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

L,UNARIl I ROUARVITIE8$. 1 3-1.
S aldl let tIhe parallelogram K(F be described, ha.vig".i IA:
for its diagomIal, anlld havinig its sides parallel to EM and ES.
JAIlth fori'.c M 1G-may 1) res i olved into two, Al'P and M'iN, of
whlich, M..., directed toward I, the celttoer of the earthl, increases tihe gravity of the moon to tie ceartl, atd does not;
h-inder thec arneas dscribed by the radius vector- firom lcilncl
pl:olp.orItional to thlc times,'t'lic otlher frce At Li draws tihao.:O1101 in the dtirectioin of' the line joiling the cenltcers of th:o
sun:and cartlh. It is, however, only thle excess of thlis foree
abovve tihe forcc rptlresented 1b' SE, or that wlieb dira.ws the
carthi to the ll sutinl, which disturbs tlhe relative positionl of the
moonl and earth. 11tis is evident, fotr if KM5[ wvere just eqtal to
_iES. no disturbanc e of thie mnoon, relative to the etirtlt, ouild
arise tfrom it. if, then, ES be taken froim MNK, thle dlifi'lirenco
IlkI is thle wlthole fiorce inl tile direction parallel to SI, by which
the sun disturbs the relative position of the moon and eartlh.
JNowt, if int MN5IIN, MNb taken qc:ual to 1 ", anld if iN'() 1)O
drawn perpeldlicular to the radius vectUor E[M plrodnuccd, tile
foree AMN tlmay be resolved into two, M() a1nd ()N, thle Iirst
lesscening the uratvity of the to the earth; and thle seconid
beitg parallel to thte tangient of tlhe lltoon's orbit illn M, acccc.ratoes the moon's motion from (' to.A, anlad retards it from nA
to I), and so altcernately in tile other two quadrant s. T.Ius tloe
whv1ole solar fTi)reC directed to the center of the a carth, is com.posed of tie two parts MI? and M1O, which arc soe,'tcetinmes opP/osed to 0one antlother, Ibut wtich never affect the unitformt
dlescription of thle areas about 1. Netar the quladratures tlte
foirce All) I vanishes, and the thrce A. I., whlich inTceasces the
gravity of thet moot to the ca.arth, cointci(ls withl (IN or I.).I.
As tile moon approaches tlhe conjunction at A, the tParce A()
prevaUils ovcr A.I, and lessens t.h'e gravity of ite imoon to thl
cartlit. I'n tic oy:posite point of the orbit, weln the moon is ill
ol)pusitioln at II3, the force wAith whicIh tile sun draws the moon(.
is less than thfat with whlichl tile sun~ draws tlec eairtli,,so tlat
tthe effect of thce solar tbrce is to separate the tc moon and earth,
or to increase tlheir distanlc; that is, it is the same, as ift conceiivljg tile eart]h ot to be acted onl, tile sut{'s for)ee droew thlt
Illoot inl tilhe dircction firom IC to.I. T''hlis t'rce is negatiCve,
therefore int respect to the three at;A, anLd thle effeet in both