373 ASTRO 
peel of the Sun; and every year it goes twice through 
the fyzygies, and twice through the quadratures. In one 
whole revolution of the Moon, the nodes go back very 
faft when they are in the quadratures ; then flower till 
they come to reft, when the line of nodes is in the fyzy- 
gies. The inclination of the plane of the orbit is changed 
by the fame force with which the nodes are moved ; being 
increafed as the Moon recedes from the node, and dimi- 
niflied as fhe approaches it. The inclination of the orbit 
is the leaft of all when the nodes are come to the fyzygies. 
For in the motion of the nodes from the fyzygies to the 
quadratures, and in one entire revolution of the Moon, 
the force which increafes the inclination exceeds that which 
diminiflies it; therefore the inclination is increafed ; and it 
is the greateft of all when the nodes are in the quadratures. 
The Moon’s motion being confidered in general: her 
gravity towards the Earth is diminifhed Coming nearer the 
Sun, and the periodical time is the greateft : as alfo the 
diftance of the Moon, caeteris paribus, is the greateft when 
the Earth is in the perihelion. All the errors in the Moon’s 
motion are fomething greater in the conjunction than in the 
oppolition. All the difturbing forces'are inverfely as the 
cube of the diftance of the Sun from the Earth ; which 
when it remains the fame, they are at the diftance of the 
Moon from the Earth. Confidering all the difturbing 
forces together, the diminution of gravity prevails. 
The figure of the Moon’s path about the Earth, is, as 
has been laid, nearly an ellipfe ; but her path, in moving 
together with the Earth about the Sun, is made up of a 
feries or repetition of epicycloids, and is in every point 
concave towards the Earth. With refpeCt to the Moon’s 
acceleration, it is a term ufed toexprefs the increafeof the 
Moon’s mean motion from the Sun, compared with the 
diurnal motion of the Earth; by which it appears that, 
from fome uncertain caufe, it is now a little quicker than 
it was formerly. Dr. Halley was led to the difeovery, or 
fufpicion, of this acceleration, by comparing the ancient 
eclipfes obferved at Babylon, &c. and thofe obferved by 
Albategnius in the ninth century, with fome of his own 
time. He could not however afeertain the quantity of the 
acceleration, becaufe the longitudes of Bagdat, Alexan¬ 
dria, and Aleppo, where the obfervations were made, had 
not been accurately determined. But fince his time the 
longitude of Alexandria has been afeertained by Chazelles; 
and Babylon, according to Ptolemy’s account, lies 50' eaft 
of Alexandria. From thefe data, Mr. Dunthorne, vol. 
Xlvi. Philof. Tranfadfions, compared the recorded times 
of feveral ancient and modern eclipfes, with the calcula¬ 
tions of them by his own tables, and thereby verified the 
fufpicion that had been (farted by Dr. Halley; for he found 
that the fame tables gave the Moon’s place more back¬ 
ward than her true place in ancient elipfes, and more for¬ 
ward than her true place in later eclipfes ; and thence he 
juftly inferred that her motion in ancient times was flower, 
and in later times quicker, than the tables gave it. Not 
content however with barely afeertaining the faCt, he pro¬ 
ceeded to determine, as well as the obervations would al¬ 
low, the quantity of the acceleration ; and by means of 
the moft authentic eclipfe, of which any good account re¬ 
mains, obferved at Babylon in the year 721 before Clirift, 
he found that the obferved beginning of this eclipfe was 
about an hour and three quarters fooner than the begin¬ 
ning by the tables ; and that therefore the Moon’s true 
place preceded her place by computation by about 50' of 
a degree at that time. Then admitting the acceleration tobe 
uniform, and the aggregate of it as the fquare of the time, 
it will be at the rate of about 10" in too years. 
Dr. Long, vol. ii. p. 436 of his Aftronomy, enumerates 
the following caufes, from fome one or more of which he 
fuppofes the acceleration may arife. Either ift, the an¬ 
nual and diurnal motion of the Earth continuing the fame, 
the Moon is really carried about the Earth with a greater 
velocity than formerly : or, 2dly, the diurnal motion of 
the Earth, and the periodical revolution of the Moon, con¬ 
suming the fame, the annual motion of the Earth about 
N O M Y. 
the Sun is retarded ; which makes the Sun’s apparent mo¬ 
tion in the ecliptic a little flower than formerly ; and con- 
fequently the Moon, in palling from any conjundtion with 
the Sun, takes up a lefs time before the again overtakes 
the Sun, and forms a fubfequent conjunction: in both thefe 
cafes, the motion of the Moon from the Sun is really ac¬ 
celerated, and the fynodical month actually fliortened : 
or, 3dly, the annual motion of the Earth, and the peri¬ 
odical revolution of the Moon, continuing the fame, the 
rotation of the Earth upon its axis is a little retarded ; in 
this cafe, days, hours, minutes, &c. by which all periods 
of time mult be meafured, appear of a longer duration ; 
and confequently the fynodical month will appear to be 
fliortened, though it really contain the fame quantity of 
abfolute time as it always did. If the quantity of matter 
in the body of the Sun be leflened, by the particles of 
light continually ftreaming from it, the motion of the 
Earth about the Sun may become flower: if the Earth 
increafes in bulk, the motion of the Moon about the Earth 
may thereby be quickened. 
M. de la Place, however, in the Mem. de l’Acad. Roy. 
des Scien. for 1786, has (hewn, that this acceleration of 
the Moon’s motion arifes from the aCtion of the Sim upon 
the Moon, combined with the variation of the eccentri¬ 
city of the Earth’s orbit. The eccentricity of the Earth’s 
orbit is, at prefent, diminifhing, and this arifes from the 
aCtion of the planets upon the Earth. The major axis of 
the Earth’s orbit is not altered by this, but the eccentricity 
is. The mean force of the Sun to dilate and contract the 
orbit of the Moon depends on the fquare of the eccentri¬ 
city of the Earth’s orbit. By the diminution of the ec¬ 
centricity, the Moon’s'mean motion is accelerated, and 
this is a circumftance which takes place at prefent. When 
the eccentricity is come to its minimum, the acceleration 
of the mean motion will ceafe; after which the eccentricity 
will increafe and the Moon’s mean motion will be retarded. 
This therefore caufes a fecular equation of the Moon’s 
mean motion, the period of which is very long. If n be 
the number of centuries from 1700, M. de la Place has com¬ 
puted the fecular equation tobe -}-i 1", 13572 s -f-o",04398// 3 ; 
this however cannot be true whatever be the value of n, 
becaufe the acceleration would then continually increafe ; 
but it may be extended back to the moft ancient obferva¬ 
tions of the Moon, and for 1000 or 1200 years to come, 
without any fenfible error. M. de la Lambre, from com¬ 
paring the modern obfervations at about the diftance of a 
century, found that the fecular mean motion of the Moon 
in the laft Tables of Mayer was too great by 25" ; and 
that the place of the Moon, calculated by thefe tables, 
ought to be corrected by the quantity —25"??-j-2", 135/2* 
-|-o"o043 98/2 3 . If the ancient obfervations of the Moon 
be compared with the places calculated by Mayer’s Tables 
with this correction, the errors will be comparatively very 
fmall, and no greater titan what might arife from the in¬ 
accuracy of their obfervations. M. de la I.ande, in his 
Tables of the Moon, has thus corrected Mayer’s Tables. 
Hence it appears, that the prefent acceleration of the 
Moon is nothing more than an equation, the period of 
which is very long; it will be accelerated and retarded by 
the fame quantity, and therefore, if the mean motion be 
taken for the whole time of acceleration or retardation, it 
will be found never to vary. 
The mean motion of the nodes and apogee of the Moon’s 
orbit is fubjeCt to a fecular equation. The fecular equa¬ 
tion of the nodes is >—2",784/2*—o’'oi0995/2 3 , which be¬ 
ing negative fhews that it is to be applied contrary to their 
mean motion. This fecular equation is ^ of the fecular 
equation of the mean motion. The fecular equation of 
the apogee is 1 of the fecular equation of the mean mo¬ 
tion, and is therefore —19",486/2*—cy',07697/2 3 , where 
the negative fign fhews that it is to be applied contrary to 
its mean motion. Hence all the irregularities of the Moon 
are but fo many equations, which return again in their re¬ 
gular order ; and the fame is (hewn to be true of the irre¬ 
gularities of Jupiter and Saturn 3 alfo as the major axes of 
Slseis 
