More than twenty years elapsed between Newton's first
conception of gravitation and the publication, in 1686-7, of Newton's
great work on gravity and physics, the *Philosophiae Naturalis
Principia Mathematica*, known to posterity as the *Principia.*
In these two decades, scientific inquiry did not stand still, and
other minds had pondered versions of Newton's initial idea--that
the force of attraction holding planets in their orbits varied
inversely with the square of their distance from the sun. One
of these minds belonged to Robert Hooke. In 1680, while Newton
labored furiously on his theory of gravitation, trying to make
it work out in all particulars, Hooke wrote a letter to him in
which he suggested that a formula involving inverse squares might
explain the attraction between planets. He made the same case
four years later, in a conversation with Halley and Christopher
Wren. Whether Hooke was actually close to hitting on something
like Newton's law of universal gravitation has been a matter of
debate among historians for generations. Hooke would always feel,
later, that he had been robbed of his discovery, but this seems
untenable, as Wren and Halley's response to his suggestion makes
clear. They agreed with his suggestion, but pointed out that a
mathematical demonstration was needed, and Wren famously offered
Hooke and Halley forty shillings if either would bring him a mathematical
proof of gravitation. It was a challenge that Hooke would be unable
to meet--but one that Newton would succeed at, and within two years.

In August of 1684, Halley visited Newton in Cambridge,
and idly asked what shape the orbit of a planet would take if its
attraction to the sun followed the inverse square of the distance
between them. Newton, who had been working on this problem for
years now, immediately replied that the orbit would be an ellipse--exactly the
shape that Johannes Kepler, the 16th century German astronomer,
had hypothesized as the shape of the planets' path. Astronomy and
physics thus coincided. Meanwhile, in the 1670s, a Frenchman named
Jean Picard had recalculated the Earth's size and distance from
the sun, producing more accurate values than what scientists had
calculated before--values that worked well with Newton's mathematical
formulas. Newton could now test the inverse square law, using
a comparison between an apple on a tree branch and the moon. The
moon was roughly sixty times as far from the center of the earth
as the apple was, and so the moon, in Newton's scheme, would be
pulled toward Earth at 1/602 (or 1/3600) of the apple's rate of
fall. This calculation harmonized closely with Kepler's calculations
of planetary orbits, and Newton felt confident enough to tell Halley,
in November 1684, that the apple and the moon both experience a
pull from the same force, and that this universal gravity applied
to all bodies in the solar system.

Halley, recognizing the importance of this discovery,
urged Newton to publish his findings. In February 1685, Newton
sent to the Royal Society a brief treatise entitled *Propositions
de Motu,* which laid out the general principles that he
had discovered. Throughout the following year, he worked to produce
a full exposition, and in April, 1686, he published the first volume
of the *Philosophiae Naturalis Principia Mathematica,* or
"Mathematical Principles of Natural Philosophy." The second two
books would be published in September 1687, at Edmund Halley's
expense--the Society being short on funds at the time. The work
would make Newton the most famous scientist in Europe.

Upon the publication of the first book, Hooke immediately pointed
out that he had anticipated Newton's law of inverse squares, and
flatly accused Newton of plagiarism. Newton, furious as ever in
defense of his discoveries, denied having taken anything from Hooke,
and went so far as to threaten to withdraw from publication the
third book of the *Principia,* complaining that
"philosophy is such an impertinently litigious Lady that a man had
as good be engaged in Law suits as have to do with her." Halley,
who had invested so much of himself in Newton's great work, mollified
him, and tried to make peace between Newton and Hooke. But the break
was final. Newton did insert a brief acknowledgement of "our friends
Wren, Hooke, and Halley" in his discussion of the law of inverse
squares, but this pat on the head did nothing to mollify Hooke.
Hooke's beloved niece died the same year that *Principia* was
published, and he went into a slow decline. As Newton's reputation
grew and his own shrank, he grew bitter and came to loathe the
very sight of his rival; he now took every opportunity to slight the
other man. Thus Hooke, knowing full well that Newton would be
the next man to be elected president of the Society, refused to retire
from his position until death claimed him in 1703; until the very
end, he refused to give his rival any satisfaction.