**Life**

Early life

Main article: Early life of Isaac Newton

Isaac Newton was born on 4 January 1643 [OS: 25 December 1642][1] at Woolsthorpe Manor in Woolsthorpe-by-Colsterworth, a hamlet in the county of Lincolnshire. At the time of Newton's birth, England had not adopted the Gregorian calendar and therefore his date of birth was recorded as Christmas Day, 25 December 1642. Newton was born three months after the death of his father, a prosperous farmer also named Isaac Newton. Born prematurely, he was a small child; his mother Hannah Ayscough reportedly said that he could have fit inside a quart mug (≈ 1.1 litre). When Newton was three, his mother remarried and went to live with her new husband, the Reverend Barnabus Smith, leaving her son in the care of his maternal grandmother, Margery Ayscough. The young Isaac disliked his stepfather and held some enmity towards his mother for marrying him, as revealed by this entry in a list of sins committed up to the age of 19: "Threatening my father and mother Smith to burn them and the house over them."[10]

Newton in a 1702 portrait by Godfrey Kneller

Isaac Newton (Bolton, Sarah K. Famous Men of Science. NY: Thomas Y. Crowell & Co., 1889)From the age of about twelve until he was seventeen, Newton was educated at The King's School, Grantham (where his signature can still be seen upon a library window sill). He was removed from school, and by October 1659, he was to be found at Woolsthorpe-by-Colsterworth, where his mother, widowed by now for a second time, attempted to make a farmer of him. He hated farming.[11] Henry Stokes, master at the King's School, persuaded his mother to send him back to school so that he might complete his education. Motivated partly by a desire for revenge against a schoolyard bully, he became the top-ranked student.[12]

In June 1661, he was admitted to Trinity College, Cambridge as a sizar — a sort of work-study role.[13] At that time, the college's teachings were based on those of Aristotle, but Newton preferred to read the more advanced ideas of modern philosophers, such as Descartes, and of astronomers such as Copernicus, Galileo, and Kepler. In 1665, he discovered the generalised binomial theorem and began to develop a mathematical theory that would later become infinitesimal calculus. Soon after Newton had obtained his degree in August 1665, the university temporarily closed as a precaution against the Great Plague. Although he had been undistinguished as a Cambridge student,[14] Newton's private studies at his home in Woolsthorpe over the subsequent two years saw the development of his theories on calculus, optics and the law of gravitation. In 1667, he returned to Cambridge as a fellow of Trinity.[15]

Middle years

Mathematics

Newton's mathematical work has been said "to distinctly advance every branch of mathematics then studied".[16]

Newton's early work on the subject usually referred to as fluxions or calculus is seen, for example, in a manuscript of October 1666, now published among Newton's mathematical papers.[17] A related subject of his mathematical work was infinite series. Newton's manuscript "De analysi per aequationes numero terminorum infinitas" ("On analysis by equations infinite in number of terms") was sent by Isaac Barrow to John Collins in June 1669: in August 1669 Barrow identified its author to Collins as "Mr Newton, a fellow of our College, and very young ... but of an extraordinary genius and proficiency in these things".[18]

Newton later became involved in a dispute with Leibniz over priority in the development of infinitesimal calculus. Most modern historians believe that Newton and Leibniz developed infinitesimal calculus independently, although with very different notations. Occasionally it has been suggested that Newton published almost nothing about it until 1693, and did not give a full account until 1704, while Leibniz began publishing a full account of his methods in 1684. (Leibniz's notation and "differential Method", nowadays recognised as much more convenient notations, were adopted by continental European mathematicians, and after 1820 or so, also by British mathematicians.) Such a suggestion, however, fails to notice the content of calculus which critics of Newton's time and modern times have pointed out in Book 1 of Newton's Principia itself (published 1687) and in its forerunner manuscripts, such as De motu corporum in gyrum ("On the motion of bodies in orbit"), of 1684. The Principia is not written in the language of calculus either as we know it or as Newton's (later) 'dot' notation would write it. But Newton's work extensively uses an infinitesimal calculus in geometric form, based on limiting values of the ratios of vanishing small quantities: in the Principia itself Newton gave demonstration of this under the name of 'the method of first and last ratios'[19] and explained why he put his expositions in this form,[20] remarking also that 'hereby the same thing is performed as by the method of indivisibles'.

Because of this content the Principia has been called "a book dense with the theory and application of the infinitesimal calculus" in modern times[21] and "lequel est presque tout de ce calcul" ('nearly all of it is of this calculus') in Newton's time.[22] Newton's use of methods involving "one or more orders of the infinitesimally small" is present in Newton's De Motu Corporum in Gyrum of 1684[23] and in his papers on motion "during the two decades preceding 1684".[24]

Newton had been reluctant to publish his calculus because he feared controversy and criticism.[25] Newton had a very close relationship with Swiss mathematician Nicolas Fatio de Duillier, who from the beginning was impressed by Newton's gravitational theory. In 1691, Duillier planned to prepare a new version of Newton's Principia, but never finished it. However, in 1693 the relationship between the two men changed. At the time, Duillier had also exchanged several letters with Leibniz.[26]

Starting in 1699, other members of the Royal Society (of which Newton was a member) accused Leibniz of plagiarism, and the dispute broke out in full force in 1711. Newton's Royal Society proclaimed in a study that it was Newton who was the true discoverer and labelled Leibniz a fraud. This study was cast into doubt when it was later found that Newton himself wrote the study's concluding remarks on Leibniz. Thus began the bitter Newton v. Leibniz calculus controversy, which marred the lives of both Newton and Leibniz until the latter's death in 1716.[27]

Newton is generally credited with the generalised binomial theorem, valid for any exponent. He discovered Newton's identities, Newton's method, classified cubic plane curves (polynomials of degree three in two variables), made substantial contributions to the theory of finite differences, and was the first to use fractional indices and to employ coordinate geometry to derive solutions to Diophantine equations. He approximated partial sums of the harmonic series by logarithms (a precursor to Euler's summation formula), and was the first to use power series with confidence and to revert power series.

He was elected Lucasian Professor of Mathematics in 1669. In that day, any fellow of Cambridge or Oxford had to be an ordained Anglican priest. However, the terms of the Lucasian professorship required that the holder not be active in the church (presumably so as to have more time for science). Newton argued that this should exempt him from the ordination requirement, and Charles II, whose permission was needed, accepted this argument. Thus a Opticsconflict between Newton's religious views and Anglican orthodoxy was averted.[28 ]

Optics

A replica of Newton's second Reflecting telescope that he presented to the Royal Society in 1672[29]From 1670 to 1672, Newton lectured on optics. During this period he investigated the refraction of light, demonstrating that a prism could decompose white light into a spectrum of colours, and that a lens and a second prism could recompose the multicoloured spectrum into white light.[30]

He also showed that the coloured light does not change its properties by separating out a coloured beam and shining it on various objects. Newton noted that regardless of whether it was reflected or scattered or transmitted, it stayed the same colour. Thus, he observed that colour is the result of objects interacting with already-coloured light rather than objects generating the colour themselves. This is known as Newton's theory of colour.[31]

From this work, he concluded that the lens of any refracting telescope would suffer from the dispersion of light into colours (chromatic aberration). As a proof of the concept, he constructed a telescope using a mirror as the objective to bypass that problem.[32] Building the design, the first known functional reflecting telescope, today known as a Newtonian telescope,[32] involved solving the problem of a suitable mirror material and shaping technique. Newton ground his own mirrors out of a custom composition of highly reflective speculum metal, using Newton's rings to judge the quality of the optics for his telescopes. In late 1668[33] he was able to produce this first reflecting telescope. In 1671, the Royal Society asked for a demonstration of his reflecting telescope.[34] Their interest encouraged him to publish his notes On Colour, which he later expanded into his Opticks. When Robert Hooke criticised some of Newton's ideas, Newton was so offended that he withdrew from public debate. Newton and Hooke had brief exchanges in 1679-80, when Hooke, appointed to manage the Royal Society's correspondence, opened up a correspondence intended to elicit contributions from Newton to Royal Society transactions,[35] which had the effect of stimulating Newton to work out a proof that the elliptical form of planetary orbits would result from a centripetal force inversely proportional to the square of the radius vector (see Newton's law of universal gravitation - History and De motu corporum in gyrum). But the two men remained generally on poor terms until Hooke's death.[36]

Newton argued that light is composed of particles or corpuscles, which were refracted by accelerating into a denser medium. He verged on soundlike waves to explain the repeated pattern of reflection and transmission by thin films (Opticks Bk.II, Props. 12), but still retained his theory of ‘fits’ that disposed corpuscles to be reflected or transmitted (Props.13). Later physicists instead favoured a purely wavelike explanation of light to account for the interference patterns, and the general phenomenon of diffraction. Today's quantum mechanics, photons and the idea of wave–particle duality bear only a minor resemblance to Newton's understanding of light.

In his Hypothesis of Light of 1675, Newton posited the existence of the ether to transmit forces between particles. The contact with the theosophist Henry More, revived his interest in alchemy. He replaced the ether with occult forces based on Hermetic ideas of attraction and repulsion between particles. John Maynard Keynes, who acquired many of Newton's writings on alchemy, stated that "Newton was not the first of the age of reason: He was the last of the magicians."[37] Newton's interest in alchemy cannot be isolated from his contributions to science; however, he did apparently abandon his alchemical researches.[5] (This was at a time when there was no clear distinction between alchemy and science.) Had he not relied on the occult idea of action at a distance, across a vacuum, he might not have developed his theory of gravity. (See also Isaac Newton's occult studies.)

In 1704, Newton published Opticks, in which he expounded his corpuscular theory of light. He considered light to be made up of extremely subtle corpuscles, that ordinary matter was made of grosser corpuscles and speculated that through a kind of alchemical transmutation "Are not gross Bodies and Light convertible into one another, ...and may not Bodies receive much of their Activity from the Particles of Light which enter their Composition?"[38] Newton also constructed a primitive form of a frictional electrostatic generator, using a glass globe (Optics, 8th Query).

Mechanics and gravitation

Newton's own copy of his Principia, with hand-written corrections for the second editionFurther information: Writing of Principia Mathematica

In 1679, Newton returned to his work on mechanics, i.e., gravitation and its effect on the orbits of planets, with reference to Kepler's laws of planetary motion. This followed stimulation by a brief exchange of letters in 1679-80 with Hooke, who had been appointed to manage the Royal Society's correspondence, and who opened a correspondence intended to elicit contributions from Newton to Royal Society transactions.[35] Newton's reawakening interest in astronomical matters received further stimulus by the appearance of a comet in the winter of 1680-1681, on which he corresponded with John Flamsteed.[39] After the exchanges with Hooke, Newton worked out a proof that the elliptical form of planetary orbits would result from a centripetal force inversely proportional to the square of the radius vector (see Newton's law of universal gravitation - History and De motu corporum in gyrum). Newton communicated his results to Edmond Halley and to the Royal Society in De motu corporum in gyrum, a tract written on about 9 sheets which was copied into the Royal Society's Register Book in December 1684.[40] This tract contained the nucleus that Newton developed and expanded to form the Principia.

The Principia was published on 5 July 1687 with encouragement and financial help from Edmond Halley. In this work, Newton stated the three universal laws of motion that were not to be improved upon for more than 200 years. He used the Latin word gravitas (weight) for the effect that would become known as gravity, and defined the law of universal gravitation.

In the same work, Newton presented a calculus-like method of geometrical analysis by 'first and last ratios', gave the first analytical determination (based on Boyle's law) of the speed of sound in air, inferred the oblateness of the spheroidal figure of the Earth, accounted for the precession of the equinoxes as a result of the Moon's gravitational attraction on the Earth's oblateness, initiated the gravitational study of the irregularities in the motion of the moon, provided a theory for the determination of the orbits of comets, and much more.

Newton made clear his heliocentric view of the solar system – developed in a somewhat modern way, because already in the mid-1680s he recognised the "deviation of the Sun" from the centre of gravity of the solar system.[41] For Newton, it was not precisely the centre of the Sun or any other body that could be considered at rest, but rather "the common centre of gravity of the Earth, the Sun and all the Planets is to be esteem'd the Centre of the World", and this centre of gravity "either is at rest or moves uniformly forward in a right line" (Newton adopted the "at rest" alternative in view of common consent that the centre, wherever it was, was at rest).[42]

Newton's postulate of an invisible force able to act over vast distances led to him being criticised for introducing "occult agencies" into science.[43] Later, in the second edition of the Principia (1713), Newton firmly rejected such criticisms in a concluding General Scholium, writing that it was enough that the phenomena implied a gravitational attraction, as they did; but they did not so far indicate its cause, and it was both unnecessary and improper to frame hypotheses of things that were not implied by the phenomena. (Here Newton used what became his famous expression Hypotheses non fingo).

With the Principia, Newton became internationally recognised.[44] He acquired a circle of admirers, including the Swiss-born mathematician Nicolas Fatio de Duillier, with whom he formed an intense relationship that lasted until 1693, when it abruptly ended, at the same time that Newton suffered a nervous breakdown.[45]

Later life

Isaac Newton in old age in 1712, portrait by Sir James Thornhill

Personal coat of arms of Sir Isaac Newton[46]Main article: Later life of Isaac Newton

In the 1690s, Newton wrote a number of religious tracts dealing with the literal interpretation of the Bible. Henry More's belief in the Universe and rejection of Cartesian dualism may have influenced Newton's religious ideas. A manuscript he sent to John Locke in which he disputed the existence of the Trinity was never published. Later works – The Chronology of Ancient Kingdoms Amended (1728) and Observations Upon the Prophecies of Daniel and the Apocalypse of St. John (1733) – were published after his death. He also devoted a great deal of time to alchemy (see above).

Newton was also a member of the Parliament of England from 1689 to 1690 and in 1701, but according to some accounts his only comments were to complain about a cold draught in the chamber and request that the window be closed.[47]

Newton moved to London to take up the post of warden of the Royal Mint in 1696, a position that he had obtained through the patronage of Charles Montagu, 1st Earl of Halifax, then Chancellor of the Exchequer. He took charge of England's great recoining, somewhat treading on the toes of Master Lucas (and securing the job of deputy comptroller of the temporary Chester branch for Edmond Halley). Newton became perhaps the best-known Master of the Mint upon Lucas' death in 1699, a position Newton held until his death. These appointments were intended as sinecures, but Newton took them seriously, retiring from his Cambridge duties in 1701, and exercising his power to reform the currency and punish clippers and counterfeiters. As Master of the Mint in 1717 in the "Law of Queen Anne" Newton moved the Pound Sterling from the silver standard to the gold standard by setting the bimetallic relationship between gold coins and the silver penny in favour of gold. This caused silver sterling coin to be melted and shipped out of Britain. Newton was made President of the Royal Society in 1703 and an associate of the French Académie des Sciences. In his position at the Royal Society, Newton made an enemy of John Flamsteed, the Astronomer Royal, by prematurely publishing Flamsteed's Historia Coelestis Britannica, which Newton had used in his studies.[48]

In April 1705, Queen Anne knighted Newton during a royal visit to Trinity College, Cambridge. The knighthood is likely to have been motivated by political considerations connected with the Parliamentary election in May 1705, rather than any recognition of Newton's scientific work or services as Master of the Mint.[49] Newton was the first scientist ever to be knighted.[46]

Towards the end of his life, Newton took up residence at Cranbury Park, near Winchester with his niece and her husband, until his death in 1727.[50] Newton died in his sleep in London on 31 March 1727 [OS: 20 March 1726],[1] and was buried in Westminster Abbey. His half-niece, Catherine Barton Conduitt,[51] served as his hostess in social affairs at his house on Jermyn Street in London; he was her "very loving Uncle,"[52] according to his letter to her when she was recovering from smallpox. Newton, a bachelor, had divested much of his estate to relatives during his last years, and died intestate.

After his death, Newton's body was discovered to have had massive amounts of mercury in it, probably resulting from his alchemical pursuits. Mercury poisoning could explain Newton's eccentricity in late life.[53]

After death

Fame

French mathematician Joseph-Louis Lagrange often said that Newton was the greatest genius who ever lived, and once added that Newton was also "the most fortunate, for we cannot find more than once a system of the world to establish."[54] English poet Alexander Pope was moved by Newton's accomplishments to write the famous epitaph:

Nature and nature's laws lay hid in night;

God said "Let Newton be" and all was light.

Newton himself had been rather more modest of his own achievements, famously writing in a letter to Robert Hooke in February 1676:

If I have seen further it is by standing on the shoulders of Giants.[55][56]

Two writers think that the above quote, written at a time when Newton and Hooke were in dispute over optical discoveries, was an oblique attack on Hooke (said to have been short and hunchbacked), rather than – or in addition to – a statement of modesty.[57][58] On the other hand, the widely-known proverb about standing on the shoulders of giants published among others by 17th-century poet George Herbert (a former orator of the University of Cambridge and fellow of Trinity College) in his Jacula Prudentum (1651), had as its main point that "a dwarf on a giant's shoulders sees farther of the two", and so its effect as an analogy would place Newton himself rather than Hooke as the 'dwarf'.

In a later memoir, Newton wrote:

I do not know what I may appear to the world, but to myself I seem to have been only like a boy playing on the sea-shore, and diverting myself in now and then finding a smoother pebble or a prettier shell than ordinary, whilst the great ocean of truth lay all undiscovered before me.[59]

Newton remains influential to scientists, as demonstrated by a 2005 survey of members of Britain's Royal Society (formerly headed by Newton) asking who had the greater effect on the history of science, Newton or Albert Einstein. Royal Society scientists deemed Newton to have made the greater overall contribution.[8] In 1999, an opinion poll of 100 of today's leading physicists voted Einstein the "greatest physicist ever;" with Newton the runner-up, while a parallel survey of rank-and-file physicists by the site PhysicsWeb gave the top spot to Newton.[60]

Commemorations

Newton statue on display at the Oxford University Museum of Natural HistoryNewton's monument (1731) can be seen in Westminster Abbey, at the north of the entrance to the choir against the choir screen, near his tomb. It was executed by the sculptor Michael Rysbrack (1694–1770) in white and grey marble with design by the architect William Kent. The monument features a figure of Newton reclining on top of a sarcophagus, his right elbow resting on several of his great books and his left hand pointing to a scroll with a mathematical design. Above him is a pyramid and a celestial globe showing the signs of the Zodiac and the path of the comet of 1680. A relief panel depicts putti using instruments such as a telescope and prism.[61] The Latin inscription on the base translates as:

Here is buried Isaac Newton, Knight, who by a strength of mind almost divine, and mathematical principles peculiarly his own, explored the course and figures of the planets, the paths of comets, the tides of the sea, the dissimilarities in rays of light, and, what no other scholar has previously imagined, the properties of the colours thus produced. Diligent, sagacious and faithful, in his expositions of nature, antiquity and the holy Scriptures, he vindicated by his philosophy the majesty of God mighty and good, and expressed the simplicity of the Gospel in his manners. Mortals rejoice that there has existed such and so great an ornament of the human race! He was born on 25 December 1642, and died on 20 March 1726/7. — Translation from G.L. Smyth, The Monuments and Genii of St. Paul's Cathedral, and of Westminster Abbey (1826), ii, 703–4.[61]

From 1978 until 1988, an image of Newton designed by Harry Ecclestone appeared on Series D £1 banknotes issued by the Bank of England (the last £1 notes to be issued by the Bank of England). Newton was shown on the reverse of the notes holding a book and accompanied by a telescope, a prism and a map of the Solar System.[62]

A statue of Isaac Newton, standing over an apple, can be seen at the Oxford University Museum of Natural History.

In popular culture

Main article: Isaac Newton in popular culture

Religious views

Main article: Isaac Newton's religious views

Newton's grave in Westminster AbbeyHistorian Stephen D. Snobelen says of Newton, "Isaac Newton was a heretic. But ... he never made a public declaration of his private faith — which the orthodox would have deemed extremely radical. He hid his faith so well that scholars are still unravelling his personal beliefs."[6] Snobelen concludes that Newton was at least a Socinian sympathiser (he owned and had thoroughly read at least eight Socinian books), possibly an Arian and almost certainly an antitrinitarian.[6] In an age notable for its religious intolerance there are few public expressions of Newton's radical views, most notably his refusal to take holy orders and his refusal, on his death bed, to take the sacrament when it was offered to him.[6]

On the other hand, latitudinarian and Newtoni

In a view disputed by Snobelen,[6] T.C. Pfizenmaier argues that Newton held the Eastern Orthodox view of the Trinity rather than the Western one held by Roman Catholics, Anglicans, and most Protestants.[63] In his own day, he was also accused of being a Rosicrucian (as were many in the Royal Society and in the court of Charles II).[64]

Although the laws of motion and universal gravitation became Newton's best-known discoveries, he warned against using them to view the Universe as a mere machine, as if akin to a great clock. He said, "Gravity explains the motions of the planets, but it cannot explain who set the planets in motion. God governs all things and knows all that is or can be done."[65]

His scientific fame notwithstanding, Newton's studies of the Bible and of the early Church Fathers were also noteworthy. Newton wrote works on textual criticism, most notably An Historical Account of Two Notable Corruptions of Scripture. He also placed the crucifixion of Jesus Christ at 3 April, AD 33, which agrees with one traditionally accepted date.[66] He also attempted, unsuccessfully, to find hidden messages within the Bible.

In his own lifetime, Newton wrote more on religion than he did on natural science. He believed in a rationally immanent world, but he rejected the hylozoism implicit in Leibniz and Baruch Spinoza. Thus, the ordered and dynamically informed Universe could be understood, and must be understood, by an active reason. In his correspondence, Newton claimed that in writing the Principia "I had an eye upon such Principles as might work with considering men for the belief of a Deity".[67] He saw evidence of design in the system of the world: "Such a wonderful uniformity in the planetary system must be allowed the effect of choice". But Newton insisted that divine intervention would eventually be required to reform the system, due to the slow growth of instabilities.[68] For this Leibniz lampooned him: "God Almighty wants to wind up his watch from time to time: otherwise it would cease to move. He had not, it seems, sufficient foresight to make it a perpetual motion."[69] Newton's position was vigorously defended by his follower Samuel Clarke in a famous correspondence.

Effect on religious thought

Newton and Robert Boyle's mechanical philosophy was promoted by rationalist pamphleteers as a viable alternative to the pantheists and enthusiasts, and was accepted hesitantly by orthodox preachers as well as dissident preachers like the latitudinarians.[70] Thus, the clarity and simplicity of science was seen as a way to combat the emotional and metaphysical superlatives of both superstitious enthusiasm and the threat of atheism,[71] and, at the same time, the second wave of English deists used Newton's discoveries to demonstrate the possibility of a "Natural Religion".

"Newton", by William Blake; here, Newton is depicted as a "divine geometer".The attacks made against pre-Enlightenment "magical thinking", and the mystical elements of Christianity, were given their foundation with Boyle's mechanical conception of the Universe. Newton gave Boyle's ideas their completion through mathematical proofs and, perhaps more importantly, was very successful in popularising them.[72] Newton refashioned the world governed by an interventionist God into a world crafted by a God that designs along rational and universal principles.[73] These principles were available for all people to discover, allowed people to pursue their own aims fruitfully in this life, not the next, and to perfect themselves with their own rational powers.[74]

Newton saw God as the master creator whose existence could not be denied in the face of the grandeur of all creation.[75][76][77] His spokesman, Clarke, rejected Leibniz' theodicy which cleared God from the responsibility for l'origine du mal by making God removed from participation in his creation, since as Clarke pointed out, such a deity would be a king in name only, and but one step away from atheism.[78] But the unforeseen theological consequence of the success of Newton's system over the next century was to reinforce the deist position advocated by Leibniz.[79] The understanding of the world was now brought down to the level of simple human reason, and humans, as Odo Marquard argued, became responsible for the correction and elimination of evil.[80]

an ideas taken too far resulted in the millenarians, a religious faction dedicated to the concept of a mechanical Universe, but finding in it the same enthusiasm and mysticism that the Enlightenment had fought so hard to extinguish.[81]

Views of the end of the world

See also: Isaac Newton's occult studies and eschatology

In a manuscript he wrote in 1704 in which he describes his attempts to extract scientific information from the Bible, he estimated that the world would end no earlier than 2060. In predicting this he said, "This I mention not to assert when the time of the end shall be, but to put a stop to the rash conjectures of fanciful men who are frequently predicting the time of the end, and by doing so bring the sacred prophesies into discredit as often as their predictions fail."[82]

Enlightenment philosophers

Enlightenment philosophers chose a short history of scientific predecessors — Galileo, Boyle, and Newton principally — as the guides and guarantors of their applications of the singular concept of Nature and Natural Law to every physical and social field of the day. In this respect, the lessons of history and the social structures built upon it could be discarded.[83]

It was Newton's conception of the Universe based upon Natural and rationally understandable laws that became one of the seeds for Enlightenment ideology.[84] Locke and Voltaire applied concepts of Natural Law to political systems advocating intrinsic rights; the physiocrats and Adam Smith applied Natural conceptions of psychology and self-interest to economic systems and the sociologists criticised the current social order for trying to fit history into Natural models of progress. Monboddo and Samuel Clarke resisted elements of Newton's work, but eventually rationalised it to conform with their strong religious views of nature.

Counterfeiters

As warden of the Royal Mint, Newton estimated that 20% of the coins taken in during The Great Recoinage were counterfeit. Counterfeiting was high treason, punishable by being hanged, drawn and quartered. Despite this, convictions of the most flagrant criminals could be extremely difficult to achieve; however, Newton proved to be equal to the task.[85] Disguised as an habitué of bars and taverns, he gathered much of that evidence himself.[86] For all the barriers placed to prosecution, and separating the branches of government, English law still had ancient and formidable customs of authority. Newton had himself made a justice of the peace in all the home counties and between June 1698 and Christmas 1699 conducted more than 100 cross-examinations of witnesses, informers and suspects. Newton successfully prosecuted 28 coiners.[87]

One of Newton's cases as the King's attorney was against William Chaloner.[88] Chaloner's schemes included setting up phoney conspiracies of Catholics and then turn in the hapless conspirators whom he 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.[89] 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.[88] 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.[90]

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Main article: Newton's laws of motion

The famous three laws of motion (stated in modernised form): Newton's First Law (also known as the Law of Inertia) states that an object at rest tends to stay at rest and that an object in uniform motion tends to stay in uniform motion unless acted upon by a net external force.

Newton's Second Law states that an applied force, , on an object equals the rate of change of its momentum, , with time. Mathematically, this is expressed as

Since the second law applies to an object with constant mass (dm/dt = 0), the first term vanishes, and by substitution using the definition of acceleration, the equation can be written in the iconic form

The first and second laws represent a break with the physics of Aristotle, in which it was believed that a force was necessary in order to maintain motion. They state that a force is only needed in order to change an object's state of motion. The SI unit of force is the newton, named in Newton's honour.

Newton's Third Law states that for every action there is an equal and opposite reaction. This means that any force exerted onto an object has a counterpart force that is exerted in the opposite direction back onto the first object. A common example is of two ice skaters pushing against each other and sliding apart in opposite directions. Another example is the recoil of a firearm, in which the force propelling the bullet is exerted equally back onto the gun and is felt by the shooter. Since the objects in question do not necessarily have the same mass, the resulting acceleration of the two objects can be different (as in the case of firearm recoil).

Unlike Aristotle's, Newton's physics is meant to be universal. For example, the second law applies both to a planet and to a falling stone.

The vector nature of the second law addresses the geometrical relationship between the direction of the force and the manner in which the object's momentum changes. Before Newton, it had typically been assumed that a planet orbiting the sun would need a forward force to keep it moving. Newton showed instead that all that was needed was an inward attraction from the sun. Even many decades after the publication of the Principia, this counterintuitive idea was not universally accepted, and many scientists preferred Descartes' theory of vortices.[91]

Apple

Reputed descendants of Newton's apple tree, at the Cambridge University Botanic Garden and the Instituto Balseiro library gardenNewton himself often told the story that he was inspired to formulate his theory of gravitation by watching the fall of an apple from a tree.[92]

Cartoons have gone further to suggest the apple actually hit Newton's head, and that its impact somehow made him aware of the force of gravity. It is known from his notebooks that Newton was grappling in the late 1660s with the idea that terrestrial gravity extends, in an inverse-square proportion, to the Moon; however it took him two decades to develop the full-fledged theory.[93] John Conduitt, Newton's assistant at the Royal Mint and husband of Newton's niece, described the event when he wrote about Newton's life:

In the year 1666 he retired again from Cambridge to his mother in Lincolnshire. Whilst he was pensively meandering in a garden it came into his thought that the power of gravity (which brought an apple from a tree to the ground) was not limited to a certain distance from earth, but that this power must extend much further than was usually thought. Why not as high as the Moon said he to himself & if so, that must influence her motion & perhaps retain her in her orbit, whereupon he fell a calculating what would be the effect of that supposition.[94]

The question was not whether gravity existed, but whether it extended so far from Earth that it could also be the force holding the moon to its orbit. Newton showed that if the force decreased as the inverse square of the distance, one could indeed calculate the Moon's orbital period, and get good agreement. He guessed the same force was responsible for other orbital motions, and hence named it "universal gravitation".

A contemporary writer, William Stukeley, recorded in his Memoirs of Sir Isaac Newton's Life a conversation with Newton in Kensington on 15 April 1726, in which Newton recalled:

when formerly, the notion of gravitation came into his mind. It was occasioned by the fall of an apple, as he sat in contemplative mood. Why should that apple always descend perpendicularly to the ground, thought he to himself. Why should it not go sideways or upwards, but constantly to the Earth's centre? Assuredly the reason is, that the Earth draws it. There must be a drawing power in matter. And the sum of the drawing power in the matter of the Earth must be in the Earth's centre, not in any side of the Earth. Therefore does this apple fall perpendicularly or towards the centre? If matter thus draws matter; it must be proportion of its quantity. Therefore the apple draws the Earth, as well as the Earth draws the apple."[95]

In similar terms, Voltaire wrote in his Essay on Epic Poetry (1727), "Sir Isaac Newton walking in his gardens, had the first thought of his system of gravitation, upon seeing an apple falling from a tree."

Various trees are claimed to be "the" apple tree which Newton describes. The King's School, Grantham, claims that the tree was purchased by the school, uprooted and transported to the headmaster's garden some years later. The staff of the [now] National Trust-owned Woolsthorpe Manor dispute this, and claim that a tree present in their gardens is the one described by Newton. A descendant of the original tree can be seen growing outside the main gate of Trinity College, Cambridge, below the room Newton lived in when he studied there. The National Fruit Collection at Brogdale[96] can supply grafts from their tree, which appears identical to Flower of Kent, a coarse-fleshed cooking variety.[97]

His writings

Method of Fluxions (1671)

Of Natures Obvious Laws & Processes in Vegetation (unpublished, c. 1671–75)[98]

De Motu Corporum in Gyrum (1684)

Philosophiae Naturalis Principia Mathematica (1687)

Opticks (1704)

Reports as Master of the Mint (1701–25)

Arithmetica Universalis (1707)

The System of the World, Optical Lectures, The Chronology of Ancient Kingdoms, (Amended) and De mundi systemate (published posthumously in 1728)

Observations on Daniel and The Apocalypse of St. John (1733) An Historical Account of Two Notable Corruptions of Scripture (1754

Newton’s Life

In 1642, the year Galileo died, Isaac Newton was born in Woolsthorpe, Lincolnshire, England on Christmas Day. His father had died three months earlier, and baby Isaac, very premature, was also not expected to survive. It was said he could be fitted into a quart pot. When Isaac was three, his mother married a wealthy elderly clergyman from the next village, and went to live there, leaving Isaac behind with his grandmother. The clergyman died, and Isaac’s mother came back, after eight years, bringing with her three small children. Two years later, Newton went away to the Grammar School in Grantham, where he lodged with the local apothecary, and was fascinated by the chemicals. The plan was that at age seventeen he would come home and look after the farm. He turned out to be a total failure as a farmer.

His mother’s brother, a clergyman who had been an undergraduate at Cambridge, persuaded his mother that it would be better for Isaac to go to university, so in 1661 he went up to Trinity College, Cambridge. Isaac paid his way through college for the first three years by waiting tables and cleaning rooms for the fellows (faculty) and the wealthier students. In 1664, he was elected a scholar, guaranteeing four years of financial support. Unfortunately, at that time the plague was spreading across Europe, and reached Cambridge in the summer of 1665. The university closed, and Newton returned home, where he spent two years concentrating on problems in mathematics and physics. He wrote later that during this time he first understood the theory of gravitation, which we shall discuss below, and the theory of optics (he was the first to realize that white light is made up of the colors of the rainbow), and much mathematics, both integral and differential calculus and infinite series. However, he was always reluctant to publish anything, at least until it appeared someone else might get credit for what he had found earlier.

On returning to Cambridge in 1667, he began to work on alchemy, but then in 1668 Nicolas Mercator published a book containing some methods for dealing with infinite series. Newton immediately wrote a treatise, De Analysi, expounding his own wider ranging results. His friend and mentor Isaac Barrow communicated these discoveries to a London mathematician, but only after some weeks would Newton allow his name to be given. This brought his work to the attention of the mathematics community for the first time. Shortly afterwards, Barrow resigned his Lucasian Professorship (which had been established only in 1663, with Barrow the first incumbent) at Cambridge so that Newton could have the Chair.

Newton’s first major public scientific achievement was the invention, design and construction of a reflecting telescope. He ground the mirror, built the tube, and even made his own tools for the job. This was a real advance in telescope technology, and ensured his election to membership in the Royal Society. The mirror gave a sharper image than was possible with a large lens because a lens focusses different colors at slightly different distances, an effect called chromatic aberration. This problem is minimized nowadays by using compound lenses, two lenses of different kinds of glass stuck together, that err in opposite directions, and thus tend to cancel each other’s shortcomings, but mirrors are still used in large telescopes.

Later in the 1670’s, Newton became very interested in theology. He studied Hebrew scholarship and ancient and modern theologians at great length, and became convinced that Christianity had departed from the original teachings of Christ. He felt unable to accept the current beliefs of the Church of England, which was unfortunate because he was required as a Fellow of Trinity College to take holy orders. Happily, the Church of England was more flexible than Galileo had found the Catholic Church in these matters, and King Charles II issued a royal decree excusing Newton from the necessity of taking holy orders! Actually, to prevent this being a wide precedent, the decree specified that, in perpetuity, the Lucasian professor need not take holy orders. (The current Lucasian professor is Stephen Hawking.)

In 1684, three members of the Royal Society, Sir Christopher Wren, Robert Hooke and Edmond Halley, argued as to whether the elliptical orbits of the planets could result from a gravitational force towards the sun proportional to the inverse square of the distance. Halley writes:

Mr. Hook said he had had it, but that he would conceal it for some time so that others, triing and failing might know how to value it, when he should make it publick.

Halley went up to Cambridge, and put the problem to Newton, who said he had solved it four years earlier, but couldn’t find the proof among his papers. Three months later, he sent an improved version of the proof to Halley, and devoted himself full time to developing these ideas, culminating in the publication of the Principia in 1686. This was the book that really did change man’s view of the universe, as we shall shortly discuss, and its importance was fully appreciated very quickly. Newton became a public figure. He left Cambridge for London, where he was appointed Master of the Mint, a role he pursued energetically, as always, including prosecuting counterfeiters. He was knighted by Queen Anne. He argued with Hooke about who deserved credit for discovering the connection between elliptical orbits and the inverse square law until Hooke died in 1703, and he argued with a German mathematician and philosopher, Leibniz, about which of them invented calculus. Newton died in 1727, and was buried with much pomp and circumstance in Westminster Abbey—despite his well-known reservations about the Anglican faith.

An excellent, readable book is The Life of Isaac Newton, by Richard Westfall, Cambridge 1993, which I used in writing the above summary of Newton’s life.

A fascinating collection of articles, profusely illustrated, on Newton’s life, work and impact on the general culture is Let Newton Be!, edited by John Fauvel and others, Oxford 1988, which I also consulted.

Projectiles and Planets

Let us now turn to the central topic of the Principia, the universality of the gravitational force. The legend is that Newton saw an apple fall in his garden in Lincolnshire, thought of it in terms of an attractive gravitational force towards the earth, and realized the same force might extend as far as the moon. He was familiar with Galileo’s work on projectiles, and suggested that the moon’s motion in orbit could be understood as a natural extension of that theory. To see what is meant by this, consider a gun shooting a projectile horizontally from a very high mountain, and imagine using more and more powder in successive shots to drive the projectile faster and faster.

The parabolic paths would become flatter and flatter, and, if we imagine that the mountain is so high that air resistance can be ignored, and the gun is sufficiently powerful, eventually the point of landing is so far away that we must consider the curvature of the earth in finding where it lands.

In fact, the real situation is more dramatic—the earth’s curvature may mean the projectile never lands at all. This was envisioned by Newton in the Principia. The following diagram is from his later popularization, A Treatise of the System of the World, written in the 1680’s:

The mountaintop at V is supposed to be above the earth’s atmosphere, and for a suitable initial speed, the projectile orbits the earth in a circular path. In fact, the earth’s curvature is such that the surface falls away below a truly flat horizontal line by about five meters in 8,000 meters (five miles). Recall that five meters is just the vertical distance an initially horizontally moving projectile will fall in the first second of motion. But this implies that if the (horizontal) muzzle velocity were 8,000 meters per second, the downward fall of the cannonball would be just matched by the earth’s surface falling away, and it would never hit the ground! This is just the motion, familiar to us now, of a satellite in a low orbit, which travels at about 8,000 meters (five miles) a second, or 18,000 miles per hour. (Actually, Newton drew this mountain impossibly high, no doubt for clarity of illustration. A satellite launched horizontally from the top would be far above the usual shuttle orbit, and go considerably more slowly than 18,000 miles per hour.)

For an animated version of Newton’s cannon on a mountain, click here!

The Moon is Falling

Newton realized that the moon’s circular path around the earth could be caused in this way by the same gravitational force that would hold such a cannonball in low orbit, in other words, the same force that causes bodies to fall.

To think about this idea, let us consider the moon’s motion, beginning at some particular instant, as deviating downwards—falling—from some initial “horizontal” line, just as for the cannonball shot horizontally from a high mountain. The first obvious question is: does the moon fall five meters below the horizontal line, that is, towards the earth, in the first second? This was not difficult for Newton to check, because the path of the moon was precisely known by this time. The moon’s orbit is approximately a circle of radius about 384,000 kilometers (240,000 miles), which it goes around in a month (to be precise, in 27.3 days), so the distance covered in one second is, conveniently, very close to one kilometer. It is then a matter of geometry to figure out how far the curved path falls below a “horizontal” line in one second of flight, and the answer turns out to be not five meters, but only a little over one millimeter! (Actually around 1.37 millimeters.)

It’s completely impossible to draw a diagram showing how far it falls in one second, but the geometry is the same if we look how far it falls in one day, so here it is:

The Moon in orbiting the Earth goes from A to D in one day. Without the Earth’s pull, it would have gone in a straight line to B.

It has therefore fallen below the straight line in one day by the distance between D and B.

Since we know the radius of the orbit, and we know how far the Moon travels in one day, we can find the distance DB using Pythagoras’ theorem for the triangle CAB, where C is the center of the Earth.

A

B

C

D

For one second, AB would be only one kilometer, so since AC is 384,000 km., the triangle ABC is really thin, but we can still use Pythagoras’ theorem!

Thus the “natural acceleration” of the moon towards the earth, measured by how far it falls below straight line motion in one second, is less than that of an apple here on earth by the ratio of five meters to 1.37 millimeters, which works out to be about 3,600.

What can be the significance of this much smaller rate of fall? Newton’s answer was that the natural acceleration of the moon was much smaller than that of the cannonball because they were both caused by a force—a gravitational attraction towards the earth, and that the gravitational force became weaker on going away from the earth.

In fact, the figures we have given about the moon’s orbit enable us to compute how fast the gravitational attraction dies away with distance. The distance from the center of the earth to the earth’s surface is about 6,350 kilometers (4,000 miles), so the moon is about 60 times further from the center of the earth than we and the cannonball are.

From our discussion of how fast the moon falls below a straight line in one second in its orbit, we found that the gravitational acceleration for the moon is down by a factor of 3,600 from the cannonball’s (or the apple’s).

Putting these two facts together, and noting that 3,600 = 60 x 60, led Newton to his famous inverse square law: the force of gravitational attraction between two bodies decreases with increasing distance between them as the inverse of the square of that distance, so if the distance is doubled, the force is down by a factor of four.

Isaac Newton Resources

The Newton Institute

The Isaac Newton Institute for Mathematical Sciences is an international research institute running a series of visitor programmes across the spectrum of the mathematical sciences. Established in 1992, the 350th anniversary of Newton's birth, the Institute itself has no direct historical links with Newton, but was named after him because of his great achievements in the fields of mathematics, optics, physics and astronomy. The Newton Institute continues in this tradition of crossing the boundaries between scientific disciplines.

At the Institute we are often asked about Newton's life and work. We do have a collection of books about Newton and Newton artefacts but they are purely for the benefit of our researchers. However, there are many excellent and informative websites about Newton's life and works and we have put together this guide to help you find out more.

Biography

Isaac Newton's life from Microsoft Encarta by A. Rupert Hall

Entry for Newton by Richard S. Westfall. This information is taken from the Galileo Project, which places Newton in context with his scientific contemporaries

Sir Isaac Newton (1642 - 1727) taken from A Short Account of the History of Mathematics by W. W. Rouse Ball (4th Edition, 1908). Detailed and authoritative biography with high mathematical content.

Newton Excellent biography with lots of links to related topics and a detailed list of references. Part of the MacTutor History of Mathematics archive at the University of St Andrews.

Newton's Birthplace

Woolsthorpe Manor, Lincolnshire Illustrated guide to Newton's birthplace from the 'Tour UK' site.

The National Trust has an entry for Woolsthorpe Manor, giving opening hours, directions etc

Newton at Cambridge

Trinity College contains about five portraits of Newton and the famous statue by Roubiliac can be seen in the Chapel. The rooms Newton occupied when he was a Fellow can be seen externally but not entered.

The Wren Library at Trinity College contains the largest intact portion of Newton's library, and some correspondence and papers, which can be viewed by appointment. It also contains two busts of Newton (including one by Roubiliac), a display of Newton memorabilia (including walking sticks, watches, mathematical instruments and a lock of hair) and a stained glass window by Cipriani (1771) depicting an allegorical scene in which Newton is presented to George III. These can be seen during opening hours or by appointment.

Papers of Sir Isaac Newton in Cambridge University Library The most complete collection of Newton's scientific papers (held on microfilm, viewing by appointment).

The Keynes' Collection in the Modern Archive Centre at King's College contains many of Newton's non-scientific manuscripts, bequeathed to King's by JM Keynes (viewing by appointment).

The Whipple Museum contains a replica Newtonian reflecting telescope, and a number of portraits of Newton.

Isaac Newton Exhibition at Cambridge University Library entitled Footprints of the Lion which ran in 2002

Newton's Works

Newton's 'Principia' Book Two. Lemma II. Latin or English text, in a variety of electronic formats. From the History of Mathematics site at Trinity College, Dublin

The Newton Project Created in 1998, the Newton Project seeks to make facsimiles and transcriptions of Newton's manuscripts available in electronic form and to display their original connections, along with full documentation relating to Newton's reading such as written notes and annotations.

Newton's Three Laws of Motion

Sir Isaac Newton: The Universal Law of Gravitation

Sir Isaac Newton and the Unification of Physics & Astronomy

These three links are all part of the Astronomy Web Syllabus at the University of Tennessee. A clear, accessible and well-illustrated guide to Newton's laws.

Newton's Monument

Newton died at Kensington on 20 March 1727 and was buried in Westminster Abbey on 28 March. Newton's Monument dates from 1731. It was designed by William Kent and was executed by Michael Rysbrack. (mohsen_zahy66@hotmail.com)

**[b]Mohsen Zahy[/b**] .