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

CINS'T'RT.'ronlREs. 97
o0ce orbit, but it is true also, that all the different bodics of a
sy.steml, describiung orbits about tle saell center of forc (, art
urged( tow-ard that center by attractions whiclt vtary, from oto
orbit to anotelr, invernselty ias the square of the distanuce.
et, a be the sicli-ilajor, land b the seomi-tmixnorx axis of ally
elliptic orbit. Theal a iUs the ilcan distance of all points of the
orbit flroli the. focus. liy Ca rule of mensuration, thle (aret of
the cllipsc:-:::,qb. If s:::: tl area describeld )by tle ratdius veetor in a unit of time, as one econd, and n:u........ te tl utber of sconwds in tlhe whole p)eriod of revolution, tlCen tllC ellipse also..:':t.
T-hetrtcefore italy Is ad; and 6; and:..... l.. eplcrs
third law (A.rt. 17 1),.. a';;.. ca; 8- t lnt, bcause the semi-parameter J2, is a third proportionall to the
sermi-axes ua and b6, o.... _ile ncc, substitutingP(t 2' 2 ~' 2
for s2, thlat is, F A Nr, in thle equation for IMt (Art. 1`79), we
fainldc! ~. in[ slM.-;''.'.yq a.fo. distance Or, thte force
variCS inversely as te squarellt of thle distalfnce, in diiffrCnlt 01orbits, as vwell as; inl different parts of tlhe satame orbit.'The s;atellites whlichl revolve al)out tlhe planets, are foi)und to
conf)rltr to eli]:,ler's lawts, atnId thcreforet the fthre whiclt urges
tellm toward tlteir rceSpt(ctite prilmtarics, varies it caclt case iilvcrsely as the square of the distalnce.
182. IBut thle inquiry still remains, does the, law of gravity,
as demonstrated in tlet ftorcgoint articles, lol4d good at tlhe
smwatle.st distances also? F'or example, do the tendencies of
bodies restiltg onl the ear'tl, ald of those elevated ill thle ir,
andl of the moon, toward the carth's center, come ln 1der thel
sae tc encral law? This is tIl very question \whiclh preslented
itself to the l.lind of INewton, after he had discovered that the
force wtvtich deflects tilc planets friom their lines of n-motion
toward the slnl varies inversely (as the squlare of their distance
firom it. As he noticed tle fall of an apple, tlhe inquiry arose
ItIay not tlisfill- be of tlhe,same natureltt as the /( rblinf of t tle