to explain only one limited class of perturbations. There are some which may be described as a slow increase and decrease of the eccentricities of the orbits, and a slow change in the direction of the longer axes of the orbits; but there are others of which no intelligible account can be given to you.
In order, however, to bring these theories into actual calculation, it is necessary to know, not only the general tendency of the disturbances, but also their actual magnitude. In the perturbations produced by the earth, by Jupiter, and by Saturn, there is no difficulty in doing this. I have already shown you how we can calculate the number of miles through which the earth's attraction draws the moon in one hour. We are certain from most careful experiments made by Newton and (in the present century) by Bessel, that the earth's attraction draws every body at the earth's surface through the same space in the same time; or in other words, that a ball of lead, a cricket ball, and a feather, will fall to the ground with equal speed, if the resistance of the air is removed. We say, therefore, that the earth's attraction would draw a planet through the same space as the moon, provided the planet were at the moon's distance; and for the greater distance of the planet, we must, on the law of gravitation, diminish that space in the inverse proportion of the square of the distance. Now I have already shown you how to compute the space through which the sun draws a planet in one hour; and therefore the problem now is, to compute the motion of a planet, knowing exactly how far and in what direction the sun will draw it in one hour, and also knowing exactly how far and in what direction the earth will draw it in one hour. Without pretending to explain to you
