Sir Isaac Newton, an English philosopher, born at Woolsthorpe, Lincolnshire, Dec. 25, 1642, died in Kensington, a suburb of London, March 20, 1727. He was a posthumous and only child, like Kepler, and was born prematurely. He was descended, according to his own account, from Sir John Newton of West-by in Lincolnshire, and according to another from a Scotch family in East Lothian. When he was three years of age, his mother, having married again, gave him to the charge of his maternal grandmother. He went to school at Skillington and Stoke till his 12th year, when he was sent to the free school at Grantham, six miles from his native hamlet, taught by a Mr. Stokes. He ranked low in his classes for some time, but being ill treated by the boy who stood next above him he determined to defeat his opponent in class work, and applied himself with such resolution to his books that he at length stood at the head of the whole school. He was usually less interested in the sports of his schoolmates than in constructing little mechanical contrivances, in which he showed marked facility of imitation and invention.

He arranged a set of pins or gnomons upon the adjacent houses so as to mark the time of day by their shadows; the arrangement served as a sort of town clock, and was known as " Isaac's dial." On the outside wall of his house at Woolsthorpe there is still a sun dial which he must have carved there. There were formerly two, but the stone on which the other was cut was removed in 1844 and presented to the royal society. In 1656 his mother, again a widow, took him to help in the management of the farm at Woolsthorpe; but such was his passion for study that he found little time to look after the concerns of the farm. His mother sent him back to Grantham, where he was fitted to enter Trinity college, Cambridge, in 1661. It does not appear that he showed a marked preeminence in the studies of the university, but he extended his acquirements beyond the prescribed routine in several directions. In the winter of the year in which he was elected scholar (1664), or earlier, he invented his binomial theorem, to which he had been led by investigations into the problem of the quadrature of the circle, and directed his attention to the subject of circles or halos around the moon, of which he gave the theory in his treatise on optics.

In 1665 he took the degree of B. A., and probably in the same year invented fluxions. - At this period the thoughts of philosophers were strongly directed to the telescope. Huygens had constructed instruments which revealed the rings and satellites of Saturn. Descartes had explained the theory of refraction, and had pointed out how glasses could be ground of such a shape as to unite parallel rays of light in a focus. Still these glasses had the great defect of giving a confused image, which was thought to be owing to imperfect manufacture, and Newton applied himself to grinding them with more accuracy. But he also experimented with a ray of light, and soon came to the conclusion "that light was not homogeneous, but composed of rays, some of which were more refrangible than others." This showed him that the defect of the lens of the refracting telescope was inherent and not accidental. He accordingly abandoned his attempts to improve that instrument, and devoted himself to the construction of a reflecting telescope, which James Gregory of Aberdeen, in view of the defects of the refracting medium, had already invented. While Newton was engaged on this, the plague forced him to retire to Woolsthorpe (1666), and it was more than two years before he resumed his researches.

During his retreat at Woolsthorpe (whether in this or the previous year is uncertain) he first conceived the identity of gravity with the force which holds the planets to their orbits, and made his first test calculations; but, starting with the erroneous estimate then entertained of the earth's mass, he failed to verify the happy conjecture (see Astronomy); and it was not till about 1680 that he resumed work upon the problem. On the cessation of the plague he returned to Cambridge, was made junior fellow in October, 1667, and senior fellow in March, 1668, and graduated M. A. in July of the same year. In the autumn of 1668 he completed a reflecting telescope 6 in. in length, magnifying 40 times, which enabled him to see Jupiter's satellites and the phases of Venus. This was the first reflecting telescope ever directed to the heavens, for Gregory never completed the instrument which he had invented. Compared with the much earlier refractors of Hevelius and Huygens, however, this was a small and ill-made instrument.

In the autumn of 1671 Newton made another, which was sent up in December "for his majesty's perusal." It is carefully preserved in the library of the royal society of London. His mind appears to have been much occupied at this time and for many years afterward with "chemical studies and practices." His celebrated letter (1669) of advice to Mr. Aston, who was about to set out for a tour of the continent, reveals a strong belief in the doctrines of alchemy; and he certainly pursued his experiments to a late period of his life in the hope of effecting some valuable transmutations. - In 1669 he became Luca-sian professor of mathematics at Cambridge, and during that and the next year spent considerable time in writing notes for a Latin translation of Kinckhuysen's algebra. In 1669-'72 he delivered a course of lectures on optics in the university, and from time to time communicated to the royal society the results of his researches on light and colors. The new doctrine of the compound nature of light involved Newton in a long and acrimonious controversy both at home and abroad. Newton considered light to consist of material particles. Hooke believed it to result from a series of undulations of an elastic medium pervading all bodies.

With this theory, which Huygens maintained in common with Hooke, Newton's alleged discovery seemed incompatible, and was accordingly strenuously resisted. On the other side Newton himself rejected Huygens's beautiful law of double refraction in Iceland spar, " founded on the finest experimental analysis of the phenomena," because it was presented as a corollary of the un-dulatory theory. Hooke in the one case, and Newton in the other, failed alike to see, or refused to admit, that the principle in question was true or false independently of what light is, or how it is propagated. It is remarkable that Newton should have missed, in the course of his optical experiments and the controversy which followed, the discovery of the different dispersive powers of different bodies. The opinion that all bodies produce spectra of equal length under the same angle of refraction, though "unsupported by experiments," observes Brewster, " and not even sustained by any theoretical views, seems to have been impressed upon his mind with all the force of an axiom; and when, under the influence of this blind conviction, he pronounced the improvement of the refracting telescope to be desperate, he checked for a long time the progress of this branch of science, and furnished to future philosophers a lesson which cannot be too deeply studied." From 1671 to 1676 his optical researches and the disputes in which they involved him seem to have occupied most of his time.

He wrote to Leibnitz, Dec. 9, 1675: "I was so persecuted with discussions arising out of my theory of light, that I blamed my own imprudence for parting with so substantial a blessing as my quiet to run after a shadow." In January, 1672, he was elected fellow of the royal society; but he offered his resignation in March, 1673, on the ground of being unable to attend the meetings. An interesting document in Newton's handwriting, entitled "A Scheme for establishing the Royal Society," has been brought to light by Sir David Brewster. His desire, it seems, was to convert the royal society into an institution like the academy of sciences in Paris. On Dec. 9, 1675, he sent to the society his " Hypothesis explaining the Properties of Light" (reprinted in the "Philosophical Magazine," September, 1846), and his "Explanation of the Colors of Thin Plates and of Natural Bodies," which Brewster says "is perhaps the loftiest of all his speculations." The phenomena of colors he ascribes to a supposed property of light, which he calls "fits of easy reflection and transmission." The theory is that every particle of light, from its first discharge from a luminous body, possesses, at equally distant intervals, dispositions to be reflected from and transmitted through the surfaces of bodies upon which it is incident.

This appears to have been his last communication to the society on optical subjects. In 1704 he published his great work on optics; much of it was written as early as 1675, and most of the remainder about 1687. - In 1679 Newton's attention was recalled to the subject of universal gravitation by a letter from Hooke, who declared that "if gravity decreased according to the reciprocal of the square of the distance, the path of a projectile would be an ellipse having the centre of the earth in the focus." Newton had hitherto confined his researches to bodies revolving in circular orbits. lie now demonstrated the mathe-. matical necessity of the three laws of Kepler as applied to the motion of a body projected in free space, and acted upon continually by a force directed toward the focus and varying inversely as the square of the distance. Newton could not consider the law of gravitation established so long as the serious discrepancy found in his calculations upon the moon remained unaccounted for. In 1680, hearing of a new measurement of a degree of the meridian by Picard, the French astronomer, which differed materially from the commonly received estimate, he went over the calculation again on the basis of the new measure, and the result was in exact agreement with observation.

He perceived that the earth, by its axial rotation and the mutual attraction of the particles of matter composing its mass, must be flattened at the poles, and he determined the amount of this flattening, though according to an incorrect law for the variation of the earth's density. He showed that the spheroidal figure of the earth, combined with its diurnal motion, would cause the weights of bodies at the surface to vary in different latitudes; and this result of pure theory explained a singular fact first noticed by the French astronomer Richer, who in 1672 had found that a clock regulated to mean time of Paris lost 2m. 28s. daily at Cayenne, within 5° of the equator. This led him to an explanation of the precession of the equinoxes. Kepler and others before him had spoken of an attraction of the waters of the earth by the moon. Newton explained the tides. He saw that the masses of the planetary bodies could be determined by observing the effects of their mutual attraction, and that from this cause their several motions would be disturbed. Thus he was conducted to an elucidation of the intricate subject of the moon's motions which had long been a stumbling-block to astronomers.

He deduced theoretically the two lunar inequalities known as the variation and the annual equation, and also the progression of the apogee and the regression of the nodes, though it was reserved for the mathematicians of the next century to complete the lunar theory. It is not known that he made any public announcement of his discoveries before February, 1085, when he sent to the royal society a paper containing his early researches on centripetal forces, Halley, who had endeavored in 1084 to calculate the law of the solar force directed to the planets moving in elliptical orbits, consulted Newton, and, finding that he had gone over the whole ground, induced him to communicate to the royal society the paper already alluded to. On its presentation Hooke raised a violent reclamation relative to the asserted discovery of the law of gravitation. As early as 1660 he had arrived at very accurate notions of centripetal forces. He had published in 1674 "An Attempt to prove the Motion of Earth from Observations," in which, as Mr. Grant observes, he describes the general nature of gravity with remarkable clearness and accuracy. (There is a Latin translation of this work, printed in 1679.) But he had not attempted to compute the law of the variation of the force at different distances from the centre, which, as applied to the elliptical orbits of the planets, was the very problem which Newton had solved.

The pretensions of Hooke called forth from Newton a long letter, dated June 20, 1686, in which he recounts the progress of his researches, and intimates his resolution to sup-press the third book of his Principle/, rather than have his peace of mind disturbed by a controversy with envious rivals. By Halley's persuasion, however, Newton consented to let the whole appear. In April, 1686, the first book of the Principia was exhibited at the royal society; in June Halley undertook its publication at his own expense, although it involved him in considerable pecuniary risk; and it appeared the next year, bearing the following title page: Philosophioe Naturalis Principia Mathematica. Imprimatur Julii 5, 1686. Londini, 1687. It is divided into three books. The first treats of motion in free space; the second treats chiefly of resisted motion; and the third deduces from these the system of the world. The doctrines of the Principia, like all discoveries which tend to overthrow cherished opinions, were hotly combated for many years.

The philosophy of Descartes, which the Newtonian theories at length supplanted, was predominant throughout Europe; and Voltaire said that at the time of his death Newton had not more than 20 followers outside of England. "The language of the French mathematicians," observes the author of the "History of the Inductive Sciences," "is Cartesian for almost half a century after the publication of the Principia of Newton." "The profound and intricate reasoning which Newton was compelled to adopt," says Mr. Grant, "formed a serious impediment to the early dissemination of his doctrines." The British universities, however, early introduced the Newtonian philosophy as a subject of study. The university of St. Andrew's in Scotland took the lead in 1690, followed by Cambridge in 1699, and by Oxford in 1704. Dr. Bentley made the new principles the basis of a theological argument in the Boyle lectures preached in London in 1692-'3. - After the publication of the Principia, Newton was content to extend and develop the principles of his philosophy without advancing into any new fields of science; and even these developments appear to have been based for the most part on experiments and observations previously made.

He was elected to represent the university in parliament in 1689, and again in 1701; and though he was rejected in 1705, those who opposed him acknowledged him to be " the glory of the university," but considered that he was sent to " tempt them from their duty by the great and just veneration they had for him." On the dissolution of parliament in 1690 he resumed his philosophical and mathematical studies at Cambridge. After this his health became impaired. In December, 1692, and January and February, 1693, he wrote the four celebrated letters to Dr. Bentley on the existence of a Deity. He was greatly affected about the beginning of 1692 by the loss of valuable manuscripts, which were consumed in his study by the upsetting of a candle. The notable story of his little dog Diamond having occasioned the mischief, and of Newton's remarkable equanimity on seeing what had happened, Brewster considers a fiction. In a letter to Pepys, dated Sept. 13, 1693, and one to Locke about the same time, there are evidences of loss of judgment.

A fortnight after the former was written, Newton told a common friend "that he had writ a very odd letter to Pepys, at which he was much concerned;" adding " that it was in a distemper that much seized his head, and that kept him awake for above five nights together." Not many days after his painful letter to Locke was written he wrote again with child-like simplicity and tenderness, asking to be forgiven for thinking ill of him, and subscribing himself, " Your most humble and unfortunate servant." About this time began the celebrated quarrel between Newton and Flamsteed, the astronomer royal, which was only terminated by Flam-steed's death (1719). They had been on terms of cordial intimacy till 1696, when a coolness began to spring up. Newton was engaged on his lunar theory, and required observations of the moon's places. Flamsteed, who at his own expense had put himself in possession of the proper instruments, was the only one who could furnish the observations. They were supplied, though not as promptly as Newton wished. Complaint followed, with little outbreaks of temper on both sides. Newton was at the summit of his fame, and Flamsteed saw the vast importance of his own labors, then unappreciated, but since fully allowed. Halley, devoted to Newton, embittered the difference.

The quarrel culminated in the publication, under Halley's name, of Flamsteed's celestial observations, which Halley had mutilated. (See Flamsteed.) Newton received in 1695 the appointment of warden of the mint, worth between £500 and £600 a year; and in 1699 he was promoted to the mastership of the mint, worth £1,200 to £1,500, which office he held during the rest of his life. The chancellor of the exchequer declared that he could not have carried on the recoinage of 1699 without his assistance. On his promotion he appointed Mr. Winston to be his deputy at Cambridge, with the full profits of the place; and in 1701 he resigned the chair. In 1699 he was elected foreign associate of the academy of sciences at Paris. He was chosen president of the royal society in 1703, and annually reelected during his life. In 1705 he was knighted by Queen Anne. In 1713 he communicated a paper to the royal society on the different kinds of years in use among the nations of antiquity; it was published in the "Gentleman's Magazine " for January, 1755, and the original is in the British museum. In 1757 he prepared two reports on the state of the coinage, which were laid before the houses of parliament.

They were followed by a proclamation in December, 1717, reducing the value of guineas from 21s. 6d. to 21s. - In 1705 began the famous dispute with Leibnitz. Newton and Leibnitz, it is now clear, were both original inventors of the infinitesimal analysis, Newton being the earlier. But Leibnitz published his method in 1684, while Newton's did not appear till 1687. The geometry of the former spread rapidly over Europe; he was considered as the sole inventor, and Newton, in the first edition of the Princi-via, acknowledged his claims as an independent inventor. In 1699 a remark was dropped in the royal society casting suspicion upon the originality of Leibnitz's discovery. Leibnitz replied in the Leipsic Journal without asperity, assertinghis claim. On Jan. 1, 1705, the same publication criticised with marked severity Newton's "Quadrature of Curves," then lately published, in which the method of fluxions was for the first time announced to the world, asserting in effect that the fluxionary method was not an original discovery.

Newton and lis friends were justly indignant, and Keill, an astronomer, undertook his defence, but was betrayed into doing similar injustice to Leib-litz, charging him in effect with having borrowed his calculus from hints thrown out by Newton. Leibnitz appealed to the royal society, which appointed a commission in the premises. Their report, which vindicates Newton's claims, forms what is called the Commercium Epistolicum (1712); for the contents of which, as also of a second edition with a review entitled Recensio (1722), Newton was himself fully responsible. In a new edition, edited by MM. Biot and Lefort (4to, Paris, 1856), this report is shown to be in many points unfair. The dissension continued without abatement up to Leibnitz's death (1716). Newton published soon after what Biot characterizes as a "bitter refutation." In the first edition of the Principia (book ii., scholium to lemma 2) justice was done to Leibnitz's claim. In the third edition (1725) another scholium is substituted, in which Leibnitz's name is not mentioned. - During his residence at Cambridge Newton was in the habit, as he expresses it, " of refreshing himself with history and chronology when he was weary with other studies." Hence grew up a system of chronology, which however was very imperfect and only existed in separate papers till the princess of Wales (afterward queen consort of George II.), who enjoyed the privilege of his conversation during the latter part of his life, requested a copy of it for her private use.

The manuscript after some years was printed in Paris (1725) surreptitiously, and involved Newton in an annoying controversy, in consequence of which he was induced to prepare a larger work, which was interrupted by his death. It appeared toward the end of 1727, under the title, "The Chronology of Ancient Kingdoms amended, to which is prefixed a Short Chronicle from the first Memory of Things in Europe to the Conquest of Persia by Alexander the Great." His system was based on the astronomical observations of the ancients. - Previous to 1692 Newton was known by the appellation of an "excellent divine." It is therefore probable that his posthumous papers on religious subjects were composed in the prime of life, at Cambridge. His " Observations on the Prophecies of Daniel and the Apocalypse of St. John " appeared in London in 1733 (4to). His "Historical Account of two Notable Corruptions of Scripture," mainly composed prior to 1690, but finished in that year, was first published in 1754, under the erroneous title of " Two Letters from Sir Isaac Newton to M. Le Clerc." In some catalogues of Newton's works another edition is mentioned, entitled "Two Letters to Mr. Clarke, late Divinity Professor of the Remonstrants in Holland" (1734). It appears to have been first published entire in Horsley's edition of Newton's works, under the title, "Historical Account of two Notable Corruptions of Scripture, in a Letter to a Friend." That friend was probably Locke. In this work he considers the two noted texts, 1 John v. 7, and 1 Tim. iii. 16. The former he attempts to prove spurious, and the latter he considers a false reading.

The publication of several of his private papers in Sir David Brewster's memoir places the fact of his entertaining Arian opinions beyond question. About the beginning of 1691 Locke contemplated going to Holland, and Newton sent him the above mentioned tract in strict confidence, requesting him to take it with him and procure its translation and publication in French, anonymously, as is evident: the object being apparently to ascertain the judgment of Biblical critics before bringing it out under his own name in English. Locke abandoned his intention of visiting Hol-land, but sent the manuscript to his friend Le Clerc in that country, who in January of the next year informed Locke that he was about to publish it in Latin. Newton, hearing of this, became alarmed at the risk of detection, and stopped the publication. He left many manuscripts on religious subjects, which have never been published. Besides a Latin dis-sertation on the sacred cubit of the Jews, printed in 1737 among the miscellaneous Works of Mr. John Greaves, Newton's only other published religious writings are the four celebrated letters addressed to Dr. Bentley, first printed in 1756. They are directed against atheism, and aim to show that matter could never have arrayed itself in its present forms without a divine power being impressed upon it.

Except a short tract on the nature of acids, his only chemical paper is one printed in the "Philosophical Transactions" for March and April, 1701, under the title of Scala Graduum Caloris. It contains a comparative scale of temperatures, from that of melting ice to that of a small kitchen coal fire. To the second English edition of the "Optics" are appended several queries, the 18th and 24th of which contain his opinions in favor of the existence of an elastic ether diffused through all space. " much subtler than air." - During the last 20 years of his life, which he spent in London, the charge of his domestic concerns, as he was never married, devolved upon his niece, Mrs. Catharine Conduitt. For two or three years prior to 1725 he had been troubled with a disorder of the bladder, accompanied with cough and gout. In January of that year he was seized with a violent cough and inflammation of the lungs, in consequence of which he removed his residence to Kensington, where his health improved. From this time the duties of his office at the mint were discharged by Mr. Conduitt. On Feb. 28, 1727, he went to London to preside at a meeting of the royal society, and became greatly fatigued. His old complaint returned with increased violence, and soon proved fatal.

He was buried with great pomp in Westminster abbey, where a monument to him was erected in 1731. Though lie had accumulated a personal estate worth at his death £32,000, he does not appear to have lived narrowly. He often evinced great generosity; to his relatives in particular he was lavish. He was of medium stature, and in the latter part of his life inclined to corpulency. In old age he had a fine head of hair, as white as silver, without any baldness. He never wore spectacles, and it is said he never lost more than one tooth to the day of his death. The house in which Newton was born was purchased in 1858 by Miss Charlwood of Grantham, to be pulled down, that a scientific college might be erected on its site. His statue was inaugurated at Grantham, Sept. 21, 1858. His dwelling house, with an observatory which he built on the top, still remains in St. Martin's street, London, and is a place of scientific pilgrimage. - Besides the first edition of the Principia above noticed, a second was published at Cambridge in 1713, under the superintendence of Cotes, whose correspondence with Newton at the time has been published (London, 1850), under the editorship of Mr. Edleston. A third edition appeared in London in 1726 (4to), edited by Pemberton; a fourth in 1729 (2 vols. 8vo), Englished by Motto; and a fifth in 1730 (2 vols. 8vo). Several editions have been published on the continent, the most famous of which is the Jesuits' edition (4 vols. 4to, Geneva, 1739-42), republished in Glasgow under the editorship of Wright (4 vols. 8vo, 1822). A Latin translation of the "Optics," by Dr. Clarke, appeared in 1706 (4to), for which Newton presented the translator with £500. Many other editions have been published.

Of his "Universal Arithmetic" there are several editions, both English and continental. The " Optical Lectures" appeared in 1728; "Fluxions," with a commentary, in 1736. His principal works were collected by Bishop Horsley (5 vols. 4to, London, 1779-'85). His communications to the royal society are comprised in vols. vii. to xi. of the "Transactions." - See Sir David Brewster's "Memoirs of the Life, Writings, and Discoveries of Sir Isaac Newton" (2 vols., 1855; new ed., revised by W. T. Lynn, 1875).