Principia Mathematica (Motte Translation, 1848) — part 2 of 45

" To these I may add some general heads for inquiries or ob- servations, such as at present I can think on. As, 1. To observe the policies, wealth, and state affairs of nations, so far as a soli- tary traveller may conveniently do. 2. Their impositions upon ail sorts of people, trades, or commodities, that are remarkable. 3. Their laws and customs, how far they differ from ours. 4. Their trades and arts wherein they excel or come short of us in England. 5. Such fortifications as you shall meet with, their fashion, strength, and advantages for defence, and other such mili- tary affairs as are considerable. 6. The power and respect be- longing to their degrees of nobility or magistracy. 7. It will not be time misspent to make a catalogue of the names and excellen- cies of those men that are most wise, learned, or esteemed in any nation. 8. Observe the mechanism and manner of guiding ships.

9. Observe the products of Nature in several places, especially in mines, with the circumstances of mining and of extracting metals or minerals out of their ore, and of refining them ; and if you meet with any transmutations out of their own species into another (as out of iron into copper, out of any metal into quick- silver, out of one salt into another, or into an insipid body, &c.), those, above all, will be worth your noting, being the most lucif- erous, and many times lucriferous experiments, too, in philosophy.

10. The prices of diet and other things. 11. And the staple commodities of places.

" These generals (such as at present I could think of), if they will serve for nothing else, yet they may assist you in drawing up a model to regulate your travels by. As for particulars, these that follow are all that I can now think of, viz. ; whether at Schem- nitium, in Hungary (where there are mines of gold, copper, iron, vitriol, antimony, &c.), they change iron into copper by dissolving it in a vitriolate water, which they find in cavities of rocks in the mines, and then melting the slimy solution in a strong fire, which in the cooling proves copper. The like is said to be done in other places, which I cannot now remember ; perhaps, too, it may be lone in Italy. For about twenty or thirty years agone there was

LIFE OP SIR ISAAC NEWTON. 21

a certain vitriol came from thence (called Roman vitriol), but of a nobler virtue than that which is now called by that name ; which vitriol is not now to be gotten, because, perhaps, they make a greater gain by some such trick as turning iron into copper with it than by selling it. 2. Whether, in Hungary, Sclavonia, Bohemia, near the town Eila, or at the mountains of Bohemia near Silesia, there be rivers whose waters are impregnated with gold ; perhaps, the gold being dissolved by some corrosive water like aqua regis, and the solution carried along with the stream, that runs through the mines. And whether the practice of laying mercury in the rivers, till it be tinged with gold, and then strain- ing the mercury through leather, that the gold may stay behind, be a secret yet, or openly practised. 3. There is newly con- trived, in Holland, a mill to grind glasses plane withal, and I think polishing them too ; perhaps it will be worth the while to see

it. 4. There is in Holland one Borry, who some years since

was imprisoned by the Pope, to have extorted from him secrets (as I am told) of great worth, both as to medicine and profit, but he escaped into Holland, where they have granted him a guard. I think he usually goes clothed in green. Pray inquire what you can of him, and whether his ingenuity be any profit to the Dutch. You may inform yourself whether the Dutch have any tricks to keep their ships from being all worm-eaten in their voyages to the Indies. Whether pendulum clocks do any service in finding out the longitude, &c.

" I am very weary, and shall not stay to part with a long compliment, only I wish you a good journey, and God be with you."

It was not till the month of June, 1669, that our author made known his Method of Fluxions. He then communicated the work which he had composed upon the subject, and entitled. Analysis per Equationes numero terminorum Infinitas, to his friend Dr. Barrow. The latter, in a letter dated 20th of the same month, mentioned it to Mr. Collins, and transmitted it to him, on the 31 st of July thereafter. Mr. Collins greatly approv- ed of the work ; took a copy of it ; and sent the original back to Dr. Barrow. During the same and the two following years, Mr..

22 LIFE OP SIR ISAAC NEWTON.

Collins, by his extensive correspondence, spread the knowledge of this discovery among the mathematicians in England, Scotland, France, Holland and Italy.

Dr. Barrow, having resolved to devote himself to Theology, resigned the Lucasian Professorship of Mathematics, in 1669, in favour of Newton, who accordingly received the appointment to the vacant chair.

During the years 1669, 1670, and 1671, our author, as such Professor, delivered a course of Optical Lectures. Though these contained his principal discoveries relative to the different re- frangibility of light, yet the discoveries themselves did not be- come publicly known, it seems, till he communicated them to the Royal Society, a few weeks after being elected a member there- of, in the spring of 1671-2. He now rose rapidly in reputation, and was soon regarded as foremost among the philosophers of the age. His paper on light excited the deepest interest in the Eoyal Society, who manifested an anxious solicitude to secure the author from the " arrogations of others," and proposed to publish his discourse in the monthly numbers in which the Transactions were given to the world. Newton, gratefully sensible of these expres- sions of esteem, willingly accepted of the proposal for publication. sHe gave them also, at this time, the results of some further ex- periments in the decomposition and re-composition of light : — that the same degree of refrangibility always belonged to the same colour, and the same colour to the same degree of refrangibility : th.at the seven different colours of the spectrum were original, or simple, and that lohiteness, or white light was a compound of all these seven colours.

The publication of his new doctrines on light soon called forth violent opposition as to their soundness. Hooke and Huygens — men eminent for ability and learning — were the most conspicuous of the assailants. And though Newton effectually silenced all his adversaries, yet he felt the triumph of little gain in comparison with the loss his tranquillity had sustained. He subsequently re- marked in allusion to this controversy — and to one with whom he was destined to have a longer and a bitterer conflict — " I was :so persecuted with discussions arising from the publication of my

LIFE OP SIR ISAAC NEWTON. 23

theory of light, that I blamed my own imprudence for parting with so substantial a blessing as my quiet to run after a shadow."

In a communication to Mr. Oldenburg, Secretary of the Royal Society, in 1672, our author stated many valuable suggestions re- lative to the construction of Reflecting Microscopes which he considered even more capable of improvement than telescopes. He also contemplated, about the same time, an edition of Kinck- huysen's Algebra, "with notes and additions; partially arranging, as an introduction to the work, a treatise, entitled, A Method of Fluxions ; but he finally abandoned the design. This treatise, however, he resolved, or rather consented, at a late .period of his life, to put forth separately ; and the plan would probably have been carried into execution had not his death intervened. It was translated into English, and published in 1736 by John Colson, Professor of Mathematics in Cambridge.

Newton, it is thought, made his discoveries concerning the Inflection and Diffraction of light before 1674. The phe- nomena of the inflection of light had been first discovered more than ten years before by Grimaldi. And Newton began by re- peating one of the experiments of the learned Jesuit — admitting a beam of the sun's light through a small pin hole into a dark chamber : the light diverged from the aperture in the form of a cone, and the shadows of all bodies placed in this light were larger than might have been expected, and surrounded with three coloured fringes, the nearest being widest, and the most remote the narrowest. Newton, advancing upon this experiment, took exact measures of the diameter of the shadow^ of a human hair, and of the breadth of the fringes, at different distances behind it, and discovered that these diameters and breadths were not pro- portional to the distances at which they were measured. He hence supposed that the rays which passed by the edge of the hair were deflected or turned aside from it, as if by a repulsive force, the nearest rays suffering the greatest, the more rem.ote a less degree of deflection. In explanation of the coloured fringes, he queried : whether the rays which differ in refrangibility do not differ also in flexibility, and whether they are not, by these dif- ferent inflections, separated from one another, so as af^er separa-

24 LIFE OF SIR ISAAC NEWTON.

tion to make the colours in the three fringes above described ? Also, whether the rays, in passing by the edges and sides of bodies, are not bent several times backwards and forwards with an eel-like motion — the three fringes arising from three such bendings ? His inquiries on this subject were here interrupted I and never renewed.

His Theory of the Colours of Natural Bodies was commu- nicated to the Royal Society, in February, 1675. This is justly regarded as one of the profoundest of his speculations. The fun- damental principles of the Theory in brief, are : — That bodies possessing the greatest refractive powers reflect the greatest quantity of light ; and that, at the confines of equally refracting media, there is no reflection. That the minutest particles of al- most all natural bodies are in some degree transparent. That between the particles of bodies there are pores, or spaces, either empty or filled with media of a less density than the particles themselves. That these particles, and pores or spaces, have some definite size. Hence he deduced the Transparency, Opacity, and colours of natural bodies. Transparency arises from the particles and their pores being too small to cause reflection at their com- mon surfaces — the light all passing through ; Opacity from the opposite cause of the particles and their pores being sufficiently large to reflect the light which is " stopped or stifled" by the multitude of reflections ; and colours from the particles, accord- ing to their several sizes, reflecting rays of one colour' and trans- mitting those of another — or in other words, the colour that meets the eye is the colour reflected, while all the other rays are transmitted or absorbed.

Analogous in origin to the colours of natural bodies, he con- sidered the COLOURS OF THIN PLATES. This subjcct was interest- ing and important, and had attracted considerable investigation. He, however, was the first to determine the law of the produc- tion of these colours, and, during the same year made known the results of his researches herein to the Royal Society. His mode of procedure in these experiments was simple and curious. He placed a double convex lens of a large known radius of curvature, upon the flat surface of a plano-convex object glass. Thus, from

LIFE OF SIR ISAAC NEWTON. 25

their point of contact at the centre, to the circumference of the lens, he obtained plates of air, or spaces varying from the ex- tremest possible thinness, by slow degrees, to a considerable thick- ness. Letting the light fall, every different thickness of this plate of air gave different colours — the point of contact of the lens and glass forming the centre of numerous concentric colored rings. Now the radius of curvature of the lens being known, the thickness of the plate of air, at any given point, or where any par- ticular colour appeared, could be exactly determined. Carefully noting, therefore, the order in which the different colours ap- peared, he measured, with the nicest accuracy, the different thick- nesses at which the most luminous parts of the rings were pro- duced, whether the medium were air, water, or mica — all these substances giving the same colours at different thicknesses ; — the ratio of which he also ascertained. From the phenomena obser- ved in these experiments, Newton deduced his Theory of Fits of Easy Reflection and Transmission of light. It consists in suppos- ing that every particle of light, from its first discharge from a lumi- nous body, possesses, at equally distant intervals, dispositions to be reflected from, or transmitted through the surfaces of bodies upon which it may fall. For instance, if the rays are in a Fit of Easy Reflection, they are on reaching the surface, repelled, thrown off, or reflected from it ; if, in a Fit of Easy Transmission, they are attracted, drawn in, or transmitted through it. By this Theory of Fits, our author likewise explained the colours of thick plates.

He regarded light as consisting of small material particles emitted from shining substances. He thought that these parti- cles could be re-combined into solid matter, so that '' gross bodies and light were convertible into one another ;" that the particles of light and the particles of solid bodies acted mutually upon each other ; those of light agitating and heating those of soHd bodies, and the latter attracting and repelling the former. Newton was the first to suggest the idea of the Polarization of light.

In the paper entitled An Hypothesis Explaining Properties of Lights December, 1675, our author first introduced his opinions re- specting Ether — opinions which he afterward abandoned and again

26 LIFE OF SIR ISAAC NEWTON.

permanently resumed — '' A most subtle spirit which pervades" all bodies, and is expanded through all the heavens. It is electric, and almost, if not quite immeasurably elastic and rare. " 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 at 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 com- mand of the will, namely, by the vibrations of this spirit, mutu- ally propagated along the solid filaments of the nerves, from the outward organs of sense to the brain, and from the brain into the muscles." This " spirit" was no aiiima mundi ; nothing further from the thought of Newton ; but was it not, on his part, a par- tial recognition of, or attempt to reach an ultimate material force, or primary element, by means of which, " in the roaring loom of time," this material universe, God's visible garment, may be woven for us ?

The Royal Society were greatly interested in the results of some experiments, which our author had, at the same time, com- municated to them relative to the excitation of electricity in glass ; and they, after several attempts and further direction from him, succeeded in re-producing the same phenomena.

One of the most curious of Newton's minor inquiries related to the connexion between the refractive powders and chemical com- position of bodies. He found on comparing the refractive powers and the densities of many different substances, that the former were very nearly proportional to the latter, in the same bodies. Unctuous and sulphureous bodies were noticed as remarkable excep- tions— as well as the diamond — their refractive powders being two or three times greater in respect of their densities than in the case of other substances, while, as among themselves, the one was generally proportional to the other. He hence inferred as to the diamond a great degree of combustibility ; — a conjecture which the experiments of modern chemistry have shown to be true.

The chemical researches of our author were probably pursued with more or less diligence from the time of his witnessing some

LIFE OF SIR ISAAC NEWTON. 2T

of the practical operations in that science at the Apothecary's at Grantham. De Natura Acidorum is a short chemical paper, on various topics, and published in Dr. Horsley's Edition of his works. Tabula Quantitatum et Graduum Coloris was in- serted in the Philosophical Transactions ; it contains a compara- tive scale of temperature from that of melting ice to that of a small kitchen coal-lire. He regarded fire as a body heated so hot as to emit light copiously ; and flame as a vapour, fume, or ex- halation heated so hot as to shine. To elective attraction, by the operation of which the small particles of bodies, as he con- ceived, act upon one another, at distances so minute as to escape observation, he ascribed all the various chemical phenomena of precipitation, combination, solution, and crystallization, and the mechanical phenomena of cohesion and capillary attraction. New- ton's chemical views were illustrated and confirmed, in part, at least, in his own life-time. As to the structure of bodies, he was of opinion " that the smallest particles of matter may cohere by the strongest attractions, and compose bigger particles of weaker virtue ; and many of these may cohere and compose bigger par- ticles whose virtue is still weaker ; and so on for divers succes- sions, until the progression end in the biggest particles, on which the operations in chemistry and the colours of natural bodies de- pend, and which by adhering, compose bodies of sensible magni- tude."

There is good reason to suppose that our author was a diligent student of the writings of Jacob Behmen ; and that in conjunction with a relative, Dr. Newton, he was busily engaged, for several months in the earlier part of life, in quest of the philosopher's tincture. " Great Alchymist," however, very imperfectly de- scribes the character of Behmen, whose researches into things material and things spiritual, things human and things divine, af- ford the strongest evidence of a great and original mind.

More appropriately here, perhaps, than elsewhere, may be given Newton's account of some curious experiments, made in his own person, on the action of light upon the retina. Locke, who was an intimate friend of our author, wrote to him for his opinion on a certain fact stated in Boyle's Book of Colours. Newton, in

28 LIFE OF SIR ISAAC NEWTON.

his reply, dated June 30th, 1691, narrates the following circum- stances, which probably took place in the course of his optical researches. Thus : —

" The observation you mention in Mr. Boyle's Book of Colours I once tried upon myself with the hazard of my eyes. The manner was this ; I looked a very little while upon the sun in the looking-glass with my right eye, and then turned my eyes into a dark corner of my chamber, and winked, to observe the impres- sion made, and the circles of colours which encompassed it, and how they decayed by degrees, and at last vanished. This I re- peated a second and a third time. At the third time, when the phantasm of light and colours about it were almost vanished, in- tending my fancy upon them to see their last appearance, I found, to my amazement, that they began to return, and by little and little to become as lively and vivid as when I had newly looked upon the sun. But when I ceased to intend my fancy upon them, they vanished again. After this, I found, that as often as I went into the dark, and intended my mind upon them, as when a man looks earnestly to see anything which is difficult to be seen, I could make the phantasm return without looking any more upon the sun ; and the oftener I made it return, the more easily I could make it return again. And, at length, by repeating this, without looking any more upon the sun, I made such an impression on my eye, that, if I looked upon the clouds, or a book, or any bright object, I saw upon it a round bright spot of light like the sun, and, which is still stranger, though I looked upon the sun with my right eye only, and not with my left, yet my fancy began to make an impression upon my left eye, as well us upon my right. For if I shut my right eye, or looked upon a book, or the clouds, with my left eye, I could see the spectrum of the sun almost as plain as with my right eye, if I did but intend my fancy a little while upon it ; for at first, if I shut my right eye, and looked with my left, the spectrum of the sun did not appear till I intended my fancy upon it ; but by repeating, this appeared every time more easily. And now, in a few hours' time, I had brought my eyes to such a pass, that I could look upon no bright object with either eye, but I saw the sun before me, so that I durst neither write

LIFE OF SIR ISAAC NEWTON. 29

nor read ; but to recover the use of my eyes, shut myself up in my chamber made dark, for three days together, and used all means to divert my imagination from the sun. For if I thought upon him, I presently saw his picture, though I was in the dark. But by keeping in the dark, and employing my mind about other things, I began in three or four days to have some use of my eyes again ; and by forbearing to look upon bright objects, recovered them pretty well, though not so well but that, for some months after, the spectrum of the sun began to return as often as I began to meditate upon the phenomena, even though I lay in bed at mid- night with my curtains drawn. But now I have been very well for many years, though I am apt to think, if I durst venture my eyes, I could still make the phantasm return by the power of my fancy. This story I tell you, to let you understand, that in the observation related by Mr. Boyle, the man's fancy probably con- curred with the impression made by the sun's light to produce that phantasm of the sun which he constantly saw in bright ob- jects. And so your question about the cause of phantasm in- volves another about the power of fancy, which I must confess is too hard a knot for me to untie. To place this effect in a constant motion is hard, because the sun ought then to appear perpetually. It seems rather to consist in a disposition of the sensorium to move the imagination strongly, and to be easily moved, both by the imagination and by the light, as often as bright objects are looked upon.'^

Though Newton had continued silent, yet his thoughts were by no means inactive upon the vast subject of the planetary mo- tions. The idea of Universal Gravitation, first caught sight of, so to speak, in the garden at Woolsthorpe, years ago, had gradually expanded upon him. We find him, in a letter to Dr. Hooke, Secretary of the Royal Society, dated in November, 1679, pro- posing to verify the motion of the earth by direct experiment, namely, by the observation of the path pursued by a body falling from a considerable height. He had concluded that the path would be spiral ; but Dr. Hooke maintained that it would be an eccentric ellipse in vacuo, and an ellipti-spiral in a resisting me- dium. Our author, aided by this correction of his error, and by

30 LIFE OF SIR ISAAC NEWTON.

the discovery that a projectile would move in an elliptical orbit when under the influence of a force varying inversely as the square of the distance, was led to discover " the theorem by which he afterwards examined the ellipsis ;" and to demonstrate the celebrated proposition that a planet acted upon by an attrac- tive force varying inversely as the squares of the distances will describe an elliptical orbit, in one of whose foci the attractive force resides.

When he was attending a meeting of the Royal Society, in June 1682, the conversation fell upon the subject of the measure- ment of a degree of the meridian, executed by M. Picard, a French Astronomer, in 1679. Newton took a memorandum of the result ; and afterward, at the earliest opportunity, computed from it the diameter of the earth : furnished with these new data, he resumed his calculation of 1666. As he proceeded therein, he saw that his early expectations were now likely to be realized ; the thick rushing, stupendous results overpowered him ; he be- came unable to carry on the process of calculation, and intrusted its completion to one of his friends. The discoverer had, indeed, grasped the master-fact. The law of falling bodies at the earth's surface was at length identified with that which guided the moon in her orbit. And so his Great Thought, that had for sixteen years loomed up in dim, gigantic outline, amid the first dawn of a plausible hypothesis, now stood forth, radiant and not less grand, in the mid-day light of demonstrated truth.

It were difficult, nay impossible to imagine, even, the influence of a result like this upon a mind like Newton's. It was as if the keystone had been fitted to the glorious arch by which his spirit should ascend to the outskirts of infinite space — spanning the immea- surable— weighing the imponderable — computing the incalculable — mapping out the marchings of the planets, and the far-wander- ings of the comets, and catching, bring back to earth some clearer notes of that higher melody which, as a sounding voice, bears perpetual witness to the design and omnipotence of a creating Deity.

Newton, extending the law thus obtained, composed a series of about twelve propositions on the motion of the primary planets

LIFE OF SIR ISAAC NEWTON. 31

about the sun. These were sent to London, and communicated to the Royal Society about the end of 16S3. At or near this pe- riod, other philosophers, as Sir Christopher Wren, Dr. Halley, and Dr. Hooke, were engaged in investigating the same subject ; but with no definite or satisfactory results. Dr. Halley, having seen, it is presumed, our author's propositions, went in August, 1684, to Cambridge to consult w^ith him upon the subject. Newton assured him that he had brought the demonstration to perfection. In November, Dr. Halley received a copy of the work ; and, in the following month, announced it to the Royal Society, with the author's promise to have it entered upon their Register. Newton, subsequently reminded by the Society of his promise, proceeded in the diligent preparation of the v/ork, and, though suffering an interruption of six weeks, transmitted the manuscript of the first book to London before the end of April, The work was entitled Philosophic Naturalis Principia Mathematica, dedicated to the Royal Society, and presented thereto on the 28th of April, 1685-6. The highest encomiums were passed upon it ; and the council resolved, on the 19th of May, to print it at the expense of the Society, and under the di- rection of Dr. Halley. The latter, a few days afterward, com- municated these steps to Newton, who, in a reply, dated the 20th of June, holds the following language : — " The proof you sent me I like very well. I designed the whole to consist of three books ; the second was finished last summer, being short, and only wants transcribing, and drawing the cuts fairly. Some nevv^ propositions I have since thought on, which I can as well let alone. The third wants the theory of comets. In autumn last, I spent two months in calculation to no purpose for want of a good method, which made me afterward return to the first book, and enlarge it with diverse propositions, some relating to comets, others to other things found out last winter. The third I now design to sup- press. Philosophy is such an impertinently litigious lady, that a man had as good be engaged in liiw-suits as have to do with her. I found it so formerly, and now I can no sooner come near her again, but she gives me warning. The first two books without the third will not so well bear the title of Philosophice Naturalis;

3

32 LIFE OF SIR ISAAC NEWTON.

Principia Mathematicia ; and thereupon I had altered it to this, De Motu Corjjorum Libri duo. But after second thought I re- tain the former title. It will help the sale of the book, which I ought not to diminish now 'tis yours."

This " warning" arose from some pretensions put forth by Dr. Hooke. And though Newton gave a minute and positive refuta- tions of such claims, yet, to reconcile all differences, he gener- ously added to Prop. IV. Cor. 6, Book I, a Scholium, in which Wren, Hooke and Halley are acknowledged to have indepen- dently deduced the law of gravity from the second law of Kepler.

The suppression of the third book Dr. Halley could not endure to see. " I must again beg you" says he, " not to let your re- sentments run so high as to deprive us of your third book, where- in your applications of your mathematical doctrine to the theory of comets, and several curious experiments, which, as I guess by what you write ought to compose it, will undoubtedly render it acceptable to those who will call themselves philosophers without mathematics, which are much the greater number." To these solicitations Newton yielded. There were no " resentments," how- ever, as we conceive, in his " design to suppress." He sought peace ; for he loved and valued it above all applause. But, in spite of his efforts for tranquillity's sake, his course of discovery was all along molested by ignorance or presumptuous rivalry.

The publication of the great work now went rapidly forwards. The second book was sent to the Society, and presented on the 2d March ; the third, on the 6th April ; and the whole was com- pleted and published in the month of May, 1686-7, In the sec- ond Lemma of the second book, the fundamental principle of his fiuxionary calculus was, for the first time, given to the world ; but its algorithm or notation did not appear till published in the second volume of Dr. Wallis's works, in 1693.

And thus was ushered into existence The Principia — a work to which pre-eminence above all the productions of the human intellect has been awarded — a work that must be esteemed of priceless worth so long as Science has a votary, or a single wor- shipper be left to kneel at the altar of Truth.

LIFE OF SIR ISAAC NEWTON. 33

The entire work bears the general title of The Mathematical Principles of Natural Philosophy. It consists of three books: the first two, entitled, Op the Motion of Bodies, are occupied with the laws and conditions of motions and forces, and are illus- trated with many scholia treating of some of the most general and best established points in philosophy, such as the density and resistance of bodies, spaces void of matter, and the motion of sound and light. From these principles, there is deduced, in the third book, drawn up in as popular a style as possible and entitled, Of the System of the World, the constitution of the system of the world. In regard to this book, the author says — " I had, indeed, composed the third Book in a popular method, that it might be read by many ; but afterwards, considering that such as had not suf- ficently entered into the principles could not easily discover the strength of the consequences, nor lay aside the prejudices to which they had been many years accustomed, therefore, to prevent dis- putes which might be raised upon such accounts, I chose to reduce the substance of this 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 : not that I would advise any one to the previous study of every Proposition of those Books." — " It is enough if one carefully reads the Definitions, the Laws of Motion, and the three first Sections of the first Book. He may then pass on to this Book, and consult such of the remaining Propositions of the first two Books, as the references in this, and his occasions shall re- quire." So that " The System of the Vf orld" is composed both " in a popular method," and in the form of mathematical Propo- sitions.

The principle of Universal Gravitation, namely, that every particle of matter is attracted by, or gravitates to, every other pa7'ticle of matter, with a force inversely proportional to the squares of their distances — is the discovery which characterizes The Principia. This principle the author deduced from the mo- tion of the moon, and the three laws of Kepler — laws, which Newton, in turn, by his greater law, demonstrated to be true.

From the first law of Kepler, namely, the proportionality of

34 LIFE OF SIR ISAAC NEWTON.