305
hours ; from the Sun to the Sun again in 29J-5UJ clays: the former isthe length of her sidereal day, and the latter the length of her solarday. A body moving round the Sun would have a solar day inevery revolution, without turning on its axis; the same as if ithad been at rest, and the Sun moved round it: but without turn-ing round its axis it could never have one sidereal day, because itwould always keep the same side towards any particular star. Ifthe Earth had no annual motion, the Moon would go round it soas to complete a lunation, a sidereal, and a solar clay, all in thesame time. But, because the Earth goes forward in its orbit, whilethe Moon goes round the Earth in her orbit, the Moon must go asmuch more than round her orbit, from change to change in com-pleting a solar day, as the Earth has gone forward in its orbit dur-ing that lime, i. c. almost a twelfth part of a circle. If the Earth had no annual motion, the Moon’s motion round the Earth , and hertrack in open space, would bgalways the same. But aS the Earth and Moon move round the Sun, the Moon ’s real path in the hea-vens is very different from Iter visible path round the Earth ; thelatter being in a progressive circle, and the former in a curve ofdifferent degrees of concavity ; which would always be the samein the same parts of the heavens, if the Moon performed a com-plete number of lunations in a year without any fraction. '1 oillustrate Ibis, let the nail in the end of the axle of a chariot-wheelrepresent the Earth, and a pin in the nave the Moon : if the bodyof the chariot be propped up so as to keep that wheel from touch-ing the ground, and the wheel be then turned round by hand, thepin will describe a circle both round the nail and in the space itmoves through. But if the props be taken away, the horses putto, and the chariot driven over a piece of ground which is circu-larly convex ; the nail in the axle will describe a circular curve,and the pin in the nave will still describe a circle round the pro-gressive nail in the axle, hut not in the space through which itmoves. In this case, the curve described by the nail will resem-ble in miniature as much of the Earth ’s annual path round theSun, as it describes whilst the Moon goes as often- round the Earth as the pin does round the nail: and the curve described by thepin will have some resemblance to the Moon ’s path during somany lunations. The surface of the Moon being uneven, someare surprised that her edge does not appear jagged, as well as thecurve bounding the light and dark places. But if we consider,that what we call the edge of the Moon ’s disk is not a single lineset round with mountains, in which case it would appear irregu-larly indented, but a large zone, having many mountains lytngbehind one another from the observer’s eye, we shall find thatthe mountains in some rows will be opposite to the vales in others ;and thus fill up tlie inequalities so as to make her appear quiteround; just as when one looks at an orange, although its rough-ness be very discernible on the side next the eye, especially ifthe Sun or a candle shines ’ " nely upon that side, yet the lineterminating the visible part still appears smooth and even.
(154.) Principal Elements oftheLunarTheory taken from the ob-servations of several eminent Astronomers . [See De La Lande’sThird Edition of his Astronomy, Tom. II. Art. 1479, 1480.]
r Kepler and Ilorrox.
10
7
48
51
Mean motion of the
Newton, Flamsteed, and
Halley.
io
7
50
25
years, of which
La Hire...
10
7
50
1
25 are Bissextiles
Cassini.
10
7
49
52
i. e. in 36525 davs
Mayer’s First Tables.
10
7
52
20
of 24 hours
-Second Tables.
10
7
53
35
'•M. de Lambre.
10
7
a 3
12
f Kepler and La Hire.
3
H)
14
16
Ilorrox.
3
19
4
10
Motion of the Apo-
Flamsteed, Halley, and
eee in 100 Julian-1 Mayeri.
3
19
11
15
■years
Cassini.
3
19
14
16
Badly, (Mem. Academ.
1763)..... 3 19 5 0
[Kepler, Ilorrox, and La
4
4
Morton of the Node 1 Flamstecc , and Ha lley...
14
14
11
11
7
15
m 100 Juhanyears | Cas ,. ni .'...
4
14
11
5
4
14
11
15
VOL. 1. —NO. 20.
s.
©
/
V
,Kepler...
6
8
13
49
Horrox..-.
6
8
12
49
La Hire.
6
8
18
5
Flamsteed..
6
8
16
19
mean longitude for
Halley.
6
8
15
19
the beginning of’
Cassini.
6
8
14
55
1750.
Mayer, (First'Fables)...
6
8
16
53
-(Second Tables)
6
8
17
19
Mason, in 1780....
6
8
17
16
^ M. de Lambre, in 1787.
6
8
17
15
f Kepler.
5
21
30
33
Ilorrox.
5
20
30
33
I .a Hire.
5
20
40
54
Longitude of the
Flamsteed..
5
20
58
52
Apogee, for the-(
Halley.
5
20
58
52
beginning of 1750.
Cassini.
5
21
1
21
Mayer, (Old Tables)....
5
20
56
47
- (New 'fables)...
5
20
55
51
Mason, in 1780 .
5
20
54
53
, Kepler.
9
10
33
14
Ilorrox.
9
10
15
14
Longitude of the As-
Ea Hire.
9
10
21
' 0
ceuding Node for.
Flamsteed.
9
10
15
0
the beginning of
Halley.
9
10
13
59
1750.
Cassini.
9
10
18
8
Mayer.
9
10
19
9
^•Mason, in 1780.
9
10
20
0
[ Flamsteed.
0
6
18
43
Euler.
0
6
18
18
Mean Elliptic Equa-
0
6
18
43
tion of the Lunar<
Clairaut..
0
6
18
I
Orbit.
Mayer, (First Tables)...
0
6
18
44
- (Second’Fables)
0
6
18
32
.Mason.
0
6
18
32
(155.) The different circumstances oftheMoon, necessary in con-structing Lunar Tables, as deduced by M. de La Lande from thebest observations, are as below:
Tropic Revolution of the Moon ..
Sidereal or periodic Revolution, the pre- 4cession of the Equinoxes in a century / 27
being supposed 1° 23' 45". )
Synodic Revolution for 1700, according Xto Mayer, the motion of the Sun over ( „„
100 Revolutions, in 100 Julian years, l
being supposed 46' 0". *
Hence the Lunar Year of 12 synodic |
Revolutions consists of.)
Synodic revolution in the time of Pto- )lemy, according to his observations... (
Synodic revolution, B. C. .300, accord-)
ing to Mayer.$
Hence the diminution of a synodic)
month in 2000 years amounts to.$
Or, in sexagesimal parts of a second ; to
Anomalistic revolution.
Revolution from the ascending or de- 4scending node to the same again, or >
her nodical revolution. >
Tropical revolution of the apogee, 8)
years, 311 days, or.$
Sidereal or periodic revolution of the )
apogee.ji
Tropic revolution of the node, 18 com- ^
moil years, and 22S days, or.)
Sidereal or periodic revolution of the )
node. J
Diurnal mean motion with respect to 4the equinox, or her tropical diurnal Vmoiion ............... J
4 1 Relative
D. H.
M.
s.
27 7
43
4,6795
27 7
43
11,5259
29 12
44
2,8283
354 8
48
33,9396
29 12
44
3,2622?
29 12
44
3,4015
0,5732
34'" 23*'
x>. ;
FJ. M.
s.
27 13 18
33,9499
27
5 5
35,6030
3231
8 34
57,6177
3232 1
!1 11
39,4089
6798
4 52
52,0296
6793
7 13
17,7440
o
©
' 35",
,02784394