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 velocities proportional to their distances from the sun. In this case, the moon, being constantly in opposition to the sun, would have described 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."[1]
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 without 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[2] illustrates Laplace's proposed arrangement. 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 800,000 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 phenomena? 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-
