Isaac Newton (18 page)

The birth of universal gravitation: Newton proves by geometry that if a body Q orbits in an ellipse, the implied force toward the focus S (not the center C) varies inversely with the square of distance
.
(illustration credit 11.2)

The alchemical furnaces went cold; the theological manuscripts were shelved. A fever possessed him, like none since the plague years. He ate mainly in his room, a few bites standing up. He wrote standing at his desk. When he did venture outside, he would seem lost, walk erratically, turn and stop for no apparent reason, and disappear inside once again.
²⁷
Thousands of sheets of manuscript lay all around, here and at Woolsthorpe, ink fading on parchment, the jots and scribbles of four decades, undated and disorganized. He had never written like this: with a great purpose, and meaning his words to be read.

Though he had dropped alchemy for now, Newton had learned from it. He embraced invisible forces. He knew he was going to have to allow planets to influence one another from a distance. He was writing the principles of philosophy. But not just that: the
mathematical
principles of
natural
philosophy. “For the whole difficulty of philosophy,” he wrote, “seems to be to discover the forces of nature from the phenomena of motions and then to demonstrate the other phenomena from these forces.”
²⁸
The planets, the comets, the moon, and the sea. He promised a mechanical program—no occult qualities. He promised proof. Yet there was mystery in his forces still.

First principles. “Time, space, place, and motion”—he wished to blot out everyday knowledge of these words. He gave them new meanings, or, as he saw it, redeemed their true and sacred meanings.
²⁹
He had no authority to rely on—this unsocial, unpublished professor—so it was a sort of bluff, but he made good on it. He established time as independent of our sensations; he established space as independent of matter. Thenceforth
time
and
space
were special words, specially understood and owned by the virtuosi—the scientists.

Absolute, true, and mathematical time, in and of itself, and of its own nature, without reference to anything external, flows uniformly.…

Absolute space, of its own true nature without reference to anything external, always remains homogeneous and immovable.…
³⁰

Our eyes perceive only relative motion: a sailor’s progress along his ship, or the ship’s progress on the earth. But the earth, too, moves, in reference to
space
—itself immovable because it is purely mathematical, abstracted from our senses. Of time and space he made a frame for the universe and a credo for a new age.

12
 
Every Body Perseveres

I
T WAS ORDERED
, that a letter of thanks be written to Mr N
EWTON
,” recorded Halley, as clerk of the Royal Society, on April 28, 1686, “… and that in the meantime the book be put into the hands of Mr H
ALLEY
.”
¹

Only Halley knew what was in “the book”—a first sheaf of manuscript pages, copied in Cambridge by Newton’s amanuensis
²
and dispatched to London with the grand title
Philosophiæ Naturalis Principia Mathematica
. Halley had been forewarning the Royal Society: “a mathematical demonstration of the Copernican hypothesis”; “makes out all the phenomena of the celestial motions by the only supposition of a gravitation towards the centre of the sun decreasing as the squares of the distances therefrom reciprocally.”
³
Hooke heard him.

It was Halley, three weeks later, who undertook the letter of thanks: “Your Incomparable treatise,” etc. He had persuaded the members, none of whom could have read the manuscript, to have it printed, in a large quarto, with woodcuts for the diagrams. There was just one thing more he felt obliged to tell Newton: “viz, that Mr Hook has some pretensions upon the invention of the rule of the decrease of
Gravity.… He sais you had the notion from him [and] seems to expect you should make some mention of him, in the preface.…”
⁴

What Newton had delivered was Book I of the
Principia
. He had completed much of Book II, and Book III lay not far behind. He interrupted himself to feed his fury, search through old manuscripts, and pour forth a thunderous rant, mostly for the benefit of Halley. He railed that Hooke was a bungler and a pretender:

This carriage towards me is very strange & undeserved, so that I cannot forbeare in stating that point of justice to tell you further … he should rather have excused himself by reason of his inability. For tis plain by his words he knew not how to go about it. Now is this not very fine? Mathematicians that find out, settle & do all the business must content themselves with being nothing but dry calculators & drudges & another that does nothing but pretend & grasp at all things must carry away all the invention.…

Mr Hook has erred in the invention he pretends to & his error is the cause of all the stirr he makes.…

He imagins he obliged me by telling me his Theory, but I thought my self disobliged by being upon his own mistake corrected magisterially & taught a Theory which every body knew & I had a truer notion of it then himself. Should a man who thinks himself knowing, & loves to shew it in correction & instructing others, come to you when you are busy, & notwithstanding your excuse, press discourses upon you & through his own mistakes correct you & multiply discourses & then make this use of it, to boast that he taught you all he spake & oblige you to acknowledge it & cry out injury & injustice if you do not, I beleive you would think him a man of a strange unsociable temper.
⁵

In his drafts of Book II, Newton had mentioned the most illustrious Hooke—“Cl[arissimus] Hookius”
⁶
—but now he struck all mention of Hooke and threatened to give up on Book III. “Philosophy is such an impertinently litigious Lady that a man had as good be engaged in Law suits as have to do with her. I found it so formerly & now I no sooner come near her again but she gives me warning.”
⁷
Hooke had not been the first to propose the inverse-square law of attraction; anyway, for him it was a guess. It stood in isolation, like countless other guesses at the nature of the world. For Newton, it was embedded, linked, inevitable. Each part of Newton’s growing system reinforced the others. In its mutual dependency lay its strength.

Halley, meanwhile, found himself entangled in the business of publishing. The Royal Society had never actually agreed to print the book. Indeed, it had only underwritten the publication of one book before, a lavish and disastrously unsuccessful two-volume
History of Fishes
.
⁸
After much discussion the council members did vote to order the
Principia
printed—but by Halley, at his own expense. They offered him leftover copies of
History of Fishes
in place of his salary. No matter. The young Halley was a believer, and he embraced his burden: the proof sheets mangled and lost, the complex abstruse woodcuts, the clearing of errata, and above all the nourishing of his author by cajolement and
flattery. “You will do your self the honour of perfecting scientifically what all past ages have but blindly groped after.”
⁹
The flattery was sincere, at least.

Halley sent sixty copies of
Philosophiæ Naturalis Principia Mathematica
on a wagon from London to Cambridge in July 1687. He implored Newton to hand out twenty to university colleagues and carry forty around to booksellers, for sale at five or six shillings apiece.
¹⁰
The book opened with a florid ode of praise to its author, composed by Halley. When an adulatory anonymous review appeared in the
Philosophical Transactions
, this, too, was by Halley.
¹¹

Without further ado, having defined his terms, Newton announced the laws of motion.

Law 1. Every body perseveres in its state of being at rest or of moving uniformly straight forward, except insofar as it is compelled to change its state by forces impressed
. A cannonball would fly in a straight line forever, were it not for air resistance and the downward force of gravity. The first law stated, without naming, the principle of inertia, Galileo’s principle, refined. Two states—being
at rest
and
moving uniformly
—are to be treated as the same. If a flying cannonball embodies a force, so does the cannonball at rest.

Law 2. A change in motion is proportional to the motive force impressed and takes place along the straight line in which that force is impressed
. Force generates motion, and these are quantities, to be added and multiplied according to mathematical rules.

Law 3. To any action there is always an opposite and equal reaction; in other words, the actions of two bodies upon each other
are always equal and always opposite in direction
. If a finger presses a stone, the stone presses back against the finger. If a horse pulls a stone, the stone pulls the horse. Actions are interactions—no preference of vantage point to be assigned. If the earth tugs at the moon, the moon tugs back.
¹²

He presented these as axioms, to serve as the foundation for an edifice of reasoning and proof. “Law”—
lex
—was a strong and peculiar choice of words.
¹³
Bacon had spoken of laws, fundamental and universal. It was no coincidence that Descartes, in his own book called
Principles of Philosophy
, had attempted a set of three laws,
regulæ quædam sive leges naturæ
, specifically concerning motion, including a law of inertia. For Newton, the laws formed the bedrock on which a whole system would lie.

A law is not a cause, yet it is more than a description. A law is a rule of conduct: here, God’s law, for every piece of creation. A law is to be obeyed, by inanimate particles as well as sentient creatures. Newton chose to speak not so much of God as of nature. “Nature is exceedingly simple and conformable to herself. Whatever reasoning holds for greater motions, should hold for lesser ones as well.”
¹⁴

Newton formed his argument in classic Greek geometrical style: axioms, lemmas, corollaries;
Q.E.D
. As the best model available for perfection in knowledge, it gave his physical program the stamp of certainty. He proved facts about triangles and tangents, chords and parallelograms, and from there, by a long chain of argument, proved facts about the moon and the tides. On his own path to these discoveries, he had invented a new mathematics, the integral and differential calculus. The calculus and the discoveries were of a piece. But he severed the connection now. Rather
than offer his readers an esoteric new mathematics as the basis for his claims, he grounded them in orthodox geometry—orthodox, yet still new, because he had to incorporate infinities and infinitesimals. Static though his diagrams looked, they depicted processes of dynamic change. His lemmas spoke of quantities that
constantly tend to equality
or
diminish indefinitely
; of areas that
simultaneously approach
and
ultimately vanish
;
of momentary increments
and
ultimate ratios
and
curvilinear limits
. He drew lines and triangles that looked finite but were meant to be on the point of vanishing. He cloaked modern analysis in antique disguise.
¹⁵
He tried to prepare his readers for paradoxes.

It may be objected that there is no such thing as an ultimate proportion of vanishing quantities, inasmuch as before vanishing the proportion is not ultimate, and after vanishing it does not exist at all.… But the answer is easy.… the ultimate ratio of vanishing quantities is to be understood not as the ratio of quantities before they vanish or after they have vanished, but the ratio with which they vanish.
¹⁶

The diagrams appeared to represent space, but time kept creeping in: “Let the time be divided into equal parts.… If the areas are very nearly proportional to the times …”