An introduction to astronomy: designed as a text-book for the use of students in college. By Denison Olmsted ...

i 3 TrI1, M~OON.
In like manner, we shlall finld the glreater inequalities of t]he
m10oon's motions are tlhemselves subject to stbordinate ilnequalities whiclh give rise to smallelr equatiolls, anlld these to smaller
still, to the last dtcogrc of refinement.
I3t. IN'cxt to the equatiol of the center, te gr'catcst colrrection to be alpplied to tile moon's longitude, is tlhat which
belongs to the.]t'C.ction..I1e Ceection is a ch4angcye qf Si' in
t/de tluna(t' orbit, by w\licht its eccentricity is sometimes ineret sctd,
and sometimes (liminishied. It depends on thlc position of the
line of the apsides withl respect to the line of the syzygies.
TThis irregularity, and its connlction with tthe pllace of the
pe'igee withl respect to tlet place of conjullnction l or oosition,
was' known 1as a. ft(Gt to the ancienlt astronomer's, I tipparftius
and Ptolemy; but its cause vwas fitrst explalined by Newton inl
conformity w\itI the law of univer'sal gravitation. It was
founld, y observation, tlhat the equationt of tle center itself
Mwtas silubjct to a periodic:al vaxria.tion, being greater than its
mean, andl greatest of all when the conjunction or opposition
takes place at the perigee or lapogree, and least of till when the
conjunctioll or opposition takes pl:ace at at poiltt llalf wSay betw\eelln the perl'igee 1an(ld apogee; or, in thle mnore colnloln Iangmuage-; of astronomlers, tle eqltuation of the center is incrleased
whtlten the line oft tlie apsides is ill szy'gy, and dilminishll wlell
that line is in qadriature. itf, for exat ple) when thle line of
tie apsi(les is it syzygY) we compuitell l the moon's place by dcducting the equation of the center fi'om thle mean atnom.aly (see
Art. 200), seven days after cotjunletion, the comllutel Ilongituide will bo greater than flhat detcrmiined by actual obserltvation, by about 80 lminltes; tbut if tlhe same estimate is made
wihen i te line of the apsildes is in qua(lrature, the comlputed
longitude Nwill be less than the obscrved, by tihe same quantity.
1Theso resullts plainly show fa connection between the velocity
of tie moonl's motions and the position of the line of tle apsides
wvith re1spect to tle linle of the syzygics.
239. iNoQw any cause which, at tlhe plerigee, should havo
tle effcct to increase the mooon's gravitation toward the ear'th
beyond its c mean, anld, at the apogee, to (limlillisli the mloon's
gravitation toward the cartl, would augment the diftrenceo