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Soon after the invention of the telescope it was found that comets resembled the planets in moving in orbits around the sun. Sir Isaac Newton showed that their motions were ruled by the sun's gravitation in the same way as the motions of the planets. The great difference was that, instead of the orbits being nearly circular, like those of the planets, they were so elongated that, in most cases, it could not be determined where the aphelion, or farther end, was. As many of our readers may desire an exact statement of the nature of cometary orbits, and the laws governing them, we shall enter into some
Fig. 45.—Parabolic Orbit of a Comet. explanations of the subject.

It was shown by Newton that a body moving under the influence of the sun's attraction would always describe a conic section. This curve is of three kinds, an ellipse, a parabola, and a hyperbola. The first, as we all know, is a closed curve returning into itself. But the parabola and the hyperbola are not such; each of them extends out without end in two branches. In the case of the parabola these two branches approach more nearly to having the same direction as we get out farther, but in the case of the hyperbola they always diverge from each other.