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

:128'itI MtOfi.
results halve eons-pired, witll those of ontg-(ontiin edttl otb)servatioll, to finrnislh th te nmeans of aseertailnillll \witlt grea t t xacttst ss,
the place of thil moontl ill tie h ]cavcns at anty givenll inIstant of
tine, l:)St or futurel, d ttus to enable astro'mllersl to letertellto longitudes, to calctulate eclipses, and to solve vtarious othtrt
problelmts of thle ighlest interest. A coi)mlete ultlerstanldinlg
of all thel irregulloaritics of tile hmoont's mnotionlls lmust f)be.soug'ht
for iln nore extcnsi\c t.reatises of atstrtoltonolm thaltn the~ pre senlt
but somtie cneral aequlaintalnc witlt t}he subject, clear land intelligible, as fatr uis it goes, tlmay e acquired b'y first tfgainilg a
distinlet idea of the mutual actionts of the sun,) the m11oo1n, and
the eartlh.
225. 7The iirretulat-Zi ties ff the.rmoon's imotionrs at fe /drjl cMfi
to ther cdist'uterinqly/ inlu/ence oqf thCe sun,, w/ itfh ofpr,'a/ttf irn two.wayts J niinst, btin unequally on1 the earit and moo'n, a!nd,
srcondl/, //y (tctiny obqti/u'uely oz /e thmoan.
If the sul acted equally on the earth and moon, and always
int parallel lniets, tlis action would s8crve oiily to re'stnrain It hemt
iln ttlcir anul lt otions round thle still, a1d would not af1iect
t.lcir actionsl ol caII otier', or their motions abolut tlheir coinlmion center of gravity. Inl that case, if theyl were allowed to
fall directly toward the smi, they would fall equally, tand their
rlesl)ctive sittmations would not be affected by their delscclldilg
equally toward it. AW'e iniglt tihen conceive tthem as iln a
piacn, every part, of wlhicll being equalltly acted oil by thIe su1,
tle w\}ole plane would descend towardt the sun, but t}he respe.cctivc motions of tlhe earth dlll the nmoon ill thlis phlane would
be thle samtl as if it were qutlicscelt. tllpposiing, thlten, this
planlle: lan1d all iln it'to have anr annual Imotion imprinted o1 it,
it would move regularl y roum d the sun, till ]til the earth andl
mooin woulld move ill it, \itht respect to eachl otler, as if thie
planle were;at rest, without any"01 irretgulcarities. Liut becIause
tlie mlooln is inearer thel sunl ill oneha-llf of her orbit tlitan the
earthl is, ald in tle oticir half of h~er orbit is at a greater distanlc tlhatnt thle eartlh friom tile suntl, wlile the power of gravity
is always greater at a less distaance, it follows, tlhat in one-half
of ler orbit time tmoon is mtiorle attractedt tian t ellc arthIt towuard
tlhe sun, and lin the otlier half less attracted thanl tlhe eart}h.
Tllc e7ace(-a-s's of the attractionl in tie first case, atnd\ thla e d<cct in