There is a certain beautiful curve known to geometricians by the name of the parabola. Its form is shown in the adjoining figure; it is a curved line which bends in towards and around a certain point known as the focus. This would not be the occasion for any allusion to the geometrical properties of this curve; they should be sought in works on mathematics. It will here be only necessary to point to the connection which exists between the parabola and the ellipse. In a former chapter we have explained the construction of the latter curve, and we have shown how it possesses two foci. Let us suppose that a series of ellipses are drawn, each of which has a greater distance between its foci than the preceding one. Imagine the process carried on until at length the distance between the foci became enormously great in comparison with the distance from each focus to the curve, then each end of this long ellipse will practically have the same form as a parabola. We may thus look on the latter curve represented in Fig. 69 as being one end of an ellipse of which the other end is at an indefinitely great distance. In 1681 Doerfel, a clergyman of Saxony, proved that the great comet then recently observed moved in a parabola, in the focus of which the sun was situated. Newton showed that the law of gravitation would permit a body to move in an ellipse of this very extreme type no less than in one of the more ordinary proportions. An object revolving in a parabolic orbit about the sun at the focus moves in gradually towards the sun, sweeps around the great luminary, and then begins to retreat. There is a necessary distinction between parabolic and elliptic motion. In the latter case the body, after its retreat to a certain distance, will turn round and again draw in towards the sun; in fact, it must make periodic circuits of its orbit, as the planets are found to do. But in the case of the true parabola the body can never return; to do so it would have to double the distant focus, and as that is infinitely remote, it could not be reached except in the lapse of infinite time.