In Saturn the proportion of the greatest distance to the least is something less, than the proportion of 9 to 8, but much nearer to this, than to the proportion of 10 to 9. In Jupiter this proportion is a little greater, than that of 11 to 10. In Mars it exceeds the proportion of 6 to 5. In the earth it is about the proportion of 30 to 29. In Venus it is near to that of 70 to 69. And in Mercury it comes not a great deal short of the proportion of 3 to 2.
7. Each of these planets so moves through its ellipsis, that the line drawn from the sun to the planet, by accompanying the planet in its motion, will describe about the sun equal spaces in equal times, after the manner spoke of in the chapter of centripetal forces[144]. There is also a certain relation between the greater axis’s of these ellipsis’s, and the times, in which the planets perform their revolutions through them. Which relation may be expressed thus. Let the period of one planet be denoted by the letter A, the greater axis of its orbit by D; let the period of another planet be denoted by B, and the greater axis of this planet’s orbit by E. Then if C be taken to bear the same proportion to B, as B bears to A; likewise if F be taken to bear the same proportion to E, as E bears to D; and G taken to bear the same proportion likewise to F, as E bears to D; then A shall bear the same proportion to C, as D bears to G.
8. The secondary planets move round their respective primary, much in the same manner as the primary do round the sun. But the motions of these shall be more fully explained hereafter[145]. And there is, besides the planets, another sort of bodies, which in all probability move round the sun; I mean the comets. The farther description of which bodies I also leave to the place, where they are to be particularly treated on[146].
9. Far without this system the fixed stars are placed. These are all so remote from us, that we seem almost incapable of contriving any means to estimate their distance. Their number is exceeding great. Besides two or three thousand, which we see with the naked eye, telescopes open to our view vast numbers; and the farther improved these instruments are, we still discover more and more. Without doubt these are luminous globes, like our sun, and ranged through the wide extent of space; each of which, it is to be supposed, perform the same office, as our sun, affording light and heat to certain planets moving about them. But these conjectures are not to be pursued in this place.
10. I shall therefore now proceed to the particular design of this chapter, and shew, that there is no sensible matter lodged in the space where the planets move.
[11.] That they suffer no sensible resistance from any such matter, is evident from the agreement between the observations of astronomers in different ages, with regard to the time, in which the planets have been found to perform their periods. But it was the opinion of Des Cartes[147], that the planets might be kept in their courses by the means of a fluid matter, which continually circulating round should carry the planets along with it. There is one appearance that may seem to favour this opinion; which is, that the sun turns round its own axis the same way, as the planets move. The earth also turns round its axis the same way, as the moon moves round the earth. And the planet Jupiter turns upon its axis the same way, as his satellites revolve round him. It might therefore be supposed, that if the whole planetary region were filled with a fluid matter, the sun, by turning round on its own axis, might communicate motion first to that part of the fluid, which was contiguous, and by degrees propagate the like motion to the parts more remote. After the same manner the earth might communicate motion to this fluid, to a distance sufficient to carry round the moon, and Jupiter communicate the like to the distance of its satellites. Sir Isaac Newton has particularly examined what might be the result of such a motion as this[148]; and he finds, that the velocities, with which the parts of this fluid will move in different distances from the center of the motion, will not agree with the motion observed in different planets: for instance, that the time of one intire circulation of the fluid, wherein Jupiter should swim, would bear a greater proportion to the time of one intire circulation of the fluid, where the earth is; than the period of Jupiter bears to the period of the earth. But he also proves[149], that the planet cannot circulate in such a fluid, so as to keep long in the same course, unless the planet and the contiguous fluid are of the same density, and the planet be carried along with the same degree of motion, as the fluid. There is also another remark made upon this motion by our author; which is, that some vivifying force will be continually necessary at the center of the motion[150]. The sun in particular, by communicating motion to the ambient fluid, will lose from it self as much motion, as it imparts to the fluid; unless some acting principle reside in the sun to renew its motion continually. If the fluid be infinite, this gradual loss of motion would continue till the whole should stop[151]; and if the fluid were limited, this loss of motion would continue, till there would remain no swifter a revolution in the sun, than in the utmost part of the fluid; so that the whole would turn together about the axis of the sun, like one solid globe[152].
[12.] It is farther to be observed, that as the planets do not move in perfect circles round the sun; there is a greater distance between their orbits in some places, than in others. For instance, the distance between the orbit of Mars and Venus is near half as great again in one part of their orbits, as in the opposite place. Now here the fluid, in which the earth should swim, must move with a less rapid motion, where there is this greater interval between the contiguous orbits; but on the contrary, where the space is straitest, the earth moves more slowly, than where it is widest[153].
13. Farther, if this our globe of earth swam in a fluid of equal density with the earth it self, that is, in a fluid more dense than water; all bodies put in motion here upon the earth’s surface must suffer a great resistance from it; where as, by Sir Isaac Newton’s experiments mentioned in the preceding chapter, bodies, that fell perpendicularly down through the air, felt about 1/860 part only of the resistance, which bodies suffered that fell in like manner through water.