*44

Mechanics.

C £ : C N : : £ 2 : g — f x and if in this Hypothesis theEarth were to revolve in 84/ 43", or g —f, then wouldC E be infinitely greater than C N ; that is, C N wouldbe nothing, or the Spheroid would then become a cir-cular Plane.

32. If Gravity be supposed inversely as the Square ofthe Distance, we have n — — 2 ; and then we shall

1 1

have 2 g — n -j- 1 : 2 £ -f- « y— f— h -j- 1 : : C E : C N ::

1 1

2 g~ l ■ 2 g+f~ 1 :: 2 £+/:*£ s : 579 : 578 . Andsince of all the above Hypotheses, this last is found tobe the only true one (fee Art. 19.) it follows that theEarth in its Chaotic or Fluid State, revolving about itsAxis, tnujl necejsarily put on a Spheroidical Figure, hav-ing the Equatorial Diameter E Q, to the Axis N S, as

5 79 : 578 - . „ ,

33. And this would be the Cafe, were all the Cir-cumstances of the Hypothesis the fame in Nature as wehave presumed in the Theory ; but since they are foundto be otherwise, the Mathematical Theory (which givesonly the true Sort of Figure, but not the true Figureitself) must be adapted to Nature, and the Figure whichthe Earth really has investigated from other Principles;For Bodies on the Earth’s Surface do gravitate in suchDirections as pass not thro’ the Centre C (as has beensupposed) any where but in the Equator or under thePoles, viz. at E and N.

34. In order to find the true Proportion betweenEQ_and N S, Sir Isaac Newton makes a Suppositionthey are as 101 to 100, and then by a Method (too pro-lix to be here explained) he finds the Gravity at E andN to be as 500 to 501. Now supposing the Matter ofthe Earth uniform and at Rest, the Weight of the Co-lumn of Particles E C will be to that of the ColumnN C in the Ratio of their Magnitudes 101 to xoo, andof their specific Gravities 500 to 501 conjointly, (SeeAnnot. LVIII. 10.) that is, as 505 to 501.

35. Now it is plain if the Weight of each Particle inthe Column C E were divided into 505 equal Parts, aCentrifugal Force, that should take off four of those

equal