclination of the Earth’s Axis _F_. _S_♋ and _S_♑ are, as it were, a ray of light proceeding from the Sun to the Earth; and shews that when the Earth is at _e_, the Sun is above the Horizon, vertical to the Tropic of Cancer; and when the Earth is at _E_, he is below the Horizon, vertical to the Tropic of Capricorn.