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
51-1/2 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.
[Sidenote: 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.
+------+-----------+--------+---------+
| | Signs | Rising | Setting |
| | | Diff. | Diff. |
| Days | +--------+---------+
| | Degrees | 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 |
+------+-----------+--------+---------+
[Sidenote: 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]13-1/6 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_, 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.