We owe much to Halley; at the time the Royal Society was in difficulties as to funds he took the whole cost on himself. Hooke, when the first book was presented, claimed that he had f ore stalled Newton in a great part of it, and in the correspondence which followed Halley did all he could to smooth over the diffi culties and persuade Newton to continue his work. Newton's letter quoted above indicates his own feelings and in a letter to Halley of July 14, i686 he had written, "I have considered how best to compose the present dispute, and I think it may be done by the enclosed scholium to the fourth proposition." In a corollary to the fourth proposition Newton showed that Kepler's third law was a consequence of the elliptic path of a planet under an inverse square law; the scholium runs : "The case of the sixth corollary applies to the heavenly bodies as our friends Wren, Hooke and Halley have already inferred and therefore I have decided to develope fully all the consequences of a force decreasing as the inverse square." The great work did this : the Principia established Newton's fame; some little time elapsed before it was fully accepted on the Continent but for more than 200 years it reigned supreme, and all theories of cosmogony were based on the principles laid down by Newton. His mechanics guided astronomers and men of science in their search for natural knowledge. And if in these last years Einstein has carried us some steps further, has picked up some few more of the jewels of truth, which Newton sought on the shore, Newton's laws re main, included it may be, in a more comprehensive statement of the truth.
In 1687 James II. tried to force the University to admit as a Master of Arts, Father Alban Francis, a Benedictine monk, with out taking the oaths of allegiance and supremacy. Newton was one of those who led the resistance to the royal action, and appeared before Lord Jeffreys to argue the case for Cambridge.
In the end the deputies were reprimanded, and Pechell the Vice Chancellor was deprived of his office. Newton's share in the affair led to his being elected member for the University in 1689, retaining the seat till the dissolution next year. He was elected again in 5701, but he never took any prominent part in politics.
On the dissolution of Parliament in 1690 he returned to Cam bridge and continued for a time his mathematical work; this was interrupted in 1692-94 by a serious illness. He was suffering from insomnia and nervous trouble. There was a report that he was going out of his mind. Huyghens in June 1694 wrote to Leibnitz "I do not know if you are acquainted with the accident to the good Mr. Newton, namely, that he has had an attack of phrenitis which lasted eighteen months and of which they say his friends have cured him by means of remedies and keeping him shut up." For some time his friends had been anxious to obtain for him some recognition of his work; this came in 1695. Wren, his friend
Charles Montague, Lord Halifax, a former Fellow of Trinity who was Chancellor of the Exchequer, offered him the post of Warden of the Mint. This he accepted and four years later became Master. In the same year he was elected one of the eight Foreign Associates of the French Academy of Science.
In 1696 John Bernoulli addressed a letter to the mathemati cians of Europe challenging them to solve two problems and giving six months for the solution. On January 29, 1697 Newton received from France two copies of the printed paper containing the prob lems and the following day sent the solution to Montague, then President of the Royal Society. They were transmitted anony mously to Bernoulli, who recognised the author in his disguise "tanquam ex ungue leonem." As Warden of the Mint Newton had retained his Cambridge offices, but soon after his appointment as Master he named Whis ton as Deputy, and in 1701 he resigned his Professorship and the Fellowship at Trinity. Whiston became Lucasian Professor. New ton had moved to London, and continued his duties as Master with marked efficiency until his death in 1727.
The remainder of his life calls for little notice; in 1703 he became President of the Royal Society and was re-elected annually until his death. Queen Anne visited Cambridge in 1705 as the guest at Trinity Lodge of the Master, Dr. Bentley, and on this occasion Newton was knighted. About the same time the contro versy with Leibnitz as to the invention of the differential calculus began. In a review published anonymously of Newton's tract on quadrature, Leibnitz, in 1705, implied that Newton had borrowed from him the idea of Fluxions.
The controversy lasted many years. Leibnitz died in 1716 but it continued to affect English mathematics for more than a cen tury. The matter is discussed very fully in the article "Newton" in the Dictionary of National Biography and in Ball's short His tory of Mathematics. Leibnitz had used the method in his note books of 1675, it occurs in a letter to Newton of 1677, and was published in 1684. Newton used his method of Fluxions in 1666, gave an account of it in manuscript to friends and among others to Collins, in letters from 1669 onwards but did not publish it until 1693. It was some of these letters which Leibnitz saw when in London in 1676, and previously to that, copies of one at least of Newton's letters to Collins had been sent to him. During this visit it appears probable that he saw Newton's tract on the subject. In the middle of 1708 Newton, at the urgent request of Dr. Bent ley, consented to let Roger Cotes, a Fellow of Trinity, edit a second edition of the Principia; the volume was published in 1713, a third edition by Pemberton appeared in 1726.