Jupiter and Saturn, which are the largest and principal planets of the solar system, have retained the relation between their density and impulsive motions, in the most exact proportions; the density of Saturn is to that of Jupiter as 67 to 94-1/2 and their velocities are nearly as 88-2/3 to 120-1/72, or as 67 to 90-11/16; it is seldom that pure conjectures can draw such exact relations. It is true, that by following this relation between the velocity and density of planets, the density of the earth ought to be only as 206-7/18, and not 400, which is its real density; from hence it may be conceived, that our globe was formerly less dense than it is at present. With respect to the other planets, Mars, Venus, and Mercury, as their densities are known only by conjecture, we cannot be certain whether this circumstance will destroy or confirm our hypothesis. The opinion of Newton is, that density is so much the greater, as the heat to which the planet is exposed is the stronger; and it is on this idea that we have just said that Mars is one time less dense than the Earth, Venus one time, Mercury seven times, and the comet in 1680, 28,000 times denser than the earth: but this proportion between the density of the planets and the heat which they sustain, seems not well founded, when we consider Saturn and Jupiter, which are the principal objects; for, according to this relation between the density and heat, the density of Saturn would be about 4-7/18, and that of Jupiter as 14-17/22, instead of 67 and 94-1/2, a difference too great to be admitted, and must destroy the principles upon which it was founded. Thus, notwithstanding the confidence which the conjectures of Newton merit, I can but think that the density of the planets has more relation with their velocity than with the degree of heat to which they are exposed. This is only a final cause, and the other a physical relation, the preciseness of which is remarkable in Jupiter and Saturn: it is nevertheless true, that the density of the earth, instead of being 206-7/8, is found to be 400, and that consequently the terrestrial globe must be condensed in this ratio of 206-7/8 to 400.
But have not the condensations of the planets some relation with the quantity of the heat of the sun which they sustain? If so, Saturn, which is the most distant from that luminary, will have suffered little or no condensation; and Jupiter will be condensed from 90-11/16 to 94-1/2. Now the heat of the sun in Jupiter being to that of the sun upon the earth as 14-17/22 are to 400, the condensations ought to be in the same proportion. For instance, if Jupiter be condensed, as 90-11/16 to 94-1/2, and the earth had been placed in his orbit, it would have been condensed from 206-7/8 to 215-990/1451, but the earth being nearer the sun, and receiving a heat, whose relation to that which Jupiter receives is from 400 to 14-17/22, the quantity of condensation it would have experienced on the orbit of Jupiter by the proportion of 400 to 14-17/22, which gives nearly 234-1/3 for the quantity which the earth would be condensed. Its density was 206-7/8, by adding the quantity of its acquired condensation, we find 400-7/8 for its actual density, which nearly approaches the real density 400, determined to be so by the parallax of the moon. As to other planets, I do not here pretend to give exact proportions, but only approximations, to point out that their densities have a strong relation to their velocity in their respective orbits.