Mechanics.

143

• £ X X n ss % X

will be as --= - impelling it towards the Ccn-

a n a

ter C. Such a Particle will be represented by x, andtherefore its Weight will be - * * * — f. s .L x . x . 2n( jas this is the Fluxion of the whole Weight of the Co-lumn C B, the Fluent thereof x __f ssx . will

n -f-1 a" 2 s

be the Weight of the said Column of Particles C B.

27. If now we consider the Column of ParticlesCE, which is of equal Weight, since in this Cafe theAngle N C E is a Right one, we shall have x = a, andf= I; wherefore the Weight of the Column C E wil]h Z X (2 n + 1 f Q Q

be --j therefore the Weight of a

n + ia* 2 ct 0

Column every where is equal

2n + i

/ £ X * + 1 /n* ! \

( — -- ---1 therefore we have (by pro

« -f- 1 a n % a J

per Reduction) 2 g x ” ‘ — ?r -j- 1 X f s s 1

x* — 2 g — n f—f X a ” -f- 1 for a general Equation.

28. Whence, putting s =. 0, we have 2 g x —

_ I

2 g —n f —f X an -{- ' j and therefore a : x :: 2 g « -j- *

r

: 2 g — nf — f " -f- ' :: C E : C N, so is the Diameterof the Equator to the Axis of the Earth.

29. Hence, upon the Hypothesis of an uniform Gra-vity, we have n — o\ in that Cafe 2 g : 2 g — f :C E : C N. But the Gravity (g) is to the Centrifu-gal Force (f) under the Equator, as 289 to 1 ( per Art.20.) Wherefore in this Cafe CE : C N :: 578 : 577.

30. If the Earth were to revolve in 84' 43", theCentrifugal Force would be equal to Gravity (Art. 18.)or g and then C E : C N :: 2 : 1. If the Earthwere to revolve quicker than that, the Particles wouldfly off, and the Earth be reduced to a single Atom.

31. If the Gravity be supposed proportional to theDistance from the Center; then n n x, and we have

C£: