NEWTON, ISAAC (b. Woolsthorpe, England, 25 December 1642; d. London, England, 20 March 1727), mathematics, dynamics, celestial mechanics, astronomy, optics, natural philosophy.

    diverges from a rectilinear progress into the unmoved spaces”; while proposition 50 gives a method of finding “the distances of the pulses,” or the wavelength. In a scholium, Newton stated that the previous propositions “respect the motions of light and sound” and asserted that “since light is propagated in right lines, it is certain that it cannot consist in action alone (by Prop. XLI and XLII)”; there can be no doubt that sounds are “nothing else but pulses of the air” which “arise from tremulous bodies.” This section concludes with various mathematical theorems concerning the velocity of waves or pulses, and their relation to the “density and elastic force of a medium.”

In section 9, Newton showed that in wave motion a disturbance moves forward, but the parts (particles) of the medium in which the disturbance occurs only vibrate about a fixed position; he thereby established the relation between wavelength, frequency, and velocity of undulations. Proposition 47 (proposition 48 in the first edition) analyzes undulatory motion in a fluid; Newton disclosed that the parts (or particles) of an undulating fluid have the same oscillation as the bob of a simple pendulum. Proposition 48 (proposition 47 in the first edition) exhibits the proportionality of the velocity of waves to the square root of the elastic force divided by the density of an elastic fluid (one whose pressure is proportional to the density). The final scholium (much rewritten for the second edition) shows that Newton's propositions yield a velocity of sound in air of 979 feet per second, whereas experiment gives a value of 1,142 feet per second under the same conditions. Newton offered an ingenious explanation (including the supposition, in the interest of simplicity, that air particles might be rigid spheres separated from one another by a distance of some nine times their diameter), but it remained for Laplace to resolve the problem in 1816.160

Section 9, the last of book II, is on vortices, or “the circular motion of fluids.” In all editions of the Principia, this section begins with a clearly labeled “hypothesis” concerning the “resistance arising from the want of lubricity in the parts of a fluid . . . other things being equal, [being] proportional to the velocity with which the parts of the fluid are separated from one another.” Newton used this hypothesis as the basis for investigating the physics of vortices and their mathematical properties, culminating in a lengthy proposition 52 and eleven corollaries, followed by a scholium in which he said that he has attempted “to investigate the properties of vortices” so that he might find out “whether the celestial phenomena can be explained by them.” The chief “phenomenon” with which Newton was here concerned is Kepler's third (or harmonic) law for the motion of the satellites of Jupiter about that planet, and for the primary “planets that revolve about the Sun”--although Newton did not refer to Kepler by name. He found “the periodic times of the parts of the vortex” to be “as the squares of their distances.” Hence, he concluded, “Let philosophers then see how that phenomenon of the 3/2th power can be accounted for by vortices.”

Newton ended book II with proposition 53, also on vortices, and a scholium, in which he showed that “it is manifest that the planets are not carried round in corporeal vortices.” He was there dealing with Kepler's second or area law (although again without naming Kepler), in application to elliptic orbits. He concluded “that the hypothesis of vortices is utterly irreconcilable with astronomical phenomena, and rather serves to perplex than to explain the heavenly motions.” Newton himself noted that his demonstration was based on “an hypothesis,” proposed “for the sake of demonstration . . . at the beginning of this Section,” but went on to add that “it is in truth probable that the resistance is in a less ratio than that of the velocity.” Hence “the periodic times of the parts of the vortex will be in a greater ratio than the square of the distances from its centre.” But it must be noted that it is in fact probable that the resistance would be in a greater “ratio than that of the velocity,” not a lesser, since almost all fluids give rise to a resistance proportional to the square (or higher powers) of the velocity.161

Book III, “The System of the World.”

In the Newtonian system of the world, the motions of planets and their satellites, the motions of comets, and the phenomena of tides are all comprehended under a single mode of explanation. Newton stated that the force that causes the observed celestial motions and the tides and the force that causes weight are one and the same; for this reason he gave the name “gravity” to the centripetal force of universal attraction. In book III he showed that the earth must be an oblate spheroid, and he computed the magnitude of the equatorial bulge in relation to the pull of the moon so as to produce the long-known constant of precession; he also gave an explanation of variation in weight (as shown by the change in the period of a seconds pendulum) as a function of latitude on such a rotating non-spherical earth. But above all, in book III Newton stated the law of universal gravitation. He showed that planetary motion must be subject to interplanetary perturbation--most apparent in the most massive planets, Jupiter and Saturn, when they are in near conjunction--and he explored the perturbing action of the sun on the motion of the moon.

Book III opens with a preface in which Newton