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

Book II of the “Principia.”

explain the elasticity and compressibility of gases
according to Boyle's law, he could explore what he
believed might be actual physical reality. But he
nonetheless reminded his readers (as in the scholium
at the end of section 1) that the condition of resistance
that he was discussing was “more a mathematical
hypothesis than a physical one.” Even in his final
argument against Cartesian vortices (section 9), he
admitted the implausibility of the proposed hypothesis
that “the resistance . . . is, other things being equal,
proportional to the velocity.” Although a scholium
to proposition 52 states that “it is in truth probable that
the resistance is in a less ratio than that of the velocity,”
Newton in fact never explored the consequences of this
probable assumption in detail. Such a procedure is in
marked contrast to book I, in which Newton examined
a variety of conditions of attractive and centripetal
forces, but so concentrated on the inverse-square force
as to leave the reader in no doubt that this is the chief
force acting (insofar as weight is concerned) on the sun,
the planets, the satellites, the seas, and all terrestrial
objects.

Book II differs further from book I in having a
separate section devoted to each of the imagined
conditions of resistance. In section 1, resistance to the
motions of bodies is said to be as “the ratio of the
velocity”; in section 2, it is as “the square of their
velocities”; and in section 3, it is given as “partly in
the ratio of the velocities and partly as the square of
the same ratio.” Then, in section 4, Newton introduced
the orbital “motion of bodies in resisting
mediums,” under the mathematical condition that
“the density of a medium” may vary inversely as the
distance from “an immovable centre”; the “centripetal
force” is said in proposition 15 to be as the square of
the said density, but is thereafter arbitrary. In a
very short scholium, Newton added that these conditions
of varying density apply only to the motions
of very small bodies. He supposed the resistance of
a medium, “other things being equal,” to be proportional
to its “density.”

In section 5, Newton went on to discuss some
general principles of hydrostatics, including properties
of the density and compression of fluids. Historically,
the most significant proposition of section 5 is
proposition 23, in which Newton supposed “a fluid
[to] be composed of particles fleeing from each other,”
and then showed that Boyle's law (“the density” of a
gas varying directly as “the compression”) is a
necessary and a sufficient condition for the centrifugal
forces to “be inversely proportional to distances of
their [that is, the particles'] centers.”

Then, in the scholium to this proposition, Newton
generalized the results, showing that for the compressing
forces to “be as the cube roots of the power
En+2,” where E is “the density of
the
compressed
fluid,” it is both a necessary and sufficient condition
that the centrifugal forces be “inversely as any power
Dn of the distance [between particles].” He made it
explicit that the “centrifugal forces” of particles must
“terminate in those particles that are next [to] them,
or are diffused not much farther,” and drew upon the
example of magnetic bodies. Having set such a model,
however, Newton concluded that it would be “a
physical question” as to “whether elastic fluids [gases]
do really consist of particles so repelling each other,”
and stated that he had limited himself to demonstrating
“mathematically the property of fluids
consisting of particles of this kind, that hence
philosophers may take occasion to discuss that
question.”157

Section 6 introduces the “motion and resistance of
pendulous bodies.” The opening proposition (24)
relates the quantity of matter in the bob to its weight,
the length of the pendulum, and the time of oscillation
in a vacuum. Because, as corollary 5 states,
“in general, the quantity of matter in the pendulous
body is directly as the weight and the square of the
time, and inversely as the length of the pendulum,”
a method is at hand for using pendulum experiments
to compare directly “the quantity of matter” in bodies,
and to prove that the mass of bodies is proportional
“to their weight.” Newton added that he had tested
this proposition experimentally, then further stated,
in corollary 7, that the same experiment may be used
for “comparing the weights of the same body in
different places, to know the variation of its
gravity.”158 This is the first clear recognition that
“mass” determines both weight (the amount of
gravitational action) and inertia (the measure of
resistance to acceleration)--the two properties of
which the “equivalence” can, in classical physics, be
determined only by experiment.

In section 6 Newton also considered the motion of
pendulums in resisting mediums, especially oscillations
in a cycloid, and gave methods for finding “the
resistance of mediums by pendulums oscillating
therein.” An account of such experiments makes up
the “General Scholium” with which section 6
concludes.159 Among them is an experiment Newton
described from memory, designed to confute “the
opinion of some that there is a certain aethereal
medium, extremely rare and subtile, which freely
pervades the pores of all bodies.”

Section 7 introduces the “motion of fluids,” and
“the resistance made to projected bodies,” and
section 8 deals with wave motion. Proposition 42
asserts that “All motion propagated through a fluid