Mechanics. 141

4.2000000 Feet in the Diameter of the Earth, we have■P = 5083 Seconds, or 84' 43"; which is the Timeof Revolution to acquire a Centrifugal Force equal tothat of Gravity at the Earth’s Surface. Consequentlywere the Earth to revolve in 84' 43" instead of 24Hours, the Bodies on its Surface would lose all theirWeight, and be as liable to fall off as to abide thereon.

19. From what has been demonstrated we may dis-cover the Law of Gravitation at the Moon ; for sincethe Distance of the Moon from the Earth’s Centre isto the Distance of the Earth’s Surface as 60 to 1 ; andsince the periodical Time at the Earth’s Surface is5083"’, therefore the Periodical Time at the Moon

may be found (by Art. ir.) thus; i 3 : 60 3 : : 5083*

: P 1 ; whence P — 5083 X 6oi — 2362000'' — 27,3Days, the Periodical Time of the Moon, if moved bya Centripetal Power, as Gravity decreasing with theSquares of the Disances inversely : And therefore sincethe Periodical Time , thus found , is equal very nearly tothe real Periodical Time of the Moon , it shews that Lawtakes Place between the Earth and Moon. This mightalso be shewn, from the Time of the Moon’s Revolu-tion, but one Proof is enough. I shall also hereaftershew, that this is the general Law of the whole Plane-tary System.

20. Since we had — =: the Central Force, when

a is given, the Force will be as ^ ; that is, in equal

Circles the Centrifugal Forces will be as the Squares ofthe Velocities inversely. And therefore since in theTime of the Earth’s Revolution, viz. 24 Hours, there

are 68400''; if we fay, as 5083^ : 68400* : : 1 : 289nearly ; that is, the Centrifugal Force under the Equator ,arising from the Earth's Rotation , is to the Power of Gra-vity on its Surface as I to 289 nearly.

21. Since the Time of Revolution of a Body under P] a teVL

the Equator EQ_, and in any parallel of Latitude B G, ^

is equal, the Centrifugal Forces are as the Distances

EC, B A, from the Centre of Motion (by Art. 16.)or, as Radius C B to the Cc-fme A B of the Latitude.

22. But