Take a single instance of the perturbations of Jupiter and Saturn which can be rendered evident. The times of orbital revolution of Saturn and Jupiter are nearly as five to two. Suppose the orbits of the planets to be, as in Fig. 3, both ellipses, but not necessarily equally distant in all parts. The planets are as near as possible at 1, 1. Drawn toward each other by mutual attraction, Jupiter's orbit bends outward, and Saturn's becomes more nearly straight, as shown by the dotted lines. A partial correction of this difficulty immediately follows. As Jupiter moves on ahead of Saturn it is held back--retarded in its orbit by that body; and Saturn is hastened in its orbit by the attraction of Jupiter. Now greater speed means a straighter orbit. A rifle-ball flies nearer in a straight line than a thrown stone. A greater velocity given to a whirled ball pulls the elastic cord far enough to give the ball a larger orbit. Hence, being hastened, Saturn stretches out nearer its proper orbit, and, retarded, Jupiter approaches the smaller curve that is its true orbit. But if they were always to meet at this point, as they would if Jupiter made two revolutions to Saturn's one, it would be disastrous. In reality, when Saturn has gone around two-thirds of its orbit to 2, Jupiter will have gone once and two-thirds around and overtaken [Page 12] Saturn; and they will be near again, be drawn together, hastened, and retarded, as before; their next conjunction would be at 3, 3, etc. Now, if they always made their conjunction at points equally distant, or at thirds of their orbits, it would cause a series of increasing deviations; for Jupiter would be constantly swelling his orbit at three points, and Saturn increasingly contracting his orbit at the same points. Disaster would be easily foretold. But as their times of orbital revolutions are not exactly in the ratio of five and two, their points of conjunction slowly travel around the orbit, till, in a period of nine hundred years, the starting-point is again reached, and the perturbations have mutually corrected one another.