A S T R O N O M Y. 
tvTien the line of the apfes coincides with that of the fyzy- 
gies, and lead when thefe lines are at right angles to each 
other. Nor is the apogee of the Moon without an irre¬ 
gularity ; being found to move forward, when it coincides 
“with the line of the fyzygies ; and backward, when it cuts 
that line at right angles. Neither is this progrefs or re¬ 
grefs uniform ; for in the conjunction or oppofitlbn, it goes 
Drilldy forward ; and in the quadratures, it either moves 
flowly forward, (lands (till, or goes backward. The mo¬ 
tion of the nodes is alfo variable; being quicker and flower 
jn different politions. 
The phyfical caufe of the Moon’s motion about the 
Earth, is the fame as that of all the primary planets about 
the Sun, and of the fatellites about their primaries, viz. 
the mutual attraction between the Earth and Moon. As 
for the particular irregularities in the Moon’s motion, to* 
which the Earth and other planets are not fubjed't, they 
arife from the Sun, which acts on and diflurbs her in her 
ordinary courfe through her orbit; and are all mechani¬ 
cally deducible from the fame great law by which her ge¬ 
neral motion is directed, viz. the law of gravitation and 
attraction. The other Secondary planets, as thofe of Ju¬ 
piter, Saturn, &c. are alfo fubjeCt to the like irregularities 
with the Moon ; as they are expofed to the fame pertur- 
bating or difturbing force of the Sun ; but their diflance 
feCures them from being fo greatly affeCted as the Moon 
is, and alfo from being fo well obferved by us. For a fa¬ 
miliar idea of this matter, it mult firft be conlidered, that 
if the Sun aCted equally on the Earth and Moon, and al¬ 
ways in parallel lines, this action would ferve only to re- 
itrain them in their annual motions round the Sun, and no 
way affeCt their aftions on each other, or their motions 
about their common centre of gravity. But becaufe the 
Moon is nearer the Sun, in one half of her orbit, than the 
Earth is, but farther off in the other half of her orbit; 
and becaufe the power of gravity is always lefs at a greater 
diflance; it follows, that in one half of her orbit the Moon 
is more attracted than the Earth towards the Sun, and lefs 
attracted than the Earth in the other half: and hence ir¬ 
regularities neceffarily arife in the motions of the Moon • 
the excefs of attraction in the firft cafe, and the defeCt in 
the fecond, becoming a force that difturbs her motion : 
and befides, the aCtion of the Sun, on the Earth and Moon, 
is not directed in parallel lines, but ii: lines that meet in 
the centre of the Sun ; which makes the effeCt of the dif¬ 
turbing force ffill the more complex and eipbarrafling. 
And hence, as well as from the various fituations of the 
Moon, arife the numerous irregularities in her motions, 
and the equations, or corrections, employed in calculating 
her places, &c. 
Sir Ifaac Newton, as well as others, has computed the 
quantities of thefe irregularities from their caufes. He 
finds that the force added to the gravity of the Moon in 
her quadratures, is to the gravity with which (he would 
revolve in a circle about the Earth, at Iter prefent mean 
diflance, if the Sun had no effeft on her, as i to 178^: 
he finds that the force fnbduCted from her gravity in the 
conjunctions and oppofitions, is double of this quantity ; 
and that the area deferibed in a given time in the quarters, 
is to the area deferibed in the fame time in the conjunctions 
and oppofitions, as 10973 to 11073 : and he finds that, in 
fuch an orbit, her diflance from the Earth in her quarters, 
would be to her diftance in the conjunctions and oppofitions, 
as 70 to 69. As to the figure of the Moon, fuppofing her 
at firft to have been a fluid, like the fea, Sir Ifaac calcu¬ 
lates, that the Earth’s attraction would raife the water 
there near ninety feet high, as the attraction of the Moon 
raifes our fea twelve feet : whence the figure of the Moon 
muft be a fpheroid, whofe greateft diameter extended will 
pafs through the centre of the Earth ; and will be longer 
than the other diameter, perpendicular to it, by 180 feet; 
and hence it comes to pafs, that we always fee the fame 
face of the Moon ; for (he cannot reft in any other pofition, 
but always endeavours to conform herfelf to this fituation : 
Princip. lib. 3, prop. 38. The denlity of the Moon he 
Voj.. II. No, 77. 
concludes is to that of the Earth, as 9 to 5 nearly ; and 
that the mafs, or quantity of matter, in tile Moon, is to 
that of the Earth, as 1 to 26 nearly. 
The plane of the Moon’s orbit is inclined to that of the 
ecliptic, and makes with it an angle of about five degrees: 
but this inclination varies, being greateft when (lie is in tire- 
quarters, and leaft when in her fyzygies. As to tire ine¬ 
quality of the Moon’s motion, (he moves fwifter, and by 
the radius drawn from her to the Earth defcribcs a greater 
area in proportion to the time, alfo has an orbit lefs curved, 
and by that means comes nearer to the Earth, in her fyzy¬ 
gies or conjunctions, than in the quadratures, unlefs the 
motion of her eccentricity hinders it: which eccentricity 
is the greateft when the Moon’s apogee falls in the con* 
junction, but leaft when this falls in-1lie quadratures: her 
motion is alfo fwifter in the Earth’s aphelion than in its 
perihelion. The apogee alfo goes forward fwifter in the 
conjunction, and goes (lower at the quadratures : but her 
nodes are at reft in the conjrtnCtions, and recede fwifteft 
of all in the quadratures. The Moon alfo perpetually 
changes the figure of her orbit, or the fpecies of the eilipCe 
flic moves in. 
There are likewife fome other inequalities In the motion 
of this planet, which it is very difficult to reduce to any 
certain rule : as the velocities or horary motions of the 
apogee and nodes, and their equations, with the difference 
between the greateft eccentricity in the conjunctions, and 
the leaft in the quadratures ; and that inequality which is 
called the variation of the Moon. Thefe increafe and de- 
creafe annually, in a triplicate ratio of the apparent dia¬ 
meter of the Sun : and this variafusn is increafed and di- 
miniftied in a duplicate ratio of the time between the qua¬ 
dratures; as is proved by Newton in many parts of his 
Principia. He alio found that the apogees in the Moon’s 
fyzygies go forward, in refpeft of the fixed ftars, at the 
rate of 23' each day ; and backwards in the quadratures 
165' per day : and therefore the mean annual motions he 
eftimates at forty degrees. 
The gravity of the Moon towards the Earth is increafed 
by the aCtion of the Sun, w hen the Moon is in the qua¬ 
dratures, and dimini (lied in the fyzygies : and, from the 
fyzygies to the quadrature, the gravity of the Moon to¬ 
wards the Earth is continually increafed, and (lie is con¬ 
tinually retarded in her motion : but from the quadrature 
to the fyzygy, the Moon’s motion is perpetually dimini filed, 
and the motion in her orbit is accelerated. The Moon is 
lefs diftant from the Earth at the fyzygies, and more at 
the quadratures. As radius is to of the line of double; 
the Moon’s diftance from the fyzygy, fo is the addition of 
gravity in the quadratures, to the force which accelerates 
or retards the Moon in her orbit. And as radius is to 
the fum or difference of \ the radius and -| the cofine of 
double the diftance of the Moon from the fyzygy, fo is 
the addition of gravity in the quadratures to the decreafe. 
or increafe of the gravity of the Moon at that diftance. 
The apfes of the Moon go forward w hen (lie is in the 
fyzygies, and backward in the quadratures. But, in a 
whole revolution of the Moon, the progrefs exceeds the 
regrefs. In a whole revolution, the apfes go forward the 
fafteft of all when the line of the apfes is in the nodes; 
and in the fame cafe they go back the (lowed of all in the 
fame revolution. When the line of the apfes is in the 
quadratures, the apfes are carried in confequentia, the 
leaft of all in the fyzygies ; but they return tiie fwifteft in 
the quadratures ; and in this cafe the regrefs exceeds the 
progrefs, in one entire revolution of the Moon. The ec¬ 
centricity of the orbit undergoes various changes every re¬ 
volution. It is the greateft of all when the line of the 
apfes is in the fyzygies, and the lead when that line is in 
the quadratures. 
Confidering one entire revolution of the Moon, caeteris 
paribus, the nodes move in anfecedentia fwifteft of all 
when (lie is in the fyzygies ; then (lower and dower, till 
they are at reft, when (lie is in the quadratures. The line 
of nodes acquires fucceffively all ooffible lituations in ref. 
5 D F ca 
