Mechanics

The common Centre of Gravity of anyNumber of Bodies being supported, none

of

them affect the other by their gravitating on the LineA B ; and also every Particle of that Line will be af-fected with those Gravities, or be carried downwards,but with an unequal Force, except one, on which theForce of each Body is equal; and since we shewed theForce of any Body A or B arises from its Quantity ofMatter multiplied into its Velocity, it is evident, thatone Particle must be so situated at C, that B : A( :: v : V) : : AC : BC. Because then we have

BX V = AXn = BXAC=AXBC, Or the Pro-duct of each Body into its Velocity is the fame at thePoint C, but no other.

2. The Point C is therefore called the common Centrees Gravity of both the Bodies. If the Distance be-tween the Centres of the Bodies be given, and theMagnitude of each, the Distance of the Point C fromeither may be thus found ; asB-[-A:B:;AC-[-BC(r AB) : AC. Let A represent the Earth, and Bthe Moon; then will A : B :: 40 : i, nearly; andsince A B — 60 Semidiameters of the Earth; we have

40 — 1 : 1 :: 60 : — = AC; and since a Semidiame-4i

ter contains about 4000 Miles, we have

60 X 400041

— 5854 — AC, from whence taking one Semidiame-ter AG =4000, there will remain GC = 1584 Miles,for the Distance of the Point C from the Earth’s Surface.

3. Since the Earth and Moon act on each other byAttraction, it is evident they must both revolve aboutthe coijimon Centre of Gravity C ; whence this PointC, and not the Centre of the Earth A, is that which theMoon regards in her periodical Revolutions, and werethere no other Bodies in the Heavens but the Earth andMoon, this common Centre of Gravity C would be atrest, or a fixed Point.

4. But since the large Body of the Sun commands(by the fame Power of Attraction) the Earth and Moon

to