- Isaac Newton: The ‘Principia’ Mathematical Principles of Natural Philosophy translated by I. Bernard Cohen
California, 974 pp, £22.00, September 1999, ISBN 0 520 08817 4
‘This incomparable author having at length been prevailed upon to appear in public, has in this treatise given a most notable instance of the extent of the powers of the mind.’ This is how the very first review of the Principia began, in summer 1687: from the start, you were forced to admire Newton’s modesty, and his genius. The reviewer, the young astronomer Edmond Halley, knew what he was talking about. Three years earlier, during a visit to Cambridge, he had posed the puzzle which started Newton on the path to his Principia. What is the orbit of a planet under the influence of an attractive force varying inversely as the square of the distance? Halley reminded his readers that the great Kepler had long before identified vital patterns in planets’ motion: their elliptical paths with the Sun at their focus, the mathematical regularities which governed their orbital speeds.
Newton himself was never quite so generous in honouring his predecessors. Others, including Halley and his London colleague, the irascible natural philosopher Robert Hooke, had the idea that orbiting bodies tended to move in straight lines while at the same time being pulled towards some force-centre. Only Newton fully exploited its implications. He defined forces by the changes they produced in the motions of bodies on which they acted, then invented the term ‘centripetal force’ to describe this pull. Using Kepler’s regularities and the most recent data from the Royal Observatory, French expeditions to Africa and the West Indies, and cometary and tidal observations from the Straits of Magellan to the Gulf of Tonkin, he was able to identify the centripetal force acting on planets, moons and the Earth itself with a universally acting gravity to which every particle of matter was susceptible. It was proportional to the bodies’ masses and weakened as the square of their distance from the force-centre. Newton did not, at least publicly, claim to know the cause of gravity, an omission which would generate much heat and some light among his readers. If all matter gravitated, gravity could not have a material cause; if gravity depended directly on God, the proper topic of natural philosophy, then, some alleged, the Principia would turn the world-order into an inexplicable miracle.
Newton could afford to shrug. Using a newfangled geometrical treatment of continuously changing quantities he analysed the motions of the solar system, the path of the Moon and the shape of the Earth. He never doubted that the world showed God’s wise design – he was impressed, for example, by the fact that only if a centripetal force varied exactly as the inverse square of the distance would bodies act as though their mass was concentrated at their centres or generate stable orbits. This wisdom was best evidenced by the success of Newton’s own sums. Even though he grossly mistook the Moon’s mass, he proved what Galileo had sneeringly denied as mere astrology, the lunar influence on the tides, and explained for the first time why there are two tides a day. Even though he could not compute a comet’s orbit precisely from just one transit, he knew what Kepler did not, that comets move under gravitation in orbits round the Sun. For the first time, a work of natural philosophy presented astonishingly, sometimes suspiciously precise numbers to back up its claims about universal forces acting through empty space. Armed with a pendulum to time echoes in a court of Trinity College, Newton ingeniously got his theoretical and experimental estimates of the speed of sound to match. He had a local joiner build a large glass water-tank to test his theory of the fall of bodies in resisting fluids, and was not deflected when the tank smashed, nor when his numbers didn’t quite answer experiment. ‘No closer to the gods can any mortal rise,’ Halley exclaimed. It had been hard for him to get the five hundred copies of Newton’s masterwork to the public, who, at least in his own country, greeted them with adulation. Halley cajoled Newton into releasing his labours and ignoring his critics, offered advice on correction and revision, wrote a fulsome poem for the front of the book, paid for its publication, presented it to the King, and reviewed it in the Royal Society’s journal, which he himself edited. He made a profit of at least £10 out of the sales of the book.