Page:On the connexion of the physical sciences (1834).djvu/24

12 force in the tangent cease, the planet would fall to the sun by its gravity; were the sun not to attract it, the planet would fly off in the tangent. Thus, when the planet is in aphelion, or at the point where the orbit is farthest from the sun, his action overcomes the planet’s velocity, and brings it towards him with such an accelerated motion, that, at last, it overcomes the sun's attraction, and, shooting past him, gradually decreases in velocity, until it arrives at the aphelion where the sun's attraction again prevails. In this motion the radii vectores, or imaginary lines joining the centres of the sun and the planets, pass over equal areas in equal times.

If the planets were attracted by the sun only, this would ever be their course; and because his action is proportional to his mass, which is much larger than that of all the planets put together, the elliptical is the nearest approximation to their true motions, which are extremely complicated, in consequence of their mutual attraction, so that they do not move in any known or symmetrical curve, but in paths now approaching to, now receding from, the elliptical form; and their radii vectores do not describe areas exactly proportional to the time. Thus the areas become a test of disturbing forces.

To determine the motion of each body, when disturbed by all the rest, is beyond the power of