The great principle on which the whole philosophy is founded is the pow er of gravity : this principle is not new ; Kepler, long ago, hinted at it in his In troduct. ad Martin. He even disco vered some of the properties thereof; and their effects in the motions of the primary planets : but the glory of bring ing it to a physical demonstration was re served to the English philosopher. See GlIATITATIOW. Ilia proof of this princi ple from phenomena, together with the application of the same principle to the various other appearances of nature, or the deducing those appearances from that principle, constitute the Newtonian system ; which, drawn in miniature, will stand thus : I. The phenomena are, 1. That the sa tellites of Jupiter do, by radii drawn to the centre of the planet, describe areas proportional to the times ; and that their periodical times are in a sesquiplicate ra tio of their distances from its centre ; in which the observations of all astronomers agree. 2. The same phenomenon holds of the satellites of Saturn, with regard to Saturn ; and of the Moon, with regard to the Earth. 3. The periodical times of the primary planets about the Sun are in a sesquiplicate ratio of their mean distances from the Sun. But, 4. The primary pla nets do not describe areas any way pro portionsl to their periodical times about the Earth; as being sometimes seen std! tionary, and sometimes retrograde, with regard thereto.
H. The powers whereby the satellites of Jupiter are constantly drawn out of their rectilinear course, and retained in their orbits, respect the centre of Jupi ter, and are reciprocally as the squares of their distances from the same centre. The same 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. See Csirraar. micas.
Ill. The moqn gravitates towards the Earth, and by the power of that gravity is retained in her orbit : and the same holds of the other satellites, with respect to their primary planets; and of the primary planets, with respect to the Sun.
As to the Moon, the proposition is thus proved ; the Moon's mean distance is 60 semidiameters of the Earth ; her period, with regard to the fixed stars, is 27 days, 7 hours, 43 minutes ; and the Earth's cir cumference 123,249,600 Paris feet. Now, supposing the Moon to have lost all her motion, and to be let drop to the Earth, with the power which retains her in her orbit, in the space of one minute she will fall Paris feet ; the arch she de scribes in her mean motion, at the dis tance of 60 diameters of the Earth, be ing the versed sign of 15.6 Paris feet. Hence, as the power, as it approaches the Earth, increases in a duplicate ratio of the distance inversely ; so as at the surface of the Earth it is 60 x 60 greater than at the Moon; a body falling with that force in our region must, in a mi nute's time, describe the space of 60 x 60x Paris feet, or Paris feet in the space of one second.
But this is the rate at which bodies fall by their gravity at the surface of our Earth, as Huygens has demonstrated by experiments with pendulums. Conse. quently, the power whereby the Moon is retained in her orbit is the very same we call gravity ; for, if they Were differ ent, a body falling with both powers to. gether would descend with double the velocity, and in a second of time describe 301 feet.
As to the other secondary planets, their phenomena, with respect to their primary ones, being of the same kind with those of the Moon about the Earth, it is argued, by analogy, that they depend on the same causes ; it being a rule or axiom all philosophers agree to, that ef fects of the same kind have the same causes. Again, attraction is always mu tual,i. e. the reaction is equal to the ac tion : consequently the primary planets gravitate towards their secondary ones, the Earth towards the Moon, and the Sun towards them all. And this gravity, with regard to each several planet, is re ciprocally as the square of its distance from the centre of gravity. See Arra.sc 'nom, 8tc.
IV. All bodies gravitate towards all the planets : and their weight towards any one planet, at equal distances from the centre of the planet, is proportional to the quantity of matter in each For the law of the descent of heavy bodies towards the Earth, setting aside their unequal retardation from the re sistance of the air, is this, that all bodies fall equal spaces in equal times ; but the nature of gravity or weight, no doubt, is the same on the other planets as on the Earth.
Suppose, e.gr. such bodies raised to the surface of the Moon, and, together with the Moon, deprived at once of all pro gressive motion, and dropped towards the Earth : it is shown, that in equal times they will describe 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 since Jupiter a satellites re. volve in times that are in a sesquiplicate ratio of their distances from the centre of Jupiter, and consequently at equal dis. tutees from Jupiter, their accelerating gravities are equal ; therefore, falling equal altitudes in equal times, they will describe equal spaces; just as in heavy bodies on our Earth. And the same ar gument will hold of the primary planets with regard to the Sun, and the powers whereby unequal bodies are equally ac celerated as the bodies, i. e. the weights are as the quantities of matter in the pla nets, and the weight of the primary and secondary planets towards the Sun are as the quantities of matter in the planets and satellites.