And hence are several corollaries drawn relating to the weights of bodies on the surface of the Earth, magnetism, and the existence of a vacuum.
V. Gravity extends itself towards all bodies, and is in proportion to the quan tity of matter in each.
That all planets gravitate towards each other has been already shewn ; likewise, that the gravity towards any one, consi dered apart, is reciprocally as the squares of its distance from the centre of the planet ; consequently, gravity is propor tionable to the matter therein. Further, as all the parts of any planet, A, gravi tate 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 matter of the whole ; and as reaction is equal to action ; the planet B will gra vitate towards all the 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 the me thods of finding and comparing weights of bodies towards different planets ; of finding the quantity of matter in the se veral planets, and their densities ; since the weights of equal bodies, revolving about planets, are as the diameter of their orbits directly, and as the squares of the periodical times inversely ; and the weights at any distance from the centre of the planet are greater or less in a du plicate ratio of their distances inversely.
And since the quantities of matter in the planets are as their powers at equal dis tances from their centres ; and, lastly, since the weights of equal and homoge neous bodies towards homogeneous spheres are, at the surface of the spheres, as the diameters of those spheres; and consequently, the densities of heteroge. neon bodies are as the weights at the di ameters of the spheres.
VI. The common centre of gravity of the Sun and all the planets is at rest; and the Sun, though always in motion, yet never recedes far from the common cen tre of all the planets.
For the matter in the Sun being to that in Jupiter as 1033 to 1; and Jupiter's dis tance from the Sun to the semi-diameter of the Sun in a ratio somewhat bigger; the common centre of gravity of Jupiter and the Sun will be a point a little with out the Sun's surface ; and by the same means the common centre of Saturn and the Sun will be a point a little within the Sun's surface ; and the common centre of the Earth, and all the planets, will be scarce one diameter of the Sun distant from the centre thereof; but the centre is always at rest : therefore, though the Sun will have a motion this and that way, according to the various situa tions of the planets, yet it Lim never recede far from the centre ; so that the common centre of gravity of the Earth, Sun, and Planets, may be esteem. ed the centre of the whole world. See