54. SIR ~ISAAC NEWTON~ shews farther, how, by comparing the periods of the motion of the satellites, which revolve round Jupiter and Saturn, with the period of our moon round the earth, and the periods of those planets round the sun with the period of our earth’s motion, the inequalities in the motion of those satellites may be derived from the inequalities in the moon’s motion; excepting only in regard to that motion of the axis of the orbit, which in the moon makes the motion of the apogeon; for the orbits of those satellites, as far as can be discerned by us at this distance, appearing little or nothing eccentric, this motion, as deduced from the moon, must be diminished. ~CHAP. IV.~ Of ~Comets~. IN the former of the two preceding chapters the powers have been explained, which keep in motion those celestial bodies, whose courses had been well determined by the astronomers. In the last chapter we have shewn, how those powers have been applied by our author to the making a more perfect discovery of the motion of those bodies, the courses of which were but imperfectly understood; for some of the inequalities, which we have been describing in the moon’s motion, were unknown to the astronomers. In this chapter we are to treat of a third species of the heavenly bodies, the true motion of which was not at all apprehended before our author writ; in so much, that here Sir ~ISAAC NEWTON~ has not only explained the causes of the motion of these bodies, but has performed also the part of an astronomer, by discovering what their motions are. 2. THAT these bodies are not meteors in our air, is manifest; because they rise and set in the same manner, as the sun and stars. The astronomers had gone so far in their inquiries concerning them, as to prove by their observations, that they moved in the etherial spaces far beyond the moon; but they had no true notion at all of the path, which they described. The most prevailing opinion before our author was, that they moved in straight lines; but in what part of the heavens was not determined. DESCARTES[205] removed them far beyond the sphere of Saturn, as finding the straight motion attributed to them, inconsistent with the vortical fluid, by which he explains the motions of the planets, as we have above related[206]. But Sir ISAAC NEWTON distinctly proves from astronomical observation, that the comets pass through the region of the planets, and are mostly invisible at a less distance, than that of Jupiter[207].