So far we have supposed that the planets were all on what we should call a level--that is to say, we have regarded them as if they were floating in a sea of water around the sun; but this is only approximately correct, for the orbits of the planets are not all at one level. If you had a number of slender hoops or rings to represent the planetary orbits, you would have to tilt one a little this way and another a little that way, only never so far but that a line through the centre of the hoop from one side to another could pass through the sun. The way in which the planetary orbits are tilted is slight in comparison with that of the orbits of comets, for these are at all sorts of angles--some turned almost sideways, and others slanting, and all of them are ellipses long drawn out and much more irregular than the planetary orbits; but erratic as they are, in every case a line drawn through the sun and extended both ways would touch each side of the orbits. A great astronomer called Halley, who was born in the time of the Commonwealth, was lucky enough to see a very brilliant comet, and the sight interested him so much that he made all the calculations necessary to find out just in what direction it was travelling in the heavens. He found out that it followed an ellipse which brought it very near to the sun at one part of its journey, and carried it far beyond the orbit of the earth, right out to that of Neptune, at the other. Then he began to search the records for other comets which had been observed before his time. He found that two particularly bright ones had been carefully noted--one about seventy-five years before that which he had seen, and the other seventy-five years before that again. Both these comets had been watched so scientifically that the paths in which they had travelled could be computed. A brilliant inspiration came to Halley. He believed that instead of these three, his own and the other two, being different comets, they were the same one, which returned to the sun about every seventy-five years. This could be proved, for if this idea were correct, of course the comet would return again in another seventy-five years, unless something unforeseen occurred. But Halley was in the prime of life: he could not hope to live to see his forecast verified. The only thing he could do was to note down exact particulars, by means of which others who lived after him might recognize his comet. And so when the time came for its return, though Halley was in his grave, numbers of astronomers were watching eagerly to see the fulfilment of his prediction. The comet did indeed appear, and since then it has been seen once again, and now we expect it to come back in the year 1910, when you and I may see it for ourselves. When the identity of the comet was fully established men began to search further back still, to compare the records of other previous brilliant comets, and found that this one had been noticed many times before, and once as