distance from the sun. Thus it is proved that the attraction of the sun on each planet, at its different distances, is inversely proportional to the square of the distance. The same thing also is proved with regard to those planets which have satellites; for several of the known orbits of satellites are elliptical (the others being circular).
There is, however, another very remarkable set of bodies, each of which in its motions sometimes goes nearer to the sun than any other known body, and sometimes passes further from the sun than any other known body; I mean the comets, the explanation of whose motions is one of the most remarkable of Newton's discoveries. A very few comets (not more than five or six,) it is now known, move in very long ellipses, and return periodically to our sight; and to these the same remarks apply which have been above applied to the motion of planets. But at the time when Newton investigated the motions of comets, the idea of periodical comets was totally unknown, and Newton's investigations in regard to comets proceeded entirely on the supposition that the comet did not return. It is difficult for me to attempt to explain here how the orbit of a comet is investigated; the best way perhaps will be to give you something like a history of the thing.
When Newton had investigated the forces which apply to the motion in an ellipse, it was very natural that he should endeavour to see whether the same law of force (namely, that the force is inversely as the square of the distance) which accounts for motion in an ellipse, would account for motion in any other curve. You will see easily that there are two things upon which the motions of a planet depend. One is the force of the attraction of the sun; the other the
