explained by supposing that the planet is at all times drawn by some force toward the sun. Secondly, supposing a planet put in motion, and then continually acted upon by any force whatever, directed always to the sun, it is found that it will describe equal areas in equal times by the line connecting it with the sun. Thirdly, taking for granted Kepler's first law, which was ascertained from observation only, "that the planets in their revolutions describe ellipses," we can ascertain what is the force with which they are drawn towards the sun, and which causes them to describe ellipses: it is found to be an attraction towards the sun following the law of the inverse square of the distance; that is to say, when the planet is half-way distant from the sun, it will be drawn with four times the strength, or, when the planet is one-third distant from the sun, it will be drawn with nine times the strength. Fourthly, we may propose to ourselves this problem: suppose the planet to be once put in motion, and then continually attracted by the sun with a force inversely as the square of the distance from the sun, what curve will it describe? It is found by the investigation which I have spoken of, that the curve which it will describe will be one or other of the following a circle, an ellipse, a parabola, or a hyperbola; and that the sun will be in the centre of the circle, or in the focus of the ellipse, parabola, or hyperbola. In nature we do not know any instance of the hyperbola; comets, as we shall see hereafter, for the most part move in parabolas; some comets and all the planets move in ellipses; and some of these ellipses approach very nearly to circles. I am exceedingly sorry that it is impossible for me to give you an idea of the steps of these investigations; but I say, and I am sure you
