Juft fo, if the Figure [Fig. 5. Plate II.] PAM PS reprefent a fluid fphere, which we may imagin compofed of a great many communicating Canals or Tubes, the fluid in every one of which preffes upon the Centre, now if the fluid in every one of these Tubes was of equal weight or gravity, it is plain that by that means they would be alfo of an equal height from the Centre; for by that means only would the Centre be equally preffed by the weight of all the Tubes; but if the fluid in the canal E OM were lighter than the fluid in the canal POS, it is plain that in this cafe the fluid POS preffing more on the Centre than the fluid in Æ OM, the surface of the fluid in the canal EOM will rife to a greater height or distance from the Centre, fo that by its greater height which recompenfes its leffer gravitation it will prefs equally upon the Centre, with the fluid in the canal P O S. After the fame manner * if the fluid in the canal GO H, were heavier than the fluid in the canal EOM, but lighter than that which is in POS, then would the canal, GOH be fhorter than ÆOM but longer than POS, and the Figure compofed of all these Tubes would be in the form of a fpheroid which is generated by the circumrotation of a femi elipfis round its axis, but as I have already fhowed that if Æ OM represent the femidia

*See Figure 6. Plate III.

meter

meter of the Equator, that all Bodies in it are lighter than in POS, the Axis of the Equator (we take the Diameters and Axis here not as pure Mathematical lines, but as fmall Canals or Tubes,) and just so those Bodies which are in the Tube GOH, I have proved to be lighter than thofe in PÓS, but heavier than the Bodies which are in OM, the centrifugal force in G H, being less than that which is in EM, and there is no centrifugal force in the Poles, PS. It is plain therefore that the Tube EOM, will be longer than GOH, and GOH will be longer than POS, that is, the Diameter of the Æquator will be longer than the Axis of the Earth, and confequently the Figure of [Fig. 6. Plate III.] the Earth will be after the fashion of a broad fpheroid which is rated by the rotation of a femi Ellipfis round geneits leffer Axis. This I hope will be fufficient to convince the Theorift of the falfenefs of his own affertion, fince it is plain demonftration, that an Earth formed from a Chaos muft have a very different Figure from what he supposes it had.

But I will now proceed farther and enquire, how much the gravity is diminished at the Equator, or any other parallel by the centrifugal force, which all bodies acquire by being turned round the Earths Axis, that from thence we may endeavour to determine what proportion the Diameter of the Earths Æqua

tor

tor has to its Axis, to Calculate which, I will firft fuppofe that the mean femidiameter of the Earth is 19615800 Paris feet according to the late obfervations of the French Mathematicians, and since the Earth turns round its Axis in the space of 23 hours 56', for in that time the fame meridian returns to the fame immoveable point of the Heaven again (but the Sun in the mean time seeming to be moved a degree according to the feries of the figns is the cause why there is four minutes more required, before the meridian can overtake him) from thence it follows, that a Body under the Æquator moves through 142688 feet in the space of one fecond of time. Now according to the Theorem given us by Mr. Newton in his Philofophia Naturalis principia Mathematicia Schol. prop. 4. Lib. 1. The centrifugal force of any body, has the fame proportion to the force of gravity, that the fquare of the arch which a body describes in a given time divided by its diameter, has to the space through which a heavy body moves in falling from a place in which it was at reft in the fame time, and supposing a heavy body falls 15 foot in a fecond of time, by Calculation it will from thence follow, that the force of gravity has the fame proportion to the centrifugal force at the Equator, that 289 has to unity; and therefore by this centrifugal force which arifes from the Diurnal rotation of the Earth round its axis, any body placed

placed in the Æquator lofes part of its gravity which it would have were the Earth at reft, or which is the fame thing, a heavy body placed at either of the Poles (where there is no diurnal rotation, and confequently no centrifugal force,) which weighs 289 pounds if it were brought to the Aquator will weigh only 288 pounds.

Having thus determined the proportion of the centrifugal force at the Aquator to the force of gravity, it will be eafy from thence to fhew their proportions in any parallel, for it is compounded of the proportion of 1 to 289, and of the co-fine of the Latitude to the Radius; for if two bodies defcribe different peripheries in the fame time, their centrifugal forces are proportional to their peripheries or to the femi-diameters of thefe Peripheries, as is determined by Monf. Hugens in his Theoremata de vi centrifuga & motu circulari: but the Periphery which a body in the æquator defcribes has its femi-diameter equal to the radius or femi-diameter of the Earth, and in any other place the parallels in which Bodies move have the co-fines of their Latitude for their femi-diameters, and therefore it will follow that the force of gravity is to the centrifugal force in a proportion compounded of the radius to the co-fine of the Latitude and of 289 to 1. and therefore at the Latitude of 51 degrees, 46 minutes (for example) it will be as 466 to i. H

But

But we must obferve that it does not from thence follow, that a body in that Latitude lofes part of its abfolute gravity which it would have were the Earth at reft; for that could not be, unless the centrifugal force acted directly contrary to the force of gravity, which it doth no where but at the Equator, for in the Figure [Fig. 7. Plate III.] let the circle QPE reprefent the Earth, QE the diameter of the Equator, O its Centre, and let B reprefent a Body which we suppose to hang by the thread A B, and is placed any where between the Pole P and the Equator

and let B D be drawn perpendicular to the axis. It is plain that if the Earth had no diurnal rotation, the Body B would draw the thread A B into the pofition A C, fince by that means it defcends as near as it can to the Centre, and there it would stretch the thread with all the force of its gravity; or if we will fuppofe that the centrifugal force acted according to the fame direction A C, it would then directly oppofe the force of gravity, and the thread would remain in the fame pofition, but it would be stretched with a force proportional to the differences of these two forces.

But because the Body B turns round the Centre D, it will endeavour to recede from it according to the line CB, in which direction the centrifugal force acting, it will not directly oppofe the force of gravity, but