exist in the movement—­I had almost said in the countenance—­of the moon a sort of impress of the spheroidal figure of the earth.  Such was the idea as it originally occurred to Laplace.  By means of a minutely careful investigation, he discovered in its motion two well-defined perturbations, each depending on the spheroidal figure of the earth.  When these were submitted to calculation, each led to the same value of the ellipticity.  It must be recollected that the ellipticity thus derived from the motions of the moon is not the one corresponding to such or such a country, to the ellipticity observed in France, in England, in Italy, in Lapland, in North America, in India, or in the region of the Cape of Good Hope; for, the earth’s crust having undergone considerable upheavals at different times and places, the primitive regularity of its curvature has been sensibly disturbed thereby.  The moon (and it is this which renders the result of such inestimable value) ought to assign, and has in reality assigned, the general ellipticity of the earth; in other words, it has indicated a sort of average value of the various determinations obtained at enormous expense, and with infinite labor, as the result of long voyages undertaken by astronomers of all the countries of Europe.

Certain remarks of Laplace himself bring into strong relief the profound, the unexpected, the almost paradoxical character of the methods I have attempted to sketch.  What are the elements it has been found necessary to confront with each other in order to arrive at results expressed with such extreme precision?  On the one hand, mathematical formulae deduced from the principle of universal gravitation; on the other, certain irregularities observed in the returns of the moon to the meridian.  An observing geometer, who from his infancy had never quitted his study, and who had never viewed the heavens except through a narrow aperture directed north and south,—­to whom nothing had ever been revealed respecting the bodies revolving above his head, except that they attract each other according to the Newtonian law of gravitation,—­would still perceive that his narrow abode was situated upon the surface of a spheroidal body, whose equatorial axis was greater than its polar by a three hundred and sixth part.  In his isolated, fixed position he could still deduce his true distance from the sun!

Laplace’s improvement of the lunar tables not only promoted maritime intercourse between distant countries, but preserved the lives of mariners.  Thanks to an unparalleled sagacity, to a limitless perseverance, to an ever youthful and communicable ardor, Laplace solved the celebrated problem of the longitude with a precision even greater than the utmost needs of the art of navigation demanded.  The ship, the sport of the winds and tempests, no longer fears to lose its way in the immensity of the ocean.  In every place and at every time the pilot reads in the starry heavens his distance from the meridian of Paris.  The extreme perfection of these tables of the moon places Laplace in the ranks of the world’s benefactors.