Page:Cyclopaedia, Chambers - Volume 2.djvu/280

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Author, then a Fellow of Trm/ry- Co liege, Camhrigde ; and in the Year 1713, republi/hed with confidcrable Improve- ments. Several other Authors have fince attempted to make it plainer ; by fetting afide many of the more fublime Mathematical Refearches, and fubftituting either more obvious Reafonings, or Experiments, in lieu thereof; particularly Wbifion in his FrateB. Fbyf. Mathemat. and Gravefande in Element. £5? Injiit.

Notwithstanding the great Merit of this Philofophy, and the univerfal Reception it has met with at home, it gains ground very ilowly abroad ; Nezotonianifm has fcarce two or three Adherents in a Nation ; but Cartejianifm, Huyge- niamfm, and Leibnitz ianifm remain flill in pofleflion.

The Philofophy itfelf is laid down chiefly in the third Book of the Frincipia. The two preceding Books are taken up in preparing the way, and laying down fuch Prin- ciples ot Mathematicks as have the moft relation to Philo- fophy : Such are the Laws and Conditionsof Powers. And tneie, to render them lefs dry and geometrical, the Author illustrates by Scholia in Philofophy, relating chiefly to the Denfity and Refiitance of Bodies, the Motion of Light, and Sounds, a "Vacuum, ££?c.

In the third Book he proceeds to the Philofophy itfelf 5 and from the fame Principles deduces the Structure of the Univerfe ; and the Powers of Gravity, whereby Bodies tend towards the Sun and Planets; and from thefe Powers, the Motions of the Planets and Comets, the Theory of the Moon and the Tides.

This Book, which he calls de Mundi Syfiemate, he tells us, was firft wrote in the popular way : But coniuiering, that fuch as are unacquainted with the faid Principles, would not conceive the force of the Confequences, nor be induced to lay afide their antient Prejudices 3 for this Reafon, and to prevent the thing from being in continual Difpute 5 he di- gested the Sum of that Book into Propo fit ions, in the Ma- thematical manner ; fo as it might only come to be read by fuch as had fjrit confider'd the Principles. Not that it is neceffary, a Man fhould matter them all. Many of them, even the firfl-rate Mathematicians, would find a Difficulty in getting over. 'Tis enough to have read the Definitions, Laws of Motion, and the three firft Sections of the firft Book j after which, the Author himfeif directs us to pafs on to the Book de Syfiemate Mundi.

Tbe feveral Articles of this Fhilofopby, are delivered under tbch refpeBive Heads in this DiBionary ; as Sun, Moon, Planet, Comet, Earth, Air, Centripetal Force, Resistance, Medium, Matter, Space, Elasti- city, &c. A general Idea, or Abflracl of the Whole, we ihallhere gratify the Reader withal ; to flic w in what Relation the feveral Parts Aandto each other.

The great Principle on which the whole Philofophy is founded, is the Power of Gravity. This Principle is not new : Kepler, long ago, hinted it in his Introdubl. ad Mot. Martis. He even difcovered fame of the Properties thereof, and their Effects in the Motions of the primary Planets : But the Glory of bringing it to a Phytical Demonstration was refcrved to the Eagl'ft Fbilofopher. SeeGRAviTY.

His Proof of the Principle from Phenomena ; together with the Application of the fame Principle to the various other Appearances of Nature, or the deducing thofe Ap- pearances from that Principle, constitute the Nezvtonian Syjlem ; which, drawn in Miniature, willftand thus.

I. The Phenomena are, 1. That the Satellites of Jupiter do, by Radii drawn to the Center of the Planet, detcribe Areas proportional to their Times ; and that their Periodical Times are in a fefquiplicate Ratio of their Diflances from its Centre : in which all Observations of all Aftronomers agree. 2. The fame Phenomenon holds of the Satellites of Saturn, with regard to Saturn ; and of the Moon with regard to the Earth, 5. The periodical Times of the primary Planets about the Sun, are in a fefquiplicate Ratio of their mean diflances from the Sun. But, 4. The primary Planets do not defcribe Areas any way proportional to their periodi- cal Times, about the Earth 5 as being fometimes feen Sta- tionary, andfometimes Retrograde with regard thereto. See Satellites, Periods, ££c.

II. The Powers whereby the Satellites of Jupiter are constantly drawn out of their rectilinear Courfe, and re- tained in their Orbits, do refpect the Center of Jupiter, and are reciprocally as the Squares of their diflances from the fame Centre. 2. The feme holds of the Satellites of Sa- turn with regard to Saturn ; of the Moon with regard to the Earth : And of the primary Planets with regard to the Sun. SeeCENTRiPETAL Force.

III. The Moon gravitates towards the Earth, and by the Power of that Gravity is retain'd in her Orbit : And the fame holds of the other Satellites with refpeft to their primary Planets 5 and of the Primaries with refpeft to th e Sun. See Moon.

As to the Moon, the Propofiti'on is thus proved : The Moon's mean diflance is 60 Semidiameters of the Earth 5 her Perkd, with regard to the fiVd Stars, is 27 Days, 7

Hours, 43 Minutes; and the Earth's Circumference 123249600 Fans Beet. Now, fuppofing the Moon to have lolt all its Motion, and to be let drop to the Earth with the Power which retains her in her Orbit ; in the fpace of one Mmute fhe will fall i 5t \ Paris Feet-; the Arch me describes m her mean Motion at the diflance of 60 Semi- diameters of the Earth being the verfed Sine of 15 T V Paris Feet Hence, as the Power as it approaches the Earth, in- creofes m a duplicate Ratio of the diflance inverfly ; fo as at the Surface of the Earth, 'tis do X 60 greater than 'the Moon : A Body tailing with that Force in our Region muit, in a Minute's time, defcribe the fpace of 60 X 60 X 15 ft Pans Feet ; and 1 5 Paris Feet in the fpace of one oecond.

t But this is the Rate at which Bodies fall, by their Gra- vity, at the Surface of our Earth ; as Buygens has demon- Anted, by Experiments with Pendulums. Confequently, the Power whereby the Moon is retain'd in her Orbit, is the very lame we call Gravity ; Forif they were different, a Body taiimg with both Powers together, would defcend with double the Velocity, and in a Second of Time de- fcribe 3c J Feet. See Descent of Bodies.

As to iheoiher fecundary Pianets, their Phenomena with refpett to their primary ones, being of the fame kind with thoie ot the Moon about the Earth ; 'tis argued, by Ana- logy, they depend on the fame Caufes: It being a Rule" or Axiom all Philofophers agree to, That Effcds of the fame kind, ha\e the fame Caufes. Again, Attraction is always mutual, i. e. the Reaction is equal to the Action. Confequently, the primary Planets gravitate towards their fecundary ones ; the Earth towards the Moon, and the Sun towards 'em all. And this Gravity, with regard to each fe- veral Planer, is reciprocally as the Square of its diflance from its Centre ot Gravity. See Attraction, Reaction ££?e.

IV. All Bodies gravitate towards all the Planets ;' and* their Weights towards any one PI; net, at equal diflances from the Centre of the Planet, are proportional to the Quantity of Matter in each.

For the Law of the Defcent of heavy Bodies towards the Earth, fetting afide their unequal Retardation from the Refiflance of the Air, is this ; that all Bodies fall equal fpacesin equal times : But the nature of Gravity or Weight no doubt, is the fame on the other Planets, as on the Earth. See Weight.

Suppofe, e.gr. fuch Bodies raifed to the Surface of the Moon, and together with the Moon deprived at once of all Progreflive Motion, and drop'd towards the Earth : 'Tis /hewn, that in equal Times they will defcribe equal Spaces with the Moon ; and, therefore, that their Quantity of Matter is to that of the Moon, as their Weights to its Weight.

Add, that fince Jupiter's Satellites revolve in times that are in a fefquiplicate Ratio of their diflances from the Centre oiJuptter t and confequently at equal diflances from Jupiter their accelerating Gravities are equal ; therefore, falling equal Altitudes in equal Times, they will defcribe equal Spaces: jultasin heavy Bodies on our Earth. And rhe fame Argument will hold of the primary Planets with re- gard to the Sun. And the Powers whereby unequal Bodies are equally accelerated, are as the Bodies; i. e. the Weights are as the Quantities of Matter in the Planets. And the Weights of the primary and fecundary Planets towards the Sun, are as the Quantities ot Matter in the Planets and Sa- tellites.

And hence are feveral Corollaries drawn relating to tht Weights q{ Bodies on the Surface of the Earth, Magnetifm, and the Exiftence of a Vacuum. Which fee under the Articles Vacuum, Weight, and Magnetism.

V. Gravity extends itfelf towards all Bodies, and is in proportion to the Quantity of Matter in each.

That all the Planets gravitate towards each other, has been already fliewn ; likewife, that the Gravity towards any one confider'd apart, is reciprocally as the Squares of its Diflance from the Centre of the Planet : Confequently, Gravity is proportional to the Matter therein. Further, As all the Parts of any Planet, A, gravitate, towards another Planet, B ; and the Gravity of any part is to the Gravity of the whole, as the Matter of the part to the Matterof the whole ; and Reaction equal to Action: The Planet B will gravitate towards all tbe Parts of the Planet A ; and its Gravity towards any part, will be to its Gravity towards the whole, as the Matter of the part to the Matter of the whole.

Hence, we derive Methods of finding and comparing the Weights of Bodies towards different Planets ; of finding the Quantity of Matter in the feveral Planets ; and their Den- sities : Since the Weights of equal Bodies revolving about Planets, are as the Diameters of their Orbits directly, and as the Squares of the Periodical Times, inverfly 5 and the Weights at any diflance from the Centre of the Planet are greater or lefs in a duplicate Ratio of their di- flances, inverfly: And fince the Quantities of Matter 7 X in-