ent size of the moon would be reduced to one ninth of its present value. With increasing distance the phenomena would still further change, till at the orbit named by Laplace the month would be equal to the year, and the moon's enlightened hemisphere would be turned constantly to the earth. But the great astronomer's dream of perpetual moonlight—how long would it be realized?
Another question of vital importance is here involved in the theory under consideration—the variation of the earth's attraction on the moon supposed to be removed to a greater distance. This variation is more rapid than that of the sun's attractive force on the same body, as the distance between the sun and moon Is four hundred times that between the moon and the earth. At what point, then, would our satellite escape from the earth's controlling influence and commence to revolve as an independent planet about the sun? This question, strangely enough, seems never to have received Laplace's consideration; at least his statement was continued without change in a later edition of his Systeme du Monde. This problem touching the moon's limit of stability was not solved until sixteen years after Laplace's death.
The relative distances as well as the direction and force of the impulses necessary to produce the required motions in the scheme of Laplace were given by himself in the paragraph quoted. The state of things at double the moon's distance has also been estimated. At four times the distance, or somewhat more, we find Laplace's position of perpetual moonlight; but just here we find the region where the earth loses its control over the moon's motion. The moon escapes from the earth's influence, and henceforth owns allegiance only to the sun. She becomes a primary planet, with a year somewhat greater than ours and a day of doubtful length. As regards the earth, lunar tides can no longer exist. Moonlight and the moon would forsake us together; and the new condition of things, could it be realized, would be worse than the first.
From the case here considered we may learn (1) that dogmatism in regard to the divine plan in the structure and constitution of the universe is not always wise. Final causes may engage the attention of thoughtful minds, but who shall set limits to their extent or application? "Touching the Almighty," said Elihu, "we can not find him out." (3) The wisdom manifested in the adaptations of material things around us transcends that of man's highest efforts. Attempts to disparage the skill of Nature's handiwork must end in failure and disappointment.
- The solution was first given by M. Liouville in 1842.