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, ♋TR the Tropic of Cancer, LT♑ the Tropic of Capricorn, ♋EU♑ 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 ♈ Aries and ♎ Libra. K is the Hour circle with its Index, F the North pole of the Globe elevated to the Latitude of London[[60]], namely 511⁄2 degrees above the Horizon; and P the South Pole depressed as much below it. Because of the oblique position of the Sphere in this Latitude, the Ecliptic has the high elevation N♋ above the Horizon, making the Angle NU♋ of 62 degrees with it when ♋ Cancer is on the Meridian, at which time ♎ Libra rises in the East. But let the Globe be turned half round its Axis, till ♑ Capricorn comes to the Meridian and ♈ Aries rises in the East, and then the Ecliptic will have the low elevation NL above the Horizon making only an Angle NUL of 15 degrees, with it; which is 47 degrees less than the former Angle, equal to the distance between the Tropics.
Least and greatest, when.
276. The smallest Angle made by the Ecliptic and Horizon is when Aries rises, 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 [[61]]Sidereal 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.
| Days | Signs | Degrees | Rising Diff. | Setting Diff. | ||
|---|---|---|---|---|---|---|
| H. | M. | H. | M. | |||
| 1 | ♋ | 13 | 1 | 5 | 0 | 50 |
| 2 | 26 | 1 | 10 | 0 | 43 | |
| 3 | ♌ | 10 | 1 | 14 | 0 | 37 |
| 4 | 23 | 1 | 17 | 0 | 32 | |
| 5 | ♍ | 6 | 1 | 16 | 0 | 28 |
| 6 | 19 | 1 | 15 | 0 | 24 | |
| 7 | ♎ | 2 | 1 | 15 | 0 | 20 |
| 8 | 15 | 1 | 15 | 0 | 18 | |
| 9 | 28 | 1 | 15 | 0 | 17 | |
| 10 | ♏ | 12 | 1 | 15 | 0 | 22 |
| 11 | 25 | 1 | 14 | 0 | 30 | |
| 12 | ♐ | 8 | 1 | 13 | 0 | 39 |
| 13 | 21 | 1 | 10 | 0 | 47 | |
| 14 | ♑ | 4 | 1 | 4 | 0 | 56 |
| 15 | 17 | 0 | 46 | 1 | 5 | |
| 16 | ♒ | 1 | 0 | 40 | 1 | 8 |
| 17 | 14 | 0 | 35 | 1 | 12 | |
| 18 | 27 | 0 | 30 | 1 | 15 | |
| 19 | ♓ | 10 | 0 | 25 | 1 | 16 |
| 20 | 23 | 0 | 20 | 1 | 17 | |
| 21 | ♈ | 7 | 0 | 17 | 1 | 16 |
| 22 | 20 | 0 | 17 | 1 | 15 | |
| 23 | ♉ | 3 | 0 | 20 | 1 | 15 |
| 24 | 16 | 0 | 24 | 1 | 15 | |
| 25 | 29 | 0 | 30 | 1 | 14 | |
| 26 | ♊ | 13 | 0 | 40 | 1 | 13 |
| 27 | 26 | 0 | 50 | 1 | 7 | |
| 28 | ♋ | 9 | 1 | 0 | 1 | 58 |
Quantity of this Angle at London.
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.
Why the Moon is always Full in different Signs.
Her periodical and synodical Revolution exemplified.