277. On the Parallel of London, as much of the Ecliptic rises about Pisces and Aries in two hours as the Moon goes through in six days: and therefore whilst the Moon is in these Signs, she differs but two hours in rising for six days together; that is, 20 minutes later every day or night than on the preceding. But in fourteen days afterwards, the Moon comes to Virgo and Libra; which are the opposite Signs to Pisces and Aries; and then she differs almost four times as much in rising; namely, one hour and about fifteen minutes later every day or night than the former, whilst she is in these Signs; for by § 275 their rising Angle is at least four times as great as that of Pisces and Aries. The annexed Table shews the daily mean difference of the Moon’s rising and setting on the Parallel of London, for 28 days; in which time the Moon finishes her period round the Ecliptic, and gets 9 degrees into the same Sign from the beginning of which she set out. So it appears by the Table, that while the Moon is in ♍ and ♎ she rises an hour and a quarter later every day than the former; and differs only 24, 20, 18 or 17 minutes in setting. But, when she comes to ♓ and ♈, she is only 20 or 17 minutes later of rising; and an hour and a quarter later in setting.

278. All these things will be made plain by putting small patches on the Ecliptic of a Globe, as far from one another as the Moon moves from any Point of the celestial Ecliptic in 24 hours, which at a mean rate is ^[62] 13¹⁄₆ degrees; and then in turning the globe round, observe the rising and setting of the patches in the Horizon, as the Index points out the different times in the hour circle. A few of these patches are represented by dots at 0 1 2 3 &c. on the Ecliptic, which has the position LUI when Aries rises in the East; and by the dots 0 1 2 3, &c. when Libra rises in the East, at which time the Ecliptic has the position EU♑: making an angle of 62 degrees with the Horizon in the latter case, and an angle of no more than 15 degrees with it in the former; supposing the Globe rectified to the Latitude of London.

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, 13¹⁄₆ 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.

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 27¹⁄₂ degrees: so that the Moon must go 27¹⁄₂ degrees more than round; and as much farther as the Sun advances in that interval, which is 2¹⁄₁₅ 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 12¹⁄₃ 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.

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.

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 66¹⁄₂ 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.

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.

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 5¹⁄₃ 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 19²⁄₃ 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 5¹⁄₃ 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 5¹⁄₃ 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 9²⁄₃ degrees on the parallel of London when Aries rises. But when the Descending Node comes to Aries, the Angle is 20¹⁄₃ 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 10²⁄₃ 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.

292. As there is a compleat revolution of the Nodes in 18²⁄₃ 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.

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.

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 23¹⁄₂ 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 23¹⁄₂ 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.