Newton's Principia (1687): Gravity and the Laws of Motion

Newton’s Principia, or Philosophiae Naturalis Principia Mathematica (Mathematical Principles of Natural Philosophy), was published in London in July 1687. In it Isaac Newton set out three laws of motion and a single law of universal gravitation, and showed that they explained the paths of planets, the Moon, comets and the rise and fall of the tides. It is widely regarded as one of the most important scientific books ever written, and it would not have appeared when it did without the astronomer Edmond Halley.

Background: the problem of the planets

By the 1680s astronomers knew from Johannes Kepler’s work that planets move in ellipses around the Sun (see Kepler’s laws of planetary motion). What nobody could yet show was why. Several thinkers suspected that the Sun pulled on the planets with a force that weakened with the square of distance, the so-called inverse-square law, but proving that such a force would produce an ellipse required mathematics that no one had demonstrated.

In January 1684 three Fellows of the Royal Society, Edmond Halley, Christopher Wren and Robert Hooke, discussed the question in London. Hooke claimed he could prove it but did not produce a proof. Wren reportedly offered a book worth forty shillings to anyone who could supply one within two months, and no one did.

Isaac Newton, then Lucasian Professor of Mathematics at Cambridge, had worked on gravity and motion since his youth (see Newton’s annus mirabilis). He was, however, secretive and had published little since a bitter dispute over his theory of light in the 1670s.

Halley’s visit and De motu

In August 1684 Halley travelled to Cambridge and asked Newton what curve a planet would follow if it were attracted to the Sun by an inverse-square force. According to the account later recorded by the mathematician Abraham de Moivre, Newton answered at once that it would be an ellipse, saying he had calculated it. He could not find the paper, but promised to send the proof.

In November 1684 Newton sent Halley a short treatise of about nine pages, known as De motu corporum in gyrum (“On the motion of bodies in orbit”). It proved the link between an inverse-square force and elliptical orbits and derived Kepler’s laws. Halley immediately grasped its importance and urged Newton to develop it for publication.

What followed was an extraordinary burst of work. Over roughly eighteen months Newton expanded the short tract into a large treatise, refining his concepts of mass, force and inertia and extending the argument from the planets to every body in the universe.

Writing, the Royal Society and the Hooke dispute

The manuscript of Book I was presented to the Royal Society on 28 April 1686. The Society agreed to publish it, and its President, the naval administrator Samuel Pepys, signed the imprimatur (licence to print) dated 5 July 1686. That is why Pepys’s name appears on the title page of a book on mathematical physics.

The Society, however, had little money, having recently spent heavily on Francis Willughby’s illustrated History of Fishes (1686). Halley, who was not wealthy and held the modest post of clerk to the Society, agreed to pay the costs himself. He also edited the text, corrected the proofs and handled the printer.

A crisis arose when Robert Hooke claimed that he had given Newton the idea of the inverse-square law and expected acknowledgement. Newton reacted furiously, removed several references to Hooke and threatened to withhold the third book altogether. Halley used tactful letters to persuade him to go ahead. The quarrel between Newton and Hooke was never healed.

Publication in July 1687

Printing was completed in the summer of 1687, and on 5 July 1687 Halley wrote to Newton to report that the work was finally finished. The first edition was a quarto in Latin, the common language of European learning. The size of the print run is not recorded precisely; older estimates suggested about 250 to 400 copies, while a recent census of surviving copies points to roughly 600 to 750.

Halley added a Latin ode in praise of Newton at the front of the book and wrote a review for the Royal Society’s Philosophical Transactions. He also presented a copy to King James II with a summary explaining the theory of the tides.

What the Principia contains

The book opens with definitions of quantities such as mass and momentum, followed by the three “axioms or laws of motion”:

• First law: a body continues at rest or in uniform straight-line motion unless compelled to change by a force (inertia).
• Second law: a change of motion is proportional to the force applied and takes place along the line of that force.
• Third law: to every action there is always an equal and opposite reaction.

The work is then divided into three books:

In Book III Newton showed that the same force that makes an apple fall also holds the Moon in its orbit. He calculated that the Earth should be slightly flattened at the poles, explained the tides as the combined pull of the Moon and Sun, and treated comets as bodies moving under gravity on very long orbits. He also stated “rules of reasoning” for natural philosophy, guiding how to argue from observed effects to causes.

Although Newton had developed his own form of calculus (which he called fluxions), the Principia was largely written in the language of classical geometry. This made it extremely difficult to read; only a handful of mathematicians in Europe could follow it fully at first. The later priority quarrel over calculus is told in the Newton–Leibniz calculus controversy.

Reception and later editions

In Britain the book quickly established Newton’s reputation. On the Continent many scholars, including Christiaan Huygens and Gottfried Wilhelm Leibniz, admired the mathematics but objected that gravity acting across empty space was an “occult” quality without a mechanical cause. Newton answered in the General Scholium added to the second edition with the famous phrase hypotheses non fingo, “I frame no hypotheses”: he described how gravity behaves without claiming to know its cause.

A second edition, edited by the Cambridge mathematician Roger Cotes, appeared in 1713 with significant revisions. A third edition, edited by Henry Pemberton, followed in 1726, the year before Newton died. Andrew Motte’s English translation was published in 1729, and Émilie du Châtelet’s French translation with commentary appeared in 1759, ten years after her death.

Over the eighteenth century, Newton’s theory won the argument through successful predictions. The French expedition to Lapland led by Pierre-Louis Maupertuis in 1736–1737 confirmed that the Earth is flattened at the poles. The return of the comet predicted by Halley, recalculated by Alexis Clairaut and colleagues and first seen on 25 December 1758, was another striking success (see Halley’s comet prediction).

Myths and facts

The falling apple. Newton himself told the story of seeing an apple fall at his family home at Woolsthorpe, as recorded by his friend William Stukeley. The apple did not hit him on the head; that detail is a later embellishment, and the story describes the start of a train of thought, not a sudden discovery.

Newton “discovered” gravity. People had always known that things fall. Newton’s achievement was to show that one mathematical law governed both falling objects on Earth and the motion of heavenly bodies.

The Principia was instantly understood. It was not. Its difficulty meant that the ideas spread mainly through summaries, lectures and popular books in the decades after 1687.

Timeline

• 1684, January: Halley, Wren and Hooke discuss the inverse-square problem in London.
• 1684, August: Halley visits Newton in Cambridge.
• 1684, November: Newton sends Halley the short treatise De motu corporum in gyrum.
• 1686, 28 April: The manuscript of Book I is presented to the Royal Society.
• 1686, 5 July: Samuel Pepys signs the imprimatur as President of the Royal Society.
• 1687, 5 July: Halley tells Newton that printing is complete.
• 1713: Second edition, edited by Roger Cotes, with the General Scholium.
• 1726: Third edition, edited by Henry Pemberton.
• 1729: Andrew Motte’s English translation is published.

Legacy

The Principia gave science a model of how to work: state precise laws in mathematical form, deduce their consequences and test them against observation. Newtonian mechanics became the basis of engineering, navigation, ballistics and astronomy, and it is still used to plan spacecraft trajectories.

In the twentieth century Albert Einstein’s theories of relativity showed that Newton’s laws are an approximation that breaks down at very high speeds and in very strong gravitational fields. For everyday conditions and most of astronomy, however, Newton’s equations remain accurate. Several copies of the first edition survive, including Newton’s own annotated copies at Cambridge, and the printer’s manuscript is preserved by the Royal Society.

Why it matters

The Principia united the physics of the Earth and the heavens under one set of laws for the first time. It turned the Scientific Revolution’s scattered discoveries into a coherent system and shaped the Enlightenment belief that nature follows rational, knowable rules. It also shows how much a single book can owe to an editor: without Halley’s persistence and money, it might never have been published.