The devout Kepler, after his last great discovery, sat down content “to wait a century for a reader.” He had not long passed away ere the reader was sent, one who read his book to good purpose indeed. Kepler had been able to discover three laws to which the planets were obedient, but as to whether there was any connection between those laws, why the planets followed them rather than any others which might have been framed, and what laws the satellites and comets of the system were subject to, Kepler could not tell. Newton, on the contrary, discovered the great underlying principle, of which the laws of Kepler were only some of the necessary consequences, and showed not merely how the planets moved, but also to a great extent why they did so. Newton had not long established his law of gravitation before he arrived at a strange discovery. Assuming his theory to be correct, he worked out by rigid mathematical processes the shape of the orbits which the planets must follow. Since we know that they travel in ellipses, we should naturally have expected that an ellipse would be the resulting orbit, but instead Newton found he had arrived at an expression which embraced not one curve but four. Of these four, one was the oval or ellipse, another the circle, but the other two were curves of a very different shape indeed, curves which did not enclose a space, but which had each two ends, which, however far they were prolonged, could never meet. And directly this fact was recognized, an unlooked-for truth was made plain. Comets, which had hitherto been regarded as perfectly lawless bodies, as irregular and uncontrolled as the thoughts of an opium-dreamer seem to be, were now seen to be integral parts of our solar system. For though so many of them enter our system but once, never having visited it before, never to visit it again, yet since these all travel, in obedience to the sun’s attraction, in one or other of these strange unending curves, curves which are a necessary consequence of the law of gravitation, they are manifestly members of the solar family; without them it would be imperfect, without them the law of gravitation were but partially illustrated.