16. SEE how all this naturally follows from the foregoing principles in those planets, which have satellites moving about them. By the times, in which these satellites perform their revolutions, compared with their distances from their respective primary, the proportion between the power, with which one primary attracts his satellites, and the force with which any other attracts his will be known; and the proportion of the power with which any planet attracts its secondary, to the power with which it attracts a body at its surface is found, by comparing the distance of the secondary planet from the center of the primary, to the distance of the primary planet’s surface from the same: and from hence is deduced the proportion between the power of gravity upon the surface of one planet, to the gravity upon the surface of another. By the like method of comparing the periodical time of a primary planet about the sun, with the revolution of a satellite about its primary, may be found the proportion of gravity, or of the weight of any body upon the surface of the sun, to the gravity, or to the weight of the same body upon the surface of the planet, which carries about the satellite.
17. BY these kinds of computation it is found, that the weight of the same body upon the surface of the sun will be about 23 times as great, as here upon the surface of the earth; about 10⅗ times as great, as upon the surface of Jupiter; and near 19 times as great, as upon the surface of Saturn[257].
18. THE quantity of matter, which composes each of these bodies, is proportional to the power it has upon a body at a given distance. By this means it is found, that the sun contains 1067 times as much matter as Jupiter; Jupiter 158⅔ times as much as the earth, and 2-5/6 times as much as Saturn[258]. The diameter of the sun is about 92 times, that of Jupiter about 9 times, and that of Saturn about 7 times the diameter of the earth.
19. BY making a comparison between the quantity of matter in these bodies and their magnitudes, to be found from their diameters, their respective densities are readily deduced; the density of every body being measured by the quantity of matter contained under the same bulk, as has been above remarked[259]. Thus the earth is found 4¼ times more dense than Jupiter; Saturn has between ⅔ and ¾ of the density of Jupiter; but the sun has one fourth part only of the density of the earth[260]. From which this observation is drawn by our author; that the sun is rarified by its great heat, and that of the three planets named, the more dense is nearer the sun than the more rare; as was highly reasonable to expect, the densest bodies requiring the greatest heat to agitate and put their parts in motion; as on the contrary, the planets which are more rare, would be rendered unfit for their office, by the intense heat to which the denser are exposed. Thus the waters of our seas, if removed to the distance of Saturn from the sun, would remain perpetually frozen; and if as near the sun as Mercury, would constantly boil[261].