82

HISTORY OF PHYSICAL ASTRONOMY.

force in various curves. In the third section, he considers the motion of !

a body compelled to revolve in any of the conic sections by a force '

directed continually to the focus. The fourth and fifth sections are ;

purely geometrical, relating to methods of drawing conic sections through j

given points and touching given straight lines. The sixth section treatsof the motion of a body in a given orbit. The seventh treats of the J

motion of a body ascending or descending in a straight line relative to the 1

centre of force. The eighth contains the investigation of the orbitdescribed by a body when the law of the centripetal force is given. Theninth relates to the motion of bodies in moveable orbits. This sectioncontains the famous investigation of the motion of the apsides. Thetenth treats of bodies moving on given surfaces, and of the motion ofpendulums.

Hitherto Newton has been considering only the motion of materialpoints. In the eleventh section he investigates the motion of bodiesexposed to their mutual attraction. The twelfth treats of the attractionof spheres. The thirteenth of the attraction of bodies not spherical.

The fourteenth relates to the motion of small particles passing from onemedium into another.

The second book is divided into nine sections, and contains fifty-three j

propositions. It treats of bodies moving in resisting media upon different j

hypotheses of the resistance; and, whether moving in straight lines, or j

curves, or vibrating like pendulums. It also takes cognizance of the j

more recondite parts of several other branches of the Physico-mathematical j

sciences. The second lemma to the eighth proposition contains an J

exposition of the method of Fluxions, which is rendered necessary in most j

of the investigations of this and the following book.

The third book contains forty-two propositions. From the first to the jeighteenth inclusive, Newton demonstrates various general theorems <relative to the attraction of the sun, moon, and planets. In the nineteenthand twentieth he investigates the ratio of the earth’s axes, and comparesthe weights of bodies at the surface in different latitudes. In the fourfollowing propositions, he shows that the precession of the equinoxes, theirregularities of the moon and the other satellites, and the phenomena ofthe tides, are all explicable by the principle of gravitation. From thetwenty-fifth to the thirty-fifth inclusive, he computes the various in-equalities of the moon's motion. The thirty-sixth aud thirty-seventhtreat of the tides. The thirty-eighth, of the figure of the moon. Thethirty-ninth, of the precession of the equinoxes. The remaining threepropositions are devoted to the theory of comets. At the conclusion is ascholium to the whole work, containing general reflections on the con-stitution of the material universe, and on the eternal and omnipotentBeing who presides over it *.

The publication of the Principia marks by far the most importantepoch in the history of physical science. Previous to its appearance theresearches of philosophers may he said to have resembled the voyages ofthe early navigators, who continued creeping timidly along the coasts,without daring to launch their barks into the boundless ocean. Newton, ,like another Columbus, disdained to confine himself within the common- .

* Besides the original edition of the Principia , tivo others wore published during ;the life of the author. The second edition was published at Cambridge in 1713, under ;the superintendence of Cotes. The third edition was published at London in 1726, by 1Pemberton. ;