the circle, and it is what mathematicians call a parabola.
The same consideration is applied to the motion of a planet, in this manner. We must suppose that the planet has been put in motion; we cannot tell how the planets have been put in motion, but they are in motion; that is sufficient for our purpose. The planets, if there were nothing to pull them aside, would go on in a straight course, without altering their velocity. The supposition which Newton made, and on which is founded the theory of gravitation, and which is perfectly conformable with every result of observation, is, that all the planets are attracted towards the sun; that the force is different in different parts, but still always directed towards the sun; that the force is of such a character that it is greater the nearer they go to the sun. Thus, if a planet started from P, Figure 30, in the direction PQ, it would go on in a straight line if it were not pulled by the attraction of the sun; but, by the attraction of the sun, the orbit becomes bent, and the planet describes the curved orbit PklMKL. Now, though this reasoning shows most clearly that the planet will move in a curved orbit of some kind, it is entirely impossible for me in this oral lecture to tell you how the precise nature of this curved orbit is found out; it is, however, found out completely; and I must beg of non-mathematicians to take my word for the result. When the investigation is conducted thoroughly we obtain these results. First, taking for granted Kepler's second law "that each planet, considered without reference to other planets, does in equal times describe equal areas by the line connecting it with the sun," which law was ascertained purely from observation: it is found that this is
