Distance from the Center; the Section of the Torrent will be a Conic Section. And if it fhould be moreover required that the Points, P, Q and C unite, the Figure will be com pounded of two Ellipfes conjoined in C. If the Distance Cy vanishes, or if the two Centers unite, you will have bo and c=a, and the Torrent will become a Spheroid. If moreover we fuppofe m=n and *=0; the general Equation of the Section of the Torrent will become 2p+1-(n+1) fal bbrr=(2p—nƒ—ƒ) a"+1. Or in the Case of n = −1; 2pal (—) = Sbbrr — fa, as in the a first Problem, which is but a particular Cafe of this. CHAP. Of the Figures of the Cœleftial Bodies; of the of the Stars which Seem to alter their Magnitude, and of Saturn's Ring. A LL we have been faying is felf applicable to the Coeleftial Bodies that turn about an Axis, if we fuppofe their parts to have taken the exact place which Gravity and the Centrifugal Force allotted them. All the Planets, we know, are very nearly Spheres, excepting Jupiter whofe Oblatenefs is confiderable enough to be observed by Aftronomers; but they are not therefore the lefs liable to all the Figures we have mentioned: There needs only lefs denfity in the Matter they are compounded of, or more Rapidity in their Revolution, to make them affume all thefe Figures: And why fhould the kind of uniformity we fee in fome Planets prevent us from fufpecting, at leaft, the variety of thofe, the immenfity of the Heavens, perhaps, hides from our Sight. Confined to a corner of the Universe, with circumfcribed Intellects, why should we bound Things to the little we perceive? We We have feen that Spheroids may affume infinite Figures, according to the Gravity of their parts and their Centrifugal Force; and that, in feveral Hypothefes, a Planet may from a Spheroid the leaft oblate, take on it the Figure of a Molary or Milftone, or be reduced even to a circular Plane. Perhaps it is the distance only that hinders our feeing of fuch Planets. But even without being at any very great distance from us, they may be hid from our Sight, if their Orbits happening to be in the Plane of the Ecliptic, or but a little diftant from it, the Axis of their Revolution fhould be perpendicular, or nearly fo, to the fame Plane. Suppofing this, the Earth being always in the Plane, or nearly fo, of the Equator of thefe Molaries, their thinnefs would conceal them from our Eyes. Here then you have a new kind of Planets in the Heavens; at least, fuch there may be But let us pufh the thought a little farther. The fixed Stars are Suns like ours; it is very poffible then, that like ours they revolve about an Axis. They must then according to the Rapidity of their Motion, be subject to a flat Form; and why fhould there not be fuch very oblate Stars in the Heavens? efpecially if it be confidered that we by no Obfervation have come at the precife Figure of the fixed Stars. But But again, it is very probable that the fixed Stars have their Planets that move round them, as our Sun has his. If then any mighty and very excentric Planet or Comet fhould go round a flat Star, in an Orbit inclined to the plane of the Equator of the Star, what would happen? The gravitation of the Star towards the Planet, when near its Perihelion, would alter the inclination of the faid Star, which must therefore appear more or lefs luminous. Such a Star even as we perceive not, because its edge is towards us, will be visible when it shews us a part of its difc; and having made its appearance would difappear again. Thus is it we may account for the change of Magnitude obferved in fome Stars, and for Stars that have appeared and disappeared. The Comets are no more, as we have feen, than very excentric Planets, fome of which having bordered very near upon the Sun,. leave him again, traverfing the Orbits of the more regular Planets, and then hold on their Journey through the different Regions of the Heavens. When they return from their Perihelion they fweep long Tails after them, and these Tails are immenfe Torrents of Vapour which the heat of the Sun has raised from them. If a Comet in this State fhould pass by some mighty Planet, the force of Gravity towards towards the Planet might divert this Torrent, and bring it to circulate about itself, in the direction of fome Ellipfis, or fome Circle. And the Comet continuing to fupply fresh Matter, or that already fupplied, being fufficient, a continued flux of Matter would be formed, or a kind of Ring about the Planet. The Planet will attract the Matter of this Torrent in a reciprocal proportion to the Square of its diftance; but, within the Torrent there will be a fecond Gravitation of its parts mutually. In fhort the parts of the Torrent will have still a third Force, or a Centrifugal Force which they will acquire from their revolutionary Motion. Now altho' the Body of Matter, that forms the Torrent, be at firft Cylindrical, or Conic, or of any other Figure poffible; it will neceffarily affume fome Figure bordering upon those I have determined in the fecond Problem. The Centrifugal Force will continually tend to flatten the Ring, and may be fuch, as well with regard to the Gravitation towards the Planet, as of the parts mutually within themfelves, that the thickness of the Ring fhall be very inconfiderable, in comparison of its breadth. In the mean time, the Body even of the Comet may be attracted alfo to the Planet, and be forced to move round it. What I have here faid of oblate Planets that may perhaps be in the Syftem of the World, |