NEWTON (Sir Isaac)

, one of the greatest philosophers and mathematicians the world has produced, was born at Woolstrop in Lincolnshire on Christmas day 1642. He was descended from the eldest branch of the family of Sir John Newton, bart. who were lords of the manor of Woolstrop, and had been possessed of the estate for about two centuries before, to which they had removed from Westley in the same county, but originally they came from the town of Newton in Lancashire. Other accounts say, I think more truly, that he was the only child of Mr. John Newton of Colesworth, near Grantham in Lincolnshire, who had there an estate of about 120l. a year, which he kept in his own hands. His mother was of the ancient and opulent family of the Ayscoughs, or Askews, of the same county. Our author losing his father while he was very young, the care of his education devolved on his mother, who, though she married again after his father's death, did not neglect to improve by a liberal education the promising genius that was observed in her son. At 12 years of age, by the advice of his maternal uncle, he was sent to the grammar school at Grantham, where he made a good proficiency in the languages, and laid the foundation of his future studies. Even here was observed in him a strong inclination to figures and philosophical subjects. One trait of this early disposition is told of him: he had then a rude method of measuring the force of the wind blowing against him, by observing how much farther he could leap in the direction of the wind, or blowing on his back, than he could leap the contrary way, or opposed to the wind: an early mark of his original infantine genius.

After a few years spent here, his mother took him home; intending, as she had no other child, to have the pleasure of his company; and that, after the manner of his father before him, he should occupy his own estate.

But instead of minding the markets, or the business of the farm, he was always studying and poring over his books, even by stealth, from his mother's knowledge. On one of these occasions his uncle discovered him one day in a hay-loft at Grantham, whither he had been sent to the market, working a mathematical problem; and having otherwise observed the boy's mind to be uncommonly bent upon learning, he prevailed upon his sister to part with him; and he was accordingly sent, in 1660, to Trinity College in Cambridge, where his uncle, having himself been a member of it, had still many friends. Isaac was soon taken notice of by Dr. Barrow, who was soon after appointed the first Lucasian professor of mathematics; and observing his bright genius, contracted a great friendship for him. At his outsetting here, Euclid was first put into his hands, as usual, but that author was soon dismissed; seeming to him too plain and easy, and unworthy of taking up his time. He understood him almost before he read him; and a cast of his eye upon the contents of his theorems, was sufficient to make him master of them: and as the analytical method of Des Cartes was then much in vogue, he particularly applied to it, and Kepler's Optics, &c, making several improvements on them, which he entered upon the margins of the books as he went on, as his custom was in studying any author.

Thus he was employed till the year 1664, when he opened a way into his new method of Fluxions and Infinite Series; and the same year took the degree of bachelor of arts. In the mean time, observing that the mathematicians were much engaged in the business of improving telescopes, by grinding glasses into one of the figures made by the three sections of a cone, upon the principle then generally entertained, that light was homogeneous, he set himself to grinding of optic glasses, of other figures than spherical, having as yet no distrust of the homogeneous nature of light: but not hitting presently upon any thing in this attempt to satisfy his mind, he procured a glass prism, that he might try the celebrated phenomena of colours, discovered by Grimaldi not long before. He was much pleased at first with the vivid brightness of the colours produced by this experiment; but after a while, considering them in a philosophical way, with that circumspection which was natural to him, he was surprised to see them in an oblong form, which, according to the received rule of refractions, ought to be circular. At first he thought the irregularity might possibly be no more than accidental; but this was what he could not leave without further enquiry: accordingly, he soon invented an infallible method of deciding the question, and the result was, his New Theory of Light and Colours.

However, the theory alone, unexpected and surprising as it was, did not satisfy him; he rather considered| the proper use that might be made of it for improving telescopes, which was his first design. To this end, having now discovered that light was not homogeneous, but an heterogeneous mixture of differently refrangible rays, he computed the errors arising from this different refrangibility; and, finding them to exceed some hundreds of times those occasioned by the circular figure of the glasses, he threw aside his glass works, and took reflections into consideration. He was now sensible that optical instruments might be brought to any degree of perfection desired, in case there could be found a reflecting substance which would polish as finely as glass, and reflect as much light as glass transmits, and the art of giving it a parabolical figure he also attained: but these seemed to him very great difficulties; nay, he almost thought them insuperable, <*>hen he further considered, that every irregularity in a reflecting superficies makes the rays stray five or six times more from their due course, than the like irregularities in a refracting one.

Amidst these speculations, he was forced from Cambridge, in 1665, by the plague; and it was more than two years before he made any further progress in the subject. However, he was far from passing his time idly in the country; on the contrary, it was here, at this time, that he first started the hint that gave rise to the system of the world, which is the main subject of the Principia. In his retirement, he was sitting alone in a garden, when some apples falling from a tree, led his thoughts upon the subject of gravity; and, reflecting on the power of that principle, he began to consider, that, as this power is not found to be sensibly diminished at the remotest distance from the centre of the earth to which we can rise, neither at the tops of the loftiest buildings, nor on the summits of the highest mountains, it appeared to him reasonable to conclude, that this power must extend much farther than is usually thought. “Why not as high as the moon? said he to himself; and if so, her motion must be influenced by it; perhaps she is retained in her orbit by it: however, though the power of gravity is not sensibly weakened in the little change of distance at which we can place ourselves from the centre of the earth, yet it is very possible that, at the height of the moon, this power may differ in strength much from what it is here.” To make an estimate what might be the degree of this diminution, he considered with himself, that if the moon be retained in her orbit by the force of gravity, no doubt the primary planets are carried about the sun by the like power; and, by comparing the periods of the several planets with their distances from the sun, he found, that if any power like gravity held them in their courses, its strength must decrease in the duplicate proportion of the increase of distance. This he concluded, by supposing them to move in perfect circles, concentric to the sun, from which the orbits of the greatest part of them do not much differ. Supposing therefore the force of gravity, when extended to the moon, to decrease in the fame manner, he computed whether that force would be sufficient to keep the moon in her orbit.

In this computation, being absent from books, he took the common estimate in use among the geographers and our seamen, before Norwood had measured the earth, namely that 60 miles make one degree of latitude; but as that is a very erroneous supposition, each degree containing about 69 1/3 of our English miles, his computation upon it did not make the power of gravity, decreasing in a duplicate proportion to the distance, answerable to the power which retained the moon in her orbit: whence he concluded, that some other cause must at least join with the action of the power of gravity on the moon. For this reason he laid aside, for that time, any further thoughts upon the matter. Mr. Whiston (in his Memoirs, pa. 33) says, he told him that he thought Des Cartes's vortices might concur with the action of gravity.

Nor did he resume this enquiry on his return to Cambridge, which was shortly after. The truth is, his thoughts were now engaged upon his newly projected reflecting telescope, of which he made a small specimen, with a metallic reflector spherically concave. It was but a rude essay, chiefly defective by the want of a good polish for the metal. This instrument is now in the possession of the Royal Society. In 1667 he was chosen Fellow of his college, and took the degree of master of arts. And in 1669 Dr. Barrow resigned to him the mathematical chair at Cambridge, the business of which appointment interrupted for a while his attention to the telescope: however, as his thoughts had been for some time chiefly employed upon optics, he made his discoveries in that science the subject of his lectures, for the first three years after he was appointed Mathematical Professor: and having now brought his Theory of Light and Colours to a considerable degree of perfection, and having been elected a Fellow of the Royal Society in Jan. 1672, he communicated it to that body, to have their judgment upon it; and it was afterwards published in their Transactions, viz, of Feb. 19, 1672. This publication occasioned a dispute upon the truth of it, which gave him so much uneasiness, that he resolved not to publish any thing further for a while upon the subject; and in that resolution he laid up his Optical Lectures, although he had prepared them for the press. And the Analysis by Infinite Series, which he had intended to subjoin to them, unhappily for the world, underwent the same fate, and for the same reason.

In this temper he resumed his telescope; and observing that there was no absolute necessity for the parabolic figure of the glasses, since, if metals could be ground truly spherical, they would be able to bear as great apertures as men could give a polish to, he completed another instrument of the same kind. This answering the purpose so well, as, though only half a foot in length, to shew the planet Jupiter distinctly round, with his four satellites, and also Venus horned, he sent it to the Royal Society, at their request, together with a description of it, with further particulars; which were published in the Philosophical Transactions for March 1672. Several attempts were also made by that society to bring it to perfection; but, for want of a proper composition of metal, and a good polish<*> nothing succeeded, and the invention lay dormant, till Hadley made his Newtonian telescope in 1723. At the request of Leibnitz, in 1676, he explained his invention of Infinite Series, and took notice how far he had improved it by his Method of Fluxions, which however| he still concealed, and particularly on this occasion, by a transposition of the letters that make up the two fundamental propositions of it, into an alphabetical order; the letters concerning which are inserted in Collins's Commercium Epistolicum, printed 1712. In the winter between the years 1676 and 1677, he found out the grand proposition, that, by a centripetal force acting reciprocally as the square of the distance, a planet must revolve in an ellipsis, about the centre of force placed in its lower focus, and, by a radius drawn to that centre, describe areas proportional to the times. In 1680 he made several astronomical observations upon the comet that then appeared; which, for some considerable time, he took not to be one and the same, but two different comets; and upon this occasion several letters passed between him and Mr. Flamsteed.

He was still under this mistake, when he received a letter from Dr. Hook, explaining the nature of the line described by a falling body, supposed to be moved circularly by the diurnal motion of the earth, and perpendicularly by the power of gravity. This letter put him upon enquiring anew what was the real figure in which such a body moved; and that enquiry, convincing him of another mistake which he had before fallen into concerning that figure, put him upon resuming his former thoughts with regard to the moon; and Picart having not long before, viz, in 1679, measured a degree of the earth with sufficient accuracy, by using his measures, that planet appeared to be retained in her orbit by the sole power of gravity; and consequently that this power decreases in the duplicate ratio of the distance; as he had formerly conjectured. Upon this principle, he found the line described by a falling body to be an ellipsis, having one focus in the centre of the earth. And finding by this means, that the primary planets really moved in such orbits as Kepler had supposed, he had the satisfaction to see that this enquiry, which he had undertaken at first out of mere curiosity, could be applied to the greatest purposes. Hereupon he drew up about a dozen propositions, relating to the motion of the primary planets round the sun, which were communicated to the Royal Society in the latter end of 1683. This coming to be known to Dr. Halley, that gentleman, who had attempted the demonstration in vain, applied, in August 1684, to Newton, who assured him that he had absolutely completed the proof. This was also registered in the books of the Royal Society; at whose earnest solicitation Newton finished the work, which was printed under the care of Dr. Halley, and came out about midsummer 1687, under the title of, Philosophiæ naturalis Principia mathematica, containing in the third book, the Cometic Astronomy, which had been lately discovered by him, and now made its sirst appearance in the world: a work which may be looked upon as the production of a celestial intelligence rather than of a man.

This work however, in which the great author has built a new system of natural philosophy upon the most sublime geometry, did not meet at first with all the applause it deserved, and was one day to receive. Two reasons concurred in producing this effect: Des Cartes had then got full possession of the world. His philosophy was indeed the creature of a fine imagination, gaily dressed out: he had given her likewise some of nature's fine features, and painted the rest to a seeming likeness of her. On the other hand, Newton had with an unparalleled penetration, and force of genius, pursued nature up to her most secret abode, and was intent to demonstrate her residence to others, rather than anxious to describe particularly the way by which he arrived at it himself: he finished his piece in that elegant conciseness, which had justly gained the Ancients an universal esteem. In fact, the consequences flow with such rapidity from the principles, that the reader is often left to supply a long chain of reasoning to connect them: so that it required some time before the world could understand it. The best mathematicians were obliged to study it with care, before they could make themselves master of it; and those of a lower rank durst not venture upon it, till encouraged by the testimonies of the more learned. But at last, when its value came to be sufficiently known, the approbation which had been so slowly gained, became universal, and nothing was to be heard from all quarters, but one general burst of admiration. “Does Mr. Newton eat, drink, or sleep like other men?” says the marquis de l'Hospital, one of the greatest mathematicians of the age, to the English who visited him. “I represent him to myself as a celestial genius intirely disengaged from matter.”

In the midst of these profound mathematical researches, just before his Principia went to the press in 1686, the privileges of the university being attacked by James the 2d, Newton appeared among its most strenuous defenders, and was on that occasion appointed one of their delegates to the high-commission court; and they made such a defence, that James thought proper to drop the affair. Our author was also chosen one of their members for the Convention-Parliament in 1688, in which he sat till it was dissolved.

Newton's merit was well known to Mr. Montague, then chancellor of the exchequer, and afterwards earl of Halifax, who had been bred at the same college with him; and when he undertook the great work of recoining the money, he fixed his eye upon Newton for an assistant in it; and accordingly, in 1696, he was appointed warden of the mint, in which employment, he rendered very signal service to the nation. And three years after he was promoted to be master of the mint, a place worth 12 or 15 hundred pounds per annum, which he held till his death. Upon this promotion, he appointed Mr. Whiston his deputy in the mathematical professorship at Cambridge, giving him the full prosits of the place, which appointment itself he also procured for him in 1703. The same year our author was chosen president of the Royal Society, in which chair he sat for 25 years, namely till the time of his death; and he had been chosen a member of the Royal Academy of Sciences at Paris in 1699, as soon as the new regulation was made for admitting foreigners into that society.

Ever since the sirst discovery of the heterogeneous mixture of light, and the production of colours thence arising, he had employed a good part of his time in bringing the experiment, upon which the theory is founded, to a degree of exactness that might satisfy himself. The truth is, this seems to have been his favourite invention; 30 years he had spent in this ardu-| ous task, before he published it in 1704. In infinite series and fluxions, and in the power and rule of gravity in preserving the solar system, there had been some, though distant hints, given by others before him: whereas in diffecting a ray of light into its primary constituent particles, which then admitted of no further separation; in the discovery of the different refrangibility of these particles thus separated; and that these constituent rays had each its own peculiar colour inherent in it; that rays falling in the same angle of incidence have alternate sits of reflection and refraction; that bodies are rendered transparent by the minuteness of their pores, and become opaque by having them large; and that the most transparent body, by having a great thinness, will become less pervious to the light: in all these, which make up his new theory of light and colours, he was absolutely and entirely the first starter; and as the subject is of the most subtle and delicate nature, he thought it necessary to be himself the last finisher of it.

In fact, the affair that chiefly employed his researches for so many years, was far from being confined to the subject of light alone. On the contrary, all that we know of natural bodies, seemed to be comprehended in it; he had found out, that there was a natural action at a distance between light and other bodies, by which both the reflections and refractions, as well as inflections, of the former, were constantly produced. To ascertain the force and extent of this principle of action, was what had all along engaged his thoughts, and what after all, by its extreme subtlety, escaped his most penetrating spirit. However, though he has not made so full a discovery of this principle, which directs the course of light, as he has in regard to the power by which the planets are kept in their courses; yet he gave the best directions possible for such as should be disposed to carry on the work, and furnished matter abundantly sufficient to animate them to the pursuit. He has indeed hereby opened a way of passing from optics to an entire system of physics; and, if we look upon his queries as containing the history of a great man's first thoughts, even in that view they must be always at least entertaining and curious.

This same year, and in the same book with his Optics, he published, for the first time, his Method of Fluxions. It has been already observed, that these two inventions were intended for the public so long before as 1672; but were laid by then, in order to prevent his being engaged on that account in a dispute about them. And it is not a little remarkable, that even now this last piece proved the occasion of another dispute, which continued for many years. Ever since 1684, Leibnitz had been artfully working the would into an opinion, that he first invented this method.— Newton saw his design from the beginning, and had sufficiently obviated it in the first edition of the Principia, in 1687 (viz, in the Scholium to the 2d lemma of the 2d book): and with the same view, when he now published that method, he took occasion to acquaint the world, that he invent<*>d it in the years 1665 and 1666. In the Acta Eruditorum of Leipsic, where an account is given of this book, the author of that account ascribed the invention to Leibnitz, intimating that Newton borrowed it from him. Dr. Keill, the astronomical professor at Oxford, undertook Newton's defence; and after several answers on both sides, Leibnitz complaining to the Royal Society, this body appointed a committee of their members to examine the merits of the case. These, after considering all the papers and letters relating to the point in controversy, decided in favour of Newton and Keill; as is related at large in the life of this last mentioned gentleman; and these papers themselves were published in 1712, under the title of Commercium Epistolicum Johannis Collins, 8vo.

In 1705, the honour of knighthood was conferred upon our author by queen Anne, in consideration of his great merit. And in 1714 he was applied to by the House of Commons, for his opinion upon a new method of discovering the longitude at sea by signals, which had been laid before them by Ditton and Whiston, in order to procure their encouragement; but the petition was thrown aside upon reading Newton's paper delivered to the committee.

The following year, 1715, Leibnitz, with the view of bringing the world more easily into the belief that Newton had taken the method of fluxions from his Differential method, attempted to foil his mathematical skill by the famous problem of the trajectories, which he therefore proposed to the English by way of challenge; but the solution of this, though the most difficult proposition he was able to devise, and what might pass for an arduous affair to any other, yet was hardly any more than an amusement to Newton's penetrating genius: he received the problem at 4 o'clock in the afternoon, as he was returning from the Mint; and, though extremely fatigued with business, yet he finished the solution before he went to bed.

As Leibnitz was privy-counsellor of justice to the elector of Hanover, so when that prince was raised to the British throne, Newton came more under the notice of the court; and it was for the immediate satisfaction of George the First, that he was prevailed on to put the last hand to the dispute about the invention of Fluxions. In this court, Caroline princess of Wales, afterwards queen consort to George the Second, happened to have a curiosity for philosophical enquiries; no sooner therefore was she informed of our author's attachment to the house of Hanover, than she engaged his conversation, which soon endeared him to her. Here she found in every difficulty that full fatisfaction, which she had in vain sought for elsewhere; and she was often heard to declare publicly, that she thought herself happy in coming into the world at a juncture of time, which put it in her power to converse with him. It was at this princess's solicitation, that he drew up an abstract of his Chronology; a copy of which was at her request communicated, about 1718, to signior Conti, a Venetian nobleman, then in England, upon a promise to keep it secret. But notwithstanding this promise, the abbé, who while here had also affected to shew a particular friend<*>hip for Newton, though privately betraying him as much as lay in his power to Leibnitz, was no sooner got across the water into France, than he dispersed copies of it, and procured an antiquary to translate it into French, as well as to write a confutation of it. This, being printed at Paris in 1725, was delivered as a present from the bookseller that printed it to our author, that he might obtain, as was said, his consent| to the publication; but though he expressly refused such consent, yet the whole was published the same year. Hereupon. Newton found it necessary to publish a Defence of himself, which was inserted in the Philosophical Transactions. Thus he, who had so much all his life long been studious to avoid disputes, was unavoidably all his life time, in a manner, involved in them; nor did this last-dispute even finish at his death, which happened the year following. Newton's paper was republished in 1726 at Paris, in French, with a letter of the abbé Conti in answer to it; and the same year some dissertations were printed there by father Souciet against Newton's Chronological Index, an answer to which was inserted by Halley in the Philosophical Transactions, numb. 397.

Some time before this business, in his 80th year, our author was seized with an incontinence of urine, thought to proceed from the stone in the bladder, and deemed to be incurable. However, by the help of a strict regimen and other precautions, which till then he never had occasion for, he procured considerable intervals of ease during the five remaining years of his life. Yet he was not free from some severe paroxysms, which even forced out large drops of sweat that ran down his face. In these circumstances he was never observed to utter the least complaint, nor express the least impatience; and as soon as he had a moment's ease, he would smile and talk with his usual chearfulness. He was now obliged to rely upon Mr. Conduit, who had married his niece, for the discharge of his office in the Mint. Saturday morning March 18, 1727, he read the newspapers, and discoursed a long time with Dr. Mead his physician, having then the perfect use of all his senses and his understanding; but that night he entirely lost them all, and, not recovering them afterwards, died the Monday following, March 20, in the 85th year of his age. His corpse lay in state in the Jerusalemchamber, and on the 28th was conveyed into Westminster-abbey, the pall being supported by the lord chancellor, the dukes of Montrose and Roxburgh, and the earls of Pembroke, Sussex, and Macclesfield. He was interred near the entrance into the choir on the left hand, where a stately monument is erected to his memory, with a most elegant inscription upon it.

Newton's character has been attempted by M. Fontenelle and Dr. Pemberton, the substance of which is as follows. He was of a middle stature, and somewhat inclined to be fat in the latter part of his life. His countenance was pleasing and venerable at the same time; especially when he took off his peruke, and shewed his white hair, which was pretty thick. He never made use of spectacles, and lost but one tooth during his whole life. Bishop Atterbury says, that, in the whole air of Sir Isaac's face and make, there was nothing of that penetrating sagacity which appears in his compositions; that he had something rather languid in his look and manner, which did not raise any great expectation in those who did not know him.

His temper it is said was so equal and mild, that no accident could disturb it. A remarkable instance of which is related as follows. Sir Isaac had a favourite little dog, which he called Diamond. Being one day called out of his study into the next room, Diamond was left behind. When Sir Isaac returned, having been ab- sent but a few minutes, he had the mortification to find, that Diamond having overset a lighted candle among some papers, the nearly finished labour of many years was in flames, and almost consumed to ashes. This loss, as Sir Isaac was then very far advanced in years, was irretrievable; yet, without once striking the dog, he only rebuked him with this exclamation, “Oh Diamond! Diamond! thou little knowest the mischief thou hast done!”

He was indeed of so meek and gentle a disposition, and so great a lover of peace, that he would rather have chosen to remain in obscurity, than to have the calm of life ruffled by those storms and disputes, which genius and learning always draw upon those that are the most eminent for them.

From his love of peace, no doubt, arose that unusual kind of horror which he felt for all disputes: a steady unbroken attention, free from those frequent recoilings inseparably incident to others, was his peculiar felicity; he knew it, and he knew the value of it. No wonder then that controversy was looked on as his bane. When some objections, hastily made to his discoveries concerning light and colours, induced him to lay aside the design he had taken of publishing his Optical Lectures, we find him reflecting on that dispute, into which he had been unavoidably drawn, in these terms: “I blamed my own imprudence for parting with so real a blessing as my quiet, to run after a shadow.” It is true this shadow, as Fontenelle observes, did not escape him afterwards, nor did it cost him that quiet which he so much valued, but proved as much a real happiness to him as his quiet itself; yet this was a happiness of his own making: he took a resolution from these disputes, not to publish any more concerning that theory, till he had put it above the reach of controversy, by the exactest experiments, and the strictest demonstrations; and accordingly it has never been called in question since. In the same temper, after he had sent the manuscript to the Royal Society, with his consent to the printing of it by them; yet upon Hook's injuriously insisting that he himself had demonstrated Kepler's problem before our author, he determined, rather than be involved again in a controversy, to suppress the third book; and he was very hardly prevailed upon to alter that resolution. It is true, the public was thereby a gainer; that book, which is indeed no more than a corollary of some propositions in the first, being briginally drawn up in the popular way, with a design to publish it in that form; whereas he was now convinced that it would be best not to let it go abroad without a strict demonstration.

In contemplating his genius, it presently becomes a doubt, which of these endowments had the greatest share, sagacity, penetration, strength, or diligence; and, after all, the mark that seems most to distinguish it is, that he himself made the justest estimation of it, declaring, that if he had done the world any service, it was due to nothing but industry and patient thought; that he kept the subject of consideration constantly before him, and waited till the first dawning opened gradually, by little and little, into a full and clear light. It is said, that when he had any mathematical problems or solutions in his mind, he would never quit the subject on any account. And his servant has| said, when he has been getting up in a morning, he has sometimes begun to dress, and with one leg in his breechea, sat down again on the bed, where he has remained for hours before he has got his clothes on: and that dinner has been osten three hours ready for him before he could be brought to table. Upon this head several little anecdotes are related; among which is the following: Doctor Stukely coming in accidentally one day, when Newton's dinner was left for him upon the table, covered up, as usual, to keep it warm till he could find it convenient to come to table; the doctor lifting the cover, found under it a chicken, which he presently ate, putting the bones in the dish, and replacing the cover. Some time after Newton came into the room, and after the usual compliments sat down to his dinner; but on taking up the cover, and seeing only the bones of the fowl left, he observed with some little surprise, “I thought I had not dined, but I now find that I have.”

After all, notwithstanding his anxious care to avoid every occasion of breaking his intense application to study, he was at a great distance from being steeped in philosophy. On the contrary, he could lay aside his thoughts, though engaged in the most intricate researches, when his other affairs required his attention; and, as soon as he had leisure, resume the subject at the point where he had lest off. This he seems to have done not so much by any extraordinary strength of memory, as by the force of his inventive faculty, to which every thing opened itself again with ease, if nothing intervened to ruffle him. The readiness of his invention made him not think of putting his memory much to the trial; but this was the offspring of a vigorous intenseness of thought, out of which he was but a common man. He spent therefore the prime of his age in those abstruse researches, when his situation in a college gave him leisure, and while study was his proper business. But as soon as he was removed to the mint, he applied himself chiefly to the duties of that office; and so far quitted mathematics and philosophy, as not to engage in any pursuits of either kind afterwards.

Dr. Pemberton observes, that though his memory was much decayed in the last years of his life, yet he perfectly understood his own writings, contrary to what I had formerly heard, says the doctor, in discourse from many persons. This opinion of theirs might arise perhaps from his not being always ready at speaking on these subjects, when it might be expected he should. But on this head it may be observed, that great geniuses are often liable to be absent, not only in relation to common life, but with regard to some of the parts of science that they are best informed of: inventors seem to treasure up in their minds what they have found out, after another manner, than those do the same things, who have not this inventive faculty. The former, when they have occasion to produce their knowledge, are in some measure obliged immediately to investigate part of what they want; and for this they are not equally fit at all times: from whence it has often happened, that such as retain things chiefly by means of a very strong memory, have appeared off-hand more expert than the discoverers themselves.

It was evidently owing to the same inventive faculty that Newton, as this writer found, had read fewer of the modern mathematicians than one could have expected; his own prodigious invention readily supplying him with what he might have occasion for in the pursuit of any subject he undertook. However, he often censured the handling of geometrical subjects by algebraic calculations; and his book of algebra he called by the name of Universal Arithmetic, in opposition to the injudicious title of Geometry which Des Cartes had given to the treatise in which he shews how the geometrician may assi<*> his invention by such kind of computations. He frequently praised Slusius, Barrow, and Huygens, for not being influenced by the false taste which then began to prevail. He used to commend the laudable attempt of Hugo d'Omerique to restore the ancient analysis; and very much esteemed Apollonius's book De Se<*>ione Rationis, for giving us a clearer notion of that analysis than we had before. Dr. Barrow may be esteemed as having shewn a compass of invention equal, if not superior, to any of the Moderns, our author only excepted; but Newton particularly recommended Huygens's style and manner: he thought him the most elegant of any mathematical writer of modern times, and the truest imitator of the Ancients. Of their taste and mode of demonstration our author always professed himself a great admirer; and even censured himself for not following them yet more closely than he did; and spoke with regret of his mistake at the beginning of his mathematical studies, in applying himself to the works of Des Cartes, and other algebraic writers, before he had considered the Elements of Euclid with that attention which so excellent a writer deserves.

But if this was a fault, it is certain it was a fault to which we owe both his great inventions in speculative mathematics, and the doctrine of Fluxions and Infinite Series. And perhaps this might be one reason why his particular reverence for the Ancients is omitted by Fontenelle, who however certainly makes some amends by that just elogium which he makes of our author's modesty, which amiable quality he represents as standing foremost in the character of this great man's mind and manners. It was in reality greater than can be easily imagined, or will be readily believed: yet it always continued so without any alteration; though the whole world, says Fontenelle, conspired against it; let us add, though he was thereby robbed of his invention of Fluxions. Nicholas Mercator publishing his Logarithmotechnia in 1668, where he gave the quadrature of the hyperbola by an infinite series, which was the first appearance in the learned world of a series of this sort drawn from the particular nature of the curve, and that in a manner very new and abstracted; Dr. Barrow, then at Cambridge, where Mr. Newton, then about 26 years of age, resided, recollected, that he had met with the same thing in the writings of that young gentleman; and there not consined to the hyperbola only, but extended, by general forms, to all sorts of curves, even such as are mechanical; to their quadratures, their rectifications, and their centres of gravity; to the solids sormed by their rotations, and to the superficies of those solids; so that, when their determinations were possible, the series stopped at a certain point, or at least their sums were given by stated rules: and if the absolute determinations were impossible, they could yet be insinitely approximated; which is the happiest and most| refined method, says Fontenelle, of supplying the defects of human knowledge that man's imagination could possibly invent. To be master of so fruitful and general a theory was a mine of gold to a geometrician; but it was a greater glory to have been the discoverer of so surprising and ingenious a system. So that Newton, finding by Mercator's book, that he was in the way to it, and that others might follow in his track, should naturally have been forward to open his treasures, and secure the property, which consisted in making the discovery; but he contented himself with his treasure which he had found, without regarding the glory. What an idea does it give us of his un<*> paralleled modesty, when we find him declaring, that he thought Mercator had entirely discovered his secret, or that others would, before he should become of a proper age for writing! His manuscript upon Infinite Series was communicated to none but Mr. John Collins and the lord Brounker, then President of the Royal Society, who had also done something in this way himself; and even that had not been complied with, but for Dr. Barrow, who would not suffer him to indulge his modesty so much as he desired.

It is further observed, concerning this part of his character, that he never talked either of himself or others, nor ever behaved in such a manner, as to give the most malicious censurers the least occasion even to suspect him of vanity. He was candid and affable, and always put himself upon a level with his company. He never thought either his merit or his reputation sufficient to excuse him from any of the common offices of social life. No singularities, either natural or affected, distinguished him from other men. Though he was firmly attached to the church of England, he was averse to the persecution of the non-conformists. He judged of men by their manners; and the true schismatics, in his opinion, were the vicious and the wicked. Not that he confined his principles to natural religion, for it is said he was thoroughly persuaded of the truth of Revelation; and amidst the great variety of books which he had constantly before him, that which he studied with the greatest application was the Bible, at least in the latter years of his life: and he understood the nature and force of moral certainty as well as he did that of a strict demonstration.

Sir Isaac did not neglect the opportunities of doing good, when the revenues of his patrimony and a profitable employment, improved by a prudent œconomy, put it in his power. We have two remarkable instances of his bounty and generosity; one to Mr. Maclaurin, extra professor of mathematics at Edinburgh, to encourage whose appointment he offered 20 pounds a year to that office; and the other to his niece Barton, upon whom he had settled an annuity of 100 pounds per annum. When decency upon any occasion required expence and shew, he was magnificent without grudging it, and with a very good grace: at all other times, that pomp which seems great to low minds only, was utterly retrenched, and the expence reserved for better uses.

Newton never married; and it has been said, that “perhaps he never had leisure to think of it; that, being immersed in profound studies during the prime of his age, and afterwards engaged in an employment of great importance, and even quite taken up with the company which his merit drew to him, he was not sensible of any vacancy in life, nor of the want of a companion at home.” These however do not appear to be any sufficient reasons for his never marrying, if he had had an inclination so to do. It is much more likely that he had a constitutional indifference to the state, and even to the sex in general; and it has even been said of him, that he never once knew woman.—He left at his death, it seems, 32 thousand pounds; but he made no will; which, Fontenelle tells us, was because he thought a legacy was no gift.—As to his works, besides what were published in his life-time, there were found after his death, among his papers, several discourses upon the subjects of Antiquity, History, Divinity, Chemistry, and Mathematics; several of which were published at different times, as appears from the following catalogue of all his works; where they are ranked in the order of time in which those upon the same subject were published.

1. Several Papers relating to his Telescope, and his Theory of Light and Colours, printed in the Philosophical Transactions, numbs. 80, 81, 82, 83, 84, 85, 88, 96, 97, 110, 121, 123, 128; or vols 6, 7, 8, 9, 10, 11.

2. Optics, or a Treatise of the Reflections, Refractions, and Inflections, and the Colours of Light; 1704, 4to.— A Latin translation by Dr. Clarke; 1706, 4to.—And a French translation by Pet. Coste, Amst. 1729, 2 vols 12mo.—Beside several English editions in 8vo.

3. Optical Lectures; 1728, 8vo. Also in several Letters to Mr. Oldenburg, secretary of the Royal Society, inserted in the General Dictionary, under our author's article.

4. Lectiones Opticæ 1729, 4to.

5. Naturalis Philosophiæ Principia Mathematica; 1687, 4to.—A second edition in 17<*>3, with a Preface, by Roger Cotes.—The 3d edition in 1726, under the direction of Dr. Pemberton.—An English translation, by Motte, 1729, 2 volumes 8vo, printed in several editions of his works, in different nations, particularly an edition, with a large Commentary, by the two learned Jesuits, Le Seur and Jacquier, in 4 volumes 4to, in 1739, 1740, and 1742.

6. A System of the World, translated from the Latin original; 1727, 8vo.—This, as has been already observed, was at first intended to make the third book of his Principia.—An English translation by Motte, 1729, 8vo.

7. Several Letters to Mr. Flamsteed, Dr. Halley, and Mr. Oldenburg.—See our author's article in the General Dictionary.

8. A Paper concerning the Longitude; drawn up by order of the House of Commons; ibid.

9. Abregé de Chronologie, &c; 1726, under the direction of the abbé Conti, together with some Observations upon it.

10. Remarks upon the Observations made upon a Chronological Index of Sir I. Newton, &c. Philos. Trans. vol. 33. See also the same, vol. 34 and 35, by Dr. Halley.

11. The Chronology of Ancient Kingdoms amended, &c; 1728, 4to.

12. Arithmetica Universalis, &c; under the inspec-| tion of Mr. Whiston, Cantab. 1707, 8vo. Printed I think without the author's consent, and even against his will: an offence which it seems was never forgiven. There are also English editions of the same, particularly one by Wilder, with a Commentary, in 1769, 2 vols 8vo. And a Latin edition, with a Commentary, by Castilion, 2 vols 4to, Amst. &c.

13. Analysis per Quantitatum Series, Fluxiones, et Differentias, cum Enumeratione Linearum Tertii Ordinis; 1711, 4to; under the inspection of W. Jones, Esq. F. R. S.—The last tract had been published before, together with another on the Quadrature of Curves, by the Method of Fluxions, under the title of Tractatus duo de Speciebus & Magnitudine Figurarum Curvilinearum; subjoined to the sirst edition of his Optics in 1704; and other letters in the Appendix to Dr. Gregory's Catoptrics, &c, 1735, 8vo.—Under this head may be ranked Newtoni Genesis Curvarum per Umbras; Leyden, 1740.

14. Several Letters relating to his Dispute with Leibnitz, upon his Right to the Invention of Fluxions; printed in the Commercium Epistolicum D. Johannis Collins & aliorum de Analysi Promota, jussu Societatis Regiæ editum; 1712, 8vo.

15. Postscript and Letter of M. Leibnitz to the Abbé Conti, with Remarks, and a Letter of his own to that Abbé; 1717, 8vo. To which was added, Raphson's History of Fluxions, as a Supplement.

16. The Method of Fluxions, and Analysis by Infinite Series, translated into English from the original Latin; to which is added, a Perpetual. Commentary, by the translator Mr. John Colson; 1736, 4to.

17. Several Miscellaneous Pieces, and Letters, as follow:—(1). A Letter to Mr. Boyle upon the subject of the Philosopher's Stone. Inserted in the General Dictionary, under the article Boyle.—(2). A Letter to Mr. Aston, containing directions for his travels; ibid. under our author's article.—(3). An English Translation of a Latin Dissertation upon the Sacred Cubit of the Jews. Inserted among the miscellaneous works of Mr. John Greaves, vol. 2, published by Dr. Thomas Birch, in 1737, 2 vols 8vo. This Dissertation was found subjoined to a work of Sir Isaac's, not finished, intitled Lexicon Propheticum.—(4). Four Letters from Sir Isaac Newton to Dr. Bentley, containing some arguments in proof of a Deity; 1756, 8vo.—(5). Two Letters to Mr. Clarke, &c.

18. Observations on the Prophecies of Daniel and the Apocalypse of St. John; 1733, 4to.

19. Is. Newtoni Elementa Perspectivæ Universalis; 1746, 8vo.

20. Tables for purchasing College Leases; 1742, 12mo.

21. Corollaries, by Whiston.

22. A Collection of several pieces of our author's, under the following title, Newtoni Is. Opuscula Mathematica Philos. & Philol. collegit J. Castilioneus; Laus. 1744, 4to, 8 tomes.

23. Two Treatises of the Quadrature of Curves, and Analysis by Equations of an Infinite Number of Terms, explained: translated by John Stewart, with a large Commentary; 1745, 4to.

24. Description of an Instrument for observing the Moon's Distance from the Fixed Stars at Sea. Philos. Trans. vol. 42.

25. Newton also published Barrow's Optical Lectures, in 1699, 4to: and Bern. Varenii Geographia, &c; 1681, 8vo.

26. The whole works of Newton, published by Dr. Horsley; 1779, 4to, in 5 volumes.

The following is a list of the papers left by Newton at his death, as mentioned above.

A Catalogue of Sir Isaac Newton's Manuscripts and Papers, as annexed to a Bond, given by Mr. Conduit, to the Administrators of Sir Isaac; by which he obliges himself to account for any profit he shall make by publishing any of the papers.

Dr. Pellet, by agreement of the executors, entered into Acts of the Prerogative Court, being appointed to peruse all the papers, and judge which were proper for the press.

No.

1. Viaticum Nautarum; by Robert Wright.

2. Miscellanea; not in Sir Isaac's hand writing.

3. Miscellanea; part in Sir Isaac's hand.

4. Trigonometria; about 5 sheets.

5. Desinitions.

6. Miscellanea; part in Sir Isaac's hand.

7. 40 sheets in 4to, relating to Church History.

8. 126 sheets written on one side, being foul draughts of the Prophetic Stile.

9. 88 sheets relating to Church History.

10. About 70 loose sheets in small 4to, of Chemical papers; some of which are not in Sir Isaac's hand.

11. About 62 ditto, in folio.

12. About 15 large sheets, doubled into 4to; Chemical.

13. About 8 sheets ditto, written on one side.

14. About 5 sheets of foul papers, relating to Chemistry.

15. 12 half-sheets of ditto.

16. 104 half-sheets, in 4to, ditto.

17. About 22 sheets in 4to, ditto.

18. 24 sheets, in 4to, upon the Prophecies.

19. 29 half-sheets; being an answer to Mr. Hook, on Sir Isaac's Theory of Colours.

20. 87 half-sheets relating to the Optics, some of which are not in Sir Isaac's hand.

From No. 1 to No. 20 examined on the 20th of May 1727, and judged not fit to be printed.

T. Pellet.
Witness, Tho. Pilkington.

21. 328 half-sheets in folio, and 63 in sinall 4to; being loose and foul papers relating to the Revelations and Prophecies.

22. 8 half-sheets in small 4to, relating to Church Matters.

23. 24 half-sheets in small 4to; being a discourse relating to the 2d of Kings.

24. 353 half-sheets in folio, and 57 in small 4to; being foul and loose papers relating to Figures and Mathematics.

25. 201 half-sheets in folio, and 21 in small 4to; loose and foul papers relating to the Commercium Epistolicum.|

26. 91 half-sheets in small 4to, in Latin, upon the Temple of Solomon.

27. 37 half-sheets in folio, upon the Host of Heaven, the Sanctuary, and other Church Matters.

28. 44 half-sheets in folio, upon Ditto.

29. 25 half-sheets in folio; being a farther account of the Host of Heaven.

30. 51 half-sheets in folio; being an Historical Account of two notable Corruptions of Scripture.

31. 88 half-sheets in small 4to; being Extracts of Church History.

32. 116 half-sheets in folio; being Paradoxical Questions concerning Athanasius, of which several leaves in the beginning are very much damaged.

33. 56 half-sheets in folio, De Motu Corporum; the greatest part not in Sir Isaac's hand.

34. 61 half-sheets in small 4to; being various sections on the Apocalypse.

35. 25 half-sheets in folio, of the Working of the Mystery of Iniquity.

36. 20 half-sheets in folio, of the Theology of the Heathens.

37. 24 half-sheets in folio; being an Account of the Contest between the Host of Heaven, and the Transgressors of the Covenant.

38. 31 half-sheets in folio; being Paradoxical Questions concerning Athanasius.

39. 107 quarter-sheets in small 4to, upon the Revelations.

40. 174 half-sheets in folio; being loose papers relating to Church History.

May 22, 1727, examined from No. 21 to No. 40 inclusive, and judged them not fit to be printed; only No. 33 and No. 38 should be reconsidered.

T. Pellet.
Witness, Tho. Pilkington.

41. 167 half-sheets in folio; being loose and foul papers relating to the Commercium Epistolicum.

42. 21 half-sheets in folio; being the 3d letter upon Texts of Scripture, very much damaged.

43. 31 half-sheets in folio; being foul papers relating to Church Matters.

44. 495 half-sheets in folio; being loose and foul papers relating to Calculations and Mathematics.

45. 335 half-sheets in folio; being loose and foul papers relating to the Chronology.

46. 112 sheets in small 4to, relating to the Revelations and other Church Matters.

47. 126 half-sheets in folio; being loose papers relating to the Chronology, part in English and part in Latin.

48. 400 half-sheets in folio; being loose Mathematical papers.

49. 109 sheets in 4to, relating to the Prophecies, and Church Matters.

50. 127 half-sheets in folio, relating to the University; great part not in Sir Isaac's hand.

51. 18 sheets in 4to; being Chemical papers.

52. 255 quarter-sheets; being Chemical papers.

53. An Account of Corruptions of Scripture; no<*> in Sir Isaac's hand.

54. 31 quarter-sheets; being Flammell's Explication of Hieroglyphical Figures.

55. About 350 half-sheets; being Miscellaneous papers.

56. 6 half-sheets; being An Account of the Empires &c represented by St. John.

57. 9 half-sheets folio, and 71 quarter-sheets 4to; being Mathematical papers.

58. 140 half-sheets, in 9 chapters, and 2 pieces in folio, titled, Concerning the Language of the Prophets.

59. 606 half-sheets folio, relating to the Chronology; 9 more in Latin.

60. 182 half-sheets folio; being loose papers relating to the Chronology and Prophecies.

61. 144 quarter sheets, and 95 half-sheets folio; being loose Mathematical papers.

62. 137 half-sheets folio; being loose papers relating to the Dispute with Leibnitz.

63. A folio Common-place book; part in Sir Isaac's hand.

64. A bundle of English Letters to Sir Isaac, relating to Mathematics.

65. 54 half-sheets; being loose papers found in the Principia.

66. A bundle of loose Mathematical Papers; not Sir Isaac's.

67. A bundle of French and Latin Letters to Sir Isaac.

68. 136 sheets folio, relating to Optics.

69. 22 half-sheets folio, De Rationibus Motuum &c; not in Sir Isaac's hand.

70. 70 half-sheets folio; being loose Mathematical Papers.

71. 38 half-sheets folio; being loose papers relating to Optics.

72. 47 half-sheets folio; being loose papers relating to Chronology and Prophecies.

73. 40 half-sheets folio; Procestus Mysterii Magni Philosophicus, by Wm. Yworth; not in Sir Isaac's hand.

74. 5 half-sheets; being a letter from Rizzetto to Martine, in Sir Isaac's hand.

75. 41 half-sheets; being loose papers of several kinds, part in Sir Isaac's hand.

76. 40 half-sheets; being loose papers, foul and dirty, relating to Calculations.

77. 90 half-sheets folio; being loose Mathematical papers.

78. 176 half-sheets folio; being loose papers relating to Chronology.

79. 176 half-sheets folio; being loose papers relating to the Prophecies.

80. 12 half-sheets folio; An Abstract of the Chronology. 92 half-sheets, folio; The Chronology.

81. 40 half-sheets folio; The History of the Prophecies, in 10 chapters, and part of the 11th unfinished.

82. 5 small bound books in 12mo, the greatest part not in Sir Isaac's hand, being rough Calcu- lations.|

May 26th 1727, Examined from No. 41 to No. 82 inclufive, and judged not fit to be printed, except No. 80, which is agreed to be printed, and part of No. 61 and 81, which are to be reconfidered.

Th. Pellet.
Witness, Tho. Pilkington.

It is astonishing what care and industry Sir Isaac had employed about the papers relating to Chronology, Church History, &c; as, on examining the papers themselves, which are in the possession of the family of the earl of Portsmouth, it appears that many of them are copies over and over again, often with little or no variation; the whole number being upwards of 4000 sheets in folio, or 8 reams of folio paper; beside the bound books &c in this catalogue, of which the number of sheets is not mentioned. Of these there have been published only the Chronology, and Observations on the Prophecies of Daniel and the Apocalypse of St. John.

NEWTONIAN Philosophy, the doctrine of the universe, or the properties, laws, affections, actions, forces, motions, &c of bodies, both celestial and terrestrial, as delivered by Newton.

This term however is differently applied; which has given occasion to some confused notions relating to it. For, some authors, under this term, include all the corpuscular philosophy, considered as it now stands reformed and corrected by the discoveries and improvements made in several parts of it by Newton. In which sense it is, that Gravesande calls his Elements of Physics, Introductio ad Philosophiam Newtonianam. And in this sense the Newtonian is the same as the new philosophy; and stands contradistinguished from the Cartesian, the Peripatetic, and the ancient Corpuscular.

Others, by Newtonian Philosophy, mean the method or order used by Newton in philosophising; viz, the reasoning and inferences drawn directly from phenomena, exclusive of all previous hypotheses; the beginning from simple principles, and deducing the first powers and laws of nature from a few select phenomena, and then applying those laws &c to account for other things. In this sense, the Newtonian Philosophy is the same with the Experimental Philosophy, or stands opposed to the ancient Corpuscular, and to all hypothetical and fanciful systems of Philosophy.

Others again, by this term, mean that Philosophy in which physical bodies are considered mathematically, and where geometry and mechanics are applied to the solution of phenomena. In which sense, the Newtonian is the same with the Mechanical and Mathematical Philosophy.

Others, by Newtonian Philosophy, understand that part of physical knowledge which Newton has handled, improved, and demonstrated.

And lastly, others, by this Philosophy, mean the new principles which Newton has brought into Philosophy; with the new system founded upon them, and the new solutions of phenomena thence deduced; or that which characterizes and distinguishes his Philosophy from all others. And this is the sense <*>n which we shall here chiefly consider it.

As to the history of this Philosophy, consult the foregoing article. It was first published in the year 1687, the author being then professor of mathematics in the university of Cambridge; a 2d edition, with considerable additions and improvements, came out in 1713; and a 3d in 1726. An edition, with a very large Commentary, came out in 1739, by Le Seur and Jacquier; besides the complete edition of all Newton's works, with notes, by Dr. Horsley, in 1779 &c. Several authors have endeavoured to make it plainer; by setting aside many of the more sublime mathematical researches, and substituting either more obvious reasonings or experiments instead of them; particularly Whiston, in his Prælect. Phys. Mathem.; Gravesande, in Elem. & Inst.; Pemberton, in his View &c; and Maclaurin, in his Account of Newton's Philosophy.

The chief parts of the Newtonian Philosophy, as delivered by the author, except his Optical Discoveries &c, are contained in his Principia, or Mathematical Principles of Natural Philosophy. He founds his system on the following definitions.

1. Quantity of Matter, is the measure of the same, arising from its density and bulk conjointly.—Thus, air of a double density, in the same space, is double in quantity; in a double space, is quadruple in quantity; in a triple space, is sextuple in quantity, &c.

2. Quantity of Motion, is the measure of the same, arising from the velocity and quantity of matter conjunctly.—This is evident, because the motion of the whole is the motion of all its parts; and therefore in a body double in quantity, with equal velocity, the Motion is double, &c.

3. The Vis Insita, Vis Inertiæ, or innate force of matter, is a power of resisting, by which every body, as much as in it lies, endeavours to persevere in its present state, whether it be of rest, or moving uniformly forward in a right line.—This definition is proved to be just by experience, from observing the difsiculty with which any body is moved out of its place, upwards, or obliquely, or even downwards when acted on by a body endeavouring to urge it quicker than the velocity given it by gravity; and any how to change its state of motion or rest. And therefore this force is the same, whether the body have gravity or not; and a cannon ball, void of gravity, if it could be, being discharged horizontally, will go the same distance in that direction, in the same time, as if it were endued with gravity.

4. An Impressed Force, is an action exerted upon a body, in order to change its state, whether of rest or motion.—This force consists in the action only; and remains no longer in the body when the action is over. For a body maintains every new state it acquires, by its vis inertiæ only.

5. A Centripetal Force, is that by which bodies are drawn, impelled, or any way tend towards a point, as to a centre.—This may be considered of three kinds, absolute, accelerative, and motive.

6. The Absolute quantity of a centripetal force, is a measure of the same, proportional to the efficacy of the cause that urges it to the centre.

7. The Accelerative quantity of a centripetal force, is the measure of the same, proportional to the velocity which it generates in a given time.|

8. The Motive quantity of a centripetal force, is a measure of the same, proportional to the motion which it generates in a given time.—This is always known by the quantity of a force equai and contrary to it, that is just sufficient to hinder the descent of the body.

After these definitions, follow certain Scholia, treating of the nature and distinctions of Time, Space, Place, Motion, Absolute, Relative, Apparent, True, Real, &c. After which, the author proposes to shew how we are to collect the true motions from their causes, effects, and apparent differences; and vice versa, how, from the motions, either true or apparent, we may come to the knowledge of their causes and effects. In order to this, he lays down the following axioms or laws of motion.

1st Law. Every body perseveres in its state of rest, or of uniform motion in a right line, unless it be compelled to change that state by forces impressed upon it. —Thus, “Projectiles persevere in their motions, so far as they are not retarded by the resistance of the air, or impelled downwards by the force of gravity. A top, whose parts, by their cohesion, are perpetually drawn aside from rectilinear motions, does not cease its rotation otherwise than as it is retarded by the air. The greater bodies of the planets and comets, meeting with less resistance in more free spaces, preserve their motions, both progressive and circular, for a much longer time.”

2d Law. The Alteration of motion is always proportional to the motive force impressed; and is made in the direction of the right line in which that force is impressed. Thus, if any force generate a certain quantity of motion, a double force will generate a double quantity, whether that force be impressed all at once, or in successive moments.

3d Law. To every action there is always opposed an equal re-action: or the mutual actions of two bodies upon each other, are always equal, and directed to contrary parts. Thus, whatever draws or presses another, is as much drawn or pressed by that other. If you press a stone with your finger, the finger is also pressed by the stone: &c.

From this axiom, or law, Newton deduces the following corollaries.

1. A body by two forces conjoined will describe the diagonal of a parallelogram, in the same time that it would describe the sides by those forces apart.

2. Hence is explained the composition of any one direct force out of any two oblique ones, viz, by making the two oblique forces the sides of a parallelogram, and the diagonal the direct one.

3. The quantity of motion, which is collected by taking the sum of the motions directed towards the same parts, and the difference of those that are directed to contrary parts, suffers no change from the action of bodies among themselves; because the motion which one body loses, is communicated to another.

4. The common centre of gravity of two or more bodies does not alter its state of motion or rest by the actions of the bodies among themselves; and therefore the common centre of gravity of all bodies, acting upon each other, (excluding external actions and impe- diments) is either at rest, or moves uniformly in a right line.

5. The motions of bodies included in a given space are the same among themselves, whether that space be at rest, or move uniformly forward in a right line without any circular motion. The truth of this is evident from the experiment of a ship; where all motions are just the same, whether the ship be at rest, or proceed uniformly forward in a straight line.

6. If bodies, any how moved among themselves, be urged in the direction of parallel lines by equal accelerative forces, they will all continue to move among themselves, after the same manner as if they had not been urged by such forces.

The mathematical part of the Newtonian Philosophy depends chiefly on the following lemmas; especially the first; containing the doctrine of prime and ultimate ratios.

Lem. 1. Quantities, and the ratios of quantities, which in any finite time converge continually to equality, and before the end of that time approach nearer the one to the other than by any given difference, become ultimately equal.

Lem. 2 shews, that in a space bounded by two right lines and a curve, if an infinite number of parallelograms be inscribed, all of equal breadth; then the ultimate ratio of the curve space and the sum of the parallelograms, will be a ratio of equality.

Lem. 3 shews, that the same thing is true when the breadths of the parallelograms are unequal.

In the succeeding lemmas it is shewn, in like manner, that the ultimate ratios of the sine, chord, and tangent of arcs infinitely diminished, are ratios of equality, and therefore that in all our reasonings about these, we may safely use the one for the other:—that the ultimate form of evanescent triangles, made by the arc, chord, or tangent, is that of similitude, and their ultimate ratio is that of equality; and hence, in reasonings about ultimate ratios, these triangles may safely be used one for another, whether they are made with the sine, the arc, or the tangent.—He then demonstrates some properties of the ordinates of curvilinear figures; and shews that the spaces which a body describes by any finite force urging it, whether that force is determined and immutable, or continually varied, are to each other, in the very beginning of the motion, in the duplicate ratio of the forces:—and lastly, having added some demonstrations concerning the evanescence of angles of contact, he proceeds to lay down the mathematical part of his system, which depends on the following theorems.

Theor. 1. The areas which revolving bodies describe by radii drawn to an immoveable centre of force, lie in the same immoveable planes, and are proportional to the times in which they are described.—To this prop. are annexed several corollaries, respecting the velocities of bodies revolving by centripetal forces, the directions and proportions of those forces, &c; such as, that the velocity of such a revolving body, is reciprocally as the perpendicular let fall from the centre of force upon the line touching the orbit in the place of the body, &c.

Theor. 2. Every body that moves in any curve| line described in a plane, and, by a radius drawn to a point either immoveable or moving forward with an uniform rectilinear motion, describes about that point areas proportional to the times, is urged by a centripetal force directed to that point.—With corollaries relatinig to such motions in resisting mediums, and to the direction of the forces when the areas are not proportional to the times.

Theor. 3. Every body that, by a radius drawn to the centre of another body, any how moved, deseribes areas about that centre proportional to the times, is urged by a force compounded of the centripetal forces tending to that other body, and of the whole accelerative force by which that other body is impelled.—With several corollaries.

Theor. 4. The centripetal forces of bodies, which by equal motions describe different circles, tend to the centres of the same circles; and are one to the other as the squares of the arcs described in equal times, applied to the radii of the circles.—With many corollaries, relating to the velocities, times, periodic forces, &c. And, in scholium, the author farther adds, Moreover, by means of the foregoing proposition and its corollaries, we may discover the proportion of a centripetal force to any other known force, such as that of gravity. For if a body by means of its gravity revolve in a circle, concentric to the earth, this gravity is the centripetal force of that body. But from the descent of heavy bodies, the time of one entire revolution, as well as the arc described in any given time, is given by a corol. to this prop. And by such propositions, Mr. Huygens, in his excellent book De Horologio Oscillacorio, has compared the force of gravity with the centrifugal forces of revolving bodies.

On these, and such-like principles, depends the Newtonian Mathematical Philosophy. The author farther shews how to find the centre to which the forces impelling any body are directed, having the velocity of the body given: and finds that the centrifugal force is always as the versed sine of the nascent arc directly, and as the square of the time inversely; or directly as the square of the velocity, and inversely as the chord of the nascent arc. From these premises, he deduces the method of finding the centripetal force directed to any given point when the body revolves in a circle; and this whether the central point be near hand, or at immense distance; so that all the lines drawn from it may be taken for parallels. And he shews the same thing with regard to bodies revolving in spirals, ellipses, hyperbolas, or parabolas. He shews also, having the figures of the orbits given, how to find the velocities and moving powers; and indeed resolves all the most difficult problems relating to the celestial bodies with a surprising degree of mathematical skill. These problems and demonstrations are all contained in the first book of the Principia: but an account of them here would neither be generally understood, nor easily comprized in the limits of this work.

In the second book, Newton treats of the properties and motion of fluids, and their powers of resistance, with the motion of bodies through such resisting mediums, those resistances being in the ratio of any powers of the velocities; and the motions being either made in right lines or curves, or vibrating like pendulums. And here he demonstrates such principles as entirely overthrow the doctrine of Des Cartes's vortices, which was the fashionable system in his time; concluding the book with these words: “So that the hypothesis of vortices is utterly irreconcileable with astronomical phenomena, and rather serves to perplex than explain the heavenly motions. How these motions are performed in free spaces without vortices, may be understood by the first book; and I shall now more fully treat of it in the following book Of the System of the World.”— In this second book he makes great use of the doctrine of Fluxions, then lately invented; for which purpose he lays down the principles of that doctrine in the 2d Lemma, in these words: “The moment of any Genitum is equal to the moments of each of the generating sides drawn into the indices of the powers of those sides, and into their coefficients continually:” which rule he demonstrates, and then adds the following scholium concerning the invention of that doctrine: “In a letter of mine, says he, to Mr. J. Collins, dated December 10, 1672, having described a method of tangents, which I suspected to be the same with Slusius's method, which at that time was not made public; I subjoined these words: ‘This is one particular, or rather a corollary, of a general method which extends itself, without any troublesome calculation, not only to the drawing of tangents to any curve lines, whether geometrical or mechanical, or any how respecting right lines or other curves, but also to the resolving other abstruser kinds of problems about the curvature, areas, lengths, centres of gravity of curves, &c; nor is it (as Hudden's method de Maximis' & Minimis) limited to equations which are free from surd quantities. This method I have interwoven with that other of working in equations, by reducing them to infinite series.’ So far that letter. And these last words relate to a Treatise I composed on that subject in the year 1671.” Which, at least, is therefore the date of the invention of the doctrine of Fluxions.

On entering upon the 3d book of the Principia, Newton briefly recapitulates the contents of the two former books in these words: “In the preceding books I have laid down the principles of philosophy; principles not philosophical, but mathematical; such, to wit, as we may build our reasonings upon in philosophical enquiries. These principles are, the laws and conditions of certain motions, and powers or forces, which chiefly have respect to philosophy. But lest they should have appeared of themselves dry and barren, I have illustrated them-here and there with some philosophical scholiums, giving an account of such things, as are of a more general nature, and which philosophy seems chiefly to be founded on; such as the density and the resistance of bodies, spaces void of all matter, and the motion of light and sounds. It remains, he adds, that from the same principles I now demonstrate the frame of the system of the world. Upon this subject, I had indeed composed the 3d book in a popular method, that it might be read by many. But afterwards considering that such as had not sufficiently entered into the principles could not easily discern the strength of the consequences, nor lay aside the prejudices to which they had been many years accustomed; therefore to prevent the disputes which| might be raised upon such accounts, I chose to reduce the substance of that book into the form of propositions, in the mathematical way, which should be read by those only, who had first made themselves masters of the principles established in the preceding books.”

As a necessary preliminary to this 3d part, Newton lays down the following rules for reasoning in natural philosophy:

1. We are to admit no more causes of natural things, than such as are both true and sufficient to explain their natural appearances.

2. Therefore to the same natural effects we must always assign, as far as possible, the same causes.

3. The qualities of bodies which admit neither intension nor remission of degrees, and which are found to belong to all bodies within the reach of our experiments, are to be esteemed the universal qualities of all bodies whatsoever.

4. In experimental philosophy, we are to look upon propositions collected by general induction from phenomena, as accurately or very nearly true, notwithstanding any contrary hypotheses that may be imagined, till such time as other phenomena occur, by which they may either be made more accurate, or liable to exceptions.

The phenomena first considered are, 1. That the satellites of Jupiter, by radii drawn to his centre, describe areas proportional to the times of description; and that their periodic times, the fixed stars being at rest, are in the sesquiplicate ratio of their distances from that centre. 2. The same thing is likewise observed of the phenomena of Saturn. 3. The five primary planets, Mercury, Venus, Mars, Jupiter, and Saturn, with their several orbits, encompass the sun. 4. The fixed stars being supposed at rest, the periodic times of the said five primary planets, and of the earth, about the sun, are in the sesquiplicate proportion of their mean distances from the sun. 5. The primary planets, by radii drawn to the earth, describe areas no ways proportional to the times: but the areas which they describe by radii drawn to the sun are proportional to the times of description. 6. The moon, by a radius drawn to the centre of the earth, describes an area proportional to the time of description. All which phenomena are clearly evinced by astronomical observations. The mathematical demonstrations are next applied by Newton in the following propositions.

Prop. 1. The forces by which the satellites of Jupiter are continually drawn off from rectilinear motions, and retained in their proper orbits, tend to the centre of that planet; and are reciprocally as the squares of the distances of those satellites from that centre.

Prop. 2. The same thing is true of the primary planets, with respect to the sun's centre.

Prop. 3. The same thing is also true of the moon, in respect of the earth's centre.

Prop. 4. The moon gravitates towards the earth; and by the force of gravity is continually drawn off from a rectilinear motion, and retained in her orbit.

Prop. 5. The same thing is true of all the other planets, both primary and secondary, each with respect to the centre of its motion.

Prop. 6. All bodies gravitate towards every planet; and the weights of bodies towards any one and the same planet, at equal distances from its centre, are proportional to the quantities of matter they contain.

Prop. 7. There is a power of gravity tending to all bodies, proportional to the several quantities of matter which they contain.

Prop. 8. In two spheres mutually gravitating each towards the other, if the matter in places on all sides, round about and equidistant from the centres, be similar; the weight of either sphere towards the other, will be reciprocally as the square of the distance between their centres.—Hence are compared together the weights of bodies towards different planets: hence also are discovered the quantities of matter in the several planets: and hence likewise are found the desities of the planets.

Prop. 9. The force of gravity, in parts downwards from the surface of the planets towards their centres, decreases nearly in the proportion of the distances from those centres.

These, and many other propositions and corollaries, are proved or illustrated by a great variety of experiments, in all the great points of physical astronomy; such as, That the motions of the planets in the heavens may subsist an exceeding long time:—That the centre of the system of the world is immoveable:—That the common centre of gravity of the earth, the sun, and all the planets, is immoveable:—That the sun is agitated by a perpetual motion, but never recedes far from the common centre of gravity of all the planets:—That the planets move in ellipses which have their common focus in the centre of the sun; and, by radii drawn to that centre, they describe areas proportional to the times of description:—The aphelions and nodes of the orbits of the planets are fixt:—To find the aphelions, eccentricities, and principal diameters of the orbits of the planets:—That the diurnal motions of the planets are uniform, and that the libration of the moon arises from her diurnal motion:—Of the proportion between the axes of the planets and the diameters perpendicular to those axes:—Of the weights of bodies in the different regions of our earth:—That the equinoctial points go backwards, and that the earth's axis, by a nutation in every annual revolution, twice vibrates towards the ecliptic, and as often returns to its former position:—That all the motions of the moon, and all the inequalities of those motions, follow from the principles above laid down:—Of the unequal motions of the satellites of Jupiter and Saturn:—Of the flux and reflux of the sea, as arising from the actions of the sun and moon:—Of the forces with which the sun disturbs the motions of the moon; of the varicus motions of the moon, of her orbit, variation, inclinations of her orbit, and the several motions of her nodes:—Of the tides, with the forces of the sun and moon to produce them:—Of the sigure of the moon's body:—Of the precession of the equinoxes:—And of the motions and trajectory of comets. The great author then concludes with a General Scholium, containing reflections on the principal parts of the great and beautiful system of the universe, and of the infinite, eternal Creator and Governor of it.

“The hypothesis of vortices, says he, is pressed| with many difficulties. That every planet by a radius drawn to the sun may describe areas proportional to the times of description, the periodic times of the several parts of the vortices should observe the duplicate proportion of their distances from the sun. But that the pcriodic times of the planets may obtain the sesquiplicate proportion of their distances from the sun, the periodic times of the parts of the vortex ought to be in the sesquiplicate proportion of their distances. That the smaller vortices may maintain their lesser revolutions about Saturn, Jupiter, and other planets, and swim quietly and undisturbed in the greater vortex of the sun, the periodic times of the parts of the sun's vortex should be equal. But the rotation of the sun and planets about their axes, which ought to correspond with the motions of their vortices, recede far from all these proportions. The motions of the comets are exceeding regular, are governed by the same laws with the motions of the planets, and can by no means be accounted for by the hypothesis of vortices. For comets are carried with very eccentric motions through all parts of the heavens indifferently, with a freedom that is incompatible with the notion of a vortex.

“Bodies, projected in our air, suffer no resistance but from the air. Withdraw the air, as is done in Mr. Boyle's vacuum, and the resistance ceases. For in this void a bit of fine down and a piece of solid gold descend with equal velocity. And the parity of reason must take place in the celestial spaces above the earth's atmosphere; in which spaces, where there is no air to resist their motions, all bodies will move with the greatest freedom; and the planets and comets will constantly pursue their revolutions in orbits given in kind and position, according to the laws above explained But though these bodies may indeed persevere in their orbits by the mere laws of gravity, yet they could by no means have at first derived the regular position of the orbits themselves from those laws.

“The six primary planets are revolved about the sun, in circles concentric with the sun, and with motions directed towards the same parts, and almost in the same plane. Ten moons are revolved about the earth, Jupiter and Saturn, in circles concentric with them, with the same direction of motion, and nearly in the planes of the orbits of those planets. But it is not to be conceived that mere mechanical causes could give birth to so many regular motions: since the comets range over all parts of the heavens, in very eccentric orbits, For by that kind of motion they pass easily through the orbs of the planets, and with great rapidity; and in their aphelions, where they move the slowest, and are detained the longest, they recede to the greatest distances from each other, and thence suffer the least disturbance from their mutual attractions. This most beautiful system of the sun, planets, and comets, could only proceed from the counsel and dominion of an intelligent and powerful Being. And if the fixed stars are the centres of other like systems, these being formed by the like wise counsel, must be all subject to the dominion of one; especially, since the light of the fixed stars is of the same nature with the light of the sun, and from every system light passes into all the other systems. And left the system of the fixed stars should, by their gravity, fall on each other mutually, he hath placed those systcms at immense distances one from another.”

Then, after a truly pious and philosophical descant on the attributes of the Being who could give existence and continuance to such prodigious mechanism, and with so much beautiful order and regularity, the great author proceeds,

“Hitherto we have explained the phenomena of the heavens and of our sea, by the power of gravity, but have not yet assigned the cause of this power. This is certain, that it must proceed from a cause that penetrates to the very centres of the sun and planets, without suffering the least diminution of its force; that operates, not according to the quantity of the surfaces of the particles upon which it acts, (as mechanical causes use to do,) but according to the quantity of the solid matter which they contain, and propagates its virtue on all sides, to immense distances, decreasing always in the duplicate proportion of the distances. Gravitation towards the sun, is made up out of the gravitations towards the several particles of which the body of the sun is composed; and in receding from the sun, decreases accurately in the duplicate proportion of the distances, as far as the orb of Saturn, as evidently appears from the quiescence of the aphelions of the planets; nay, and even to the remotest aphelions of the comets, if those aphelions are also quiescent. But hitherto I have not been able to discover the cause of those properties of gravity from phenomena, and I frame no hypotheses. For whatever is not deduced from the phenomena, is to be called an hypothesis; and hypotheses, whether metaphysical or physical, whether of occult qualities or mechanical, have no place in experimental philosophy. In this philosophy particular propositions are inferred from the phenomena, and afterwards rendered general by induction. Thus it was that the impenetrability, the mobility, and the impulsive force of bodies, and the laws of motion and of gravitation, were discovered. And to us it is enough, that gravity does really exist, and act according to the laws which we have explained, and abundantly serves to account for all the motions of the celestial bodies, and of our sea.

“And now we might add something concerning a certain most subtle spirit, which pervades and lies hid in all gross bodies, by the force and action of which spirit, the particles of bodies mutually attract one another at near distances, and cohere, if contiguous, and electric bodies operate to greater distances, as well repelling as attracting the neighbouring corpuscles; and light is emitted, reflected, refracted, inflected, and heats bodies; and all sensation is excited, and the members of animal bodies move at the command of the will, namely, by the vibrations of this spirit, mutually propagated along the solid filaments of the nerves, from the outward organs of sense to the brain, and from the brain into the muscles. But these are things that cannot be explained in few words, nor are we furnished with that sufficiency of experiments which is required to an accurate determination and demonstration of the laws by which this electric and elastic spirit ope- rates.”|

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ABCDEFGHKLMNOPQRSTU and VWXYZABCEGLMN

Entry taken from A Mathematical and Philosophical Dictionary, by Charles Hutton, 1796.

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NEEDHAM (John Tuberville)
NEEDLE
NEGATIVE
NEWEL
NEWTON (Dr. John)
* NEWTON (Sir Isaac)
NICHE
NICOLE (Francis)
NIEUWENTYT (Bernard)
NIGHT
NOCTILUCA