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291. To be a little more particular, when the ascending node is in Aries, the angle is only 9 de. grees on the parallel of London when Aries rises. But when the descending node comes to Aries, the angle is 20 degrees; this occasions as great a difference of the Moon's rising in the same signs eve. ry nine years, as there would be on two parallels 10 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 Ascend. In the highest pt. Full in her Descend- In the lowest pt. of ing Node. of her Orbit.
12 15 A 15! 3 M20 4 A 30 3M15 4 A 321 3M405 A 16) 3M O
321 4 2514 50 4 455 151 4 2016 0 4 15 14 5 48 5 305 15) 6 015 45 5 4016 2015 28 5 7. 421 7 2016 15! 6 5616
45| 6 32 201 8 15.6 28 3516 461 8 017 81 7 45 17 16 361 9 1216 26! 9 4517 18 91117 30) 9 15 5410 307 0 10 4018
0/10 2017 52 10 0
15 16 16 16
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 blacklead 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, ought by the table to rise just at six o'clock, or at sun-set, on the 15thday of her age; being in the ecliptic at that time. But it must be considered, that the Moon is only 14 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. 292. As there is a complete revolution of the The peri
od of the nodes in 183 years, there must be a regular period
harvesta 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 benefii of her rising nearer the time of sun-set for a few day together about the full in harvest, than when she is tull 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 tall about the ascending node. In all the columns trom Nto S the harvestmoons descend gradually in the lunar orbit, and rise to less heights above the horizon. From Sto N they ascend in the same proportion, and rise to greater heighis 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 risings, though not at the same times, are nearly the same with regard to difference on time, as in the Moon's orbit were coinci. dent with the ecliptic.
Years in which the Harvest Moons are least beneficial.
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.
1798 1799 1800 1801 1802 1803 1804 1805 1806
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. The long
294. At the poles, one half of the ecliptic never continu. sets, and the other half never rises: and therefore,
as the Sun is always half a year in describing one light at half of the ecliptic, and as long in going through the poles.
ance of moon.
the other half, it is natural to imagine that the Sun contin ues half a year together above the horizon of each pole in its 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 be comes 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 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 is 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 fulls 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 hálf 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 Capri. corn, 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 lit. tle, 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 its north pole n inclines toward the Sun, and Ethe Earth in winter, when its 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, op ons 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 polen; 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 toward him. Thus in our summer, the Moon is above the horizon of the north pole, while she describes the northern half of the ecliptic pos, or from her third quarter to her first; and below the horizon during her progress through the southern half - vg op; highest at the change, most depressed at the full. But in winter, when the Earth is at E, and its 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} degrees above the horizon at B and b, and as much below it at D and d, equal to the inclination