No one was more sagacious than Laplace in discovering intimate relations between phenomena apparently unrelated, or more skillful in deducing important conclusions from such unexpected affinities. For example, toward the close of his days, with the aid of certain lunar observations, with a stroke of his pen he overthrew the cosmogonic theories of Buffon and Bailly, which were so long in favor. According to these theories, the earth was hastening to a state of congelation which was close at hand. Laplace, never contented with vague statements, sought to determine in numbers the rate of the rapid cooling of our globe which Buffon had so eloquently but so gratuitously announced. Nothing could be more simple, better connected, or more conclusive than the chain of deductions of the celebrated geometer. A body diminishes in volume when it cools. According to the most elementary principles of mechanics, a rotating body which contracts in dimensions must inevitably turn upon its axis with greater and greater rapidity. The length of the day has been determined in all ages by the time of the earth's rotation; if the earth is cooling, the length of the day must be continually shortening. Now, there exists a means of ascertaining whether the length of the day has undergone any variation; this consists in examining, for each century, the arc of the celestial sphere described by the moon during the interval of time which the astronomers of the existing epoch call a day; in other words, the time required by the earth to effect a complete rotation on its axis, the velocity of the moon being in fact independent of the time of the earth's rotation. Let us now, following Laplace, take from the standard tables the smallest values, if you choose, of the expansions or contractions which solid bodies experience from changes of temperature; let us search the annals of Grecian, Arabian, and modern astronomy for the purpose of finding in them the angular velocity of the moon: and the great geometer will prove, by incontrovertible evidence founded upon these data, that during a period of two thousand years the mean temperature of the earth has not varied to the extent of the hundredth part of a degree of the centigrade thermometer. Eloquence cannot resist such a process of reasoning, or withstand the force of such figures. Mathematics has ever been the implacable foe of scientific romances. The constant object of Laplace was the explanation of the great phenomena of nature according to inflexible principles of mathematical analysis. No philosopher, no mathematician, could have guarded himself more cautiously against a propensity to hasty speculation. No person dreaded more the scientific errors which cajole the imagination when it passes the boundary of fact, calculation, and analogy.