newton

Newton C. Blanchard, Democrat Jared Y.

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.

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.

231), and Sir Isaac Newton in 1715 reported unfavourably on the "marine surveyor" of Henry de Saumarez, which also depended on a rotator.

West Newton is not far from Boston and we went there in the steam cars very quickly.

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 entire number of Palaearctic families are, according to Newton, 67, and of the genera 323.

Afterwards 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.

Laplace had not yet completed his twenty-fourth year when he entered upon the course of discovery which earned him the title of "the Newton of France."

Newton in 1857-1858 .

Of the suburbs, Newton, Parnell and Newmarket are in reality outlying parts of the town itself.

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.

If there is even a single body moving freely, then the laws of Kepler and Newton are negatived and no conception of the movement of the heavenly bodies any longer exists.

His reputation was helped by several clever if somewhat wrong-headed publications, including a satirical pamphlet entitled The Theology and Philosophy of Cicero's Somnium Scipionis (1751), a defence of the Hutchinsonians in A Fair, Candid and Impartial State of the Case between Sir Isaac Newton and Mr Hutchinson (1753), and critiques upon William Law (1758) and Benjamin Kennicott (1760).

But, as Newton charmingly puts it (Diet.

He made his first appearance in public as the critic of Newton, and the arbiter between d'Alembert and Euler.

Newton demonstrated these to be no strayed Phoenician products.

"It appears like the mystical ratios of Kepler which Newton so happily elucidated."

Kepler's Problem, namely, that of finding the co-ordinates of a planet at a given time, which is equivalent - given the mean anomaly - to that of determining the true anomaly, was solved approximately by Kepler, and more completely by Wallis, Newton and others.

This cannot apparently be done for insects or foi birds; Newton accordingly unites the two into the Holarctic region.

Newton and R.

We may here quote Newton (Encyclopaedia Britannica, 9th ed., " Birds," p. 738) on the remarkable differences between this region and the rest of the Old World: - " The prevalent zoological features of any Region are of two kinds - negative and positive.

The New Zealand Subregion, considered by Professors Newton and Huxley and various other zoogeographers as deserving the rank of a region, is, and to all appearance has long been, more isolated than any other portion of the globe.

The attention of Newton was also directed to the discharge of water from orifices in the bottom of vessels.

Of many genera, the so-called species found in the New World are represented in the Old by forms so like them that often none but an expert can distinguish them, and of such representative ` species ' about 80 might be enumerated " (Newton, Did.

Following Newton, he believed a gas to be made up of particles or atoms, From Dalton's Hydrogen Gas.

(Newton) Booth Tarkington >>

While at Oxford Wren distinguished himself in geometry and applied mathematics, and Newton, in his Principia, p. 19 (ed.

In 1646 he is found in partnership with two other deprived clergymen, keeping a school at Newton Hall, in the parish of Llanvihangel-Aberbythych, Carmarthenshire.

From Miall and Denny (after Newton), The Cockroach, Lovell Reeve & Co.

Bruce admitted Newton to his presence at Aldcamus or Old Cambus, and informed him that he would not receive the bulls until his title was acknowledged and he had taken Berwick.

It banished the spirits and genii, to which even Kepler had assigned the guardianship of the planetary movements; and, if it supposes the globular particles of the envelope to be the active force in carrying the earth round the sun, we may remember that Newton himself assumed an aether for somewhat similar purposes.

Newton had divined the principle of the conservation of energy, so far as it belongs purely to mechanics.

In 1777 he studied theology under the evangelical John Newton at Olney.

The next period of advance stretches from the Renaissance to Newton and Leibnitz at the end of the 17th century.

During this period logarithms were invented, trigonometry and algebra developed, analytical geometry invented, dynamics put upon a sound basis, and the period closed with the magnificent invention of (or at least the perfecting of) the differential calculus by Newton and Leibnitz and the discovery of gravitation.

Although for a time it was lost sight of on the continent, Sir Isaac Newton thought so highly of this book that he prepared an annotated edition which was published in Cambridge in 1672, with the addition of the plates which had been planned by Varenius, but not produced by the original publishers.

After the death of Newton, in 1728, his nephew, John Conduitt, applied to Maclaurin for his assistance in publishing an.

"NEWTON DIEHL BAKER (1871-), American politician, was born at Martinsburg, W.

On his return Newton was waylaid and his papers seized, not without suspicion of Bruce's connivance.

Glauber (1603-1668); by Robert Boyle (1627-1691) and, for a time at least, by Sir Isaac Newton and his rival and Cf.

Newton (1884),(1884), R.

CORNELIUS NEWTON BLISS (1833-), American merchant and politician, was born at Fall River, Massachusetts, on the 26th of January 1833.

After a fortnight more at Shawbury, he wrote to John Newton and another clergyman friend in London for advice.

The effects of friction and viscosity in diminishing the velocity of running water were noticed in the Principia of Sir Isaac Newton, who threw much light upon several branches of hydromechanics.

Newton, History of Discoveries at Cnidus, Halicarnassus and Branchidae).

Another attempt by Adam Newton, guardian of the Friars Minorite at Berwick, had a more ignominious result.

In it Maclaurin developed several theorems due to Newton, and introduced the method of generating conics which bears his name, and showed that many curves of the third and fourth degrees can be described by the intersection of two movable angles.

Of the more immediate successors of Newton in Great Britain Maclaurin is probably the only one who can be placed in competition with the great mathematicians of the continent of Europe at the time.

His method for determining approximate values of the roots of equations is far in advance of the Hindu method as applied by Cardan, and is identical in principle with the methods of Sir Isaac Newton and W.

Newton's possession.

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.

Newton he entertained a confident belief in Providence, founded not on any tenuous inference, but on personal feeling.

It was this: from the observed perturbations of a known planet to deduce by calculation, assuming only Newton's law of gravitation, the mass and orbit of an unknown disturbing body.

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.

Newton.

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.

The 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.

Sir 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.

Some clamour was raised by a publication in which blame for harsh dealings was freely imputed to Newton, but W.

Whewell vindicated his character in Flamsteed and Newton (1836).

ROGER JOSEPH BOSCOVICH (1711?-1787) mathematician and natural philosopher, one of the earliest of foreign savants to adopt Newton's gravitation theory, was born at Ragusa in Dalmatia on the 18th of May 1711, according to the usual account, but ten years earlier according to Lalande (Eloge, 1792).

NEWTON ABBOT, a market town and seaport in the Ashburton parliamentary division of Devonshire, England, 20 m.

and William of Orange, who first read his declaration to the people of England at Newton Abbot market-cross.

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.

Newton was elected Lucasian professor on the 29th of October 1669.

While 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.

Newton's Dictionary of Birds, London, 1896.

Exp.sec. From Newton's by permission of A.

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.

Newton's Dictionary of Birds (London, 1893); Cat.

Especial attention has to be drawn to the article " Geographical Distribution," in Newton's Dictionary of Birds.

The first of these supports Newton's contention of the essential unity of the Nearctic and Palaearctic areas.

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.

and made the acquaintance of Sir Isaac Newton.

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

account of Newton's life and discoveries.

After Maclaurin's death his account of Newton's philosophical discoveries was published by Patrick Murdoch, and also his algebra in 1748.

the force which holds chemically dissimilar substances together (and also similar substances as is seen in di-, tri-, and poly-atomic molecules), was introduced by Hermann Boerhaave, and made more precise by Sir Isaac Newton.

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.

Newton's Philosophical Discoveries, and dedication to John Wilkes), examines the properties of matter.

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.

The original form of the theorem was first given in a letter, dated the 13th of June 1676, from Sir Isaac Newton to Henry Oldenburg for communication to Wilhelm G.

Leibnitz, although Newton had discovered it some years previously.

Newton m m _ _ there states that (p+ pq) - = p n -}- T naq ?- m 2n n bq -?

&c., where p+pq is the quantity whoseTi power or root is required, p the first term of that quantity, and q the quotient of the rest divided by p, m the power, which may be a positive or negative integer or a fraction, and a, b, c, &c., the several terms in order, In a second letter, dated the 24th of October 1676, to Oldenburg, Newton gave the train of reasoning by which he devised the theorem.

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.

He visited England, where he was kindly received by Sir Isaac Newton and Edmund Halley (Com.

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.

" Franklin's reputation," wrote John Adams with characteristic extravagance, " was more universal than that of Leibnitz or Newton, Frederick or Voltaire; and his character more esteemed and beloved than all of them..

1875); Examples of Analytical Geometry of Three Dimensions (1858, 3rd ed., 1873); Mechanics (1867), History of the Mathematical Theory of Probability from the Time of Pascal to that of Lagrange (1865); Researches in the Calculus of Variations (1871); History of the Mathematical Theories of Attraction and Figure of the Earth from Newton to Laplace (1873); Elementary Treatise on Laplace's, Lame's and Bessel's Functions (1875); Natural Philosophy for Beginners (1877).

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 1743

Since by definition E_ - v(dp/dv) =p(dp/dp) equation (6) becomes U = (dp / dp) (7) The value U = / (E/p) was first virtually obtained by Newton (Principia, bk.

He 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).

Newton found 979 ft./sec. But, as we shall see, all the determinations give a value of Uo in the neighbourhood of 33, 000 cm./sec., or about 1080 ft./sec. This discrepancy e was not explained till 1816, when Laplace (Ann.

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.

' For the Greek priests, see, besides Schomann and other works on Greek antiquities, Newton, Essays on Art and Archaeology, p. 136 seq.

Through the influence of Sir Isaac Newton he was elected mathematical master in Christ's hospital.

xxiv., from which it was copied and reprinted in the Ada Eruditorum (1707), and also in the Memoirs of the Academy of Sciences at Paris; General Laws of Nature and Motion (1705), a work which is commended by Wolfius as illustrating and rendering easy the writings of Galileo and Huygens, and the Principia of Newton; An Institution of Fluxions, containing the First Principles, Operations, and Applications of that admirable Method, as invented by Sir Isaac Newton (1706).

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).

Long and Charles Merivale, Sir Henry Maine, Sir Charles Newton and A.

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.

N., and the more modern village of Newton, 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.

(23) Sir Isaac Newton, Dissertation upon the Sacred Cubit (1737);

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.

Newton and G.

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.

Brown's History of Alabama (New York, 1900); Newton W.

Of less interest nowadays are Robins's more purely mathematical writings, such as his Discourse concerning the Nature and Certainty of Sir Isaac Newton's Methods of Fluxions and of Prime and Ultimate Ratios (1735), "A Demonstration of the Eleventh Proposition of Sir Isaac Newton's Treatise of Quadratures" (Phil.

ROGER SHERMAN (1721-1793), American political leader, a signer of the Declaration of Independence, was born at Newton, Massachusetts, on the 19th of April 1721 (O.S.).

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.

The true order of discovery, however, was as follows: (a) Sir Christo p her Wren made many experiments before the Royal Society, which were afterwards repeated in a corrected form by Sir Isaac Newton in the Principia, experimentally proving that bodies of ascertained comparative weights, when suspended and impelled against one another, forced one another back by impressing on one another opposite changes of velocity inversely as their weights and therefore masses; that is, by impressing on one another equal and opposite changes of momentum.

(e) Newton in the Principia, repeating and correcting Wren's experiments on collision, and adding further instances from attractive forces of magnetism and gravity, induced the third law of motion as a general law of all forces.

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, a city and the county-seat of Harvey county, Kansas, U.S.A., about 27 m.

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.

Newton, Massachusetts >>

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's law of gravitation affords the most notable example of the process of verification of a law of force, and incidentally of the Galileo-Newton theory.

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.

Weston (1730); Huygens, Horologium Oscillatorium (1673); Newton, Philosophiae naturalis principia mathematica (1687; translation by A.

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.

This theory was adopted by Edme Mariotte, Sir Isaac Newton and Thomas Young; and, although certain of their assumptions were somewhat arbitrary, yet the general validity of the theory has been demonstrated by the researches of J.

Newton, A Dictionary of Birds, p. 572-575 (London, 1893-1896); E.

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.

in length and 6 in height, which has been supposed to commemorate the great naval victory of Conon over the Lacedaemonians in 394 B.C. Among the minor antiquities obtained from the city itself, or the great necropolis to the east, perhaps the most interesting are the leaden KarrccB€o oc, or imprecationary tablets, found in the temple of Demeter, and copied in facsimile in the appendix to the second volume of Newton's work.

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.

Colleges connected with the Church, besides the seminary at Lancaster, Franklin and Marshall College and Heidelberg University, are: Catawba College (1851) at Newton, North Carolina; and Ursinus College (1869), founded by the Low Church wing, at Collegeville, Pennsylvania, which had, until 1908, a theological seminary, then removed to Dayton, Ohio, where it united with Heidelberg Theological Seminary (until 1908 at Tiffin) to form the Central Theological Seminary.

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.

His merit was so well known and acknowledged by the Royal Society that they judged him a fit person to decide the famous contest between Newton and G.

This work was first printed in 1618, in 4to, and dedicated to Sir Isaac Newton.

Relying on statements made by Sir Isaac Newton, Dollond disputed this possibility (Phil.

Trans., 1753), but subsequently, after the Swedish physicist, Samuel Klingenstjerna (1698-1765), had pointed out that Newton's law of dispersion did not harmonize with certain observed facts, he began experiments to settle the question.

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.

"NEWTON WESLEY ROWELL (1867-), Canadian politician, was born Nov.

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.

Beecher, Newton Bateman (1822-1897), superintendent of public instruction of Illinois from 1865 to 1875 and president of Knox College in 1875-1893, Bishop Theodore N.

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.

Brewster, Life of Newton; R.

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."

Dollond admitted the accuracy of Euler's analysis, but disputed his hypothesis on the grounds that it was purely a theoretical assumption, that the theory was opposed to the results of Newton's experiments on the refrangibility of light, and that it was impossible to determine a physical law from analytical reasoning alone (Phil.

He did not doubt the accuracy of Newton's.

experiments quoted by Dollond, because he asserted that the difference between the law deduced by Newton and that which he assumed would not be rendered sensible by such an experiment.

4 Dollond did not reply to this memoir, but soon afterwards he received an abstract of a memoir by Samuel Klingenstierna, the Swedish mathematician and astronomer, which led him to doubt the accuracy of the results deduced by Newton on the dispersion of refracted light.

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).

Phaenomena, 4-5; prop. 2.) What Newton did, in short, was to prove by analysis that the planets, revolving by Kepler's astronomical laws round the sun, have motions such as by mechanical laws are consequences of a centripetal force to the sun.

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.

Newton Booth.

Newton in Geol.

Newton, Travels (1867), and Discoveries at Halicarnassus, &c. (1863); Dilettanti Society, Ionian Antiquities (1769-1840); J.

Newton and J.

ASHTON-IN-MAKERFIELD, an urban district in the Newton parliamentary division of Lancashire, England, 4 m.

i-it fn~xavuc&), which might more properly be restricted to the theory of mechanisms, and which was indeed used in this narrower sense by Newton, has clung to it, although the subject has long attained a far wider scope.

Newton, Philosophiae naturo~lis Principia Mathemalica (1 St ed., London, 1687); J.

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.

1774), a native of Newton, England, who emigrated to America in 1730, and became a prosperous Marblehead merchant.

owing to their containing more or less of a substance called the matter of heat," and inclines to Newton's opinion that it "consists in the internal motion of the particles of bodies."

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.

39, 61; Brewster, Newton, .ii.

Bacon has frequently been disparaged on the ground that his name is not mentioned by Sir Isaac Newton.

It can be shown, however, that Newton was not ignorant of Bacon's works, and Dr Fowler explains his silence with regard to them on three grounds: (1) that Bacon's reputation was so well established that any definite mention was unnecessary, (2) that it was not customary at the time to acknowledge indebtedness to contemporary and recent writers, and (3) that Newton's genius was so strongly mathematical (whereas Bacon's great weakness was in mathematics) that he had no special reason to refer to Bacon's experimental principles.

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.

Sir Isaac Newton was probably the discoverer of astigmation; the position of the astigmatic image lines was determined by Thomas Young (A Course of Lectures on Natural Philosophy, 1807); and the theory has been recently developed by A.

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.

Thus Sir Isaac Newton placed a magnet in a floating vessel and a piece of iron in another in order to observe their mutual action, and A.

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.

including Newton Hill (670 ft.

Epicycloids also received attention at the hands of Edmund Halley, Sir Isaac Newton and others; spherical epicycloids, in which the moving circle is inclined at a constant angle to the plane of the fixed circle, were studied by the Bernoullis, Pierre Louis M.

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.

The editor of Newton's Journal of Arts and Sciences speaks of it thus: - " The apparatus consists of a car containing the goods, passengers, engines, fuel, &c., to which a rectangular frame, made of wood or bamboo cane, and covered with canvas or oiled silk, is attached.

In 1854 he became interested, through his brother Matthew, a civil engineer, in the project of Frederick Newton Gisborne (1824-1892) for a telegraph across Newfoundland; and he was attracted by the idea of a trans-Atlantic telegraphic cable, as to which he consulted S.

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.

SIR ISAAC NEWTON (1642-1727), English natural philosopher, was born on the 25th of December 1642 (o.s.), at Woolsthorpe, a hamlet in the parish of Colsterworth, Lincolnshire, about 6 m.

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.

And in this same commonplace book the following entry made by Newton himself, many years afterwards, gives a further account of the nature of his work during the period when he was an undergraduate: " July 4, 1699.

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."

In his reply to the secretary on the 18th of January 1672, Newton writes: " I desire that in your next letter you would inform me for what time the society continue their weekly meetings; because, if they continue them for any time, I am purposing them to be considered of and examined an account of a philosophical discovery, which induced me to the making of the said telescope, and which I doubt not but will prove much more grateful than the communication of that instrument being in my judgment the oddest if not the most considerable detection which hath hitherto been made into the operations of nature."

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.

Newton carried on the discussion with the objectors with great courtesy and patience, but the amount of pain which these perpetual discussions gave to his sensitive mind may be estimated from the fact of his writing on the 18th of November 1676 to Oldenburg: " I promised to send you an answer to Mr Lucas this next Tuesday, but I find I shall scarce finish what I have designed, so as to get a copy taken of it by that time, and therefore I beg your patience a.

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.

On the 8th of March 1673 Newton wrote to Oldenburg, the secretary of the Royal Society: " Sir, I desire that you will procure that I may be put out from being any longer Fellow of the Royal Society: for though I honour that body, yet since I see I shall neither profit them, nor (by reason of this distance) can partake of the advantage of their assemblies, I desire to withdraw."

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.

to 1°, made the two results, the discrepancy between which Newton had regarded as a disproof of his conjecture, to agree so exactly that he now regarded his conjecture as fully established.

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.

" Mr Halley was desired to put Mr Newton in mind of his promise for the securing this invention to himself, till such time as he could be at leisure to publish it," and Paget was desired to join with Halley in urging Newton to do so.

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 loth, of June 1686 Newton wrote to Halley the following letter: " Sir, - In order to let you know the case between Mr Hooke and me, I give you an account of what passed between us in our letters, so far as I could remember; for 'tis long since they were writ, and I do not know that I have seen them since.

Newton."

On the 29th of June 1686 Halley wrote to Newton: - " I am heartily sorry that in this matter, wherein all mankind ought to acknowledge their obligations to you, you should meet with anything that should give you unquiet "; and then, after an account of Hooke's claim to the discovery as made at a meeting of the Royal Society, he concludes: " But I found that they were all of opinion that nothing thereof appearing in print, nor on the books of the Society, you ought to be considered as the inventor.

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.

And in a letter written to John Locke in reply to one of his about the second edition of his book, and dated the 15th of October 1693, Newton wrote: " The last winter, by sleeping too often by my fire, I got an ill habit of sleeping; and a distemper, which this summer has been epidemical, put me farther out of order, so that when I wrote to you, I had not slept an hour a night for a fortnight together, and for five days together not a wink.

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.

Pepys must have heard such rumours, as in a letter to his friend Millington, the tutor of Magdalene College at Cambridge, dated the 26th of September 1693, he wrote: " I must acknowledge myself not at the ease I would be glad to be at in reference to excellent Mr Newton; concerning whom (methinks) your answer labours under the same kind of restraint which (to tell you the truth) my asking did.

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.

In a letter to Newton announcing the news, Montague writes: " I am very glad that at last I can give you a good proof of my friendship, and the esteem the king has of your merits.

Mr Overton, the warden of the mint, is made one of the Commissioners of Customs, and the king has promised me to make Mr Newton warden of the mint.

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.

The prince had offered, on Newton's recommendation, to be at the expense of printing Flamsteed's observations, and especially his catalogue of the stars.

Afterwards the queen held a court at Trinity Lodge, where (16th of April 1705) she conferred the order of knighthood upon Sir Isaac Newton.

As soon as the first edition of the Principia was published Newton began to prepare for a second edition.

Dr Edleston, in his preface to Newton's correspondence with Cotes, justly remarks: " If Flamsteed the Astronomer-Royal had cordially co-operated with him in the humble capacity of an observer in the way that Newton pointed out and requested of him.

Newton, however, could not get the information he wanted from Flamsteed, and after the spring of 1696 his time was much occupied by his duties at the mint.

Dr Bentley, the master of Trinity College, had for a long time urged Newton to give his consent to the republication of the Principia.

In the middle of 1708 Newton's consent was obtained, but it was not till the spring of 1709 that he was prevailed upon to entrust the superintendence of it to a young mathematician of great promise, Roger Cotes, fellow of Trinity College, who had been recently appointed the first Plumian professor of astronomy and experimental philosophy.

On the 21st of May 1709, after having been that day with Newton, Bentley announced this arrangement to Cotes: - " Sir Isaac Newton," he said, " will be glad to see you in June, and then put into your hands one part of his book corrected for the press."

During the printing of this edition a correspondence went on continuously between Newton and Cotes.

On the 31st of March 1713, when the edition was nearly ready for publication, Newton wrote to Cotes: " I heare that Mr Bernoulli has sent a Paper of 40 pages to be published in the Acta Leipsica relating to what I have written upon the curve Lines described by Projectiles in resisting Mediums. And therein he partly makes Observations upon what I have written & partly improves it.

Newton's desire to have no hand in writing the preface seems. to have proceeded from a knowledge that Cotes was proposing to allude to the dispute about the invention of fluxions.

At last, about midsummer 1713, was published the long and impatiently expected second edition of the Principia, and, on the 27th of July, Newton waited on the queen to present her with a copy of the new edition.

Newton appeared before them and gave evidence.

Newton criticized all the methods, pointing out their weak points, and it is due mainly to his evidence that the committee brought in the report which was accepted by the House, and shortly afterwards was converted into a Bill, passed both Houses, and received the royal assent.

Sir Isaac Newton was a very popular visitor at the court of George I.

The translation was printed under the title Abrege de chronologie de M le Chevallier Newton, fait par lui-meme et traduit sur le manuscrit anglais.

Upon receiving a copy of this work, Sir Isaac Newton printed, in the Philosophical Transactions for 1725, a paper entitled " Remarks on the observations made on a Chronological Index of Sir Isaac Newton, translated into French by the observator, and published at Paris."

From an early period of his life Newton had paid great attention to theological studies, and it is well known that he had begun to study the subject of the prophecies before the year 1690.

That Newton's mind was even then quite clear and powerful is sufficiently proved by his ability to attack the most difficult mathematical problems with success.

Newton received this problem about 5 o'clock in the afternoon as he was returning from the mint, but, though he was fatigued with business, he solved the problem the same evening.

Being prevented from going to Holland, Locke copied the manuscript, and sent it, without Newton's name, to Le Clerc, who received it before the 11th of April 1691.

This was accordingly done; but Le Clerc sent the manuscript to the library of the Remonstrants, and it was afterwards published at London in 1754, under the title of Two Letters from Sir Isaac Newton to M le Clerc. This edition is imperfect, and in many places erroneous.

Sir Isaac Newton left behind him in manuscript a work entitled Observations on the Prophecies of Daniel and the Apocalypse of St John, which was published in London in 1733, in one volume 4to; another work, entitled Lexicon Propheticum, with a dissertation on the sacred cubit of the Jews, which was printed in 1737; and four letters addressed to Bentley, containing some arguments in proof of a Deity, which were published by Cumberland, a nephew of Bentley, in 1756.

Newton devoted much of his time to the study of chemistry; but the greater number of his experiments still remain in manuscript.

In the earlier part of his life he and his relation Dr Newton of Grantham had put up furnaces, and had wrought for several months in quest of the philosopher's tincture.

In the last few years of his life Newton was troubled with incontinence of urine, which was supposed to be due to stone; but with care he kept the disease under control.

Pemberton, A View of Sir Isaac Newton's Philosophy (1728); Colin Maclaurin, Sir Isaac Newton's Philosophical Discoveries (1775); F.

Brewster, Memoirs of the Life, Writings, and Discoveries of Sir Isaac Newton (1855; new ed.

1893); Lord Brougham and Routh's Analytical View of Sir Isaac Newton's Principia (1855); S.

A complete bibliography of Newton's writings has been given by G.

John Newton (Divine) >>

Other cities of above 5000 inhabitants were Hutchinson (9379), Emporia (8223), Parsons (7682), Ottawa (6934), Newton (6208), Arkansas City (6140), Salina (6074), Argentine (5878) and Iola (5791).

Other cities of above 5000 inhabitants each were: Chanute (9704), Emporia (8974), Winfield (7845), Salina (7829), Ottawa (7727), Arkansas City (7634), Newton (6601), Galena (6449), Argentine (6053), Junction City (5264) and Cherryvale (5089).

It may be noticed that the nine inflections of a cubic curve represented by an equation with real coefficients are three real, six imaginary; the three real inflections lie in a line, as was known to Newton and Maclaurin.

A branch is either re-entrant, or it extends both ways to infinity, and in this case, we may regard it as consisting of two legs (crura, Newton), each extending one way to infinity, but without any definite separation.

- We may now consider the various forms of cubic curves as appearing by Newton's Enumeratio, and by the figures belonging thereto.

The word usage examples above have been gathered from various sources to reflect current and historial usage. They do not represent the opinions of YourDictionary.com.