# Newton Sentence Examples

**Newton**accepted the three subclasses of Huxley, Saururae, Ratitae and Carinitae, and made a series of cautious but critical observations on the minor divisions of the Carinates.The discoveries of Johann Kepler and Bonaventura Cavalieri were the foundation upon which Sir Isaac

**Newton**and Gottfried Wilhelm Leibnitz erected that wonderful edifice, the Infinitesimal Calculus.The King's Own was a vast improvement, in point of construction, upon Frank Mildmay; and he went on, through a quick succession of tales,

**Newton**Forster (1832), Peter Simple (1834), Jacob Faithful (1834), The Pacha of Many Tales (1835), Japhet in Search of a Father (1836), Mr Midshipman Easy (1836), The Pirate and the Three Cutters (1836), till he reached his highwater mark of constructive skill in Snarley-yow, or the Dog Fiend (1837).Sir Isaac

**Newton**introduced the term Universal Arithmetic, since it is concerned with the doctrine of operations, not affected on numbers, but on general symbols.The geometrical theory, which formed the basis of the investigations of Descartes and

**Newton**, afforded no explanation of the supernumerary bows, and about a century elapsed before an explanation was forthcoming.AdvertisementAfterwards he modified his hypothesis, and referred the disturbances produced to the "nervous liquor," which he supposed to be a quantity of the "universal elastic matter" diffused through the universe, by which

**Newton**explained the phenomena of light - i.e.Shortly afterwards Barrow resigned his chair, and was instrumental in securing

**Newton**'s election as his successor.The two legs of a hyperbolic branch may belong to different asymptotes, and in this case we have the forms which

**Newton**calls inscribed, circumscribed, ambigene, &c.; or they may belong to the same asymptote, and in this case we have the serpentine form, where the branch cuts the asymptote, so as to touch it at its two extremities on opposite sides, or the conchoidal form, where it touches the asymptote on the same side.There are two non-singular kinds, the one with, the other without, an oval, but each of them has an infinite (as

**Newton**describes it) campaniform branch; this cuts the axis at right angles, being at first concave, but ultimately convex, towards the axis, the two legs continually tending to become at right angles to the axis.He also wrote biographies of Sir Isaac

**Newton**and Edmund Halley for Knight's British Worthies, various notices of scientific men for the [[Gallery]] of Portraits, and for the uncompleted Biographical Dictionary of the Useful Knowledge Society, and at least seven articles in Smith's Dictionary of Greek and Roman Biography.Advertisement**Newton**he entertained a confident belief in Providence, founded not on any tenuous inference, but on personal feeling.Its mathematical prediction was not only an unsurpassed intellectual feat; it showed also that

**Newton**'s law of gravitation, which Airy had almost called in question, prevailed even to the utmost bounds of the solar system.For

**Newton**and his writings he had a boundless admiration; many of his papers, indeed, bear the cast of**Newton**'s thought.He laboured for many years at the task of arranging and cataloguing the great collection of

**Newton**'s unpublished mathematical writings, presented in 1872 to the university by Lord Portsmouth, and wrote the account of them issued in a volume by the University Press in 1888.An international committee was formed for the purpose of erecting a monument to his memory in Westminster Abbey; and there, in May 1895, a portrait medallion, by Albert Bruce Joy, was placed near the grave of

**Newton**, and adjoining the memorials of Darwin and of Joule.AdvertisementThe original township of Cambridge was very large, and there have been successively detached from it,

**Newton**(1691), Lexington (1713), Brighton (1837) and Arlington (1867).The chief suburbs are

**Newton**, Sandy Bay, Wellington, Risdon, Glenorchy, Bellerive and Beltana.In his letters and otherwise we have pleasant pictures of its inmates and domestic life and the occasional visits of his friends, among others Lord Peterborough, Lord Shaftesbury of the Characteristics, Sir Isaac

**Newton**, William Molyneux and Anthony Collins.Letters from Locke to Thoynard, Limborch, Le Clerc, Guenellon, Molyneux, Collins, Sir Isaac

**Newton**, the first and the third Lord Shaftesbury, Lords Peterborough and Pembroke, Clarke of Chipley and others are preserved, many of them unpublished, most of them in the keeping of Lord Lovelace at Horseley Towers, and of Mr Sanford at Nynehead in Somerset, or in the British Museum.On his return from a visit to London in 1670 he became acquainted with Isaac

**Newton**at Cambridge, entered his name at Jesus college, and took, four years later, a degree of M.A.AdvertisementSir Isaac

**Newton**, who depended for the perfecting of his lunar theory upon "places of the moon" reluctantly doled out from Greenwich, led the movement for immediate communication; whence arose much ill-feeling between him and Flamsteed.Whewell vindicated his character in Flamsteed and

**Newton**(1836).The portion of

**Newton**Abbot in the parish of Highweek was formerly a separate town, known as**Newton**Bushel.Probably both

**Newton**Abbot and**Newton**Bushel were originally included under the name of**Newton**.Thereupon the Newtonian analysis which preceded this synthesis, became forgotten; until at last Mill in his Logic, neglecting the Principia, had the temerity to distort

**Newton**'s discovery, which was really a pure example of analytic deduction, into a mere hypothetical deduction; as if the author of the saying " Hypotheses non lingo" started from the hypothesis of a centripetal force to the sun, and thence deductively explained the facts of planetary motion, which reciprocally verified the hypothesis.AdvertisementWhile still an undergraduate he formed a league with John Herschel and Charles Babbage, to conduct the famous struggle of "d-ism versus dot-age," which ended in the introduction into Cambridge of the continental notation in the infinitesimal calculus to the exclusion of the fluxional notation of Sir Isaac

**Newton**.There was, however, even before

**Newton**'s time, more than a suspicion that heat was a form of energy.After

**Newton**'s time the first vigorous effort to restore the universality of the doctrine of energy was made by Benjamin Thompson, Count Rumford, and was published in the Phil.Samuel Clarke, who defended

**Newton**'s view of the world against Leibnitz's strictures, is perhaps chiefly interesting to.He was, indeed, the first to show clearly the relationship of the heron-like birds with the Steganopodes; of storklike birds with the American vultures; the great difference between the latter and the other birds of prey; the connexion of the gulls and auks with the plovers, and that of the sand-grouse with the From

**Newton**'s FIG.Especial attention has to be drawn to the article " Geographical Distribution," in

**Newton**'s Dictionary of Birds.The resulting " classification is based on the examination, mostly autoptic, of a far greater number of characters than any that had preceded it; moreover, they were chosen in a different way, discernment being exercised in sifting and weighing them, so as to determine, so far as possible, the relative value of each, according as that value may vary in different groups, and not to produce a mere mechanical ` key ' after the fashion become of late years so common " (

**Newton**'s Dictionary of Birds, Introduction, p. 103).He soon learned to call to his aid the subsidiary sciences of geography and chronology, and before he was quite capable of reading them had already attempted to weigh in his childish balance the competing systems of Scaliger and Petavius, of Marsham and

**Newton**.Special mention, however, must be made of the most important of them all - his biography of Sir Isaac

**Newton**.The following year he was elected professor of mathematics in the university of Edinburgh on the urgent recommendation of

**Newton**.After Maclaurin's death his account of

**Newton**'s philosophical discoveries was published by Patrick Murdoch, and also his algebra in 1748.**Newton**'s Hypotheses non fingo was a proud boast, but it rests upon an entire misconception of the capacities of the mind of man in dealing with external nature.Sheets of mica very often show coloured rings and bands (

**Newton**'s rings), due to the interference of light at the surfaces of internal cleavage cracks.The discordance of their results incited Laplace to a searching examination of the whole subject of planetary perturbations, and his maiden effort was rewarded with a discovery which constituted, when developed and completely demonstrated by his own further labours and those of his illustrious rival Lagrange, the most important advance made in physical astronomy since the time of

**Newton**.The phenomena thus presented were described by Grimaldi and by

**Newton**.The medicine of the i 8th century is notable, like that of the latter part of the 17th, for the striving after complete theoretical systems. The influence of the iatro-physical school was by no means exhausted; and in England, especially through the indirect influence of Sir Isaac

**Newton**'s (1642-1727) great astronomical generalizations, it took on a mathematical aspect, and is sometimes known as iatro-mathematical.Mead's treatise on The Power of the Sun and Moon over Human Bodies (1704), equally inspired by

**Newton**'s discoveries, was a premature attempt to assign the influence of atmospheric pressure and other cosmical causes in producing disease.She wrote Institutions dehysique (1740), Dissertation sur la nature et la propagation du feu (1 744), Doutes sur les religions reculees (1792), and in 1756 published a translation of

**Newton**'s Principia.When the results of this theory were compared with the quantity of water actually discharged,

**Newton**concluded that the velocity with which the water issued from the orifice was equal to that which a falling body would receive by descending through half the height of water in the reservoir.This conclusion, however, is absolutely irreconcilable with the known fact that jets of water rise nearly to the same height as their reservoirs, and

**Newton**seems to have been aware of this objection.**Newton**was also the first to investigate the difficult subject of the motion of waves (q.v.).On the reassembling of the Long Parliament he was superseded; he took no part in the Restoration, and died at

**Newton**Tony in Wiltshire on the 16th of December 1669.Watertown is served by the Fitchburg division of the Boston & Maine railway, and is connected with Boston, Cambridge,

**Newton**(immediately adjacent and served by the New York, New Haven & Hartford railway) and neighbouring towns by electric railways.Respect for his character and abilities attracted pupils irrespective of religious connexion, among them

**Newton**Ogle, afterwards dean of Westminster.Although the law was first clearly and rigorously formulated by Sir Isaac

**Newton**, the fact of the action indicated by it was more or less clearly seen by others.Hooke, contemporaries of

**Newton**, saw that Kepler's third law implied a force tending toward the sun which, acting on the several planets, varied inversely as the square of the distance.**Newton**'s researches showed that the attraction of the earth on the moon was the same as that for bodies at the earth's surface, only reduced in the inverse square of the moon's distance from the earth's centre.Sir Isaac

**Newton**, in his Opticks (1704), explains the principle of the camera obscura with single convex lens and its analogy with vision in illustration of his seventh axiom, which aptly embodies the correct solution of Aristotle's old problem.Taylor was elected a fellow of the Royal Society early in 1712, sat in the same year on the committee for adjudicating the claims of Sir Isaac

**Newton**and Gottfried Wilhelm Leibnitz, and acted as secretary to the society from the 13th of January 1714 to the 21st of October 1718.As a mathematician, he was the only Englishman after Sir Isaac

**Newton**and Roger Cotes capable of holding his own with the Bernoullis; but a great part of the effect of his demonstrations was lost through his failure to express his ideas fully and clearly.As has been justly said, if

**Newton**once suffered a cerebral attack without forfeiting our veneration for the Principia, Comte may have suffered in the same way, and still not have forfeited our respect for Positive Philosophy and Positive Polity.The binomial theorem is a celebrated theorem, originally due to Sir Isaac

**Newton**, by which any power of a binomial can be expressed as a series.Leibnitz, although

**Newton**had discovered it some years previously.**Newton**gave no proof, and it was in the Ars Conjectandi (1713) that James Bernoulli's proof for positive integral values of the exponent was first published, although Bernoulli must have discovered it many years previously.**Newton**is a burgh or barony of very ancient creation, the charter of which is traditionally said to have been granted by Robert Bruce in favour of forty-eight of the inhabitants who had distinguished themselves at Bannockburn.**Newton**and Dr Samuel Clarke is laid open, 1732; Glory or Gravity, 1733; The Religion of Satan, or Antichrist Delineated, 1736.At present we are where we were in electrical science, when

**Newton**produced curious sparks while rubbing glass with paper.His first wife was Mary, daughter of William Staunton of Staunton; and his second was Jane, daughter of Sir John

**Newton**.A follower of the positive philosophy, but in conflict with Richard Congreve as to details, he led the Positivists who split off and founded

**Newton**Hall in 1881, and he was president of the English Positivist Committee from 1880 to 1905; he was also editor and part author of the Positivist New Calendar of Great Men (1892), and wrote much on Comte and Positivism.The Chronology of Ancient Kingdoms amended, by Sir Isaac

**Newton**, remarkable as an attempt to construct a system on new bases, independent of the Greek chronologers.Jacques Bernoulli cannot be strictly called an independent discoverer; but, from his extensive and successful application of the calculus and other mathematical methods, he is deserving of a place by the side of

**Newton**and Leibnitz.He was as keen in his resentments as he was ardent in his friendships; fondly attached to his family, he yet disliked a deserving son; he gave full praise to Leibnitz and Leonhard Euler, yet was blind to the excellence of Sir Isaac

**Newton**.**Newton**defined the diameter of a curve of any order as the locus of the centres of the mean distances of the points of intersection of a system of parallel chords with the curve; this locus may be shown to be a straight line.He took orders in 1713; and the same year, at the request of Dr Richard Bentley, he published the second edition of

**Newton**'s Principia with an original preface.The exceptional genius of Cotes earned encomiums from both his contemporaries and successors; Sir Isaac

**Newton**said, "If Mr Cotes had lived, we should have known something."Under this method might be classed the expositions of Luther, Osiander, Striegel, Flacius, Gerhard and Calovius; and English writers such as Napier, Mede and

**Newton**.According to the census of 1900 there were 33 incorporated cities in Massachusetts, of which 8 had between 12,000 and 20,000 inhabitants; 5 between 20,000 and 25,000 (Everett, North Adams, Quincy, Waltham, Pittsfield); 2 io between 25,000 and 50,000 (Holyoke, Brockton, Haverhill, Salem, Chelsea, Malden,

**Newton**, Fitchburg, Taunton, Gloucester); 7 between 50,000 and ioo,000 (Lowell, Cambridge, Lynn, Lawrence, New Bedford, Springfield, Somerville); and 3 more than roo,000 inhabitants, viz.There are schools, of theology at Cambridge (Protestant Episcopal),

**Newton**(Baptist) and Waltham (New Church), as well as in connexion with Boston University (Methodist), Tufts College (Universalist) and Harvard (non-sectarian, and the affiliated Congregational Andover Theological Seminary at Cambridge).In 1718 Sir Isaac

**Newton**was made master of the Mint, and in that capacity as contractor for the coinage he amassed a considerable fortune.He also published a critical account of the system of Sir Isaac

**Newton**in French in 1743He supposed that in air Boyle's law holds in the extensions and compressions, or that p = kp, whence dp/dp = k = p/p. His value of the velocity in air is therefore U = iJ (p ip.) (

**Newton**'s formula).Sir Isaac

**Newton**introduced several important improvements into the Cambridge edition of 1672; in 1715 Dr Jurin issued another Cambridge edition with a valuable appendix; in 1733 the whole work was translated into English by Dugdale; and in 1736 Dugdale's second edition was revised by Shaw.The next years were much occupied with scientific work, especially the study of heat, light and electricity, on which he presented memoirs to the Academie des Sciences, but the academicians were horrified at his temerity in differing from

**Newton**, and, though acknowledging his industry, would not receive him among them.The results of his leisure were in 1787 a new translation of

**Newton**'s Optics, and in 1788 his Memoires academiques, ou nouvelles decouvertes sur la lumiere.**Newton**himself, however, endeavoured to account for gravitation by differences of pressure in an aether; but he did not publish his theory, ` because he was not able from experiment and observation to give a satisfactory account of this medium, and the manner of its operation in producing the chief phenomena of nature.'It could hardly have been thought of before Sir Isaac

**Newton**'s discovery of the actual facts regarding universal gravitation.In this belief he differed from his pupil, Roger Cotes, and from most of the great mathematical astronomers of the 18th century, who worked out in detail the task sketched by the genius of

**Newton**.Through the influence of Sir Isaac

**Newton**he was elected mathematical master in Christ's hospital.Although the method had been approved by Sir Isaac

**Newton**before being presented to the Board of Longitude, and successfully practised in finding the longitude between Paris and Vienna, the board determined against it.Latin was also used in works on science and philosophy, such as Sir Isaac

**Newton**'s Principia (1687), and many of the works of Leibnitz (1646-1705).The urban district (formed in 1893) is conterminous with the civil parish of

**Newton**Nottage, which, in addition to Porthcawl proper, built on the sea-front, comprises the ancient village of Nottage, 1 m.The natural harbour of

**Newton**(as it used to be called) was improved by a breakwater, and was connected by a tramway with Maesteg, whence coal and iron were brought for shipment.In 1867 he entered the British Museum as an assistant in the department of Greek and Roman antiquities under Sir Charles

**Newton**, whom he succeeded in 1886.The invention of logarithms and the calculation of the earlier tables form a very striking episode in the history of exact science, and, with the exception of the Principia of

**Newton**, there is no mathematical work published in the country which has produced such important consequences, or to which so much interest attaches as to Napier's Descriptio.The final step was made by John

**Newton**in his Trigononometria Britannica (1658), a work which is also noticeable as being the only extensive eightfigure table that until recently had been published; it contains logarithms of sines, &c., as well as logarithms of numbers.If we consider only the logarithms of numbers, the main line of descent from the original calculation of Briggs and Vlacq is Roe, John

**Newton**, Sherwin, Gardiner; there are then two branches, viz.Napier's original work, the Descriptio Canonis of 1614, contained, not logarithms of numbers, but logarithms of sines, and the relations between the sines and the logarithms were explained by the motions of points in lines, in a manner not unlike that afterwards employed by

**Newton**in the method of fluxions.Besides Napier and Briggs, special reference should be made to Kepler (Chilias, 1624) and Mercator (Logarithmotechnia, 1668), whose methods were arithmetical, and to

**Newton**, Gregory, Halley and Cotes, who employed series.This method was employed by Sir Isaac

**Newton**, whose experiments constitute the earliest systematic investigation of the phenomenon.In an experiment similar to that here represented,

**Newton**made a small hole in the screen and another small hole in a second screen placed behind the first.**Newton**also made use of the method of crossed prisms, which has been found of great use in studying dispersion.By studying the dispersion of colours in water, turpentine and crown glass

**Newton**was led to suppose that dispersion is proportional to refraction.There are several houses of interest, notably the Priory and Dr Awbrey's residence (now called Buckingham House), both built about the middle of the 16th century, but the finest specimen is

**Newton**(about a mile out, near Llanfaes) built in 1582 by Sir John Games (a descendant of Sir David Gam), but now a farmhouse.**Newton**to enable a fairly complete restoration of its design to be made.The original one, made by

**Newton**and Pullan, is obviously in error in many respects; and that of Oldfield, though to be preferred for its lightness (the Mausoleum was said anciently to be "suspended in mid-air"), does not satisfy the conditions postulated by the remains.These precise conditions were afterwards demonstrated by

**Newton**to follow necessarily from the law of gravitation.This problem, also termed the " Apollonian problem," was demonstrated with the aid of conic sections by Apollonius in his book on Contacts or Tangencies; geometrical solutions involving the conic sections were also given by Adrianus Romanus, Vieta,

**Newton**and others.As far as the circlesquaring functions are concerned, it would seem that Gregory was the first (in 1670) to make known the series for the arc in terms of the tangent, the series for the tangent in terms of the arc, and the secant in terms of the arc; and in 1669

**Newton**showed to Isaac Barrow a little treatise in manuscript containing the series for the arc in terms of the sine, for the sine in terms of the arc, and for the cosine in terms of the arc. These discoveries 1 See Euler, ” Annotationes in locum quendam Cartesii," in Nov.Probably there was as much foundation for this legend as for the more rationalistic explanation of William

**Newton**(Display of Heraldry, p. 145), that the fleur-de-lis was the figure of a reed or flag in blossom, used instead of a sceptre at the proclamation of the Frankish kings.By some of the students and tutors, by Liddell,

**Newton**, Acland and others, he was regarded as a youth of rare promise, and he made some lifelong friendships with men of mark and of power.In 1869 he issued the Queen of the Air, lectures on Greek myths, a subject he now took up, with some aid from the late Sir C.

**Newton**.The Copernican theory of the solar system - that the earth revolved annually about the sun - had received confirmation by the observations of Galileo and Tycho Brahe, and the mathematical investigations of Kepler and

**Newton**.This brought him to another difference from Leibnitz as well as from

**Newton**.Lotze's metaphysics is thus distinguished from the theism of

**Newton**and Leibnitz by its pantheism, and from the pantheism of Spinoza by its idealism.This view involves the denial of force as a cause, and the assertion that all we know about force is that the acceleration of one mass depends on that of another, as in mathematics a function depends on a variable; and that even

**Newton**'s third law of motion is merely a description of the fact that two material points determine in one another, without reciprocally causing, opposite accelerations.Now, Mach applies these preconceived opinions to " mechanics in its development," with the result that, though he shows much skill in mathematical mechanics, he misrepresents its development precisely at the critical point of the discovery of

**Newton**'s third law of motion.He quotes as an instance that

**Newton**in this way added to the planetary appearances contained in Kepler's laws the gravitation of the planets to the sun, as a notion of causality not contained in the appearances, and thus discovered that gravitation is the cause of the appearances.But

**Newton**had already discovered beforehand in the mechanics of terrestrial bodies that gravitation constantly causes similar facts on the earth, and did not derive that cause from any logical ground beyond experience, any more than he did the third law of motion.His taste for mathematics early developed itself; and he acquired Latin that he might study

**Newton**'s Principia.He graduated in 1856 at the Biblical Institute at Concord, New Hampshire (now a part of Boston University), became a minister in the Episcopal Church in 1857, and during the next three years was a rector first at North Adams, and then at

**Newton**Lower Falls, Mass.**Newton**is the centre of the settlements of the German-Russian Mennonites, a thrifty people, who immigrated in 1873 and subsequently; Bethel College (opened 1893) is a Mennonite secondary school, and there is a Mennonite hospital.**Newton**is a supply and distributing point for the surrounding agricultural and stock-raising region, and has various manufactures.**Newton**was first settled in 1871, was chartered as a city in 1872, and in 1910 adopted a commission form of government.In 1609 and 1619 Kepler published his new laws of planetary motion, which were subsequently shown by

**Newton**to agree with the results obtained by experiment for the motion of terrestrial bodies.We owe to

**Newton**(1642-1727) the consolidation of the views which were current in his time into one coherent and universal Galileo- system, sometimes called the Galileo-**Newton**theory,**Newton**Theory.**Newton**assumed the possibility of choosing a base such that, relatively to it, the motion of any particle would have only such divergence from uniform velocity in a straight line as could be expressed by laws of acceleration dependent on its relation to other bodies.Assuming such a base to exist,

**Newton**admitted at the outset the difficulty of identifying it, but pointed out that the key to the situation might be found in the identification of forces; that is to say, in the mutual character of laws of acceleration as applied to any given body and any other by whose presence its motion is influenced.**Newton**tells us that this agreement led him to adopt the law of the inverse square of the distance about 1665-1666, before Huygens's results as to circular motion had been published.There are indications of this having been

**Newton**'s own view.**Newton**called attention to the fact that a falling body moves in a curve, diverging slightly from the plumb-line vertical.**Newton**dealt with the question at the beginning of the Principia, distinguishing what he called "absolute time" from such measures of time as would be afforded by any particular examples of motion; but he did not give any clear definition.The most important extension of the principles of the subject since

**Newton**'s time is to be found in the development of the of theory of energy, the chief value of which lies in the Theory Energy.The importance of a study of the changes of the vis viva depending on squares of velocities, or what is now called the "kinetic energy" of a system, was recognized in

**Newton**'s time, especially by Leibnitz; and it was perceived (at any rate for special cases) that an increase in this quantity in the course of any motion of the system was otherwise expressible by what we now call the "work" done by the forces.It is served by the Chicago & North-Western (which has construction and repair shops here), the Chicago, Milwaukee & St Paul, and the

**Newton**& North-Western railways, and by the Fort Dodge, Des Moines & Southern (inter-urban) railway, of which it is the headquarters.**Newton**in 1857-1858; but of recent years it has become a frequent calling station of touring steamers, which can still lie safely in the southern harbour.**Newton**discovered a fine seated statue of Demeter, which now adorns the British Museum; and about 3 m.Benjamin Wills

**Newton**, head of the community there, who had been a fellow of Exeter College, Oxford, was accused of departing from the testimony of the Brethren by reintroducing the spirit of clericalism.The majority of the Brethren out of Plymouth supported Darby, but a minority remained with

**Newton**.The separation became wider in 1847 on the discovery of supposed heretical teaching by

**Newton**.The Bethesda congregation at Bristol, where George Muller was the most influential member, received into communion several of

**Newton**'s followers and justified their action.Out of this came the separation into Neutral Brethren, led by Muller, and Exclusive Brethren or Darbyites, who refused to hold communion with the followers of

**Newton**or Muller.Sir Isaac

**Newton**appears to have been the first to use a glass globe instead of sulphur (Optics, 8th Query).In 1669 he resigned his mathematical chair to his pupil, Isaac

**Newton**, having now determined to renounce the study of mathematics for that of divinity.By his English contemporaries Barrow was considered a mathematician second only to

**Newton**.He was undoubtedly a clear-sighted and able mathematician, who handled admirably the severe geometrical method, and who in his Method of Tangents approximated to the course of reasoning by which

**Newton**was afterwards led to the doctrine of ultimate ratios; but his substantial contributions to the science are of no great importance, and his lectures upon elementary principles do not throw much light on the difficulties surrounding the border-land between mathematics and philosophy.A state normal school (the first normal school in the United States, established at Lexington in 1839, removed to

**Newton**in 1844 and to Framingham in 1853) is situated here; and near South Framingham, in the township of Sherborn, is the state reformatory prison for women.The combustibility of the diamond was predicted by Sir Isaac

**Newton**on account of its high refractive power; it was first established experimentally by the Florentine Academicians in 1694.Taking

**Newton**'s law of cooling that the rate of loss of heat is simply proportional to the excess of temperature, the emissivity would be independent of the temperature.The conductivity of the same bars was independently determined by the method of Forbes, employing an ingenious formula for the heat-loss in place of

**Newton**'s law.The consequence was that, when not spending himself in vain attempts to solve the impossible problems that have always waylaid the fancy of self-sufficient beginners, he took an interest only in the elements of geometry, and never had any notion of the full scope of mathematical science, undergoing as it then was (and not least at the hands of Wallis) the extraordinary development which made it before the end of the century the potent instrument of physical discovery which it became in the hands of

**Newton**.There is more than one meaning of John

**Newton**discussed in the 1911 Encyclopedia.In 1727 also he succeeded Sir Isaac

**Newton**in the presidential chair of the Royal Society; he retired from it at the age of eighty.Rasselas and Imlac, Nekayah and Pekuah, are evidently meant to be Abyssinians of the 18th century; for the Europe which Imlac describes is the Europe of the 18th century, and the inmates of the Happy Valley talk familiarly of that law of gravitation which

**Newton**discovered and which was not fully received even at Cambridge till the 18th century.His Letters from Prison were an earlier Cardiphonia than John

**Newton**'s.Ray's quiet college life closed when he found himself unable to subscribe to the Act of Uniformity of 1661, and was obliged to give up his fellowship in 1662, the year after Isaac

**Newton**had entered the college.A year at the Ackworth school, two years at a school at York, and a year and a half at

**Newton**, near Clitheroe, completed his education.His later works include "Pioneer Monument," Salt Lake City; "Sir Isaac

**Newton**," Congressional Library, Washington; and "Don Quixote."**Newton**himself regarded this as probably incorrect.Proceeding to England, he was introduced to Sir Isaac

**Newton**, who found in him one of the earliest defenders of his discoveries.The Principia mathematica of Sir Isaac

**Newton**, which chance threw in his way, caused him to prosecute his studies with vigour, and he soon became distinguished among first-rate mathematicians.He was among the intimate personal friends of

**Newton**, and his eminence and abilities secured his admission into the Royal Society of London in 1697, and afterwards into the Academies of Berlin and Paris.This work was first printed in 1618, in 4to, and dedicated to Sir Isaac

**Newton**.These curves were investigated by Rene Descartes, Sir Isaac

**Newton**, Colin Maclaurin and others.The cartesian parabola is a cubic curve which is also known as the trident of

**Newton**on account of its three-pronged form.**Newton**discussed the five forms which arise from the relations of the roots of the cubic equation.The school, however, produced few, if any, great mathematicians between

**Newton**and George Green.In astronomy he depreciates the merits of

**Newton**and elevates Kepler, accusing**Newton**particularly, a propos of the distinction of centrifugal and centripetal forces, of leading to a confusion between what is mathematically to be distinguished and what is physically separate.As to colour, he follows Goethe, and uses strong language against

**Newton**'s theory, for the barbarism of the conception that light is a compound, the incorrectness of his observations, &c. In chemistry, again, he objects to the way in which all the chemical elements are treated as on the same level.At Woolwich he remained until 1870, and although he was not a great success as an elementary teacher, that period of his life was very rich in mathematical work, which included remarkable advances in the theory of the partition of numbers and further contributions to that of invariants, together with an important research which yielded a proof, hitherto lacking, of

**Newton**'s rule for the discovery of imaginary roots for algebraical equations up to and including the fifth degree.Formerly classified by the ancient Greeks with halos, rainbows, &c., under the general group of "meteors," they came to receive considerable attention at the hands of Descartes, Christiaan Huygens, and Sir Isaac

**Newton**; but the correct explanation of coronae was reserved until the beginning of the 19th century, when Thomas Young applied the theories of the diffraction and interference of light to this phenomenon.**Newton**'s fusible metal (named after Sir Isaac**Newton**) contains 50 parts of bismuth, 31.25 of lead and 18.75 of tin; that of Jean Darcet (1725-1801), 50 parts of bismuth with 25 each of lead and tin; and that of Valentin Rose the elder, so of bismuth with 28 1 of lead and 24 I of tin.Having reached so far as to perceive that the central force of the solar system must decrease inversely as the square of the distance, and applied vainly to Wren and Hooke for further elucidation, he made in August 1684 that journey to Cambridge for the purpose of consulting

**Newton**, which resulted in the publication of the Principia.But, as has been remarked by Dr Robert Grant (History of Physical Astronomy, p. 515), we are no more warranted in drawing so important a conclusion from casual remarks, however sagacious, than we should be justified in stating that Seneca was in possession of the discoveries of

**Newton**because he predicted that comets would one day be found to revolve in periodic orbits.Until

**Newton**'s discovery of the different refrangibility of light of different colours, it was generally supposed that object-glasses of telescopes were subject to no other errors than those which arose from the spherical figure of their surfaces, and the efforts of opticians were chiefly directed to the construction of lenses of other forms of curvature.**Newton**was the first to construct a reflecting telescope.**Newton**'s first telescope so far realized his expectations that he could see with its aid the satellites of Jupiter and the horns of Venus.After remarking that

**Newton**'s telescope "had lain neglected these fifty years," they stated that Hadley had sufficiently shown "that this noble invention does not consist in bare theory."He did not doubt the accuracy of

**Newton**'s.Klingenstierna showed from purely geometrical considerations, fully appreciated by Dollond, that the results of

**Newton**'s experiments could not be brought into harmony with other universally accepted facts.The whole history of his researches proves how fully he was aware of the conditions necessary for the attainment of achromatism in refracting telescopes, and he may be well excused if he so long placed implicit reliance on the accuracy of experiments made by so illustrious a philosopher as

**Newton**.The composition of metallic specula in the present day differs very little from that used by Sir Isaac

**Newton**.The philosophy of Descartes was the reigning system at the university; Clarke, however, mastered the new system of

**Newton**, and contributed greatly to its extension by publishing an excellent Latin version of the Traite de physique of Jacques Rohault (1620-1675) with valuable notes, which he finished before he was twenty-two years of age.Clarke's translation (1697) continued to be used as a text-book in the university till supplanted by the treatises of

**Newton**, which it had been designed to introduce.He also wrote at this time a translation of

**Newton**'s Optics, for which the author presented him with Soo.In 1727, on the death of Sir Isaac

**Newton**, he was offered by the court the place of master of the mint, worth on an average from £1200 to £1500 a year.Dr Warton, in his observations upon Pope's line, "Unthought-of frailties cheat us in the wise," says, "Who could imagine that Locke was fond of romances; that

**Newton**once studied astrology; that Dr Clarke valued himself on his agility, and frequently amused himself in a private room of his house in leaping over the tables and chairs ?"Clarke has been generally supposed to have derived the opinion that time and space are attributes of an infinite immaterial and spiritual being from the Scholium Generale, first published in the second edition of

**Newton**'s Principia (1714).The view propounded by Clarke may have been derived from the Midrash, the Kabbalah, Philo, Henry More, or Cudworth, but not from

**Newton**.**Newton**, according to Dr Pemberton, thought in 1666 that the moon moves so like a falling body that it has a similar centripetal force to the earth, 20 years before he demonstrated this conclusion from the laws of motion in the Principia.But the full value of the ancient theory of these processes cannot be appreciated until we recognize that as Aristotle planned them

**Newton**used them.Much of the Principia consists of synthetical deductions from definitions and axioms. But the discovery of the centripetal force of the planets to the sun is an analytic deduction from the facts of their motion discovered by Kepler to their real ground, and is so stated by

**Newton**in the first regressive order of Aristotle - P-M, S-P, S-M.**Newton**did indeed first show synthetically what kind of motions by mechanical laws have their ground in a centripetal force varying inversely as the square of the distance (all P is M); but his next step was, not to deduce synthetically the planetary motions, but to make a new start from the planetary motions as facts established by Kepler's laws and as examples of the kind of motions in question (all S is P); and then, by combining these two premises, one mechanical and the other astronomical, he analytically deduced that these facts of planetary motion have their ground in a centripetal force varying inversely as the squares of the distances of the planets from the sun (all S is M).It is noticeable that Wundt quotes

**Newton**'s discovery of the centripetal force of the planets to the sun as an instance of this supposed hypothetical, analytic, inductive method; as if**Newton**'s analysis were a hypothesis of the centripetal force to the sun, a deduction of the given facts of planetary motion, and a verification of the hypothesis by the given facts, and as if such a process of hypothetical deduction could be identical with either analysis or induction.Mill confused

**Newton**'s analytical deduction with hypothetical deduction; and thereupon Jevons confused induction with both.S-M, of which

**Newton**has left so conspicuous an example in his Principia.Really, we first experience that particular causes have particular effects; then induce that causes similar to those have effects similar to these; finally, deduce that when a particular cause of the kind occurs it has a particular effect of the kind by synthetic deduction, and that when a particular effect of the kind occurs it has a particular cause of the kind by analytic deduction with a convertible premise, as when

**Newton**from planetary motions, like terrestrial motions, analytically deduced a centripetal force to the sun like centripetal forces to the earth.It was because the aftermath of Newtonian science was so rich that the scientific faith of naturalism was able to retain a place besides its epistemological creed that a logician of the school could arise whose spirit was in some sort Baconian, but who, unlike Bacon, had entered the modern world, and faced the problems stated for it by Hume and by

**Newton**.His New Theory of the Earth (1696), although destitute of sound scientific foundation, obtained the praise of both

**Newton**and Locke, the latter of whom justly classed the author among those who, if not adding much to our knowledge, "at least bring some new things to our thoughts."In 1701 he resigned his living to become deputy at Cambridge to Sir Isaac

**Newton**, `Thom two years later he succeeded as Lucasian professor of mathematics.He attacked Sir Isaac

**Newton**'s chronological system with success; but he himself lost not only time but money in an endeavour to discover the longitude.After the Conquest Wigan was part of the barony of

**Newton**, and the church was endowed with a carucate of land, the origin of the manor.Some time before Henry III.'s reign the baron of

**Newton**granted to the rector of Wigan the manorial privileges.Sir Isaac

**Newton**substituted a ball of glass for sulphur in the electrical machine and made other not unimportant additions to electrical knowledge.Bacon has frequently been disparaged on the ground that his name is not mentioned by Sir Isaac

**Newton**.In 1883 the Cyprus Museum was founded by private enterprise, and on its behalf Max Ohnefalsch-Richter, who had already made trial diggings for Sir Charles

**Newton**and the British Museum, excavated sanctuaries at Voni and Kythrea (Chytri), and opened tombs on some other sites.This theory of complementary colours as due to the polarity in the qualitative action of the retina is followed by some criticism of

**Newton**and the seven colours, by an attempt to explain some facts noted by Goethe, and by some reference to the external stimuli which cause colour.**Newton**failed to perceive the existence of media of different dispersive powers required by achromatism; consequently he constructed large reflectors instead of refractors.In 1839 a state normal school for women (the first in Massachusetts and the first public training school for teachers in the United States) was opened at Lexington; it was transferred to West

**Newton**in 1844 and to Framingham in 1853.These rapidly descend in

**Newton**'s scale and at last disappear, showing that the thickness of the film is less than the tenth part of the length of a wave of light.Its status was only that of a "creek" in the port of Cardiff till 1685, when it was made an independent port with jurisdiction over

**Newton**(now Porthcawl), Neath or Briton Ferry and South Burry, its limits being defined in 1847 as extending from Nash Point on the east to Whitford Point on the west, but in 1904 Port Talbot, which was included in this area, was made into a separate port.In physics, Descartes had prepared the way for the final triumph of the mechanical explanation of the world in

**Newton**'s system.Whatever may be the future history of his other views, he will always be remembered as an originator of a principle more illuminating than any which has appeared since the days of

**Newton**, as one of its two discoverers whose scientific rivalry was only the beginning of a warm and unbroken friendship.It seems certain that these conclusions were independent of Berkeley and Malebranche, and were not drawn from Arthur Collier's Clavis universalis (1713), with which they have much in common, but were suggested, in part at least, by Locke's doctrine of ideas,

**Newton**'s theory of colours, and Cudworth's Platonism, with all of which Edwards was early familiar.Tripoli is quarried particularly in

**Newton**county, where it has been produced since 1872, and though not produced in great quantities has value from its general scarcity.The Life of Bishop White Kennett, by the Rev. William

**Newton**(anonymous), appeared in 1730.But, two years before, he had accidentally fallen in with a Latin copy of Euclid, which he eagerly devoured; and at twelve he attacked

**Newton**'s Arithmetica universalis.But they contain what is far more valuable still, the greatest addition which dynamical science had received since the grand strides made by Sir Isaac

**Newton**and Joseph Louis Lagrange.His father (also Isaac

**Newton**) who farmed a small freehold property of his own, died before his son's birth, a few months after his marriage to Hannah Ayscough, a daughter of James Ayscough of Market-Overton.When

**Newton**was little more than two years old his mother married Barnabas Smith, rector of North Witham.Of this marriage there was issue, Benjamin, Mary and Hannah Smith, and to their children Sir Isaac

**Newton**subsequently left the greater part of his property.After having acquired the rudiments of education at two small schools in hamlets close to Woolsthorpe,

**Newton**was sent at the age of twelve to the grammar school of Grantham.While attending Grantham school

**Newton**lived in the house of Mr Clark, an apothecary of that town.An unprovoked attack from the boy next above him led to a fight, in which

**Newton**'s pluck gave him the victory.In 1656 Mr Smith died, and

**Newton**'s mother came back with her three children to Woolsthorpe.**Newton**was then in his fifteenth year, and, as his mother in all probability intended him to be a farmer, he was taken away from school.He was frequently sent on market days to Grantham with an old and trusty servant, who made all the purchases, while

**Newton**spent his time among the books in Mr Clark's house.It soon became apparent to

**Newton**'s relatives that they were making a great mistake in attempting to turn him into a farmer, and he was therefore sent back again to school at Grantham.His mother's brother, William Ayscough, the rector of Burton Coggles, the next parish, was a graduate of Trinity College, Cambridge, and when he found that

**Newton**'s mind was wholly devoted to mechanical and mathematical problems, he urged upon Mrs Smith the desirability of sending her son to his own college.**Newton**tells us himself that, when he had purchased a book on astrology at Stourbridge fair, a fair held close to Cambridge, he was unable, on account of his ignorance of trigonometry, to understand a figure of the heavens which was drawn in this book.It is reported that in his examination for a scholarship at Trinity, to which he was elected on the 28th of April 1664, he was examined in Euclid by Dr Isaac Barrow, who formed a poor opinion of his knowledge, and that in consequence

**Newton**was led to read the Elements again with care, and thereby to form a more favourable estimate of Euclid's merits.The study of Descartes's Geometry seems to have inspired

**Newton**with a love of the subject, and to have introduced him to the higher mathematics.That

**Newton**must have begun early to make careful observations of natural phenomena is sufficiently testified by the following remarks about halos, which appear in his Optics, book ii.In January 1665

**Newton**took the degree of B.A.The persons appointed (in conjunction with the proctors, John Slade of Catharine Hall, and Benjamin Pulleyn of Trinity College,

**Newton**'s tutor) to examine the questionists were John Eachard of Catharine Hall and Thomas Gipps of Trinity College.It is supposed that it was in 1665 that the method of fluxions first occurred to

**Newton**'s mind.There are several papers still existing in

**Newton**'s handwriting bearing dates 1665 and 1666 in which the method is described, in some of which dotted or dashed letters are used to represent fluxions, and in some of which the method is explained without the use of dotted letters.**Newton**must have left college before August 1665, as his name does not appear in the list of those who received extra commons on that occasion, and he tells us himself in the extract from his commonplace book already quoted that he was " forced from Cambridge by the plague " in the summer of that year.A few weeks after his election to a fellowship

**Newton**went to Lincolnshire, and did not return to Cambridge till the February following.During the years 1666 to 1669

**Newton**'s studies were of a very varied kind.In a subsequent letter on the 10th of August, Barrow expressed his pleasure at hearing the favourable opinion which Collins had formed of the paper, and added, " the name of the author is

**Newton**, a fellow of our college, and a young man, who is only in his second year since he took the degree of master of arts, and who, with an unparalleled genius (eximio quo est acumine), has made very great progress in this branch of mathematics."The subject which

**Newton**chose for his lectures was optics.At the meeting at which

**Newton**was elected a description of a reflecting telescope which he had invented was read, and " it was ordered that a letter should be written by the secretary to Mr**Newton**to acquaint him of his election into the Society, and to thank him for the communication of his telescope, and to assure him that the Society would take care that all right should be done him with respect to this invention."The promise here made was fulfilled in a communication which

**Newton**addressed to Henry Oldenburg, the secretary of the Royal Society, on the 6th of February 1672, and which was read before the society two days afterwards.The publication of these discoveries led to a series of controversies which lasted for several years, in which

**Newton**had to contend with the eminent English natural philosopher Robert Hooke; Lucas, mathematical professor at Liege; Linus, a physician in Liege, and many others.Others criticized the experiments, saying that the length of the spectrum was never more than three and a half times the breadth, whereas

**Newton**found it to be five times the breadth.It appears that

**Newton**made the mistake of supposing that all prisms would give a spectrum of exactly the same length; the objections of his opponents led him to measure carefully the lengths of spectra formed by prisms of different angles and of different refractive indices; and it seems strange that he was not led thereby to the discovery of the different dispersive powers of different refractive substances.It was a fortunate circumstance that these disputes did not so thoroughly damp

**Newton**'s ardour as he at the time felt they would.This discovery was communicated by him to Edmund Halley in 17bo, but was not published, or communicated to the Royal Society, till after

**Newton**'s death, when a description of it was found among his papers.In March 1673

**Newton**took a prominent part in a dispute in the university.On the morning of the election a protest in which

**Newton**'s name appeared was read, and entered in the Regent House.But the vice-chancellor admitted Paman the same morning, and so ended the first contest of a non-scientific character in which

**Newton**took part.Nothing further seems to have been done in the matter until the 28th of January 1675, when Oldenburg informed " the Society that Mr

**Newton**is now in such circumstances that he desires to be excused from the weekly payments."On the 18th of February 1675

**Newton**was formally admitted into the Society.The most probable explanation of the cause why

**Newton**wished to be excused from these payments is to be found in the fact that, as he was not in holy orders, his fellowship at Trinity College would lapse in the autumn of 1675.This must have relieved

**Newton**'s mind from a great deal of anxiety about pecuniary matters, as we find him in November 1676 subscribing £40 towards the building of the new library of Trinity College.It is supposed that it was at Woolsthorpe in the summer of 1666 that

**Newton**'s thoughts were directed to the subject of gravity.He had his information from

**Newton**'s favourite niece Catharine Barton, who married Conduitt, a fellow of the Royal Society, and one of**Newton**'s intimate friends.The fact that heavy bodies have always a tendency to fall to the earth, no matter at what height they are placed above the earth's surface, seems to have led

**Newton**to conjecture that it was possible that the same tendency to fall to the earth was the cause by which the moon was retained in its orbit round the earth.**Newton**, by calculating from Kepler's laws, and supposing the orbits of the planets to be circles round the sun in the centre, had already proved that the force of the sun acting upon the different planets must vary as the inverse square of the distances of the planets from the sun.**Newton**regarded the discrepancy between the results as a proof of the inaccuracy of his conjecture, and " laid aside at that time any further thoughts of this matter."But in 1679 a controversy between Hooke and

**Newton**, about the form of the path of a body falling from a height, taking the motion of the earth round its axis into consideration, led**Newton**again to revery() his former conjectures on the moon.It is probable that

**Newton**had become acquainted with this measurement of Picard's, and that he was therefore led to make use of it when his thoughts were redirected to the subject.It appears that Hooke professed to have a solution of the problem of the path of .a body moving round a centre of force attracting as the inverse square of the distance; but Halley, finding, after a delay of some months, that Hooke " had not been so good as his word " in showing his solution to Wren, started in the month of August 1684 for Cambridge to consult

**Newton**on the subject.Without mentioning the speculations which had been made, he asked

**Newton**what would be the curve described by a planet round the sun on the assumption that the sun's force diminished as the square of the distance.**Newton**replied promptly, "an ellipse," and on being questioned by Halley as to the reason for his answer he replied, " Why, I have calculated it."After the latter had left Cambridge,

**Newton**set to work to reproduce the calculation.In the following November

**Newton**redeemed his promise to Halley by sending him, by the hand of Mr Paget, one of the fellows of his own college, and at that time mathematical master of Christ's Hospital, a copy of his demonstration; and very soon afterwards Halley paid another visit to Cambridge to confer with**Newton**about the problem; and on his return to London on the 10th of December 1684, he informed the Royal Society " that he had lately seen Mr**Newton**at Cambridge, who had showed him a curious treatise De Motu," which at Halley's desire he promised to send to the Society to be entered upon their register.By the middle of February

**Newton**had sent his paper to Aston, one of the secretaries of the Society, and in a letter to Aston dated the 23rd of February 1685, we find**Newton**thanking him for " having entered on the register his notions about motion."It was in them that

**Newton**composed almost the whole of his great work.During this period

**Newton**had a very extensive correspondence with John Flamsteed, who was then the astronomer-royal.Many of the letters are lost, but it is clear from one of

**Newton**'s, dated the 19th of September 1685, that he had received many useful communications from Flamsteed, and especially regarding Saturn, " whose orbit, as defined by Kepler,"**Newton**" found too little for the sesquialterate proportions."On this last point the information supplied by Flamsteed was peculiarly gratifying to

**Newton**; and it is obvious from the language of this part of his letter that he had still doubts of the universal application of the sesquialteral proportion.Upon

**Newton**'s return from Lincolnshire in the beginning of April 1685, he seems to have devoted himself to the preparation of his work.Excepting in the correspondence with Flamsteed we hear nothing more of the preparation of the Principia until the 21st of April 1686, when Halley read to the Royal Society his Discourse concerning Gravity and its Properties, in which he states " that his worthy countryman Mr Isaac

**Newton**has an incomparable treatise of motion almost ready for the press," and that the law of the inverse square " is the principle on which Mr**Newton**has made out all the phenomena of the celestial motions so easily and naturally, that its truth is past dispute."At the next meeting of the Society, on the 28th of April, " Dr Vincent presented to the Society a manuscript treatise entitled Philosophiae Naturalis Principia Mathematica, and dedicated to the Society by Mr Isaac

**Newton**."Although this manuscript contained only the first book, yet such was the confidence the Society placed in the author that an order was given " that a letter of thanks be written to Mr

**Newton**; and that the printing of his book be referred to the consideration of the council; and that in the meantime the book be put into the hands of Mr Halley, to make a report thereof to the council."At the next meeting of the Society, on the igth of May, some dissatisfaction seems to have been expressed at the delay, as it was ordered " that Mr

**Newton**'s work should be printed forthwith in quarto, and that a letter should be written to him to signify the Society's resolutions, and to desire his opinion as to the print, volume, cuts and so forth."Three days afterwards Halley communicated the resolution to

**Newton**, and stated to him that the printing was to be at the charge of the Society.At the next meeting of the council, on the 2nd of June, it was again ordered " that Mr

**Newton**'s book be printed," but, instead of sanctioning the resolution of the general meeting to print it at their charge, they added " that Mr Halley undertake the business of looking after it, and printing it at his own charge, which he engaged to do."In order to explain to

**Newton**the cause of the delay, Halley in his letter of the 22nd of May alleges that it arose from " the president's attendance on the king, and the absence of the vicepresidents, whom the good weather had drawn out of town"; but there is reason to believe that this was not the true cause, and that the unwillingness of the council to undertake the publication arose from the state of the finances of the Society.In the same letter Halley found it necessary to inform

**Newton**of Hooke's conduct when the manuscript of the Principia was presented to the Society.Halley only communicated to

**Newton**the fact " that Hooke had some pretensions to the invention of the rule for the decrease of gravity being reciprocally as the squares of the distances from the centre," acknowledging at the same time that, though**Newton**had the notion from him, " yet the demonstration of the curves generated thereby belonged wholly to**Newton**."In thus appealing to

**Newton**'s candour, Halley obviously wished that some acknowledgment of Hooke should be made.On the 30th of June 1686 the president was desired by the council to license

**Newton**'s book, entitled Philosophiae Naturalis Principia Mathematica.On the 14th of July 1686

**Newton**wrote to Halley approving of his proposal to introduce woodcuts among the letterpress, stating clearly the different things which he had from Hooke, and adding, " And now having sincerely told you the case between Mr Hooke and me, I hope I shall be free for the future from the prejudice of his letters.After this letter of

**Newton**'s the printing of the Principia was begun.While

**Newton**was writing the second and third books of the Principia, a very important event occurred at Cambridge which had the effect of bringing him before the public in a new light.**Newton**was one of the eight deputies appointed by the senate for this purpose.A compromise which was put forward by one of them was stoutly and successfully resisted by

**Newton**, and on the 21st of April the deputation, with their case carefully prepared, appeared before the court.**Newton**returned to Trinity College to complete the Principia.In 1692 and 1693

**Newton**seems to have had a serious illness, the nature of which has given rise to very considerable dispute.The loss of sleep to a person of

**Newton**'s temperament, whose mind was never fiat rest, and at times so wholly engrossed in his scientific pursuits that he even neglected to take food, must necessarily have led to a very great deal of nervous excitability.On the 30th of September 1693 Millington wrote to Pepys that he had been to look for

**Newton**some time before, but that " he was out of town, and since," he says, " I have not seen him, till upon the 28th I met him at Huntingdon, where, upon his own accord, and before I had time to ask him any question, he told me that he had writt to you a very odd letter, at which he was much concerned; added, that it was in a distemper that much seized his head, and that kept him awake for above five nights together, which upon occasion he desired I would represent to you, and beg your pardon, he being very much ashamed he should be so rude to a person for whom he hath so great an honour.He is now very well, and though I fear he is under some small degree of melancholy, yet I think there is no reason to suspect it bath at all touched his understanding, and I hope never will; and so I am sure all ought to wish, that love learning or the honour of our nation, which it is a sign how much it is looked after, when such a person as Mr

**Newton**lyes so neglected by those in power."The illness of

**Newton**was very much exaggerated by foreign contemporary writers.Huygens, in a letter dated the 8th of June 1694, wrote to Leibnitz, " I do not know if you are acquainted with the accident which has happened 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."To which Leibnitz, in a letter dated the 22nd of June, replied, " I am very glad that I received information of the cure of Mr

**Newton**at the same time that I first heard of his illness, which doubtless must have been very alarming."The active part which

**Newton**had taken in defending the legal privileges of the university against the encroachments of the crown had probably at least equal weight with his scientific reputation when his friends chose him as a candidate for a seat in parliament as one of the representatives of the university.Sir Robert stood at the head of the poll with 125 votes,

**Newton**next with 122 and Mr Finch was last with 117 votes.**Newton**retained his seat only about a year, from January 1689 till the dissolution of the Convention Parliament in February 1690.During this time

**Newton**does not appear to have taken part in any of the debates in the House; but he was not neglectful of his duties as a member.On the 12th of February 1689, the day of the coronation of William and Mary,

**Newton**intimated to the vicechancellor that he would soon receive an order to proclaim them at Cambridge.During his residence in London

**Newton**had made the acquaintance of John Locke.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 emoluments of a college fellowship and a professorship.At one time

**Newton**'s friends had nearly succeeded in getting him appointed provost of King's College, Cambridge, but the college offered a successful resistance on the ground that the appointment would be illegal, as the statutes required that the provost should be in priest's orders.Charles Montague, who was afterwards earl of Halifax, was a fellow of Trinity College, and was a very intimate friend of

**Newton**; and it was on his influence that**Newton**relied in the main for promotion to some post of honour and emolument.In one of his letters to Locke at the beginning of 1692, when Montague, Lord Monmouth and Locke were exerting themselves to obtain some appointment for him,

**Newton**wrote that he was " fully convinced that Mr Montague, upon an old grudge which he thought had been worn out, was false to him."**Newton**was now in his fifty-fifth year, 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.He had previously consulted

**Newton**upon the subject of the recoinage, and on the opportunity occurring he appointed**Newton**to the post of warden of the mint.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.This letter must have convinced

**Newton**of the sincerity of Montague's good intentions towards him; we find them living as friends on the most intimate terms until Halifax's death in 1715.**Newton**'s chemical and mathematical knowledge proved of great use in carrying out the recoinage.In 1697

**Newton**was appointed to the mastership of the mint, a post worth between £1200 and £150o per annum.While he held this office,

**Newton**drew up a very extensive table of assays of foreign coins, and composed an official report on the coinage.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.Though this new and powerful method was of great help to

**Newton**in his work, he did not exhibit it in the results.**Newton**'s admirers in Holland had informed Dr Wallis that**Newton**'s method of fluxions passed there under the name of Leibnitz's Calculus Di fferentialis.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 the reason for this method first appearing in Wallis's works.A further account of the method was given in the first edition of

**Newton**'s Optics, which appeared in 1704.In 1707 William Whiston published the algebraical lectures which

**Newton**had delivered at Cambridge, under the title of Arithmetica Universalis, sive de Compositione et Resolutione Arithmetica Liber.**Newton**'s solution of the celebrated problems proposed by John Bernoulli and Leibnitz deserves mention among his mathematical works.On the 29th of January 1696/7

**Newton**received from France two copies of the printed paper containing the problems, and on the following day he transmitted a solution of them to Montague, then president of the Royal Society.Solutions were also obtained from Leibnitz and the Marquis de L'Hopital; and, although that of

**Newton**was anonymous, yet Bernoulli recognized the author in his disguise; " tanquam," says he, " ex ungue leonem."In 1699

**Newton**'s position as a mathematician and natural philosopher was recognized by the French Academy of Sciences..Tschirnhausen were appointed on the 4th of February, James Bernoulli and John Bernoulli on the 14th of February, and

**Newton**and Olaus Roemer on the 21st of February.While

**Newton**held the office of warden of the mint, he retained his chair of mathematics at Cambridge, and discharged the duties.Whiston began his astronomical lectures as

**Newton**'s deputy in January 1701.On the 10th of December 1701

**Newton**resigned his professorship, thereby at the same time resigning his fellowship at Trinity, which he had held with the Lucasian professorship since 1675 by virtue of the royal mandate.Whiston's claims to succeed

**Newton**in the Lucasian chair were successfully supported by**Newton**himself.On the 26th of November 1701

**Newton**was again elected one of the representatives of the university in parliament, but he retained his seat only until the dissolution in the following July..**Newton**does not seem to have been a candidate at this election,.In the autumn of 1703 Lord Somers retired from the presidency of the Royal Society, and

**Newton**on the 30th of November 1703 was elected to succeed him.**Newton**was annually reelected to this honourable post during the remainder of his life.As president

**Newton**was brought into close connexion with Prince George of Denmark, the queen's husband, who had been elected a fellow of the Royal Society.