It was a visit from Halley in the year 1684 which seems to have first suggested to Newton the idea of publishing the results of his investigations on gravitation.  Halley, and other scientific contemporaries, had no doubt some faint glimmering of the great truth which only Newton’s genius was able fully to reveal.  Halley had indeed shown how, on the assumptions that the planets move in circular orbits round the sun, and that the squares of their periodic times are proportional to the cubes of their mean distances, it may be proved that the force acting on each planet must vary inversely as the square of its distance from the sun.  Since, however, each of the planets actually moves in an ellipse, and therefore, at continually varying distances from the sun, it becomes a much more difficult matter to account mathematically for the body’s motions on the supposition that the attractive force varies inversely as the square of the distance.  This was the question with which Halley found himself confronted, but which his mathematical abilities were not adequate to solve.  It would seem that both Hooke and Sir Christopher Wren were interested in the same problem; in fact, the former claimed to have arrived at a solution, but declined to make known his results, giving as an excuse his desire that others having tried and failed might learn to value his achievements all the more.  Halley, however, confessed that his attempts at the solution were unsuccessful, and Wren, in order to encourage the other two philosophers to pursue the inquiry, offered to present a book of forty shillings value to either of them who should in the space of two months bring him a convincing proof of it.  Such was the value which Sir Christopher set on the Law of Gravitation, upon which the whole fabric of modern astronomy may be said to stand.

Finding himself unequal to the task, Halley went down to Cambridge to see Newton on the subject, and was delighted to learn that the great mathematician had already completed the investigation.  He showed Halley that the motions of all the planets could be completely accounted for on the hypothesis of a force of attraction directed towards the sun, which varies inversely as the square of the distance from that body.

Halley had the genius to perceive the tremendous importance of Newton’s researches, and he ceased not to urge upon the recluse man of science the necessity for giving his new discoveries publication.  He paid another visit to Cambridge with the object of learning more with regard to the mathematical methods which had already conducted Newton to such sublime truths, and he again encouraged the latter both to pursue his investigations, and to give some account of them to the world.  In December of the same year Halley had the gratification of announcing to the Royal Society that Newton had promised to send that body a paper containing his researches on Gravitation.