138

Mechanics.

pear, that Bodies under the Equator havethe greatest centrifugal Force, which thereacts in direct Opposition to Gravity, anddiminishes towards the Poles, with theSquares of the Distances from the Earth’sAxis. Hence also it is evident , that if everthe Earth was in a fluid State, and at thefame 'Time moving about its Axis, it mujl ne-cessarily put on the Figure , not of a perse SiSphere or Globe , but os an oblate Spheroid ,fatted towards both Poles ; as is manses lysewn by Experiment (XXXIV).

Plate V. (XXXTV) 1. Let AD = a, the Diameter of theFig. 8. Circle AMD; AH the Space which a Body A movesthrough in a constant Particle of Time by an uniformProjectile Force ; HE the Distance it is drawn from theTangent AH by the Centripetal Force (which is justsufficient to retain the Body moving in a circular Orbit)in the same Time.

2. Then since AH is indefinitely small, the ArchAE, and its Chord, will nearly coincide and be equalto AH, and will therefore also represent the Projectile

Force. But A D : AE : : AE ; As - HE -

AD

— the Central Force. Now A E is infinitely small inrespect of AD, therefore HE or A a is infinitely smallwith respect to AE.

3. If the Projectile Force or Velocity A E — V,and AD — a, the general Expression of the Central

V 1

Force will be — ; which therefore in different Circlesa

will be as the Squares of the Velocities direttly, and in-versely as the Diameters or Semi-diamcters of the Circles.

4. But in the fame Circle it will be direStly as theSquares of the Velocity, ^because in that Cafe a is given.

But