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THE Arguments indeed which Authors offer to confirm the Truth of this, are handled fo obfcurely and confufedly, that they are almost insufficient to convince the ftrenuous and obftinate Defenders of the contrary Opinion. We fhall therefore as much as is poffible, clear up and examine thefe Arguments; that the Reader may have a diftinct Knowledge of them, and know the better how to use them.

WE fhall not here take notice of fuch Reasons as are of lefs Weight, and at beft.only probable, or perhaps fophiftical. Such as, 1. A fpherical Figure is the most capacious; and therefore the Earth ought to have fuch a Figure. 2. All the Parts of the Earth tend to the fame Center; therefore all these

The fame Inequality of Diameter is also found in the Planet Jupiter, by the Obfervations of those excellent Aftronomers Caffini and Flamstead, and that much more than in our Earth; because the diurnal Rotation of that Planet is more than twice as fwift as the Rotation of the Earth which plainly proves, that the Difference arifes from no other Cause than the circular Motion.

Jurin's Appendix. Dr Derham (in his PhyficoTheol. Bii. C1. Note a) doth not feem to entertain any doubts concerning the terraqueous Globe, and the other Planets, being of a prolate fpheroidal Figure; but he faith, That altho' he hath often viewed Jupiter, and other Planets, with very good Glaffes, which he hath of 72 feet, and the Royal Society's Glafs of above 120 feet, yet he never could perceive them to be otherwife than perfectly globu

lar. And he thinks it next to impoffible, to take an exact meafure of the Polar and Equatorial Diameters, by reason of the Smallness of their apparent Diameters in a Micrometer, and their Motion all the time of mea furing 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 Diftances from the Earth's Center, may cause different Vibrations; but yet he fhews, from good Experiments he made with Pendulums in the Air-Pump, that thofe Alterations might, in fome measure, be from the Rarity and Denfity of the Air, in the different Zones. And I may add to Dr Derham's Experiments, the Lengthening of Iron Rods by Heat, and their Shortening by Cold; which I have found to be very confiderable, by ve ry exact Experiments.

Parts

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 fpherical: and fo ought the Earth to remain after the feparation of the moist Parts from the dry.

I SAY, neglecting these and fuch like Arguments, let us look out for better; which are of three kinds. Of the first there is only one deduced à priori, as they call it those of the other two kinds are demonftrated à pofteriori; or from Celestial or Terrestrial Observations and Appearances.

THE firft Argument is taken from the Nature of Water, and borrowed either from Ariftotle or Archimedes. Ariftotle in his fecond Book de Calo, chap. 5th, proposes it as his own, after this manner, (tho' it is likely he borrowed it from fome Philofopher 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 neceffarily follow, that the Superficies of the Water is round or fpherical; 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 aß and ay; and from 6 to 7 the Line By; to which from alet fall the Perpendicular a. (c) It is plain the Line ad (Fig. 5.) is less than aß or ay, and therefore the Place is lower and more concave then or 2; therefore the Water must flow downwards from Band 'till the Lines aß, ay, and as are equal, that is, 'till a becomes as equal to aß, and ay; hence ß,, and being in the Periphery of the fame Circle, must make the true Superficies of the Water of a round Figure.

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(c) Euclid. Lib. i. Prop. 18.

THIS is Ariftotle's Demonftration, in which, besides the Incoherency of it, which might be eafily amended, I obferve these greater Errors. 1. He fuppofeth the Universe to have a certain Center. 2. That Places are higher or lower in refpect to that Center. Now he who denies the fpherical Figure of the Earth, will perhaps grant neither of thefe Poftulata: Tho' the Univerfe may be easily proved to have a Center, because the apparent Motion of the fixed Stars obligeth us to fuppofe 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 Demoftration, be taken for Ariftotle's central Point. But the chief Difficuly is in the fecond Suppofition; viz. that Places are higher or lower in respect of that Center; because he who will have the Superficies of the Earth to be a Plane, or fome other Figure, not round, will deny this Suppfition, and fay that Places appear higher or lower in refpect of the horizontal Plane, perpendicular to which the Earth is infinitely extended downwards; or will perhaps explain the Declivity fome other way: fo that the Argument would not be conclusive except it were first granted that the Elevation of one Place above another is only in refpect of fome Center, about which the Stars have their apparent Motion. And tho' this were true, and all other Notions of Declivity by which Water is depreffed were confuted, yet it could fcarcely be admitted for a Principle; because it precariously supposes the Earth to be of a spheric Figure, which is begging the Question.

THEREFORE fome prefer Archimedes's Demonstration (found in the first Book of his De Infidentibus Humido) which is indeed more artificial than

that

that of Ariftotle; yet labours under the fame Difficulties, in previously fuppofing the Earth to be of a fpheric Figure, to whofe Center the preffure of the Water is made. But we are far from fuppofing that the divine Archimedes could be guilty of any falfe Reasoning! No, his Defign in that Book was not to demonstrate the fpherical 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-fuppofes 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 demonftrated from other Phænomena: So that I wonder Clavius did not observe this, who, in his Commentary upon Joannes de Sacro Bofco, ufes this Demonftration of Archimedes for the fpheric Figure of the Earth: Snellius alfo does the fame in his Eratofthenes Batavus. But it was Aristotle's Design in the Place before cited to demonstrate the fpheric Figure of the Earth, Sea, and Heavens; wherefore he could not affume a Center to the Universe, or Earth, without being guilty of a manifeft Paralogifm.

SO that this Argument taken from the Nature of Water, tho' it be propofed by almost all Authors, yet labours under fome Difficulties, which more learned Mathematicians have endeavoured to remove, if poffible. I have myself spent some Time upon this Matter, and tryed feveral Methods, but 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 fome Arguments à pofteriori, taken first from celeftial 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 alfo thro' the two Poles M, N; as A B C D. And fuppofe 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 say 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, interfecting 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 aforefaid Theorem conclude the Superficies of the Earth to be of a fpherical 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 Perfon 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 impoffible if the Line he travelled in was not circular; as is plainly fhewed by the artificial terreftrial Globe. 2. The Line ABCD 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 fome Time of the Year is perpendicular to fome Place in the Line ABC; for Example, to P. If we take equal Spaces BQ, PQ (or any other) we fhall 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

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