THE BACKGROUND to Halley's visit to Cambridge in August 1684 was a chance conversation of the previous January. By his own account, Halley had been contemplating celestial mechanics. From Kepler's third law, he had concluded that the centripetal force toward the sun must decrease in proportion to the square of the distance of the planets from the sun. The context of his statement implied that he arrived at the inverse-square relation by substituting Kepler's third law into Huygens's recently published formula for centrifugal force. He was not the only one who made the substitution. After Hooke raised the cry of plagiarism in 1686, Newton recalled a conversation with Sir Christopher Wren in 1677 in which they had considered the problem “of Determining the Hevenly motions upon philosophicall principles.” He had realized that Wren had also arrived at the inverse-square law. It is clear that the problem Hooke put to Newton in the winter of 1679-80 was one that several people defined for themselves at much the same time. It was, indeed, the great unanswered question confronting natural philosophy, the derivation of Kepler's laws of planetary motion from principles of dynamics.

This same problem was discussed by Halley, Wren, and Hooke at a meeting of the Royal Society in January 1684. Hooke claimed that he could demonstrate all the laws of celestial motion from the inverse-square relation. Halley admitted that his own attempt to do so had failed. Wren was skeptical of Hooke's claim. Hooke again asserted that he had the demonstration, but he intended to keep it secret until others, by failing to solve the problem, learned how to value it. We do not know what took Halley to Cambridge. Because he allowed seven months to pass, we can hardly surmise that he rushed there, afire with curiosity, to lay the problem before Newton. Nevertheless, he did find himself in Cambridge in August, and he did seize the opportunity to consult a man he knew to be expert in mathematics.

Although Halley mentioned the visit, the best account came from Newton's recollection as he told it to Abraham DeMoivre.