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.
Dynamics, Astronomy, and the Birth of the
“Principia.”
Principia. Evidently Newton learned the law of
centrifugal force almost a decade before Huygens,
who published a similar result in 1673. One early
passage of the Waste Book also contains an entry on
Newton's theory of conical pendulums.109
According to Newton himself, the “notion of
gravitation” came to his mind “as he sat in a contemplative
mood,” and “was occasioned by the fall of an
apple.”110 He postulated that, since the moon is
sixty times as far away from the center of the earth
as the apple, by an inverse-square relation it would
accordingly have an acceleration of free fall
1/(60)2 = 1/3600 that of the apple. This “moon test”
proved the inverse-square law of force which Newton
said he “deduced” from combining “Kepler's Rule
of the periodical times of the Planets being in a
sesquialterate proportion of their distances from the
Centers of the Orbs”—that is, by Kepler's third law,
that R3/T2 = constant, combined with the
law of
central (centrifugal) force. Clearly if
F?V2/R for a
force F acting on a body moving with speed V in a
circle of radius R (with period T), it follows simply and
at once that
F?V2/R =
4π2R2/T2R =
4π2/R2 x
(R3/T2).
Since R3/T2 is a constant,
F?1/R2.
An account by Whiston states that Newton took
an incorrect value for the radius of the earth and so
got a poor agreement between theory and observation,
“which made Sir Isaac suspect that this Power was
partly that of Gravity, and partly that of Cartesius's
Vortices,” whereupon “he threw aside the Paper of
his Calculation, and went to other Studies.”
Pemberton's narration is in agreement as to the poor
value taken for the radius of the earth, but omits the
reference to Cartesian vortices. Newton himself said
(later) only that he made the two calculations and
“found them [to] answer pretty nearly.”111 In other
words, he calculated the falling of the moon and the
falling of a terrestrial object, and found the two to be
(only) approximately equal.
A whole tradition has grown up (originated by
Adams and Glaisher, and most fully expounded by
Cajori)112 that Newton was put off not so much by
taking a poor value for the radius of the earth as by
his inability then to prove that a sphere made up of
uniform concentric shells acts gravitationally on an
external point mass as if all its mass were concentrated
at its center (proposition 71, book I,
book III, of the Principia). No firm evidence
has ever been found that would support Cajori's
conclusion that the lack of this theorem was
responsible for the supposed twenty-year delay
in Newton's announcement of his “discovery”
of the inverse-square law of gravitation. Nor is there
evidence that Newton ever attempted to compute the
attraction of a sphere until summer 1685, when he
was actually writing the Principia.
An existing document does suggest that Newton
may have made just such calculations as Whiston and
Pemberton described, calculations in which Newton
appears to have used a figure for the radius of the
Earth that he found in Salusbury's version of Galileo's
Dialogue, 3,500 Italian miles (milliaria), in which one
mile equals 5,000, rather than 5,280, feet.113 Here,
some time before 1669, Newton stated, to quote him
in translation, “Finally, among the primary planets,
since the cubes of their distances from the Sun are
reciprocally as the squared numbers of their periods
in a given time, their endeavours of recess from the
Sun will be reciprocally as the squares of their
distances from the Sun,” and he then gave numerical
examples from each of the six primary planets.
A. R. Hall has shown that this manuscript is the paper
referred to by Newton in his letter to Halley of
20 June 1686, defending his claim to priority of
discovery of the inverse-square law against Hooke's
claims. It would have been this paper, too, that David
Gregory saw and described in 1694, when Newton let
him glance over a manuscript earlier than “the year
1669.”
This document, however important it may be in
enabling us to define Newton's values for the size of
the earth, does not contain an actual calculation of the
moon test, nor does it refer anywhere to other than
centrifugal “endeavours” from the sun. But it does
show that when Newton wrote it he had not found
firm and convincing grounds on which to assert what
Whiteside has called a perfect “balance between
(apparent) planetary centrifugal force and that of solar
gravity.”114
By the end of the 1660's Newton had studied the
Cartesian principles of motion and had taken a
critical stand with regard to them. His comments occur
in an essay of the 1670's or late 1660's, beginning
“De gravitatione et aequipondio fluidorum,”115 in
which he discussed extensively Descartes's Principia
and also referred to a letter that formed part of the
correspondence with Mersenne. Newton further set up
a series of definitions and axioms, then ventured “to
dispose of his [Descartes's] fictions.” A large part of
the essay deals with space and extension; for example,
Newton criticized Descartes's view “that extension is
not infinite but rather indefinite.” In this essay Newton
also defined force (“the causal principle of motion
and rest”), conatus (or “endeavour”), impetus, inertia,
and gravity. Then, in the traditional manner, he
reckoned “the quantity of these powers” in “a double