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

9o I'Ut'IV EHSAL, 0 RAVITATION.
mt0oonls path toward the ealrthl and may not the force in the
t\o e'atse.s be.Co as thle squltares of tile distlances ilnversely?
lect us then find what is the distanice through wlltich thle
mloon aI:lttatly. s!t,. d(/. ill a secolid of time. Let tile earth b)0
at E (FIlig. 3t7), altnd Ab the arc described by) the moon ill one
seconol. As shle was o (illn tow\ard:I
Fig. 37.
at tlt} poitt., 1e s twould }lave gone
over thle line A- l in olne seeol(],if.......
sotnic inil. ene latd not tlured h er
aside. T'lhiis influenc: e imust be directed to'z-lrd the eartlt E, bectause it is
arounlld ]i tlat thte radius -vet.tot describes equal areas in equal times
(Arlt. 1 73t. Thlerefore lt, olr thlo
Tversed fine Au, (which tlmay be consideret d equal to it), is thte distance
fillen thlrotugh in one second. Now
the diistance of thte mloon from the,earthl's center is 2)38,515 mtilcs (Art.
201). I1c nce, thle circumtfelrfelce is biowl. ti'te time of revolltion is 2T.32 days. (Art. 213.) Tllerefibre -A, the disattee
traveled iiit one second is obtained. Tlhis is so small, that its
versed sine Aa cant ot hbe calculated by ordinary trigonometrical tables; but is easily and accurately determinied b)y geometry; tlhus, 2A I: A:: At: A a; sitnee tite arc AB and thie
chord A1t lmay 1)e conlisidered identical. A,t) tllhus calculated,
is found to be 0.0.535 of anvSt inlch.l At t le surface of thle eartl,
a bodly fieels t in tie first sceold. I1n order to
(:iminish thlis fbr tlle 1r0o0e1's distanlce, we make thle )prolportion,
(23S8.545)': (3956)2::' 16.> ft.: 0.0523 6, agreeing'very actarattely witl tlhe distance \whiich the noon actually falls fiom at
tanlgent in a1 second of time. Wtlhen NewVtol, l}owever, first
made tl e complarison just describeld, thle result vwa's quite untsattisactorlty. tl tendelrcy of the imoon wuas about; too
greait. >Neat r 2,0 years afterward, wlen a new measuremlellnt of
at dteg'oC of tle nertidian lhad been made, and thus a corrected
nlag0,'itude of tle earth, lhe re peted thle prlocess, andl 1 f:111d
the law of attractlion it this case to be the same as elsewhere
in the solar slystelm.
Again, the nullmerous disturbances wiC the bodies of thle