Mr. Facio's ANSWER to the Objection taken from the Motion of Comets, of their Bignefs, and of their Number; and bow greatly their near Paffages or Shocks are to be feared.

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Confiderable Objection offers itfelf against my Theory concerning the Syftem of the World; which Theory will be greatly confirmed, if I give a juft Answer to that Objection. I propofe it as follows, How can it be poffible that the Aftronomical Calculations should fo exactly reprefent the wonderful Motions of fome Comets, (for inftance of that Comet which appeared in 1680) by supposing each Comet barely to describe, according to the Laws of Gravity, a long elliptical and unmovable Orbit, baving its Focus in the unmovable center of the Sun: If the Earth (to which that Comet for a long time was nearer than to the Sun) contained more Matter than the Sun itself?

2. To this I reply, That the fame Objection wants an Answer from other Aftronomers as well as from me. For furely my Demonstrations prove at least, and the Moon's Dichotomies evince, That the Earth is confiderably bigger and denfer, in reference to the Sun, than Aftronomers did fuppofe. And yet Sir Ifaac Newton himself, in the niceft Calculations of the Places of Comets, neglects wholly the Situation of the Center of Gravity of the Solar System; even tho' he afterts, p. 408, that that Cen ter may fometimes be at the changeable Dittance of near the Diameter of the Sun from the Sun's Center; and this even towards oppofite Parts of the Heavens. Therefore that Objection coming from other Aftronomers has no force against me, till they themselves have answered it, as well as my former Demonstrations.

3. However I fhall give, tho' but in part as yet, the following Answer, which is unexceptionable. Let the Bodies of the Sun, of the Earth, of the Moon, and of the Planet or Comet be called refpectively S, T, L, P. I have demonstrated univerfally, That in a Syltem of two Bodies or Globes, fuppofe the Sun S and the Earth T, from whofe Centers any Point P whatsoever is diftant by any Intervals x and z respectively; if the Gravitation in every Point P of the Solar System be toward the Globe Sas and toward the Globe T as; Those two united Gravitations

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will tend to one given or determinate Focus F placed in the common Center of Gravity of the two Bodies or Globes S and T, whether thefe Bodies or that Focus be at relt or not at reft; and whether their Dillance from one another remains the fame or no. This Propofition agrees, or is the fame with the 61st Prop. of Sir Isaac Newton's Princ. p. 164.

4. And if instead of the two Bodies or Globes T and L, or the Earth and the Moon, be fubflituted an equivalent Globe, which I call G, having its Center in the common Center of Gravity of the two Globes or Bodies T and L, and its Mafs equal to both their Maffes: Then according to the 65th Prop. the Centers of the three Bodies S, T, and L may move in Ellipfes accurately. And each Center of the two Bodies S and G will defcribe equal Areas in equal Times, about their common Center of Gra vity F; or about the Center of Gravity of the three Bodies S, T and L.

5. It

5. It is known that by our Aftronomical Theories, notwithstanding the Motion of the Earth, we account very well for the Motions of the Moon, as if the Sun and the Earth were both at reft, and the Center of the Moon defcribed her Orbit upon an unmovable Plane.

6. Likewife the apparent Motions of Comets may be, and have often been accounted for, by fuppofing that the Center of the Comet describes equal Areas in equal Times, in an unmovable Parabolical or Elliptical Orbit, about the Sun confidered also as unmovable; tho' the Centers of the four Globes or Bodies of the Sun, the Earth, the Moon and the Comet revolve also in their movable Orbits, being attracted toward the Center of Gravity of the Solar System, that is toward their common Focus, which I call O.

7. For fince any Globe or Body P is always driven or attracted directly toward O; therefore whatsoever Line PQV the Center of that Body may defcribe by any Compofition of the Forces or Gravitations to which that Body is expofed, the Areas defcribed by the Center of the Body P about the faid Focus or Center of Gravity, whether F or O, will always be proportionable to the Times of their Defcription. (See Newt. Princ. Prop. 1. & Prop. 61. & Schol. Prop. 17.) But that hinders not the Centers of Comets moving at the fame Time, according to the known Laws of Gravity, in unmovable parabolical or elliptical Orbits,about the Center of the Sun, confidered alfo as unmovable. Now this amazing Afiertion deserves to be demonstrated more particularly; which I do as follows: Beginning with a Syftem of three Bodies only, as S, T and P, or the Sun, the Earth and a Comet; and fuppofing the Comet P to be either exceeding small, or elfe of an exceeding rare Contexture; fo that the Focus F be fenfibly upon the Line ST.

8. I fay then that while the Center of fuch a Comet P defcribes an unmovable Orbit PQV about the unmovable Focus S, according to the known Laws of Gravity, that Center of the Comet often may and will neceffarily at the fame Time defcribe equal Areas about another Focus or common Center of Gravity F or O placed upon the Line ST or SG, viz. if that Line falls within a Cylinder, &c. erected upon the Orb PQVP.

9. For let RQPX be the Tangent of the Orbit in P: And let the three Parallel Lines S R, F P, TX cut the faid Tangent in the Points R, P and X: And taking P Q as infinitely fmall, or as a momentaneous Fluxion; the Areas QSP, QF P, QTP will be as the parallel Lines SR, FP, TX. And by confequence if the movable Area QFP, defcribed in equal Times, be always reprefented by an Unit; that Unit will be to the Area defcribed about S, as FP to SR: And that Unit will be to the Area defcribed about T, as FP to TX.

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10. Let Z be the movable Point where the Line T F S and the movable Tangent PR interfect each other; And let ZS be called And while the Center of a Comet defcribes for inftance the Orbit PQV, †f the Fluxion P Q be always fo taken, upon the feveral Parts of the Orbit' PQV, that the Area PQF be conftantly equal to an Unit, we fhall have thefe Proportions; y SR::y+SF. FP:: y + ST. TX. From whence it follows, that SF is to ST; as FP-SR, to TX- SR, But SF is to ST in a determinate Proportion. And fo likewife ought

to be by confequence FP-SR equal to T X-SR. And fince the Thing is really fo, as it is evident by the Figure; therefore the aforefaid origi mal Proportions involving y, from whence this true Conclufion is derived must be true alfo. And fo is it likewife, if inftead of the Globe T and the Focus F we fubftitute the aforesaid Globe G and the Focus F placed up. on the Line S G. And if the Comet P be fupposed to have too great a Weight to be neglected; then instead of the Focus F we fhall have upon the Line FP a new Focus O, for the common Center of Gravity of that whole System of the four Bodies S, T, L, P.

11. And by confequence at the fame Time that the Center of the Comet defcribes equal Areas about the Focus S confidered as unmovable; the fame Center may describe also equal Areas about the unmovable or movable Focus F or F, and likewife about the Focus O. And if the Quantity of the Defcription of the Areas be disturbed on one hand, by the further Increase of the Number of the Celeftial Globes, which are very numerous in the Solar Syftem; fo on the other hand that Quantity will remain determinate in Nature; and will be in a great meafure preferved nearly the fame in my Theory, by the fmalness of Comets, or by their weak Density; or, according to Sir If. Newton, by the Globes S and G not being unmovable, but expofed to be agitated by the fame Laws. as the rest of the Globes in the Solar Syftem. And thus far the Objection itself propofed in No. 1. p. 61. is answered. For when the Convexity of the Orbit is turned toward the Focus For O, I do not find that the Comets Motion can be accounted for in the like manner, without taking notice of the Centrifugal Forces produced by the Revolution of the Globes about the Focus F, or F or O.

12. As to the Difference between the Suppofitions that the Sun and the Earth be at reft, or that they do revolve together with the Moon for with a Comet] about a common Center of Gravity, the Reader may alfo fee how Sir Ifanc Newton would account for it in his Princ. p.432.

13. From what I have demonftrated here, it follows that the 5th Prop. of Sir Laac Newton may feem imperfectly folved. He finds indeed one Focus S of the Orbit wherein the Center of the Body P revolves: But, by what precedes, it appears that in the Syftem of the World, when that first Focus is found, there may likewife be found, under certain Suppofitions, an infinite Number of other Foci F or F, about which a very small or very rare Body P may defcribe equal Areas in equal Times, as well as about the Focus S.

14. For fuppofing S to be the unmovable Center of the Sun, let another unmovable Center T of another Globe be placed in any proper Place within the infinite rectangular Cylinder whofe Bafis is the Orbit PQV, and let the attracting or impelling Forces towards the Centers of the Bodies S and T be as in the Syftem of the World; that is, as the Bodies S and T directly, and the Square of the Distances from their Centers reciprocally: And I lay that the Body P, if its Mafs be very small, may allo defcribe Areas proportional to the Times about F he common Center of Gravity of the Bodies S and T, as well as about the Center or Focus S. For, if the Ma's of the Body P deferves to be confidered, then the Areas deAcribed about the common Center of Gravity of the four Bodies S, T, L and P, or of the three Bodies S, G and P will be proportional to the Times.

15. And

15. And if the Bodies T and S, or G and S do revolve about their common Center of Gravity, this, by means of the centrifugal Forces ge nerated thereby, may supply the Suppofition of the Bodies S and T, or S and G being at reft. For otherwile they would fall towards one another; unless we fuppofe them to be kept afunder by fome other Poweri as, for inftance, by fome inflexible Lines, or Bars, &c.

16. Here I muft warn the Reader to beware of absurd and inconfiftent Objections: For if we fuppofe a System composed only of these four Bodies, the Sun, the Earth, the Moon and a Comet, then the Comet muft defcribe equal Areas in equal Times about F the common Center of Gravity of the four Globes; and its Orbit must have its Concavity turn'd toward F. And, according to the Place where you fuppofe the Comet to be at any one Time, with its proper Direction and Switness, the Comet's Orbit becomes determined, by Sir Ifaac Newton's 17th Prop. But if the Orbit be Elliptical and encompaffes the Sun; and if at the fame time the Cylinder perpendicular to the Orbit, and whofe Bafis is the Orbit it felf, can never encompass or contain the Earth, then the Comet must be in the nature of one of the inferior Planets; which Suppofition, by con fequence, would be abfurd. For we know but two inferior Planets Venus and Mertury. Likewife if that Cylinder fhould always encompass or con tain the Earth, but fhould always leave out the Sun, then the Comet muft be like the Moon; that is, it must be a meer Satellite of the Earths which Suppofition is abfurd alfo. For if this was the Cafe, the Comet would always be within reach of our Obfervations; as one may eafily demonftrate, by determining the Stereographic Spherical Surface, in which the Gravity towards the Sun is equal to the Gravity towards the Earth..

17. Therefore the faid Cylinder, perpendicular to the Orbit of any Comet, must be capable of encompaffing at once, fometimes or always, both the Sun and the Earth; tho' the Earth may fometimes stand without, or on the convex fide of the Cylinder.

18. Sir Ifaac Newton did fometimes quote to me this Paffage of Origen, concerning the celeftial Globes or Earths, ΦΘΕΙΡΕΣΘΑΙ ΔΕ ΕΠ' ΑΛΛΗ AOTE 'ENINI TONTAE: That they are, or may be destroyed, by falling foul upon one another. The Comet of 1680 paffed, on the 11th of No member, about four times nearer to the Interfection of the Great Orh with the Plane of that Comet's Orbit, than I reckon the Center of the Moon to be diftant from the Center of the Earth. So the Earth and the Moon did then efcape a most dangerous Vifit, by the Comet's palling thro' that threatened Place, when the Earth was yet at about a Months distance from it.

19. For by the Principles of Aftronomy, fuppofing the Sun to be at reft, the Planes of the Ecliptic, and of the Orbit of the Comet are nearly unmovable: And a bare change of the Pofition of the Diurnal Axis of the Earth, from whence depends each Equinox and each Solstice, cannot hinder the Earth and the Moon from being expoted every 575th Year to the Paffages of that Comet. And they would at laft, probably, become fatal, but that it is poflible that the faid Comet may fooner de diffipated into Vapours; or fall into the Sun, and there be confumed, before it does break in upon the Syftem of the M on and of the Earth. Fu the Danger from any other known Comet cannot be prevented in this lat manner.

20. Let

20. Let us conceive the Planes of the Orbits of the Six Primary Planets, the Earth being reckoned for One of them. And if we con fider only the 22 Comets, whofe Orbits are fufficiently known; then we find 44 Interfections of the Orbits of thefe Comets with each of those Planets; which make 264 Interfections in all. Beside the proper Interfections of the Orbits of fuch Comets as are yet unknown, and which probably may with the former amount to about 70 or 100, and their Interfections with the Plane of the Ecliptic to about 140 or 200.

21. And let us mind that the Gravitation of the Comets toward the Planets, and of the Planets toward the Comets, is very great when they come near each other; and particularly when the Comets come near the Earth and the Moon, whofe Bignels and Denfities I have demonftrated to be very much greater than is commonly fuppofed. And again let us mind that the faid Gravitation expofes fo much the more the Earth and the Moon, and the other Planets, to the near Paffage, and even to the Shock of Comets.

22. Befides, let us confider on one hand that the Comets pierce thro' thofe Six Planes more or less obliquely, and fo make each time in them as it were an Oval Breach or Hole, and often a confiderably long one; And on the other hand, that thefe Breaches or Holes are almoft all of them crowded among or within the Orbits of the inferior Planets, Mars, the Earth, Venus and Mercury.

23. And if One would take the pains to mark down as I have done, the several Places of thofe Holes (for Inftance in Mr. Whifton's Scheme of the Solar System) he could not but be filled with Dread and Amaze. ment, at the View of thofe eminent Dangers from Comets, to which thofe four or five Inferior Gobes are expoled. This the Ancients feem to have likewife understood, when their Aftronomers fuppofed the Comets to be of fo mischievous a Nature; according alfo to this Verse of Virgil. Non alias diri toties fulfere Comet.

24. However, here is a threatening and most dangerous Scourge which may well frighten many People into the deepest Repentance, if ever Aftronomers by their Obfervations at a Return of the Comet of 1680, or of any other, do forefee that the Comet muft needs pafs very near the Earth. And the greater is the Sun's Parallax, the greater as alfo the Number of the Days during which our lower Syftem of the Earth and of the Moon is expofed to eminent Danger from the Pasfage of the Comet of 1620, as well as of feveral others.

25. From thefe Reflections, fome Questions feem naturally to arise, 1. Whether a very long undisturbed Difpofition of the Solar System, or at least of the Earth, the Moon and the three Inferior Planets, would not be a Proof of the Newnefs of the Creation in general; or at leaft of of the Creation of fome of thefe Inferior Globes, or of iome of the Comets ?

26. II. Whether thofe Inferior Planets can efcape, for many Thousands of Years to come, the dangerous Fffects of the Shocks or near Paffages of Comets; unless the Divine Providence will interpofe, and over-rule the fettled Laws of the Heavenly Motions?

27. III. Whether the Ruggedness of high Mountains, and the many Petrifications of Fishes found in them be not a Proof that