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

N TMmERICAI, mrEt'I1ONs. 29145
a body moves with less velocity, wlhen tfle distalnce fiom thle
sun is greater, it will be convellient, ill order toavoid firactional forms, to use the reciprocal of V, instead of V itself. Let.R (retarda tion) be equll to V; then V and V2; heneo
Jtht2:II' It2
tt2[ q "; ". 2 c 1) (1). If, thrierefore, t indicates how muchll
lowecr a planet mlovcs tlhan anotlher as thle cearthll talkel as a
standarld, the square of I.t will show low much furtler fr'om
theo slun te plalnet is thanl thle:carth. ".Agaii, since Vco f V3 B uj.' ut, by Kepler's law;")'.3 J3.;
1)2 1.... 3' or-~-3,. Ro P ] (2).
Consequently, if I.:t expresses hlow many times slower thlan
thle arth a, given plallct moves, the cubc of l.t will cxpress tho
rel ati vc lpcriod(l ic tin e.l
Finally, by the law of glra-vitation, the, folrce of gravitatioln
toward the central body varies as the squaro of tile distance
illYInvrsly, or01' G But if thl reciprocal f gravity be called I'ltvrrv, and exprel)ssed by L, telicn t.; buitoD but Rc D,.lt' co 1)2,' tll(l ].C'' 1a (3)..Thl'erefore, if it denotes how lmuch sBlower a p1lanet iloves ill
its orbit ttan the earth, Rl will denote htow nu\ch less thle
fiaml body gravitates toward the enltral: body. Collccting
thlese several re'sults, it appears that t/e reci2procal of velocity
IR, Mthe di:'tane I.), t./ui periodic time P, andl the t'ecap'rocal qf
graxity L, are respectively d(enoted( by the geomctrical scries,
t{, R,:f*,: i., in W\litch tlhe first term and tlhe ratio are cqua.
888. A mnmbcer of very useful and colnvcelient rules, may
be decived from this numlcrical relation betwree the members
of tlhe solar system t; since% whenl any one of tilhe fourl thinl's
amed l is givel ttll th o-'Tst may )e fou nd from it; and each
of the fol may 1be) found llill four dilffrent ways whCn11 thle otherC'
mClenlbclrs of the series are given Tll tis will be obvious from a
ifew examplles.