It remained for a mathematical astronomer to solve these puzzles. The man of all others competent to take the subject in hand was the French astronomer Laplace. For a quarter of a century he had devoted his transcendent mathematical abilities to the solution of problems of motion of the heavenly bodies. Working in friendly rivalry with his countryman Lagrange, his only peer among the mathematicians of the age, he had taken up and solved one by one the problems that Newton left obscure. Largely through the efforts of these two men the last lingering doubts as to the solidarity of the Newtonian hypothesis of universal gravitation had been removed. The share of Lagrange was hardly less than that of his co-worker; but Laplace will longer be remembered, because he ultimately brought his completed labors into a system, and, incorporating with them the labors of his contemporaries, produced in the Mecanique Celeste the undisputed mathematical monument of the century, a fitting complement to the Principia of Newton, which it supplements and in a sense completes. In the closing years of the eighteenth century Laplace took up the nebular hypothesis of cosmogony, to which we have just referred, and gave it definite proportions; in fact, made it so thoroughly his own that posterity will always link it with his name. Discarding the crude notions of cometary impact and volcanic eruption, Laplace filled up the gaps in the hypothesis with the aid of well-known laws of gravitation and motion. He assumed that the primitive mass of cosmic matter which was destined to form our solar system was revolving on its axis even at a time when it was still nebular in character, and filled all space to a distance far beyond the present limits of the system. As this vaporous mass contracted through loss of heat, it revolved more and more swiftly, and from time to time, through balance of forces at its periphery, rings of its substance were whirled off and left revolving there, subsequently to become condensed into planets, and in their turn whirl off minor rings that became moons. The main body of the original mass remains in the present as the still contracting and rotating body which we call the sun. Let us allow Laplace to explain all this in detail: "In order to explain the prime movements of the planetary system," he says, "there are the five following phenomena: The movement of the planets in the same direction and very nearly in the same plane; the movement of the satellites in the same direction as that of the planets; the rotation of these different bodies and the sun in the same direction as their revolution, and in nearly the same plane; the slight eccentricity of the orbits of the planets and of the satellites; and, finally, the great eccentricity of the orbits of the comets, as if their inclinations had been left to chance.