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• THE Arguments indeed which Authors offer to confirm the Truth of this, are handled so obscurely and confusedly, that they are almost insufficient to convince the strenuous and obstinate Defenders of the contrary Opinion. We shall therefore as much as is possible, clear up and examine these Arguments; that the Reader may have a distinct Knowledge of them, and know the better how to use them.

W E shall not here take notice of such Reasons as are of less Weight, and at bestjonly probable, or perhaps sophistical. Such as, i. A spherical Figure is the most capacious; and therefore the Earth ought to have such a Figure. 2. All the Parts of the Earth tend to the fame Center; therefore all these

The same Inequality os Diameter is also found in the Planet Jupiter, by the Observations of those excellent Astronomers CaJJini and Flam/lead, and that much more than in our Earth; because the diurnal Rotation of that Planet is more than twice as swift as the Rotation of the Earth: which plainly proves, that the Difference arises from 110 other Cause than the circular Motion.

Juriiss appendix. Dr Derham (in his PhystcoTheol.B'a. C 1. Note a) doth not seem to entertain any doubts concerning the terraqueous Globe, and the other Planets, being of a prolate spheroidal Figure; but he faith, That altho' he hath often viewed Jupiter, and other Planets, with very good Glasses, which he hath of 72 feet, and the Roy al Society's Glass of above 120 feet, yet he never could perceive them to be Otherwise than perfectly globu

lar. And he thinks it next to impoffible, to take an exact measure of the Polar and Æquatorial Diameters, by reason of the Smallness of their apparent Diameters in a Micrometer, and their Motion all the time of measuring them.

And as to the Variation of the Vibrations of Pendulums, under the Line, and in the Northern and Southern Latitudes, he hath no doubt, but different Distance* from the Earth's Center, may cause different Vibrations; but yet he shews, from good Experiments he made with Pendulums in the Air-Pump, that those Alterations might, in some measure, be from the Rarity and Density of the Air, in the different Zones. And I may add to Dr Derbamt Experiments, the Lengthening of Iron Rods by Heat, and their Shortening by Cold; which I have found to be very considerable, by ve* ry exact Experiment*.

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Parts ought to make up a globular Figure. 3. When at the first Creation the Waters were confusedly mixed with the Earth, it was then without doubt moist and soft; but the Figure of all moist and liquid Bodies is spherical: and so ought the Earth to remain after the separation of the moist Parts from the dry.

I S A Y, neglecting these and such like Arguments, let us look out for better; which are of three kinds. Of the first there is only one deduced a priori, as they call it: those of the other two kinds are demonstrated a posteriori; or from Celestial or Terrestrial Observations and Appearances.

THE first Argument is taken from the Nature of Water, and borrowed either from Aristotle or Archimedes. Aristotle in his second Book de Ccelo, chap. 5th, proposes it as his own, after this manner, (tho' it is likely he borrowed it from some Philosopher before him). If we take it for granted (fays he) that Water of it's own Nature tends always down to the most concave or lowest Place; it will necessarily follow, that the Superficies of the Water is round or spherical; but that Place is most concave that is nearest the Center of the Earth, therefore let there be drawn from the Center * two right Lines and a.y; and from 0 to y the Line $y; to which from * let fall the Perpendicular «<-. (c) It is plain the Line a.^ (Fig. 5.) is less than *P or *y, and therefore the Place ^ is lower and more concave then £ or y; therefore the Water must flow downwards from p and y 'till the Lines *y, and are equal, that is, 'till *^ becomes <« equal to and *y; hence 0, s, and y being in the Periphery of the fame Circle, must make the true Superficies of the Water of a round Figure.

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THIS is Aristotle's Demonstration, in which, befides the Incoherency of it, which might be easily amended, I observe these greater Errors, i. He supposeth the Universe to have a certain Center. 2. That Places are higher or lower in respect to that Center. Now he who denies the spherical Figure of the Earth, will perhaps grant neither of these Postulata: Tho' the Universe may be easily proved to have a Center, because the apparent Motion of the fixed Stars obligeth us to suppose that they themselves either revolve by a diurnal Motion, or that the Earth is turned about it's Center. If the Stars be really moved, then the Point about which they will revolve will certainly be the Center of the Universe. If the Earth; then the middle Point round which it moves, may, in the Demostration, be taken for Aristotle's central Point. But the chief Difficuly is In the second Supposition; viz. that Places are higher or lower in respect of that Center j because he who will have the Superficies of the Earth to be a Plane, or some other Figure, not round, will deny this Suppsition, and fay that Places appear higher or lower in respect of the horizontal Plane, perpendicular to which the Earth is infinitely extended downwards; or will perhaps explain the Declivity some other way: so that the Argument would not be conclusive except it were first granted that the Elevation of one Place above another is only in respect of some Center, about which the Stars have their apparent Motion. And tho' this were true, and all other Notions of Declivity by which Water is depressed were confuted, yet it could scarcely be admitted for a Principle; because it precarioufly supposes the Earth to be of a spheric Figure, which is begging the Question.

THEREFORE some prefer Archimedes'* Demonstration (found in the first Book of bis De lnfivlentibus Humido) which is indeed more artificial than

that that of Aristotle; yet labours under the fame Difficulties, in previously supposing the Earth to be of a spheric Figure, to whose Center the pressure of the "Water is made. But we are far from supposing that the divine Archimedes could be guilty of any false Reasoning! No, his Design in that Book was not to demonstrate the spherical Figure of the Earth (for then he had indeed begged the Question) but only to explain the Nature of Water and other Liquids; in order to which he pre-iuppofes the Earth to be of a spherical Figure, or to have a Center, to which all heavy Bodies in general tend; and this he takes as a Principle before known and demonstrated from other Phænomena: So that I wonder Clavius did not observe this, who, in his Commentary upon Joannes de Sacro Bosco, uses this Demonstration of Archimedes for the spheric Figure of the Earth: Snellius also does the fame in his Eratosthenes Batavus. But it was Aristotle's Design in the Place before cited to demonstrate the spheric Figure of the Earth, Sea, and Heavens; wherefore he could not assume a Center to the Universe, or Earth, without being guilty of a manifest Paralogism.

S O that this Argument taken from the Nature of Water, tho' it be proposed by almost all Authors, yet labours under some Difficulties, which more learned Mathematicians have endeavoured to remove, if possible. I have myself spent some Time upon this Matter, and tryed several Methods, bdt could not bring them to bear. I was induced to attempt the Thing, because it would be an elegant and unquestionable Demonstration of the spherical Figure of the Earth.

THEREFORE waving this; we shall now propose some Arguments a posteriori, taken first from celestial Phænomena. Let us conceive a Section made by a plane or a meridian Line (which is called the Line of Latitude) to pass thro' a Place B,

VOL. I. D or or any other Part of the Earth, and also thro' the two Poles M, N; as ABCD. And suppose another Section (or Line of Longitude) (Fig. 3.) to pass thro* the fame Point B, perpendicular to the former, and parallel to the Equator; as EBFC. I fay these two Sections or Lines on the Surface of the Earth may be proved to be circular. And it is a plain geometrical Theorem, that any Superficies whatever, when it is cut with perpendicular Planes, intersecting each other in one common Line or Axis, if the Lines produced on the Surface be circular, the Body can be no other than spherical.

THEREFORE if we can prove, that the two perpendicular Sections are circular, which pass thro' any Point, B, taken at Pleasure; we may also by the aforesaid Theorem conclude the Superficies of the Earth to be of a spherical Figure, and the Earth itself a globular Body.

NOW it is proved from divers celestial Phænomena. that a Section made from one Pole to another, according to the Latitude of the Earth, is circular. 1. If in the Line ABCD, a Person go from any Point, as B, towards either Pole, as M, or the Star near it; he will find that by equal Journies he will equally approach nearer the Pole ; which would be impossible if the Line he travelled in was not circular •, as is plainly shewed by the artificial terrestrial Globe. 2. The Line A B C D is the meridian Line, into which when the Sun comes it is Noon or Mid-Day with us and all the People who inhabit that Line, as we know by Experience; and they that fail in the Torrid Zone testify, that the Sun at some Time of the Year is perpendicular to some Place in the Line ABC-, for Example, to P. If we take equal Spaces B Q, P Q^(or any other) we shall find the Distance of the Sun from the Zenith of Q^, equal to the Interval, by which the Distance of the Sun from the Zenith of B exceeds the Distance z of

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