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Mr. Facio's ANSWER to the Obje&tion taken from the
Motion of Comets, of their Bigness, and of their Num. ber; and bow greatly their near Pasages or Shocks are to be feared. A
Considerable Objection offers itfelf againk my Theory concerning
the System of the World; which Theory will be greatly cons firmed, if I give a just Answer to that Objection, I propose it as follows, How can it be possible that the Astronomical Calculations pould fo exactly represent the wonderful Motions of fome Comets, (for instance of that Comet which appeared in 1680) by jupposing each Comet barely to describe, accordo ing 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 zobich ebat Comet for a long time was nearer than to the Sun) contained more Master sban the Sun itself?
2. To this 1 reply, That the fame Objection wants an Answer from other Astronomers as well as from me. For surely my Demonitrations prove at least, and the Moon's Dichotomies evince, 'That the Earth is conkderably bigger and denser, in reference to the Sun, than Aftronomers did suppose. And yet Sir Isaac Newton himself, in the nicest Calculationa of the Places of Comets, neglects wholly the Situation of the Center of Gravity of the Solar System; even tho' he asierts, p. 408, that that Ceri ter may sometimes be at the changeable Dittance of near the Diameter of the Sun from the Sun's Center ; and this even towards opposite Parts of the Heavcns. Therefore that Objection coming from other Astronomers has no force against me, till they themselves have answered it, as well as my former Demonstrations.
3. However I fan 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 respectively S, T, L, P. I have demonstrated universally, That in a System of two Bodies or Globes, suppose the Sun S and the Earth T, from whose Centers any Point P whatsoever is distant by any Intervals x and z respectively; it. the Gravitation in every Point P of the Solar System be toward the Globe
"and toward the Globe T as Those two united Gravitations 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 these Bodies or that Focus be at rett or not at reft; and whether their Dillance from one another remains the same or no. This Proposition agrees, or is the fame with the 6iit Prop. of Sir Ilanc Nestor's Princ. p. 164.
4. And if instead of the two Bodies or Globes T and L, or the Earth and the Moon, be substituted 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 Mass equal to both their Mafies : Then according to the 65th Prop. the Centers of the three Bodies S, T, and L may move in Ellipses accurately. And each Center of the two Bodies S and G will describe equal Areas in equal Times, about their common Center of Gran vity F; os about che Center of Gravity of the abree Bodies S, T and L.
5. It is known that by our Astronomical 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 rest, and the Center of the Moon described her Orbit upon an unmovable Plane. 5. 6. Likewise the apparent Motions of Comets may be, and have often been accounted for, by supposing that the Center of the Comet describes equal Areas in equal Times, in an unmovable Parabolical or Elliptical Orbit, about the Sun considered also as unmovable ; tho'thc 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 describe by any Composition of the Forces or Gravitations to which that Body is exposed, the Areas described by the Center of the Body P about the said Focus or Center of Gravity, whether F or O, will always be proportionable to the Times of their Description. (See Newt. Princ. Prop. 1.
& Prop. 61. & Schol. Prop. 17.) But that hinders not the Centers of Comets 'moving at the same Time, according to the known Laws of Gravity, in unmovable
parabolical or ellipticalOrbits about the Center of the Sun, considered also as unmovable. Now this amazing Aliertion deserves to be demonitrated more particularly; which I do as follows: Beginning with a System of three Bodies only, as S, T and P, or the Sun, the Earth and a Comet; and supposing the Comet P to be either exceeding small, or else of an exceeding rare Contexture; so that the Focus F be icndibly upon the Line ST.
8. I lay then that while the Center of such a Comet P describes an unmovable Orbit P Q V about the unmovable Focus S, according to the known Laws of Gravity, that Center of the Comet often may and will necessarily at the same Time describe equal Areas about another Focus or common Center of Gravity For O placed upon the Line S T or SG, viz. if that Line falls within a Cylinder, &c. erected upon the Orb POVP.
9. For let R Q P X be the Tangent of the Orbit in P: And let the three Parallel Lines SR, FP, TX cut the said Tangent in the Points R, P and X: And taking P Q as infinitely small, or as a moinentancous Fluxion; the Areas QSP, OPP, QTP will be as the parallel Lines SR, FP; T X. And by consequence if the movable Area QFP, defcribed in equal Times, be always represented by an Unit ; that Unit will be to the Area described about S, as F P to SR: And that Unit will be to the Area described about T, as F P to T X.
10. Let Z be the movable Point where the Line TFS and the mov. able Tangent P R intersect each other; And let Z S be called And while the Center of a Comet deicribes for inttance the Orbit POV, If the Fluxion P Q be always so taken, upon the several Parts of the Orbit' PRV, that the Area PQF be constantly equal to an Unii, we shall have these Proportions ; ',. SR::9 + SF. FP :: 9 + ST. TX. From whence it follows, that S F is to St; as F P-SR, to TX-SR. But SF is to ST in a dctcrminate Proportion. And so likewile ought
to be by consequence FP-SR equal to TX-SR. And fince the Thing is really so, as it is evident by the Figure; therefore the aforesaid origie nal Proportions involving y, from whence this true Conclusion is derived must be true allo. And so is it likewise, if instead of the Globe T and the Focus F we substitute the aforesaid Globe G and the Focus F placed upon the Line SG. And if the Comet P be supposed to have too great a Weight to be neglected; then instead of the Focus F we shall 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 consequence at the same Time that the Center of the Co. met describes equal Areas about the Focus S considered as unmovable ; the same Center may describe also equal Areas about the unmovable or movable Focus For F, and likewise about the Focus O. And if the Quantity of the Description of the Areas be disturbed on one hand, by the further Increale of the Number of the Celestial Globes, which are very numerous in the Solar Syltem ; fo on the other hand that Quantity will remain determinate in Nature ; and will be in a great measure preserved nearly the same in my Theory, by the smalness of Comets, or by their weak Density; or, according to Sir IJ. Newton, by the Globes S and G not being unmovable, but exposed to be agitated by the same Laws. as the relt of the Globes in the Solar System. And thus far the Objection itlelf proposed 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 For O.
12. As to the Difference between the Suppositions that the Sun and the Earth be at rett, or that they do revolve together with the Moon for with a Comet] about a common Center of Gravity, the Reader may also see how Sir Ifanc Nezoton would account for it in his Princ. p.432.
13. From what I have demonstrated here, it follows that the 5th Prop. of Sir Ianc Newton may seem 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 Syitem of the World, when that first focus is found, there may likewise be found, under certain Suppofitions, an infinite Number of other Foci F or F, about which a very jmall or very rare Body P may describe equal Areas in equal Times, as well as about the Focus S.
14. For luppoling S to be the unmovable Center of the Sun, let ano. ther unmovable Center T of another Globe be placed in any proper Place within the infinite rectangular Cylinder whose Basis is the Orbit PRV, and let the attracting or impelling Forces towards the Centers of the Bodies S and T be as in the System of the World; that is, as the Bodies $ and T directly, and he Suare of the Distances from their Centers reci. procally: And I lay that the Body P, if its Mul be very /mall, may also delcribe 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 Budy P Heleriips on be condere', then the Areas de. scribed thout the common Center of Gravity of the four Bodies S, T, L and P, or of the three Bodie, S, G and P will be proportional to the Times
is. And 13. And if the Bodies T and S, or G and S do revolve about theis common Center of Gravity, this, by means of the centrifugal Forces generated thereby, may supply the supposition of the Bodies S and T, of S and G being at rest. For otherwile they would fall towards one ano. ther; unless we suppofe them to be kept alunder by some other Power ; as, for instance, by some inflexible Lines, or Bars, &c.
16. Here I must warn the Reader to beware of absurd and inconsistent Obje&tions : For if we suppose a System composed only of these four Bodics, the Sun, the Earth, the Moon and a Comet, then the Comet muft describe 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 suppote the Comet to be at any one Time, with its proper Direction and Switness, the Comet's Orbit becomes determined, by Sir Isaac Necuton's 1766 Prop. But if the Orbit be Elliptical and encompasses the Sun; and if at the same time the Cylinder perpendicular to the Orbit, and whole Basis is the Orbit its felf, can never encompass or contain the Earth, then the Comet must be in the nature of one of the inferior Planets; which Supposition, by con• fequence, would be absurd. For we know but two inferior Planets Venus and Mercury. Likewife if that Cylinder should always encompass or contain the Earth, but should always leave out the Sun, then the Comet muft be like the Moons that is, it must be a meer Satellite of the Earths which Supposition is absurd also. For if this was the Case, the Comet would always be within reach of our Observationss as one may casily 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 said Cylinder, perpendicular to the Orbit of any Comet, muft be capable of encompassing at once, sometimes or always, both the Sun and the Earth; tho'the Earth may sometimes stand without or on the convex fide of the Cylinder.
18. Sir Ifaac Newton did sometimes quote to me this Passage of Origen, concerning the celeftial Globes or Earths, ΦΘΕΙΡΕ ΣΘΑΙ ΔΕ ΕΠ' ΑΛΛΗ. AOTS 'ENINI ITONTAL : That they are, or may be destroyed, by falling foul upon one another. The Comet of 1680 passed, on the 11th of Now pember, about four times nearer to the Interiection of the Great Orb with the Plane of that Comer'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 escape a molt dangerous Visit, by the Comet's palling thro' that threatened Place, when the Earth was yet at about a Months diltance from it.
19. For by the Principles of Astronomy, fupposing the Sun to be at rest, the Planes of the Ecliptic, and of the Orbit of the Comet are nearly unmovable : And a bare change of the Position of the Diurnal Axis of the Earth, from whence depends each Equinox and each Solstice, cannot hinder the Earth and the Moon from being expuled every 575ih Year to the Passages of thac Comct. And they would at laft, probably, beconie fatal, hut thit it is poflible that the said Comet may sooner de diffipated into Vapours; or tall into the Sun, and there be coníu ned, butore it does break in upon the Syitem of the M on and of the Earth. Pu: the Danger from any other kauwn Comet canaot be prevented in this la.. manner.
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, whose Orbits are fufficiently known; then we find 44 Intersections of the Orbits of these Comets with each of those Planets ; which make 264 Intersections in all. Beside the proper Intersections of the Orbits of such Comets as are yet unknown, and which probably may with the former amount to about 70 or 100, and their Intersections 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 tbe Earth and the Moon, whose Bignels and Densities I have demonstrated to be very much greater than is commonly supposed. And again let us mind that the said Gravitation exposes so mni ch the more the Earth and the Moon, and the other Planets, to the near Paslage, and even to the Shock of Comets.
22. Besides, let us consider on one hand that the Comets pierce thro' those Six Planes more or less obliquely, and so 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 these Breaches or Holes are almost 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 those Holes (for Instance in Mr. Whiffon's Scheme of ihe Solar System) he could not but be filled with Dread and Amaže. ment, at the View of tholc eminent Dangers from Comets, to which those four or five Inferior Gobes are exposed. This the Ancients seem to have likewise understood, when their Astronomers supposed the Comets to be of so mischievous a Nature ; according also to this Verse of Virgil. Non alias diri toties fulfere Comera.
24. However, here is a threatening and most dangerous Scourge which may well frighten many People into the deepeit Repentance, if ever Attronomers by their Observations at a Return of the Comet of 1680, or of any orber, do toʻesee that the Comet must needs pass very near the Earth. And the greater is the Sun's Parallax, the greater as also the Number of the Days during wh'ch our lower System of the Earth and of the Moon is exposed to eminent Danger from the Pasfage of the Comet of 1620, as well as of several others.
25. From these Reflections, some Questions seem naturally to arise, 1. Whether a very long undisturbed Disposition of the Solar System, or at least of the Earth, the Moon and the three inferior Planets, would not be a Proof of the Newness of the Creation in general; or at least of of the Creation of fome of these inferior Globes, or of tome of the Comets ?
26. II. Whether those Inferior Planets can escape, for many Thousands of years to come, the dangerous Effects of the Shocks or near Passages of Comets ; unless the Divine Providence will interpose, and over-rule the settled 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