7. THIS finishes the discoveries made in the action of the primary planets upon their secondary. The next thing to be shewn is, that the sun acts upon them likewise: for this purpose it is to be observed, that if to the motion of the satellite, whereby it would be carried round its primary at rest, be superadded the same motion both in regard to velocity and direction, as the primary it self has, it will describe about the primary the same orbit, with as great regularity, as if the primary was indeed at rest. The cause of this is that law of motion, which makes a body near the surface of the earth, when let fall, to descend perpendicularly, though the earth be in so swift a motion, that if the falling body did not partake of it, its descent would be remarkably oblique; and that a body projected describes in the most regular manner the same parabola, whether projected in the direction, in which the earth moves, or in the opposite direction, if the projecting force be the same[185]. From this we learn, that if the satellite moved about its primary with perfect regularity, besides its motion about the primary, it would participate of all the motion of its primary; have the same progressive velocity, with which the primary is carried about the sun; and be impelled with the same velocity as the primary towards the sun, in a direction parallel to that impulse of its primary. And on the contrary, the want of either of these, in particular of the impulse towards the sun, will occasion great inequalities in the motion of the secondary planet. The inequalities, which would arise from the absence of this impulse towards the sun are so great, that by the regularity, which appears in the motion of the secondary planets, it is proved, that the sun communicates, the same velocity to them by its action, as it gives to their primary at the same distance. For Sir ~ISAAC NEWTON~ informs us, that upon examination he found, that if any of the satellites of Jupiter were attracted by the sun more or less, than Jupiter himself at the same distance, the orbit of that satellite, instead of being concentrical to Jupiter, must have its center at a greater or less distance, than the center of Jupiter from the sun, nearly in the subduplicate proportion of the difference between the sun’s action upon the satellite, and upon Jupiter; and therefore if any satellite were attracted by the sun but 1/1000 part more or less, than Jupiter is at the same distance, the center of the orbit of that satellite would be distant from the center of Jupiter no less than a fifth part of the distance of the outermost satellite from Jupiter[186]; which is almost the whole distance of the innermost satellite. By the like argument the satellites of Saturn gravitate towards the sun, as much as Saturn it self at the same distance; and the moon as much as the earth.