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son of this.
But re. gether. At the polar circles, where the mild season
is of according
short duration, the autumnal full Moon to the dis.rises at sun-set from the first to the third quarter. tances of And at the poles, where the Sun is for half a year places from it.
absent, the winter full Moons shine constantly with
out setting from the first to the third quarter. The rea. It is soon said that all these phenomena are owing
to the different angles made by the horizon and different parts of the Moon's orbit; and that the Moon can be full but once or twice in a year in those parts of her orbit which rise with the least angles. But to explain this subject intelligibly, we must dwell much longer upon it.
274. The* plane of the equinoctial is perpendicular to the Earth's axis; and therefore, as the Earth turns round its axis, all parts of the equinoctial make equal angles with the horizon both at rising and setting; so that equal portions of it always rise or set in equal times. Consequently, if the Moon's motion were equable, and in the equinoctial, at the rate of 12 degrees 11 min. from the Sun every day, as it is in her orbit, she would rise and set 50 minutes later every day than on the preceding; for 12 deg. 11 min. of the equinoctial, rise or set in 50 minutes of time in all latitudes.
275. But the Moon's motion is so nearly in the ecliptic, that we may consider her at present as moving in it. Now the different parts of the ecliptic, on account of its obliquity to the Earth's axis, make very different angles with the horizon as they rise or set. Those parts or signs which rise with the smallest angles set with the greatest; and vice versa. In equal times, whenever this angle is least, a greater portion of the ecliptic rises than when the angle is larger; as may be seen by elevating the pole of a globe to any considerable latitude, and then
* If a globe be cut quite through upon any circle, the flat surface where it is so divided is the plane of that circle.
turning it round its axis. Consequently, when the plate Moon is in those signs which rise or set with the smallest angles, she rises or sets with the least difference of time; and with the greatest difference in Fig. III. those signs which rise or set with the greatest angles.
But, because all who read this treatise may not be provided with globes, though in this case it is requisite to know how to use them, we shall substitute the figure of a globe; in which FUP is the axis, os TR the tropic of Cancer, Lt vs the tropic of Capricorn, s EU is the ecliptic touching both the tropics, which are 47 degrees from each other, and AB the horizon. The equator being in the middle between the tropics, is cut by the ecliptic in two opposite points, which are the beginnings of op Aries and a Libra; K is the hour-circle with its index, F the north pole of the globe elevated to a , considerable latitude, suppose 40 degrees above the horizon; and P the south pole depressed as much Fig. III. below it. Because of the oblique position of the sphere in this latitude, the ecliptic has the high ele. vation N o above the horizon, making the angle The differNUS of 73, degrees with it when s Cancer is on ent angles the meridian, at which time = Libra rises in the the eclip. east. But let the globe be turned half round its axis, tic and ho
rizon. till vs Capricorn comes to the meridian and op Aries rises in the east, and then the ecliptic will have the low elevation NL above the horizon, making only an angle NUL of 26} degrees with it; which is 47 degrees less than the former angle, equal to the distance between the tropics.
276. In northern latitudes, the smallest angle Least and made by the ecliptic and horizon is when Aries rises, greatest, at which time Libra sets; the greatest when Libra rises, at which time Aries sets. From the rising of Aries to the rising of Libra (which is twelve* side
* The ecliptic, together with the fixed stars, make 366 apparent diurnal revolutions about the Earth in a year; the Sun only 365. Therefore the stars gain 3 minutes 56 sc
510 100 1410
ral hours) the angle increases ; and from the rising of Libra to the rising of Aries, it decreases in the same proportion. By this article and the preceding it appears that the ecliptic rises fastest about Aries,
and slowest about Libra. Result of 277. On the parallel of London, as much of the the quan: ecliptic rises about Pisces tity of this and Aries in two hours as
Rising Setting angle at
Diff. Diff. I.ondon. the Moon goes through in six days: and therefore
H. M. H. M. while the Moon is in these 7. 137 signs, she differs but two 2) hours in rising for six days 3 & 10
1710 together; that is, about 20%
ming 611 minutes later every day or
19/1 night than on the preced- 7+ 211 ing, at a mean rate. But 8
281 in fourteen days afterward,
10lm 1211 1510
81 130 opposite signs to Pisces 13
1010 and Aries; and then she 14118 41 410 differs almost four times as
1710 much in rising; namely, 17
911 000 time the moon finishes her.
50 43 37 32 28 24 20 18 17 22 30 39 47 56 5 8 12 15 16 17 16 15 11 15 14 13
310 1610 2910
conds upon the Sun every day; so that a sideral day contains only 23 hours 56 minutes of mean solar time ; and a natural or solar day 24 hours. Hence 12 sideral hours are one minute 58 seconds shorter than 12 solar hours.
period round the ecliptic, and gets 9 degrees into PLATE the same sign from the beginning of which she set out. Thus it appears by the table, that when the Moon is in me and she rises an hour and a quarter later every day than she rose on the former; and differs only 28, 24, 20, 18 or 17 minutes in setting. But, when she comes to * and op, she is only 20 or 17 minutes later in 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* 133 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 on the hour-circle. A few of these patches are represented by dots at () 1 2 3, &c. on the ecliptic, Fig. III. which has the position LUI when Aries rises in the east; and by the dots 0123, &c. when Libra rises in the east, at which time the ecliptic has the position EU v8: 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 in 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 remembered than any other. Then turn the globe round westward, and in that time, suppose the patch 0 to have moved thence
* The Sun advances almost a degree in the ecliptic in 24 hours, the same way that the Moon moves ; and therefore the Moon by advancing 134 degrees in that time, goes little more than 12 degrees farther from the Sun than she was on the day before.
to 1, 134 degrees, while the Earth turns once round its axis, and you will see that I 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 in setting on the western side of the horizon, which shews that the Moon's setting will be so much retarded 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. 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 while 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.