Electronic edition published by Cultural Heritage Langauge Technologies (with permission from Charles Scribners and Sons) and funded by the National Science Foundation International Digital Libraries Program. This text has been proofread to a low degree of accuracy. It was converted to electronic form using data entry.
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.