Principia Mathematica (Motte Translation, 1848) — part 1 of 45

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NEWTON'S PRINCIPIA.

THE

MATHEMATICAL PEINCIPLES

OP

NATURAL PHILOSOPHY^

BY SIR ISAAC NEWTON;

TRANSLATED INTO ENGLISH BY ANDREW MOTTE.

TO WHICH IS ADDED

IE¥TOI'S SYSTEM OE THE ¥OELD ;

With a Portrait taken from the Bust in the Royal Observatory at Greenwich.

FIRST AMERICAN EDITION, CAREFULLY REVISED AND CORRECTED,

WITH A LIFE OP THE AUTHOR, BY N. W. CHITTENDEN, M. A., &c.

NEW-YORK:

PUBLISHED BY DANIEL ADEE, 107 FULTON-STREET.

DEDICATION

TO THE

TEACHERS OE THE lORMAL SCHOOL

OF THE STATE OF NEW-YORK.

Gentlemen : —

A stirring freshness in the air, and ruddy streaks upon the horizon of the moral world betoken the grateful dawning of a new era. The days of a drivelling instruction are departing. With us is the opening promise of a better time, wherein genuine man- hood doing its noblest work shall have adequate reward. Teacher is the highest and most responsible office man can fill. Its dignity is, and will yet be held commensurate with its duty — a duty boundless as man's intellectual capacity, and great as his moral need — a duty from the performance of which shall emanate an influence not limited to the now and the here, but which surely will, as time flows into eternity and space into infinity, roll up, a measureless curse or a measureless blessing, in inconceivable swellings along the infinite curve. It is an office that should be esteemed of even sacred import in this country. Ere long a hun- dred millions, extending from the Atlantic to the Pacific, from Baffin's Bay to that of Panama, shall call themselves American citizens. What a field for those two master-passions of the hu- man soul — the love of Rule, and the love of Gain ! How shall our liberties continue to be preserved from the graspings of Am^ bition and the corruptions of Gold ? Not by Bills of Rights,

4: DEDICATION.

Constitutions, and Statute Books ; but alone by the rightly culti- vated hearts and heads of the People. They must themselves guard the Ark. It is yours to fit them for the consecrated charge. Look well to it : for you appear clothed in the majesty of great power ! It is yours to fashion, and to inform ; to save, and to perpetuate. You are the Educators of the People : you are the prime Conservators of the public weal. Betray your trust, and the sacred fires would go out, and the altars crumble into dust : knowledge become lost in tradition, and Christian no- bleness a fable ! As you, therefore, are multiplied in number, elevated in consideration, increased in means, and fulfill, well and faithfully, all the requirements of true Teachers, so shall our fa- voured land lift up her head among the nations of the earth, and call herself blessed.

In conclusion. Gentlemen, to you, as the conspicuous leaders in the vast and honourable labour of Educational Reform, and Popular Teaching, the First American Edition of the Principia of Newton — the greatest work of the greatest Teacher — is most respectfully dedicated.

N. W. CHITTENDEN.

INTRODUCTION TO THE AMERICAN EDITION.

That the Principia of Newton should have remained so gen- erally unknown in this country to the present day is a somewhat remarkable fact ; because the name of the author, learned with the very elements of science, is revered at every hearth-stone where knowledge and virtue are of chief esteem, while, abroad, in all the high places of the land, the character which that name recalls is held up as the noblest illustration of what Man may be, and may do, in the possession and manifestation of pre-eminent intellectual and moral worth ; because the work is celebrated, not only in the history of one career and one mind, but in the history of all achievement and human reason itself; because of the spirit of inquiry, which has been aroused, and which, in pursuing its searchings, is not always satisfied with stopping short of the foun- tain-head of any given truth ; and, finally, because of the earnest endeavour that has been and is constantly going on, in many sections of the Republic, to elevate the popular standard of edu- cation and give to scientific and other efforts a higher and a better aim.

True, the Principia has been hitherto inaccessible to popular use. A few copies in Latin, and occasionally one in English may be found in some of our larger libraries, or in the possession of some ardent disciple of the great Master. But a dead language in the one case, and an enormous price in both, particularly in that of the English edition, have thus far opposed very sufficient obstacles to the wide circulation of the work. It is now, how- ever, placed within the reach of all. And in performing this la- bour, the utmost care has been taken, by collation, revision, and otherwise, to render the First American Edition the most accurate and beautiful in our language. " Le plus beau monument que r on puisse elever a la gloire de Newton, c'est une bonne edition de ses ouvrages :" and a monument like unto that we would here

VI INTRODUCTION TO

set up. The Principia, above all, glows with the immortality of a transcendant mind. Marble and brass dissolve and pass away ; but the true creations of genius endure, in time and beyond time, forever : high upon the adamant of the indestructible, they send forth afar and near, over the troublous waters of life, a pure, un- wavering, quenchless light whereby the myriad myriads of barques, richly laden with reason, intelligence and various faculty, are guided through the night and the storm, by the beetling shore and the hidden rock, the breaker and the shoal, safely into havens calm and secure.

To the teacher and the taught, the scholar and the student, the devotee of Science and the worshipper of Truth, the Principia must ever continue to be of inestimable value. If to educate means, not so much to store the memory with symbol» and facts, as to bring forth the faculties of the soul and develope them to the full by healthy nurture and a hardy discipline, then, what so effec- tive to the accomplishment of that end as the study of Geometri- cal Synthesis ? The Calculus, in some shape or other, is, indeed, necessary to the successful prosecution of researches in the higher branches of philosophy. But has not the Analytical encroached upon the Synthetical, and Algorithmic Formulas been employed when not requisite, either for the evolution of truth, or even its apter illustration ? To each method belongs, undoubtedly, an appropriate use. Newton, himself the inventor of Fluxions, censured the handling of Geometrical subjects by Algebraical calculations ; and the maturest opinions which he expressed were additionally in favour of the Geometrical Method. His prefer- ence, so strongly marked, is not to be reckoned a mere matter of taste ; and his authority should bear with preponderating weight upon the decision of every instructor in adopting what may be deemed the best plan to insure the completest mental develop- ment. Geometry, the vigorous product of remote time ; blended with the earliest aspirations of Science and the earliest applica- tions of Art ; as well in the measures of music as in the move- ment of spheres ; as wholly in the structure of the atom as in that of the world ; directing Motion and shaping Appearance ; in a word, at the moulding of the created all, is, in comprehensive

THE AMERICAN EDITION. Vll

view, the outward form of that Inner Harmony of which and in which all things are. Plainly, therefore, this noble study has other and infinitely higher uses than to increase the power of ab- straction. A more general and thorough cultivation of it should be strenuously insisted on. Passing from the pages of Euclid or Legendre, might not the student be led, at the suitable time, to those of the Principia wherein Geome*try may be found in varied use from the familiar to the sublime ? The profoundest and the happiest results, it is believed, would attend upon this enlargement of our Educational System.

Let the Principia, then, be gladly welcomed into every Hall where a true teacher presides. And they who are guided to the diligent study of this incomparable work, who become strengthened by its reason, assured by its evidence, and enlight- ened by its truths, and who rise into loving communion with the great and pure spirit of its author, will go forth from the scenes of their pupilage, and take their places in the world as strong- minded, right-hearted men — such men as the Theory of our Government contemplates and its practical operation absolutely demands.

LIFE OF

SIR ISAAC NEWTON.

Nee fas est proprius mortali attingere Divos, — Halley.

From the thick darkness of the middle ages man's struggling spirit emerged as in new birth ; breaking out of the iron control of that period ; growing strong and confident in the tug and din of succeeding conflict and revolution, it bounded forwards and upwards with resistless vigour to the investigation of physical and moral truth ; ascending height after height ; sweeping afar over the earth, penetrating afar up into the heavens ; increasing in en- deavour, enlarging in endowment ; every where boldly, earnestly out-stretching, till, in the Author of the Principia, one arose, who, grasping the master-key of the universe and treading its celestial paths, opened up to the human intellect the stupendous realities of the material world, and, in the unrolling of its harmo- nies, gave to the human heart a new song to the goodness, wis- dom, and majesty of the all-creating, all-sustaining, all-perfect God.

Sir Isaac Newton, in whom the rising intellect seemed to attain, as it were, to its culminating point, was born on the 25th of De- cember, O. S. 1642 — Christmas day — at Woolsthorpe, in the parish of Colsterworth, in Lincolnshire. His father, John New- ton, died at the age of thirty-six, and only a few months after his marriage to Harriet Ayscough, daughter of James Ayscough, oi Rutlandshire. Mrs. Newton, probably wrought upon by the early loss of her husband, gave premature birth to her only and posthumous child, of which, too, from its extreme diminutiveness, she appeared likely to be soon bereft. Happily, it was otherwise decreed ! The tiny infant, on whose little lips the breath of life

10 LIFE OP SIR ISAAC NEWTON.

SO doubtingly liovered, lived ; — lived to a vigorous maturity, to a hale old age ; — lived to become the boast of his country, the v^^on- der of his time, and the "ornament of his species."

Beyond the grandfather, Robert Nev^ton, the descent of Sir Isaac cannot with certainty be traced. Two traditions were held in the family : one, that they were of Scotch extraction ; the other, that they came originally from Newton, in Lancashire, dwelling, for a time, however, at Westby, county of Lincoln, be- fore the removal to and purchase of Woolsthorpe — about a hundred years before this memorable birth.

The widow Newton was left with the simple means of a com- fortable subsistence. The Woolsthorpe estate together with a small one which she possessed at Sewstern, in Leicestershire, yield- ed her an income of some eighty pounds ; and upon this limited sum, she had to rely chiefly for the support of herself, and the educa- tion of her child. She continued his nurture for three years, when, marrying again, she confided the tender charge to the care of her own mother.

Great genius is seldom marked by precocious development ; and young Isaac, sent, at the usual age, to two day schools at Skillington and Stoke, exhibited no unusual traits of character. In his twelfth year, he was placed at the public school at Gran- tham, and boarded at the house of Mr. Clark, an apothecary. But even in this excellent seminary, his mental acquisitions con- tinued for a while unpromising enough : study apparently had no charms for him ; he was very inattentive, and ranked low in the school. One day, however, the boy immediately above our seem- ingly dull student gave him a severe kick in the stomach ; Isaac, deeply affected, but with no outburst of passion, betook himself, with quiet, incessant toil, to his books ; he quickly passed above the offending classmate ; yet there he stopped not ; the strong spirit was, for once and forever, awakened, and, yielding to its noble impulse, he speedily took up his position at the head of all.

His peculiar character began now rapidly to unfold itself. Close application grew to be habitual. Observation alternated with reflection. "A sober, silent, thinking lad," yet, the wisest and the kindliest, the indisputable leader of his fellows. Gener-

LIFE OF SIR ISAAC NEWTON. 11

osity, modesty, and a love of truth distinguished him then as ever afterwards. He did not often join his classmates in play ; but he would contrive for them various amusements of a scientific kind. Paper kites he introduced ; carefully determining their best form and proportions, and the position and number of points whereby to attach the string. He also invented paper lanterns ; these served ordinarily to guide the way to school in winter mornings, but occasionally for quite another purpose ; they were attached to the tails of kites inadarknight, to the dismay of the country people dreading portentous comets, and to the immeasureable delight of his companions. To him, however, young as he was, life seemed to have become an earnest thing. When not occupied with his studies, his mind would be engrossed with mechanical contrivances ; now imitating, now inventing. He became singularly skilful in the use of his little saws, hatchets, hammers, and other tools. A windmill was erected near Grantham ; during the operations of the workmen, he was frequently present ; in a short time, he had completed a perfect working model of it, which elicited general admiration. Not content, however, with this exact imitation, he conceived the idea of employing, in the place of sails, animal power ; and, adapting the construction of his mill accordingly, he enclosed in it a mouse, called the miller, and which by acting on a sort of treadwheel, gave motion to the machine. He invented, too, a mechanical carriage — having four wheels, and put in motion with a handle worked by the person sitting inside. The measurement of time early drew his attention. He first constructed a water clock, in proportions somewhat like an old-fashioned house clock. The index of the dial plate was turned by a piece of wood acted upon by dropping water. This instrument, though long used hy himself, and by Mr. Clark's family, did not satisfy his inquiring mind. His thoughts rose to the sun ; and, by careful and oft-re-. peated observations of the solar movements, he subsequently- formed many dials. One of these, named Isaac's dial, was the accurate result of years' labour, and was frequently referred to for the hour of the day by the country people.

May we not discern in these continual efforts — the diligent re- search; the patient meditation, the aspiring glance, and the energy

12 LIFE OF SIR ISAAC NEWTON.

of discovery — the stirring elements of that wondrous spirit, which, clear, calm, and great, moved, in after years, through deep onward through deep of Nature's mysteries, unlocking her strongholds, dispelling darkness, educing order — everywhere si- lently conquering.

Newton had an early and decided taste for drawing. Pictures, taken sometimes from copies, but often from life, and drawn, coloured and framed by himself, ornamented his apartment. He was skilled also, in j)oetical composition, " excelled in making verses ;" some of these were borne in remembrance and repeated, seventy years afterward, by Mrs. Vincent, for whom, in early youth, as Miss Storey, he formed an ardent attachment. She w^as the sister of a physician resident near Woolsthorpe ; but Newton's intimate acquaintance with her began at Grantham, where they were both numbered among the inmates of the same house. Two or three years younger than huuself, of great per- sonal beauty, and unusual talent, her society afforded him the greatest pleasure ; and their youthful friendship, it is believed, gradually rose to a higher passion ; but inadequacy of fortune prevented their union. Miss Storey was afterwards twice mar- ried ; Newton, never ; his esteem for her continued unabated during life, accompanied by numerous acts of attention and kindness.

In 1656, Newton's mother was again left a widow, and took up her abode once more at Woolsthorpe. He was now fifteen years of age, and had made great progress in his studies ; but she, desirous of his help, and from motives of economy, recalled him from school. Business occupations, however, and the manage- ment of the farm, proved utterly distasteful to him. When sent to Grantham Market on Saturdays, he would betake himself to his former lodgings in the apothecary's garret, where some of Mr. Clark's old books employed his thoughts till the aged and trust- worthy servant had executed the family commissions and announced the necessity of return : or, at other times, our young philosopher would seat himself under a hedge, by the wayside, and continue his studies till the same faithful personage — proceeding alone to the town and completing the day's business — stopped as he re-

LIFE OF SIR ISAAC NEWTON. 13

turned. The more immediate affairs of the farm received no better attention. In fact, his passion for study grew daily more absorbing, and his dislike for every other occupation more in- tense. His mother, therefore, wisely resolved to give him all the advantages v/hich an education could confer. He was sent back to Grantham school, where he remained for some months in busy preparation for his academical studies. At the recommendation of one of his uncles, who had himself studied at Trinity College, Cambridge, Newton proceeded thither, and was duly admitted, on the 5th day of June 1660, in the eighteenth year of his age.

The eager student had now entered upon a new and wider field ; and we find him devoting himself to the pursuit of know- ledge with amazing ardour and perseverance. Among other sub- jects, his attention was soon drawn to that of Judicial Astrology. He exposed the folly of this pseudo-science by erecting a figure with the aid of one or two of the problems of Euclid ; — and thus began his study of the Mathematics. His researches into this science were prosecuted with unparallelled vigour and success. Regarding the propositions contained in Euclid as self-evident truths, he passed rapidly over this ancient system" — a step which he afterward much regretted — and mastered, without further pre- paratory study, the Analytical Geometry of Descartes. Wallis's Arithmetic of Infinites, Saunderson's Logic, and the Optics of Kepler, he also studied with great care ; writing upon them many comments ; and, in these notes on Wallis's work was un- doubtedly the germ of his fluxionary calcuhis. His progress was so great that he found himself more profoundly versed than his tutor in many branches of learning. Yet his acquisitions were not gotten with the rapidity of intuition ; but they were thoroughly made and firmly secured. Quickness of apprehension, or intel- lectual nimbleness did not belong to him. He saw too far : his insight was too deep. He dwelt fully, cautiously upon the least subject ; while to the consideration of the greatest, he brought a massive strength joined with a matchless clearness, that, regard- less of the merely trivial or unimportant, bore with unerring sa- gacity upon the prominences of the subject, and, grappling with its difficulties, rarely failed to surmount them.

14 LIFE OF SIR ISAAC NEWTON.

His early and fast friend, Dr. Barrow — in compass of inven- tion only inferior to Newton — who had been elected Professor of Greek in the University, in 1660, was made Lucasian Profes- sor of Mathematics in 1663, and soon afterward delivered his Optical Lectures : the manuscripts of these were revised by New- ton, and several oversights corrected, and many important sug- gestions made by him ; but they were not published till 1669ji

In the year 1665, he received the degree of Bachelor of Arts ; and, in ] 666, he entered upon those brilliant and imposing dis- coveries which have conferred inappreciable benefits upon science, and immortality upon his own name.

Newton, himself, states that he was in possession of his Method of Fluxions, " in the year 1666, or before." Infinite quantities had long been a subject of profound investigation ; among the ancients by Archimedes, and Pappus of Alexandria ; among the moderns by Kepler, Cavaleri, Roberval, Fermat and Wallis. With consummate ability Dr. Wallis had improved upon the la- bours of his predecessors : with a higher power, Newton moved forwards from where Wallis stopped. Our author first invented his celebrated Binomial Theorem. And then, applying this Theorem to the rectification of curves, and to the determination of the surfaces and contents of solids, and the position of their centres of gravity, he discovered the general principle of deducing the areas of curves from the ordinate, by considering the area as a nascent quantity, increasing by continual fluxion in the propor- tion of the length of the ordinate, and supposing the abscissa to increase uniformly in proportion to the time. Regarding lines as generated by the motion of points, surfaces by the motion of lines, and solids by the motion of surfaces, and considering that the ordinates, abscissae, &:c., of curves thus formed, vary accord- ing to a regular law depending on the equation of the curve, he deduced from this equation the velocities with which these quantities are generated, and obtained by the rules of infinite series, the ultimate value required. To the velocities with which every line or quantity is generated, he gave the name of Flux- ions, and to the lines or quantities themselves, that of Fluents. A discovery that successively bafiied the acutest and strongest

LIFE OF SIR ISAAC NEWTON. 15

intellects : — that, variously modified, has proved of incalculable service in aiding to develope the most abstruse and the highest truths in Mathematics and Astronomy : and that was of itself enough to render any name illustrious in the crowded Annals of Science.

At this period, the most distinguished philosophers were direct- ing all their energies to the subject of light and the improvement of the refracting telescope. Newton, having applied himself to the grinding of "optic glasses of other figures than spherical," ex- perienced the impracticability of executing such lenses ; and con- jectured that their defects, and consequently those of refracting telescopes, might arise from some other cause than the imperfect convergency of rays to a single point. He accordingly "procured a triangular glass prism to try therewith the celebrated phenom- ena of colours." His experiments, entered upon with zeal, and conducted with that industry, accuracy, and patient thought, for which he was so remarkable, resulted in the grand conclusion, that Light was not homogeneous, but consisted of rays,

SOME OF which WERE MORE REFRANGIBLE THAN OTHERS. TMs

profound and beautiful discovery opened up a new era in the History of Optics. As bearing, however, directly upon the construc- tion of telescopes, he saw that a lens refracting exactly like a prism would necessarily bring the different rays to different foci, at different distances from the glass, confusing and rendering the vision indistinct. Taking for granted that all bodies produced spectra of equal length, he dismissed all further consideration of the refracting instrument, and took up the principle of reflection.. Eays of all colours, he found, were reflected regularly, so that the angle of reflection was equal to the angle of incidence, and hence he concluded that optical instruments might he brought to any degree of j^erfection imaginahle^ provided reflecting specula of the requisite fig'are and finish could be obtained. At this stage of his optical researches, he was forced to leave Cambridge oil account of the plague which was then desolating England.

He retired to Woolsthorpe. v The old manor-house, in which he was born, was situated in a beautiful little valley, on the west side.^ of the river Witham ; and here in the quiet home of his boyhood^,

2

16 LIFE OF SIR ISAAC NEWTON.

he passed his days in serene contemplation, while the stalking pestilence was hurrying its tens of thousands into undistinguisha- ble graves.

Towards the close of a pleasant day in the early autumn of 1666, he was seated alone beneath a tree, in his garden, absorbed in meditation. He was a slight young man ; in the twenty-fourth year of his age ; his countenance mild and full of thought. For a century previous, the science of Astronomy had advanced with rapid strides. The human mind had risen from the gloom and bondage of the middle ages, in unparalleled vigour, to unfold the system, to investigate the phenomena, and to establish the laws of the heavenly bodies. Copernicus, Tycho Brahe, Kepler, Galileo, and others had prepared and lighted the way for him who was to give to their labour its just value, and to their genius its true lustre. At his bidding isolated facts were to take order as parts of one harmonious whole, and sagacious conjectures grow luminous in the certain splendour of demonstrated truth. And this ablest man had come — was here. His mind, familiar with the knowledge of past effort, and its unequalled faculties develop- ed in transcendant strength, was now moving on to the very threshold of Its grandest achievement. Step by step the untrod- den path was measured, till, at length, the entrance seemed dis- closed, and the tireless explorer to stand amid the first opening wonders of the universe.

The nature of gravity — that mysterious power which causes all bodies to descend towards the centre of the earth — had, in- deed, dawned upon him. And reason busily united link to link of that chain which was yet to be traced joining the least to the vastest, the most remote to the nearest, in one harmonious bond. From the bottoms of the deepest caverns to the summits of the highest mountains, this power suffers no sensible change : may not its action, then, extend to the moon ? Undoubtedly : and further reflection convinced him that such a power might be sufficient for retaining that luminary in her orbit round the earth. But, though this powder suffers no sensible variation, in the little change of distance from the ^earth's centre, at which w^e may place our- ielves, yet, at the distance of the moon, may not its force undergo

LIFE OF SIR ISAAC NEWTON, 17

more or less diminution ? The conjecture appeared most proba- ble : and, in order to estimate what the degree of diminution might be, he considered that if the moon be retained in her orbit by the force of gravity, the primary planets must also be carried round 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 they were held in their courses by any power like gravity, its strength must decrease in the duplicate proportion of the in- crease of distance. In forming this conclusion, he supposed the planets to move in perfect circles, concentric to the sun. Now was this the law of the moon's motion ? Was such a force, em- anating from the earth and directed to the moon, sufficient, when diminished as the square of the distance, to retain her in her orbit ? To ascertain this master-fact, he compared the space through which heavy bodies fall, in a second of time, at a given distance from the centre of the earth, namely, at its surface, with the space through which the moon falls, as it were, to the earth, in the same time, while revolving in a circular orbit. He was absent from books ; and, therefore, adopted, in computing the earth's diameter, the common estimate of sixty miles to a degree of latitude as then in use among geographers and navigators. The result of his calculations did not, of course, answer his ex- pectations ; hence, he concluded that some other cause, beyond the reach of observation — analogous, perhaps, to the vortices of Des- cartes— -joined its action to that of the power of gravity upon the moon. Though by no means satisfied, he yet abandoned awhile further inquiry, and remained totally silent upon the subject.

These rapid marches in the career of discovery, combined with the youth of Newton, seem to evince a penetration the most lively, and an invention the most exuberant. But in him there was a conjunction of influences as extraordinary as fortunate. Study, unbroken, persevering and profound carried on its inform- ing and disciplining work upon a genius, natively the greatest, and rendered freest in its movements, and clearest in its vision, through the untrammelling and enlightening power of religion. And, in this happy concurrence, are to be sought the elements of those amazing abilities, which, grasping, with equal facility, the

18 LIFE OF SIR ISAAC NEWTON.

minute and the stupendous, brought these successively to light, and caused science to make them her own.

In 1667, Newton was made a Junior Fellow ; and, in the year following, he took his degree of Master of Arts, and was appoint- ed to a Senior Fellowship.

On his return to Cambridge, in 1668, he resumed his optical labours. Having thought of a delicate method of polishing metal, he proceeded to the construction of his newly projected reflect- ing telescope ; a small specimen of which he actually made with his own hands. It was six inches long ; and magnified about forty times ; — a power greater than a refracting instrument of six feet tube could exert with distinctness. Jupiter, with his four satellites, and the horns, or moon-like phases of Venus were plainly visible through it. This was the first reflecting

TELESCOPE EVER EXECUTED AND DIRECTED TO THE HEAVENS.

He gave an account of it, in a letter to a friend, dated February 23d, 1668-9 — a letter which is also remarkable for containing the first allusion to his discoveries " concernina; the nature of lidit." En- eouraged by the success of his first experiment, he again executed with his own hands, not long afterward, a second and superior instrument of the same kind. The existence of this having come to the knowledge of the Royal Society of London, in 1671, they requested it of Newton for examination. He accordingly sent it to them. It excited great admiration ; it was shown to the king ; a drawing and description of it was sent to Paris ; and the tele- scope itself was carefully preserved in the Library of the Society. Newton lived to see his invention in public use, and of eminent service in the cause of science.

In the spring of 1669, he wrote to his friend Francis Aston, Esq., then about setting out on his travels, a letter of advice and directions ; it was dated May 18th, and is interesting as exhibit- ing some of the prominent features in Newton's character. Thus :—

" Since in your letter you give me so much liberty of spending my judgment about what may be to your advantage in travelling, I shall do it more freely than perhaps otherwise would have been decent. First, then, I will lay down some general rules, most of

LIFE OF SIR ISAAC NEWTON. 19

which, I believe, you have considered already ; but if any of them be new to you, they may excuse the rest ; if none at all, yet is my punishment more in writing than yours in reading.

"When you come into any fresh company. 1. Observe their humours. 2. Suit your own carriage thereto, by which insinua- tion you will make their converse more free and open. 3. Let your discourse be more in queries and doubtings than peremptory assertions or disputings, it being the design of travellers to learn, not to teach. Besides, it will persuade your acquaintance that you have the greater esteem of them, and so make them more ready to communicate what they know to you ; whereas nothing sooner occasions disrespect and quarrels than peremptoriness. You will find little or ho advantage in seeming wiser or much more ignorant than your company. 4. Seldom discommend any- thing though never so bad, or do it but moderately, lest you be unexpectedly forced to an unhandsome retraction. It is safer to commend any thing more than it deserves, than to discommend a thing so much as it deserves; for commendations meet not so often with oppositions, or, at least, are not usually so ill re- sented by men that think otherwise, as discommendations; and you will insinuate into men's favour by nothing sooner than seem- ing to approve and commend w^iat they like ; but beware of doing it by comparison. 5. If you be affronted, it is better, in a foreign country, to pass it by in silence, and with a jest, though with some dishonour, than to endeavour revenge ; for, in the first case, your credit's ne'er the worse when you return into England, or come into other company that have not heard of the quarrel. But, in the second case, you may bear the marks of the quarrel while you live, if you outlive it at all. But, if you find yourself unavoidably engaged, 'tis best, I think, if you can command your passion and language, to keep them pretty evenly at some certain moderate pitch, not much heightening them to exasperate your adversary, or provoke his friends, nor letting them grow overmuch dejected to make him insult. In a word, if you can keep reason above passion, that and watchfulness will be your best defendants. To which purpose you may consider, that, though such excuses as this — He provok't me so much I could not forbear — may pass

20 LIFE OF SIR ISAAC NEWTON.

among friends, yet amongst strangers they are insignificant, and only argue a traveller's weakness.