About this period other philosophers had been occupied with the same subject. Sir Christopher Wren had many years before endeavoured to explain the planetary motions “by the composition of a descent towards the sun, and an impressed motion; but he at length gave it over, not finding the means of doing it.” In January, 1683–4, Dr. Halley had concluded, from Kepler’s Law of the Periods and Distances, that the centripetal force decreased in the reciprocal proportion of the squares of the distances, and having one day met Sir Christopher Wren and Dr. Hooke, the latter affirmed that he had demonstrated upon that principle all the laws of the celestial motions. Dr. Halley confessed that his attempts were unsuccessful, and Sir Christopher, in order to encourage the inquiry, offered to present a book of forty shillings’ value to either of the two philosophers who should, in the space of two months, bring him a convincing demonstration of it. Hooke persisted in the declaration that he possessed the method, but avowed it to be his intention to conceal it for some time. He promised, however, to show it to Sir Christopher; but there is every reason to believe that this promise was never fulfilled. In August, 1684, Dr. Halley went to Cambridge for the express purpose of consulting Newton on this interesting subject. Newton assured him that he had brought this demonstration to perfection, and promised him a copy of it. This copy was received in November by the doctor, who made a second visit to Cambridge, in order to induce its author to have it inserted in the register book of the society. On the 10th of December, Dr. Halley announced to the society, that he had seen at Cambridge Mr. Newton’s treatise _De Motu Corporum_, which he had promised to send to the society to be entered upon their register; and Dr. Halley was desired to unite with Mr. Paget, master of the mathematical school in Christ’s Hospital, in reminding Mr. Newton of his promise “for securing the invention to himself till such time as he can be at leisure to publish it.” On the 25th February Mr. Aston, the secretary, communicated a letter from Mr. Newton, in which he expressed his willingness “to enter in the register his notions about motion, and his intentions to fit them suddenly for the press.” The progress of his work was, however, interrupted by a visit of five or six weeks which he made in Lincolnshire; but he proceeded with such diligence on his return, that he was able to transmit the manuscript to London before the end of April. This manuscript, entitled _Philosophiæ Naturalis Principia Mathematica_, and dedicated to the society, was presented by Dr. Vincent on the 28th April, 1686, when Sir John Hoskins, the vice-president, and the particular friend of Dr. Hooke, was in the chair. Dr. Vincent passed a just encomium on the novelty and dignity of the subject; and another member added, that “Mr. Newton had carried the thing so far, that there was no more to be added.” To