LAPLACE'S PLAN FOR PERPETUAL MOONLIGHT. 37 



we are often deprived at the same time of the light of both sun 

 and moon. To have accomplished this end, it would have been 

 sufficient to have placed the moon at first in opposition to the sun 

 and in the plane of the ecliptic, at a distance from the earth equal 

 to the one hundredth part of the distance of the earth from the 

 sun, and to have impressed on the earth and moon parallel veloci- 

 ties proportional to their distances from the sun. In this case, the 

 moon, being constantly in opposition to the sun, would have de- 

 scribed round it an ellipse similar to that of the earth. These two 

 bodies would then constantly succeed each other, and as at this 

 distance the moon could not be eclipsed, its light would always 

 replace that of the sun." * 



The plan here proposed was one of startling boldness ; but 

 without assuming to defend the doctrine of final causes, it must 

 be said in fairness that to afford light by night had never been 

 claimed as the only design for which the moon was given. Other 

 purposes no less important may be readily imagined. Moreover, 

 the moon's light at the distance named by Laplace would have 

 been little more than one twentieth part of that afforded by the 

 full moon at its actual distance, or less than that of our new moon 

 two days after the change. Such moonlight, though perpetual, 

 would have had little comparative value. Again, the tidal effect 

 upon the earth would have been scarcely perceptible. But with- 

 out further insisting on these points, however important, let us 

 compare the proposed arrangement with that of Nature. Would 

 it have involved nothing inconsistent with the system's stability ? 

 or would its adoption have resulted in depriving our world of the 

 moonlight enjoyed in the existing system ? 



The annexed figure f illustrates Laplace's proposed arrange- 

 ment. The distance at which he would have placed the moon 

 from the earth is about 1,000,000 miles, or a little more than four 

 times the actual distance. An eclipse of the moon is caused by 

 its falling into the earth's shadow. This can extend into space 

 only about 860,000 miles, and, as this is less than the distance of 

 Laplace's proposed moon, the latter, as he remarks, could never 

 be eclipsed. 



Let us suppose the distance of the moon from the earth to be 

 increased, what changes would be effected in the observed phe- 

 nomena ? At 478,000 miles, twice the present distance, the length 

 of the lunar month would be seventy-seven days ; the quantity of 

 moonlight would be one fourth of what we now enjoy ; and the 

 height of tides in the open seas would be but a few inches. At 

 717,000 miles, three times the present distance, the length of the 

 month would be one hundred and forty-two days, and the appar- 



* Systeme du Monde, Hart's translation, vol. ii, p. 79. \ Figure omitted. 



