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. Halley wrote his account in the summer of 1686 after he had read two successive versions of what became Book I of the Principia. Since Newton coined the word “centripetal” after January 1684, Halley could not have framed his conclusion using that word, and he probably did not use the concept, either. 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 plagiary 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. When, at Newton's request, Halley asked Wren about the conversation, Wren told him that for many years he “had had his thoughts upon making out the Planets motions by a composition of a Descent towards the sun, & an imprest motion …,” but he had not been able to solve the problem.