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Rh, as we should if we started off with the proper velocity; and it was thought they never came back. Halley found out that they did come back, and that comets move in ellipses as other planets do, only that they are very long ellipses. It was a well-deserved reward for Halley, who took such pains to get the proof of the law of gravitation from Newton, that he should be led to this great discovery. I may add to what I have already told you, that even when Halley took Newton's great work to the Royal Society in triumph, he found to his astonishment that they were at the moment too poor to publish it. Thereupon Halley paid for it out of his own pocket, although he was not a rich man. He got his reward when he made this great discovery about comets coming back to us, and that was soon after he went back to Oxford as Savilian Professor of Geometry.

He set out to examine as many orbits of comets as he could find observations of—assuming that they went in parabolas and never came back—and he calculated the orbits of twenty-four of them. Now the calculation of an orbit is a complicated matter that I am not going to trouble you with, at present at any rate; but we can all of us understand that when figures come out the same, whatever the figures may mean, they must refer to the same thing. Look now at these figures which Halley obtained for three comets which were thought at that time to be quite different. One of them had appeared in 1531, the second in 1607, and the third in 1682; and when Halley calculated the particulars of their orbits quite separately and independently he found—