and diminutions of velocity, variations in the forms of orbits, changes in distances and inclinations, which these forces must evidently produce, the most learned geometer would fail to discover a trustworthy guide.  Forces so numerous, so variable in direction, so different in intensity, seemed to be incapable of maintaining a condition of equilibrium except by a sort of miracle.  Newton even suggested that the planetary system did not contain within itself the elements of indefinite stability.  He was of opinion that a powerful hand must intervene from time to time to repair the derangements occasioned by the mutual action of the various bodies.  Euler, better instructed than Newton in a knowledge of these perturbations, also refused to admit that the solar system was constituted so as to endure forever.

Never did a greater philosophical question offer itself to the inquiries of mankind.  Laplace attacked it with boldness, perseverance, and success.  The profound and long-continued researches of the illustrious geometer completely established the perpetual variability of the planetary ellipses.  He demonstrated that the extremities of their major axes make the circuit of the heavens; that independent of oscillation, the planes of their orbits undergo displacements by which their intersections with the plane of the terrestrial orbit are each year directed toward different stars.  But in the midst of this apparant chaos, there is one element which remains constant, or is merely subject to small and periodic changes; namely, the major axis of each orbit, and consequently the time of revolution of each planet.  This is the element which ought to have varied most, on the principles held by Newton and Euler.  Gravitation, then, suffices to preserve the stability of the solar system.  It maintains the forms and inclinations of the orbits in an average position, subject to slight oscillations only; variety does not entail disorder; the universe offers an example of harmonious relations, of a state of perfection which Newton himself doubted.

This condition of harmony depends on circumstances disclosed to Laplace by analysis; circumstances which on the surface do not seem capable of exercising so great an influence.  If instead of planets all revolving in the same direction, in orbits but slightly eccentric and in planes inclined at but small angles toward each other, we should substitute different conditions, the stability of the universe would be jeopardized, and a frightful chaos would pretty certainly result.  The discovery of the actual conditions excluded the idea, at least so far as the solar system was concerned, that the Newtonian attraction might be a cause of disorder.  But might not other forces, combined with the attraction of gravitation, produce gradually increasing perturbations such as Newton and Euler feared?  Known facts seemed to justify the apprehension.  A comparison of ancient with modern observations revealed a continual acceleration