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

102 U,7NIVERSALS (GIWAVITATION.
ing poinlt, while tlhe sut \Nil1 do( tle salme inl onse(11quence of thlo
imutual attraction between them. lFicg-ure 40 NwNill illusttrate the
case. It is proved (Nat. Phil., Art. 89) tlat a force applied to
one body of a system will prodIuce tthe same effect on the center of gravity of that system, as if the force were applied to
Fig.. 40
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0 —... _.
4
tihe entire systeim collected at that center. Therefore, let S he
thel sllun, Fi tht earth, and C their center of gravity; and let thl
impulse be stucl as to mlove thie s-11um of both bo(ies over Ca,
ab, bo, &e., in any equal times, xwhile in each unit of time it
calrries iE over a given are, say 45~ of its circle, then, whlen the
center is at a, E: is at I, 4I5' friom a perp)endicullar at.a. Bult S
xlst b)e on the opposite side of a, and tat the samel distatnce fi'om
it as from ( lcf obre, because aC's distance frionl the cenlter relmait;lS tlaltered. T!lherefore, by tefl imllls)l given to IXC, and
the mutual attraction between IC and 8, the1t ltter lhals beenl
dtrawn la long t firom S to 1'. )Dra\ting at'ain tvFo cihrcles fitrou
the center b, one flor IE, thle other fo)r 8, tle n1ext positions for
the bodies tare 2 2and','While Ei wvas on the upper side of Cd,
S was drawn tow-\ard t.hat line, and now tcrosses it, and by its
own%-l inertia continues upward, althougrh E is now bclow the
line. In this manner the two bodlies revolve about a moving
center, deseribiig circles, relatively to that, blt curves of a totalttly different challacter in space. Thezse curves are always
some variety or otller of tle curve called anl cicycloid. Inl the