3 8 THE POPULAR SCIENCE MONTHLY. 



ent size of the moon would be reduced to one ninth of its present 

 value. With increasing distance the phenomena would still fur- 

 ther 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 astrono- 

 mer's dream of perpetual moonlight how long would it be re- 

 alized ? 



Another question of vital importance is here involved in the 

 theory under consideration the variation of the earth's attrac- 

 tion 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 con- 

 trolling 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 state- 

 ment 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 esti- 

 mated. 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 mo- 

 tion. 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 dogma- 

 tism 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." (2) 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 handi- 

 work must end in failure and disappointment. 



* The solution was first given by M. Liouville in 1842. 



