During his residence in London, Isaac Newton had made the acquaintance of John Locke. Locke had taken a very great interest in the new theories of the Principia. He was one of a number of Newton's friends who began to be uneasy and dissatisfied at seeing the most eminent scientific man of his age left to depend upon the meagre remuneration of a college fellowship and a professorship.

1693 During the period 1692–1693 Newton is known to have suffered a breakdown of nervous functioning, or a supposed depression see also: FRANK E. MANUEL 1968 lasting for 18 months, as reported by Huygens. He suffered insomnia and poor digestion, in his letters to friends showing signs of irrationality.Mercury Poisoning: A Probable Cause of Isaac Newton's Physical and Mental Ills - L. W. Johnson and M. L. Wolbarsht - Notes and Records of the Royal Society of London - Vol. 34, No. 1 (July 1979), pp. 1-9 (article consists of 9 pages) JSTOR . Retrieved 28 January 2012

During exhumation the hair from Newton's dead body was found to contain high levels of mercury,Eric Weisstein's World of Biography. 1996-2007 Eric W. Weisstein . Retrieved 30 August 2006. remains of desiccated hair were later found to contain four times the lead, arsenic and antimony and fifteen times mercury than in normal range samples. Two hairs contained mercury and separately lead at levels indicating chronic poisoning.M.S. LESNEY- Newton's Hair Chemistry Chronicles . Retrieved 28 January 2012Derek Gjertsen Symptoms of mercury poisoning exhibited by Newton were apparently tremor, severe insomnia, delusions of persecution or paranoid ideas, problems with memory, mental confusion, and withdrawal or decline from personal friendships, significant in the period of time, the deterioration of his relations with his protégé Nicolas Fatio de Duillier.Milo Keynes - Balancing Newton's mind: his singular behaviour and his madness of 1692–93

Newton documented the first performed alchemy experiment during 1678, having first obtained furnaces and chemicals in 1669. Experiments with metal included analysis of taste of which there are 108 documented, including mercury: documented also by the scientist were similar experiments with arsenic, gold and lead.

Newton recorded in his notebook of experimenting with chemicals during June 1693. The limited evidence for symptomatic mental illness of Newton during this period stem from correspondences (c.f. The Royal Society) revealing melancholia, desire for withdrawal from relations including his good friends, insomnia, apathy, loss of appetite, delusion of persecution, possibly failures in memory (amnesia), and bipolar. In a letter written to Samuel Pepys, Newton stated he was

On the 30th of that month Newton reported he had been seized by a distemper

Running the Royal Mint For the last half of Newton's adult life, 30 years, he was warden of the Royal Mint as well as Master of the Mint.

Appointment to the Mint Newton got his appointment because of his renown as a scientist and because he supported the winning side in the Glorious Revolution.

At some time Locke nearly succeeded in procuring Newton an appointment as provost of King's College, Cambridge, but the college had offered a successful resistance on the grounds that the appointment would be illegal; its statutes required that the provost should be in priest's orders. Charles Montagu, afterwards Earl of Halifax, was a fellow of Trinity and an intimate friend of Newton, and it was on his influence that Newton relied for promotion to some honourable and lucrative post. However, his hopes were spoiled by long delay. In one of his letters to Locke at the beginning of 1692, when Montagu, Lord Monmouth and Locke were exerting themselves to obtain some appointment for Newton, Newton wrote that he was "fully convinced that Montagu, upon an old grudge which he thought had been worn out, was false to him."

Newton was now 55 years old, and whilst those of his own standing at the university had been appointed to high posts in church or state, he still remained without any mark of national gratitude. Montagu, after being appointed Chancellor of the Exchequer in 1694 finally put this right; he had previously consulted Newton upon the subject of the recoinage, and took the opportunity to appoint Newton to the post of warden of the Royal Mint in 1696. In a letter to Newton announcing the news, Montagu writes: "I am very glad that at last I can give you a good proof of my friendship, and the esteem the king has of your merits. Mr Overton, the warden of the mint, is made one of the Commissioners of Customs, and the king has promised me to make Mr Newton warden of the mint. The office is the most proper for you. 'Tis the chief office in the mint: 'tis worth five or six hundred pounds per annum, and has not too much business to require more attendance than you can spare."

The letter must have convinced Newton of the sincerity of Montagu's good intentions towards him; we find them living as friends on the most intimate terms until Halifax's death in 1715.

Achievements and influence Although the post was intended to be a sinecure, Newton took it seriously. By the time of his appointment the currency had been seriously weakened by an increase in clipping and counterfeiting during the Nine Years' WarThe 1696 Recoinage (1696-1699) , Richard Kleer, University of Regina, The Literary Encyclopedia to the extent that it had been decided to recall and replace all hammered silver coinage in circulation. The exercise came close to disaster due to fraud and mismanagement,The Scottish Mint after the recoinage, 1709-1836 , Athol L Murray, Society of Antiquaries of Scotland, 1999 but was salvaged by Newton's personal intervention. Newton's chemical and mathematical knowledge proved of great use in carrying out this Great Recoinage of 1696, a process that was completed in about two years. Newton was subsequently given the post of Master of the Mint in 1699, a post worth between £1,200 and £1,500 per annum.

Despite counterfeiting being considered high treason, punishable by hanging, drawing and quartering, convicting even the most flagrant criminals could be extremely difficult. Undaunted, Newton conducted more than 100 cross-examinations of witnesses, informers, and suspects between June 1698 and Christmas 1699. He himself gathered much of the evidence he needed to successfully prosecute 28 coiners.

One of Newton's cases as the King's attorney was against William Chaloner. Chaloner's schemes included setting up phony conspiracies of Catholics and then turning in the hapless conspirators whom he had entrapped. Chaloner made himself rich enough to posture as a gentleman. Petitioning Parliament, Chaloner accused the Mint of providing tools to counterfeiters (a charge also made by others). He proposed that he be allowed to inspect the Mint's processes in order to improve them. He petitioned Parliament to adopt his plans for a coinage that could not be counterfeited, while at the same time striking false coins. Newton put Chaloner on trial for counterfeiting and had him sent to Newgate Prison in September 1697. But Chaloner had friends in high places, who helped him secure an acquittal and his release. Newton put him on trial a second time with conclusive evidence. Chaloner was convicted of high treason and hanged, drawn and quartered on 23 March 1699 at Tyburn gallows. Then, he was publicly disemboweled.

Following the 1707 union between the Kingdom of England and the Kingdom of Scotland, Newton used his experience from the English recoinage to direct the 1707-1710 Scottish recoinage, resulting in a common currency for the new Kingdom of Great Britain.Sir Isaac Newton and the Scottish recoinage, 1707-10 , Athol L Murray, Society of Antiquaries of Scotland, 1997

Newton also drew up a very extensive table of assays of foreign coins.

As a result of a report written by Newton on 21 September 1717 to the Lords Commissioners of His Majesty's TreasuryOn the Value of Gold and Silver in European Currencies and the Consequences on the World-wide Gold- and Silver-Trade , Sir Isaac Newton, 21 September 1717. the bimetallic relationship between gold coins and silver coins was changed by Royal proclamation on 22 December 1717, forbidding the exchange of gold guineas for more than 21 silver shillings.By The King, A Proclamation Declaring the Rates at which Gold shall be current in Payments reproduced in the numismatic chronicle and journal of the Royal Numismatic Society, Vol V., April 1842 - January 1843 Due to differing valuations in other European countries this inadvertently resulted in a silver shortage as silver coins were used to pay for imports, while exports were paid for in gold, effectively moving Britain from the silver standard to its first gold standard, rather than the bimetallic standard implied by the proclamation.

Due to his income from the Mint Newton became very wealthy, although he lost a substantial sum in the collapse of the South Sea Bubble. Newton's niece Catherine Conduitt reported that he "lost twenty thousand pounds. Of this, however, he never much liked to hear…"William Seward, Anecdotes of Distinguished Men, 1804 This was a fortune at the time (equivalent to about £ in present-day terms), but it is not clear whether it was a monetary loss or an opportunity cost loss.

Newton continued in his position at the Royal Mint until his death in 1727.

Fluxions

Up to the time of the publication of the Principia in 1687 the method of fluxions which had been invented by Newton, and had been of great assistance to him in his mathematical investigations, was still, except to Newton and his friends, a secret. One of the most important rules of the method forms the second lemma of the second book of the Principia. Though this new and powerful method was of great help to Newton in his work, he did not exhibit it in the results. He was aware that the well known geometrical methods of the ancients would make his new creations seem less strange and uncouth to those not familiar with the new method. The Principia gives no information on the subject of the notation adopted in the new calculus, and it was not until 1693 that it was communicated to the scientific world in the second volume of John Wallis's works.

Newton's admirers in the Netherlands informed Wallis that Newton's method of fluxions passed there under the name of Gottfried Leibniz's Calculus Differentials. It was therefore thought necessary that an early opportunity should be taken of asserting Newton's claim to be the inventor of the method of fluxions, and this was why this method first appeared in Wallis's works. A further account was given in the first edition of Newton's Optics (1704).

To this work were added two treatises, entitled Accedunt tractatus duo ejusdem authoris de speciebus & magnitudine figurarum curvilinearum, the one bearing the title Introductio ad Quadratura Curvarum, and the other Enumeratio linearum tertii ordinis. The first contains an explanation of the doctrine of fluxions, and of its application to the quadrature of curves; the second, a classification of 72 curves of the third order, with an account of their properties.