The year 1666 was germinal for Newton. It saw the beginning of his work in optics; but also, he later recalled, in May “I had entrance into the inverse method of Fluxions; and in the same year I began to think of gravity extending to the orbit of the moon, . . . having thereby compared the force requisite to keep the moon in her orbit with the force of gravity at the surface of the earth, and found them to answer pretty nearly. . . . In those years I was in the prime of my age.” 21
In 1666 the plague reached Cambridge, and for safety’s sake Newton returned to his native Woolsthorpe. At this point we come upon a pretty story. Wrote Voltaire, in his Philosophie de Newton (1738):
One day, in the year 1666, Newton, then retired to the country, seeing some fruit fall from a tree, as I was told by his niece, Mme. Conduit, fell into a profound meditation upon the cause which draws all bodies in a line which, if prolonged, would pass very nearly through the center of the earth. 22
This is the oldest known mention of the apple story. It does not appear in Newton’s early biographers, nor in his own account of how he came to the idea of universal gravitation; it is now generally regarded as a legend. More likely is another story in Voltaire: that when a stranger asked Newton how he had discovered the laws of gravitation, he replied, “By thinking of them without ceasing.” 23 It is fairly clear that by 1666 Newton had calculated the force of attraction holding the planets in their orbits as varying inversely with the square of their distance from the sun. 24 But he could not as yet reconcile the theory with his mathematical reckonings. He laid it aside, and published nothing about it for the next eighteen years.
The idea of interstellar gravitation was by no means original with Newton. Some fifteenth-century astronomers thought that the heavens exert a force upon the earth like that of the magnet upon iron, and that, since the earth is equally attracted from every direction, it remains suspended in the sum total of all these forces. 25 Gilbert’s De Magnete (1600) had set many minds thinking about the magnetic influences surrounding every body, and he himself had written, in a work that would be published (1651) forty-eight years after his death:
The force which emanates from the moon reaches to the earth, and, in like manner, the magnetic virtue of the earth pervades the region of the moon; both correspond and conspire by the joint action of both, according to a proportion and conformity of motions; but the earth has more effect, in consequence of its superior mass. 26
Ismaelis Bouillard, in his Astronomia philolaica (1645), had held that the mutual attraction of the planets varies inversely as the square of the distance between them. 27 Alfonso Borelli, in Theories of the Medicean Planets (1666), held “that every planet and satellite revolves round some principal globe of the universe as a fountain of virtue [force], which so draws and holds them that they cannot by any means be separated from it, but are compelled to follow it wherever it goes, in constant and continuous revolutions”; and he explained the orbits of these planets and satellites as the resultant of the centrifugal force of their revolution (“as we find in a wheel, or a stone whirled in a sling”) countered by the centripetal attraction of their sun. 28 Kepler considered gravity inherent in all celestial bodies, and for a while he reckoned its force as varying inversely with the square of the intervening distance; this would have clearly anticipated Newton; but later he rejected this formula, and supposed the attraction to be diminished in direct proportion as the distance increased. 29 These approaches to a gravitational theory were deflected by Descartes’ hypothesis of vortices forming in a primeval mass and then determining the action and orbit of each part.
Many of the alert inquirers in the Royal Society puzzled over the mathematics of gravitation. In 1674 Hooke, in An Attempt to Prove the Annual Motion of the Earth, anticipated by eleven years Newton’s announcement of the gravitation theory:
I shall explain a system of the world, differing in many particulars from any yet known, answering in all tilings to the common rules of mechanical motions. This depends upon three suppositions: first, that all celestial bodies whatsoever have an attractive or gravitating power towards their centers, whereby they attract not only their own parts, and keep them from flying from them, . . . but that they do also attract all other celestial bodies that are within the sphere of their activity. . . . The second suggestion is this, that all bodies whatsoever, that are put into direct and simple motion, will so continue to move forward in a straight line, till they are by some other effectual powers deflected. . . . The third supposition is, that these attractive powers are so much the more powerful in operating, by how much nearer the body wrought upon is to their own centers. 30
Hooke did not, in this treatise, reckon the attraction as varying inversely with the square of the distance; but, if we may believe Aubrey, he communicated this principle to Newton, who had already arrived at it independently. 31 In January, 1684, Hooke propounded the formula of inverse squares to Wren and Halley, who themselves had already accepted it. They pointed out to Hooke that what was needed was no mere supposition, but a mathematical demonstration that the principle of gravitation would explain the paths of the planets. Wren offered to Hooke and Halley a reward of forty shillings ($100) if either would bring him, within two months, a mathematical proof of gravitation. So far as we know, none came. 32
Sometime in August, 1684, Halley went to Cambridge, and asked Newton what would be the orbit of a planet if its attraction by the sun varied inversely as the square of the distance between them. Newton replied, an ellipse. As Kepler had concluded, from his mathematical study of Tycho Brahe’s observations, that the planetary orbits are elliptical, astronomy seemed now confirmed by mathematics, and vice versa. Newton added that he had worked out the calculations in detail in 1679, but had laid them aside, partly because they did not fully accord with the then current estimates of the earth’s diameter and the distance of the earth from the moon; more probably because he was not sure that he could treat the sun, the planets, and the moon as single points in measuring their attractive force. But in 1671 Picard announced his new measurements of the earth’s radius and a degree of longitude, which last he calculated at 69.1 English statute miles; and in 1672 Picard’s mission to Cayenne enabled him to estimate the distance of the sun from the earth as 87,000,000 miles (the present figure is 92,000,000). These new estimates harmonized well with Newton’s mathematics of gravitation; and further calculations in 1685 convinced him that a sphere attracts bodies as though all its mass were gathered at its center. Now he felt more confidence in his hypothesis.
He compared the rate of fall in a stone dropped to the earth with the rate at which the moon would fall toward the earth if the gravitational pull of the earth upon the moon diminished with the square of the distance between them. He found that his results agreed with the latest astronomical data. He concluded that the force making the stone fall, and the force drawing the moon toward the earth despite the moon’s centrifugal impetus, were one and the same. His achievement lay in applying this conclusion to all bodies in space, in conceiving all the heavenly bodies as bound in a mesh of gravitational influences, and in showing how his mathematical and mechanical calculations tallied with the observations of the astronomers, and especially with Kepler’s planetary laws.*
Newton worked out his calculations anew, and communicated them to Halley in November, 1684. Recognizing their importance, Halley urged him to submit them to the Royal Society. He complied by sending the Society a treatise, Propositiones de Motu(February, 1685), which summarized his views on motion and gravitation. In March, 1686, he began a fuller exposition, and on April 28, 1686, he presented to the Society, in manuscript, Book I (De Motu Corporum) of Philosophiae Naturalis Principia Mathematica. Hooke at once pointed out that he had anticipated Newton in 1674. Newton answered, in a letter to Halley, that Hooke had taken the idea of inverse squares from Borelli and Bouillard. The dispute waxed to mutual irritation; Halley acted as peacemaker, and Newton soothed Hooke by inserting into his manuscript, under Proposition IV, a scholium in which he credited “our friends Wren, Hooke, and Halley” as having “already inferred” the law of inverse squares. But the dispute so irked him that when he announced to Halley (June 20, 1687), that Book II was ready, he added, “The third I now design to suppress. Philosophy is such an impertinently litigious lady that a man had as good be engaged in lawsuits as have to do with her.” Halley persuaded him to continue; and in September, 1687, the entire work was published under the imprint of the Royal Society and its current president, Samuel Pepys. The Society being short of funds, Halley paid for the publication entirely out of his own pocket, though he was not a man of means. So at last, after twenty years of preparation, appeared the most important book of seventeenth-century science, rivaled, in the magnitude of its effects upon the mind of literate Europe, only by the De revolutionibus orbium coelestium (1543) of Copernicus and The Origin of Species (1859) of Darwin. These three books are the basic events in the history of modern Europe.