[Sidenote: Application of Mechanics to the celestial motions.] The steps thus far taken for an explanation of the movements of the planets in curvilinear paths therefore consisted in the removal of the old misconception that for a body to continue its motion forward in a straight line a continued application of force is necessary, the first law of motion disposing of that error. In the next place, it was necessary that clear and distinct ideas should be held of the combination or composition of forces, each continuing to exercise its influence without deterioration or diminution by the other. The time had now come for it to be shown that the perpetual movement of the planets is a consequence of the first law of motion; their elliptic paths, such as had been determined by Kepler, a consequence of the second. Several persons almost simultaneously had been brought nearly to this conclusion without being able to solve the problem completely. Thus Borelli, A.D. 1666, in treating of the motions of Jupiter's satellites, distinctly shows how a circular motion may arise under the influence of a central force; he even uses the illustration so frequently introduced of a stone whirled round in a sling. In the same year a paper was presented to the Royal Society by Mr. Hooke, "explicating the inflection of a direct motion into a circular by a supervening attractive principle." Huygens also, in his "Horologium Oscillatorium," had published some theorems on circular motions, but no one as yet had been able to show how elliptical orbits could, upon these principles, be accounted for, though very many had become satisfied that the solution of this problem would before long be given. [Sidenote: Newton; publication of the "Principia."] In April, 1686, the "Principia" of Newton was presented to the Royal Society. This immortal work not only laid the foundation of Physical Astronomy, it also carried the structure thereof very far toward its completion. It unfolded the mechanical theory of universal gravitation upon the principle that all bodies tend to approach each other with forces directly as their masses, and inversely as the squares of their distances. [Sidenote: Propounds the theory of universal gravitation.] To the force producing this tendency of bodies to approach each other the designation of attraction of gravitation, or gravity, is given. All heavy bodies fall to the earth in such a way that the direction of their movement is toward its centre. Newton proved that this is the direction in which they must necessarily move under the influence of an attraction of every one of the particles of which the earth is composed, the attraction of a sphere taking effect as if all its particles were concentrated in its centre.