NEWTON

NEWTON (Sir Isaac), one of the greatest philosophers and mathematicians the world has ever produced, was the only child of Mr John Newton of Coleworth, not far from Grantham in Lincolnshire, who had an estate of about 120l. per annum, which he kept in his own hands. He was born at that place on Christmas day 1642. His father dying when he was young, his mother's brother, a clergyman of the name of Asfough, or Asket, who lived near her, and directed all her affairs after the death of Mr Newton, put her son to school at Grantham. When he had finished his school learning, his mother took him home, intending, as she had no other child, to have the pleasure of his company; and that he, as his father had done, should occupy his own estate. But his uncle happening to find him in a hay-loft at Grantham working a mathematical problem, and having otherwise observed the boy's mind to be uncommonly bent upon learning, he prevailed upon her to part with him; and she sent him to Trinity College in Cambridge, where her brother, having himself been a member of it, had still many friends. Isaac was soon taken notice of by Dr Isaac Barrow; who, observing his bright genius, contracted a great friendship for him. M. de Fontenelle tells us, "That in learning mathematics he did not study Euclid, who seemed to him too plain and simple, 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 theorema was sufficient to make him master of them. He advanced at once to the geometry of Des Cartes, Kepler's optics, &c. It is certain, that he had made his great discoveries in geometry, and laid the foundation of his two famous works the Principia and the Optics, by the time he was 24 years of age."

In 1664, he took the degree of bachelor of arts; and in 1668 that of master, being elected the year before, fellow of his college. He had before this time discovered the method of fluxions; and in 1669 he was chosen professor of mathematics in the university of Cambridge, upon the resignation of Dr Barrow. The same year, and the two following, he read a course of optical lectures in Latin, in the public schools of the university; an English translation of which was printed at London in 1728, in 8vo, as was the Latin original the next year in 4to. From the year 1671 to 1679, he held a correspondence by letters with Mr Henry Oldenburg secretary of the royal society, and Mr John Collins fellow of that society; which letters contain a variety of curious observations.

Concerning the origin of his discoveries, we are told, that as he sat alone in a garden, the falling of some apples from a tree led him into a speculation on the power of gravity; that as this power is not diminished at the remotest distance from the centre of the earth to which we can rise, it appeared to him reasonable to conclude, that it must extend much farther than was usually thought; and pursuing this speculation, 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 inquiry was dropped; but re-

fumed again, and gave rise to his writing the treatise which he published in 1687, under the name of Mathematical Principles of Natural Philosophy; a work looked upon as the production of a celestial intelligence rather than of a man. The very same year in which this great work was published, the university of Cambridge was attacked by king James II. when Mr Newton was one of its most zealous defenders, and was accordingly nominated one of the delegates of that university to the high-commission court; and the next year he was chosen one of their members for the convention-parliament, in which he sat till it was dissolved. In 1696, Mr Montague, then chancellor of the exchequer, and afterwards earl of Halifax, obtained for him of the king the office of warden of the mint; in which employment he was of signal service, when the money was called in to be recoined. Three years after, he was appointed master of the mint; a place of very considerable profit, which he held till his death. In 1699, he was elected one of the members of the royal academy of sciences at Paris. In 1701, he was a second time chosen member of parliament for the university of Cambridge. In 1704, he published his Optics; which is a piece of philosophy so new, that the science may be considered as entirely indebted to our author. In 1705, he was knighted by queen Anne. In 1707, he published his Arithmetica Universalis. In 1711, his Analytis per Quantitatem Serierum, Fluxiones et Differentias, &c. was published by William Jones, Esq. In 1712, several letters of his were published in the Commercium Epistolicum. In the reign of George I. he was better known at court than before. The princess of Wales, afterwards queen-consort of England, used frequently to propose questions to him, and to declare that she thought herself happy to live at the same time with him, and have the pleasure and advantage of his conversation. He had written a treatise of ancient chronology, which he did not think of publishing; but the princess desired an abstract, which she would never part with. However, a copy of it stole abroad, and was carried into France; where it was translated and printed, with some observations, which were afterwards answered by Sir Isaac. But, in 1728, the Chronology itself was published at London in quarto; and was attacked by several persons, and as zealously defended by Sir Isaac's friends. The main design of it was to find out, from some tracts of the most ancient Greek astronomy, what was the position of the colures with respect to the fixed stars, in the time of Chiron the centaur. As it is now known that these stars have a motion in longitude of one degree in 72 years, if it is once known thro' what fixed stars the colure passed in Chiron's time, by taking the distance of these stars from those through which it now passes, we might determine what number of years is elapsed since Chiron's time. As Chiron was one of the Argonauts, this would fix the time of that famous expedition, and consequently that of the Trojan war; the two great events upon which all the ancient chronology depends. Sir Isaac places them 500 years nearer the birth of Christ than other chronologists generally do.

This great man had all along enjoyed a settled and equal state of health to the age of 80, when he began to be afflicted with an incontinence of urine.

Newton. urine. However, for the five following years, he had great intervals of ease, which he procured by the observance of a strict regimen. It was then believed that he certainly had the stone; and when the paroxysms were so violent, that large drops of sweat ran down his face, he never uttered the least complaint, or expressed the smallest degree of impatience; but, as soon as he had a moment's ease, would smile and talk with his usual cheerfulness. Till then he always read and wrote several hours in a day. He had the perfect use of all his senses and understanding till the day before he died, which was on the 20th of March 1726-7, in the 85th year of his age.—He lay in state in the Jerusalem chamber at Westminster, and on the 28th of March his body 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. The bishop of Rochester read the funeral office, being attended by all the clergy of the church. The corpse was interred just at the entrance into the choir, where a noble monument is erected to his memory.

Sir Isaac was of a middling stature, and in the latter part of his life somewhat inclined to be fat. His countenance was pleasing, and at the same time venerable. He never made use of spectacles, and lost but one tooth during his whole life.

His temper is said to have been so equal and mild, that no accident could disturb it. Of this the following remarkable instance is related. Sir Isaac had a favourite little dog, which he called Diamond; and being one day called out of his study into the next room, Diamond was left behind. When Sir Isaac returned, having been absent but a few minutes, he had the mortification to find, that Diamond having thrown down 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 irretreivable; 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 a great lover of peace; and 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 peculiarly eminent for them. 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 under 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. Dinner has been often three hours ready for him before he could be brought to table: and his man often said, when he has been getting up in a morning, he has sometimes begun to dress, and with one leg in his breeches sat down again on the bed, where he has remained for hours before he got his

cloaths on. From his love of peace, no doubt, arose Newton. that unusual kind of horror which he had 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 of publishing his optic lectures, we find him reflecting on that dispute, into which he was unavoidably drawn thereby, 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 Mr 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 about 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 of his Principia to the Royal Society, with his consent to the printing of it by them, upon Mr Hook's injuriously insinuating that 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 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 originally 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.

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 attendance; and, as soon as he had leisure, resumed the subject at the point where he had left 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 even while study was his proper profession. But as soon as he was removed to the mint, he applied himself chiefly to the business of that office; and so far quitted mathematics and philosophy, as not to engage in any pursuits of either kind afterwards.

The amiable quality of modesty is represented 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; and

Newton. and let us add, though he was thereby robbed of his invention of fluxions. Nicholas Mercator publishing his Logarithmetica 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, at that time 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 confined 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 formed by their relations, 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 infinitely approximated; which is the happiest and most refined method, says Mr 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 Mr Newton, finding by Mercator's book, that he was in the way to it, and that others might follow in his tract, 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 unparalleled modesty, when we see him declaring, that he thought Mercator had entirely discovered his secret, or that others would, before he was of a proper age for writing? His MS. upon infinite series was communicated to none but Mr John Collins and the lord Brouncker; 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 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: 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 pru-

dent economy, put it in his power. We have two remarkable instances of his bounty and generosity; one to Mr McLaurin, professor of mathematics at Edinburgh, to whom he offered 20 l. per annum; and the other to his niece Barton, who had an annuity of 100 l. per annum settled upon her by him. 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. He never married, and perhaps he never had leisure to think of it. 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. He left 32,000 l. at his death; but made no will, which Mr 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.

Newtonian Philosophy, the doctrine of the universe, and particularly of the heavenly bodies, their laws, affections, &c. as delivered by Sir Isaac Newton.

The term Newtonian Philosophy is applied very differently; whence divers confused notions relating thereto. Some authors under this philosophy include all the corporeal philosophy, considered as it now stands corrected and reformed by the discoveries and improvements made in several parts thereof by Sir Isaac Newton. In which sense it is that Gravefande calls his elements of physics, Introductio ad Philosophiam Newtonianam. And in this sense the Newtonian is the same with the new philosophy; and stands contradistinguished from the Cartesian, the Peripatetic, and the ancient Corporeal.

Others, by Newtonian Philosophy, mean the method or order which Sir Isaac Newton observes in philosophising; viz. the reasoning and drawing of conclusions directly from phenomena, exclusive of all previous hypotheses; the beginning from simple principles; deducing the first powers and laws of nature from a few select phenomena, and then applying those laws, &c. to account for other things. And in this sense the Newtonian philosophy is the same with the experimental philosophy, and stands opposed to the ancient Corporeal.

Others, by Newtonian philosophy, mean that wherein physical bodies are considered mathematically, and where geometry and mechanics are applied to the solution of the appearances of nature. In which sense the Newtonian is the same with the mechanical and mathematical philosophy.

Others again, by Newtonian philosophy, understand that part of physical knowledge which Sir Isaac Newton has handled, improved, and demonstrated, in his Principia.

Others, lastly, by Newtonian philosophy, mean the new principles which Sir Isaac Newton has brought into philosophy; the new system founded thereon; and the new solutions of phenomena thence deduced;

Newtonian or that which characterizes and distinguishes his phi-
Philosophy. losophy from all others.—Which is the sense wherein
we shall chiefly consider it.

As to the history of this philosophy, we have no-
thing to add to what has been given in the preceding
article. It was first made public in the year 1687,
by the author, then a fellow of Trinity-college, Cam-
bridge; and in the year 1713, republished with con-
siderable improvements.—Several authors have since at-
tempted to make it plainer; by setting aside many of
the more sublime mathematical researches, and substi-
tuting either more obvious reasonings or experiments
in lieu thereof; particularly Whiston in his Prælect.
Phys. Mathemat. Gravesande in Element. & Instit. and
Dr Pemberton in his View.

The whole of the Newtonian Philosophy, as delivered
by the author, is contained in his Principia, or Ma-
thematical Principles of Natural Philosophy. He founds
his system on the following definitions.

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

2. The quantity of motion is the measure of the
same, arising from the velocity and quantity of mat-
ter conjointly. This is evident, because the motion
of the whole is the motion of all its parts; and there-
fore in a body double in quantity, with equal velocity,
the motion is double, &c.

3. The vis inertia, 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, only
by the difficulty we find in moving any thing out of
its place; and this difficulty is by some reckoned to
proceed only from gravity. They contend, that in
those cases where we can prevent the force of gravity
from acting upon bodies, this power of resistance be-
comes insensible, and the greatest quantities of matter
may be put in motion by the very least force. Thus
there have been balances formed so exact, that when
loaded with 200 weight in each scale, they would turn
by the addition of a single drachm. In this case
400 lb. of matter was put in motion by a single
drachm, i. e. by $\backslash frac\{1\}\{1750000\}$ parts of its own quantity: and
even this small weight, they say, is only necessary on
account of the inaccuracy of the machine; so that we
have no reason to suppose, that, if the friction could
be entirely removed, it would take more force to move
a tun weight than a grain of sand. This objection,
however, is not taken notice of by Sir Isaac; and he
bestows on the resisting power above-mentioned the
name of vis inertia; a phrase which is perhaps not well
chosen, and with which inferior writers have endeavoured
to make their readers merry at the expense of New-
ton. A force of inactivity, it has been said, is a forceless
force; and analogous to a black white, a cold heat, and
a tempestuous calm.

But objections of more importance have been made
to the whole of this doctrine than those which merely
respect the term vis inertia. "An endeavour to re-
main at rest (we are told*) is unnecessary, whilst no-
thing attempts to disturb the rest. It is likewise im-

possible to be conceived, as it implies a contradiction. Newtonian
A man, by opposing force to force, may endeavour Philosophy.
not to be moved; but this opposition is an endeavour
to move, not with a design to move, but by counter-
acting another force to prevent being moved. An
endeavour not to move therefore cannot exist in bod-
ies, because it is absurd; and if we appeal to fact,
we shall find every body in an actual and constant en-
deavour to move." It has been likewise observed,
and we think justly, that "if bodies could continue to
move by any innate force, they might also begin to
move by that force. For the same cause which can
move a body with a given velocity at one time, could
do it, if present, at any other time; and therefore if
the force by which bodies continue in motion were
innate and essential to them, they would begin to
move of themselves, which is not true." Newton
indeed says that this innate force is the cause of
motion under certain circumstances only, or when the
body is acted upon by a force impressed ab extra.
But if this impressed force do not continue as well
as begin the motion, if it cease the instant that
the impression is over, and the body continue to
move by its vis inertia, why is the body ever stopped?
"If in the beginning of the motion the body, by
its innate force, overcomes a certain resistance of fric-
tion and air, in any following times, the force being
undiminished, it will overcome the same resistance for-
ever. These resistances, therefore, could never change
the state of a moving body, because they cannot
change the quantity of its motive force. But this is
contrary to universal experience." For these reasons
we are inclined to think that bodies are wholly pas-
sive; that they endeavour nothing; and that they con-
tinue in motion not by any innate force or vis inertia, but
by that force, whatever it be, which begins the motion,
and which, whilst it remains with the moving body,
is gradually diminished, and at last overcome by op-
posite forces, when the body of course ceases to move.

4. An impressed force is an action exerted upon a
body, in order to change its state, either of rest, or of
moving uniformly forward in a right line.—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
inertia only.

It is here implied, and indeed fully expressed, that
motion is not continued by the same power that pro-
duces it. Now there are two grounds on which the
truth of this doctrine may be supposed to rest.

"First, On a direct proof that the impressed force
does not remain in the body, either by showing the
nature of the force to be transitory and incapable of
more than its first action; or that it acts only on the
surface, and that the body escapes from it; or that
the force is somewhere else, and not remaining in the
body. But none of these direct proofs are offered.

"Secondly, It may rest on an indirect proof, that
there is in the nature of body a sufficient cause for
the continuance of every new state acquired; and
that therefore any adventitious force to continue mo-
tion, though necessary for its production, is super-
fluous and inadmissible. As this is the very ground
on which the supposition stands, it ought to have been
indubitably certain that the innate force of the body

Newtonian Philosophy is sufficient to perpetuate the motion it has once acquired, before the other agent, by which the motion was communicated, had been dismissed from the office. But the innate force of body has been shown not to be that which continues its motion; and therefore the proof, that the impressed force does not remain in the body, fails. Nor indeed is it in this case desirable to support the proof, because we should then be left without any reason for the continuance of motion.⁶ When we mention an impressed force, we mean such a force as is communicated either at the surface of the body or by being diffused through the mass.

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

6. The absolute quantity of a centrifugal force is the measure of the same, proportional to the efficacy of the cause that propagates it from the centre, through the spaces round about.

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 equal and contrary to it, that is just sufficient to hinder the descent of the body.

I. Absolute, true, and mathematical time, of itself, and from its own nature, flows equably, without regard to any thing external, and, by another name, is called duration. Relative, apparent, and common time, is some sensible and external measure of duration, whether accurate or not, which is commonly used instead of true time; such as an hour, a day, a month, a year, &c.

II. Absolute space, in its own nature, without regard to any thing external, remains always similar and immoveable. Relative space is some moveable dimension or measure of the absolute spaces; and which is vulgarly taken for immoveable space. Such is the dimension of a subterraneous, an aerial, or celestial space, determined by its position to bodies, and which is vulgarly taken for immoveable space; as the distance of a subterraneous, an aerial, or celestial space, determined by its position in respect of the earth. Absolute and relative space are the same in figure and magnitude; but they do not remain always numerically the same. For if the earth, for instance, moves, a space of our air which, relatively and in respect of the earth, remains always the same, will at one time be one part of the absolute space into which the earth passes; at another time it will be another part of the same; and so, absolutely understood, it will be perpetually mutable.

III. Place is a part of space which a body takes up; and is, according to the space, either absolute or relative. Our author says it is part of space; not the situation, nor the external surface of the body. For the places of equal solids are always equal; but their superficies, by reason of their dissimilar figures,

are often unequal. Positions properly have no quantity, nor are they so much the places themselves as the properties of places. The motion of the whole is the same thing with the sum of the motions of the parts; that is, the translation of the whole out of its place is the same thing with the sum of the translations of the parts out of their places; and therefore the place of the whole is the same thing with the sum of the places of the parts; and for that reason it is internal, and in the whole body.

IV. Absolute motion is the translation of a body from one absolute place into another, and relative motion the translation from one relative place into another. Thus, in a ship under sail, the relative place of a body is that part of the ship which the body possesses, or that part of its cavity which the body fills; and which therefore moves together with the ship; and relative rest is the continuance of the body in the same part of the ship, or of its cavity. But real absolute rest is the continuance of the body in the same part of that immoveable space in which the ship itself, its cavity, and all that it contains, is moved. Wherefore, if the earth is really at rest, the body which relatively rests in the ship will really and absolutely move with the same velocity which the ship has on the earth. But if the earth also moves, the true and absolute motion of the body will arise, partly from the true motion of the earth in immoveable space; partly from the relative motion of the ship on the earth; and if the body moves also relatively in the ship, its true motion will arise partly from the true motion of the earth in immoveable space, and partly from the relative motions as well of the ship on the earth as of the body in the ship; and from these relative motions will arise the relative motion of the body on the earth. As if that part of the earth where the ship is, was truly moved towards the east, with a velocity of 10010 parts; while the ship itself with a fresh gale is carried towards the west, with a velocity expressed by 10 of these parts; but a sailor walks in the ship towards the east with one part of the said velocity; then the sailor will be moved truly and absolutely in immoveable space towards the east with a velocity of 10011 parts; and relatively on the earth towards the west, with a velocity of 9 of those parts.

Absolute time, in astronomy, is distinguished from relative, by the equation or correction of the vulgar time. For the natural days are truly unequal, though they are commonly considered as equal, and used for a measure of time: astronomers correct this inequality for their more accurate deducing of the celestial motions. It may be that there is no such thing as an equal motion whereby time may be accurately measured. All motions may be accelerated or retarded; but the true or equal progress of absolute time is liable to no change. The duration or perseverance of the existence of things remains the same, whether the motions are swift or slow, or none at all; and therefore ought to be distinguished from what are only sensible measures thereof, and out of which we collect it by means of the astronomical equation. The necessity of which equation for determining the times of a phenomenon is evinced, as well from the experiments of the pendulum-clock as by eclipses of the satellites of Jupiter.

Newtonian Philosophy. As the order of the parts of time is immutable, so also is the order of the parts of space. Suppose those parts to be moved out of their places, and they will be moved (if we may be allowed the expression) out of immutability of time themselves. For times and spaces are, as it were, and space. the places of themselves as of all other things. All things are placed in time as to order of succession; and in space as to order of situation. It is from their essence or nature that they are places; and that the primary places of things should be moveable, is absurd. These are therefore the absolute places; and translations out of those places are the only absolute motions.

But because the parts of space cannot be seen, or distinguished from one another by the senses, therefore in their stead we use sensible measures of them. For, from the positions and distances of things from any body, considered as immovable, we define all places; and then with respect to such places, we estimate all motions, considering bodies as transferred from some of those places into others. And so, instead of absolute places and motions, we use relative ones; and that without any inconvenience in common affairs: but in philosophical disquisitions we ought to abstract from our senses, and consider things themselves distinct from what are only sensible measures of them. For it may be, that there is no body really at rest, to which the places and motions of others may be referred.

But we may distinguish rest and motion, absolute and relative, one from the other by their properties, causes, and effects. It is a property of rest, that bodies really at rest do rest in respect of each other. And therefore, as it is possible, that, in the remote regions of the fixed stars, or perhaps far beyond them, there may be some body absolutely at rest, tho' it be impossible to know from the position of bodies to one another in our regions, whether any of these do keep the same position to that remote body; it follows, that absolute rest cannot be determined from the position of bodies in our regions.

It is a property of motion, that the parts which retain given positions to their wholes do partake of the motion of their wholes. For all parts of revolving bodies endeavour to recede from the axis of motion; and the impetus of bodies moving forwards arises from the joint impetus of all the parts. Therefore if surrounding bodies are moved, those that are relatively at rest within them will partake of their motion. Upon which account the true and absolute motion of a body cannot be determined by the translation of it from those only which seem to rest; for the external bodies ought not only to appear at rest, but to be really at rest. For otherwise all included bodies, beside their translation from near the surrounding ones, partake likewise of their true motions; and though that translation was not made, they would not really be at rest, but only seem to be so. For the surrounding bodies stand in the like relation to the surrounded, as the exterior part of a whole does to the interior, or as the shell does to the kernel; but if the shell moves, the kernel will also move, as being part of the whole, without any removal from near the shell.

A property near akin to the preceding is, that if

a place is moved, whatever is placed therein moves along with it; and therefore a body which is moved from a place in motion, partakes also of the motion of its place. Upon which account all motions from places in motion, are no other than parts of entire and absolute motions; and every entire motion is composed of the motion of the body out of its first place, and the motion of this place out of its place; and so on, until we come to some immovable place, as in the above-mentioned example of the sailor. Wherefore entire and absolute motions can be no otherwise determined than by immovable places. Now, no other places are immovable but those that from infinity to infinity do all retain the same given positions one to another; and upon this account must ever remain unmoved, and do thereby constitute what we call immovable space.

The causes by which true and relative motions are distinguished one from the other, are the forces impressed upon bodies to generate motion. True motion is neither generated nor altered, but by some force impressed upon the body moved; but relative motion may be generated or altered without any force impressed upon the body. For it is sufficient only to impress some force on other bodies with which the former is compared, that, by their giving way, that relation may be changed, in which the relative rest or motion of the other body did consist. Again, true motion suffers always some change from any force impressed upon the moving body; but relative motion does not necessarily undergo any changes by such force. For if the same forces are likewise impressed on those other bodies with which the comparison is made, that the relative position may be preserved; then that condition will be preserved, in which the relative motion consists. And therefore any relative motion may be changed when the true motion remains unaltered, and the relative may be preserved when the true motion suffers some change. Upon which account true motion does by no means consist in such relations.

The effects which distinguish absolute from relative motion are, the forces of receding from the axis of circular motion. For there are no such forces in a circular motion purely relative: but, in a true and absolute circular motion, they are greater or less according to the quantity of the motion. If a vessel, hung by a long cord, is so often turned about that the cord is strongly twisted, then filled with water, and let go, it will be whirled about the contrary way; and while the cord is untwisting itself, the surface of the water will at first be plain, as before the vessel began to move; but the vessel, by gradually communicating its motion to the water, will make it begin sensibly to revolve, and recede by little and little from the middle, and ascend to the sides of the vessel, forming itself into a concave figure; and the swifter the motion becomes, the higher will the water rise, till at last, performing its revolutions in the same times with the vessel, it becomes relatively at rest in it. This ascent of the water shows its endeavour to recede from the axis of its motion; and the true and absolute circular motion of the water, which is here directly contrary to the relative, discovers itself, and may be measured by this endeavour. At first, when the relative motion in the water was greatest, it produced no endeavour

Newtonian Philosophy. deavour to recede from the axis; the water showed no tendency to the circumference, nor any ascent towards the sides of the vessel, but remained of a plain surface; and therefore its true circular motion had not yet begun. But afterwards, when the relative motion of the water had decreased, the ascent thereof towards the sides of the vessel proved its endeavour to recede from the axis; and this endeavour showed the real circular motion of the water perpetually increasing, till it had acquired its greatest quantity, when the water rested relatively in the vessel. And therefore this endeavour does not depend upon any translation of the water in respect of the ambient bodies; nor can true circular motion be defined by such translations. There is only one real circular motion of any one revolving body, corresponding to only one power of endeavouring to recede from its axis of motion, as its proper and adequate effect: but relative motions in one and the same body are innumerable, according to the various relations it bears to external bodies; and, like other relations, are altogether destitute of any real effect, otherwise than they may perhaps participate of that only true motion. And therefore, in the system which supposes that our heavens, revolving below the sphere of the fixed stars, carry the planets along with them, the several parts of those heavens and the planets, which are indeed relatively at rest in their heavens, do yet really move. For they change their position one to another, which never happens to bodies truly at rest; and being carried together with the heavens, participate of their motions, and, as parts of revolving wholes, endeavour to recede from the axis of their motion.

Wherefore relative quantities are not the quantities themselves whose names they bear, but those sensible measures of them, either accurate or inaccurate, which are commonly used instead of the measured quantities themselves. And then, if the meaning of words is to be determined by their use, by the names time, space, place, and motion, their measures are properly to be understood; and the expression will be unusual and purely mathematical, if the measured quantities themselves are meant.

It is indeed a matter of great difficulty to discover, and effectually to distinguish, the true motions of particular bodies from those that are only apparent: because the parts of that immoveable space in which those motions are performed, do by no means come under the observation of our senses. Yet we have some things to direct us in this intricate affair; and these arise partly from the apparent motions which are the difference of the true motions, partly from the forces which are the causes and effects of the true motions. For instance, if two globes, kept at a given distance one from the other by means of a cord that connects them, were revolved about their common centre of gravity; we might, from the tension of the cord, discover the endeavour of the globes to recede from the axis of motion, and from thence we might compute the quantity of their circular motions. And then, if any equal forces should be impressed at once on the alternate faces of the globes to augment or diminish their circular motions, from the increase or decrease of the tension of the cord we might infer the increment or decrement of their motions; and thence would be found on what faces those forces ought to

be impressed, that the motions of the globes might be most augmented; that is, we might discover their hindermost faces, or those which follow in the circular motion. But the faces which follow being known, and consequently the opposite ones that precede, we should likewise know the determination of their motions. And thus we might find both the quantity and determination of this circular motion, even in an immense vacuum, where there was nothing external or sensible, with which the globes might be compared. But now, if in that space some remote bodies were placed that kept always a given position one to another, as the fixed stars do in our regions; we could not indeed determine from the relative translation of the globes among those bodies, whether the motion did belong to the globes or to the bodies. But if we observed the cord, and found that its tension was that very tension which the motions of the globes required, we might conclude the motion to be in the globes, and the bodies to be at rest; and then, lastly, from the translation of the globes among the bodies, we should find the determination of their motions.

Having thus explained himself, Sir Isaac proposes to show 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.

I. EVERY BODY PERSEVERES IN ITS STATE OF REST, OR OF UNIFORM MOTION IN A RIGHT LINE, UNLESS IT IS COMPELLED TO CHANGE THAT STATE BY FORCES IMPRESSED UPON IT.—Sir Isaac's proof of this axiom is as follows: "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. At 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."—Notwithstanding this demonstration, however, the axiom hath been violently disputed. It hath been argued, that bodies continue in their state of motion because they are subjected to the continual impulse of an invisible and subtle fluid, which always pours in from behind, and of which all places are full. It hath been affirmed that motion is as natural to this fluid as rest is to all other matter. It is said, moreover, that it is impossible we can know in what manner a body would be influenced by moving forces if it was entirely destitute of gravity. According to what we can observe, the momentum of a body, or its tendency to move, depends very much on its gravity. A heavy cannon-ball will fly to a much greater distance than a light one, though both are actuated by an equal force. It is by no means clear, therefore, that a body totally destitute of gravity would have any proper momentum of its own; and if it had no momentum, it could not continue its motion for the smallest space of time after the moving power was withdrawn. Some have imagined that matter was capable of beginning motion of itself, and consequently that the axiom was false; because we see plainly that matter in some cases hath a tendency

Newtonian to change from a state of motion to a state of rest, and
Philosophy. from a state of rest to a state of motion. A paper ap-
peared on this subject in the first volume of the Edin-
burgh Physical and Literary Essays; but the hypo-
thesis never gained any ground.

2. THE ALTERATION OF MOTION IS EVER PROPOR-
TIONAL 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 gene-
rates a certain quantity of motion, a double force will
generate a double quantity, whether that force be im-
pressed all at once, or in successive moments. To this
law no objection of consequence has ever been made.
It is founded on this self-evident truth, that every ef-
fect must be proportional to its cause. Mr Young,
who seems to be very ambitious of detecting the errors
of Newton, finds fault indeed with the expressions in
which the law is stated; but he owns, that if thus ex-
pressed, The alteration of motion is proportional to the ac-
tions or resistances which produce it, and is in the direction
in which the actions or resistances are made, it would be
unexceptionable.

13
Objections
to the third
law.

3. TO EVERY ACTION THERE ALWAYS IS OPPOSED AN
EQUAL RE-ACTION: OR THE MUTUAL ACTION OF TWO
BODIES UPON EACH OTHER ARE ALWAYS EQUAL, AND DI-
RECTED TO CONTRARY PARTS.—This axiom is also dis-
puted by many. In the above-mentioned paper in the
Physical Essays, the author endeavours to make a di-
stinction between re-action and resistance; and the
same attempt has been made by Mr Young. "When
an action generates no motion (says he), it is cer-
tain that its effects have been destroyed by a contrary
and equal action. When an action generates two con-
trary and equal motions, it is also evident that mutual

actions were exerted, equal and contrary to each
other. All cases where one of these conditions are not
found, are exceptions to the truth of the law. If a
finger presses against a stone, the stone, if it does not
yield to the pressure, presses as much upon the finger:
but if the stone yields, it re-acts less than the finger
acts; and if it should yield with all the momentum
that the force of the pressure ought to generate, which
it would do if it were not impeded by friction, or a
medium, it would not re-act at all. So if the stone
drawn by a horse, follows after the horse, it does not
re-act so much as the horse acts; but only so much as
the velocity of the stone is diminished by friction, and
it is the re-action of friction only, not of the stone.
The stone does not re-act because it does not act, it
resists, but resistance is not action.

"In the loss of motion from a striking body, equal
to the gain in the body struck, there is a plain solution
without requiring any re-action. The motion lost, is
identically that which is found in the other body; this
supposition accounts for the whole phenomenon in the
most simple manner. If it be not admitted, but the
solution by re-action is insisted upon, it will be incum-
bent on the party to account for the whole effect of
communication of motion; otherwise he will lie under
the imputation of rejecting a solution which is simple,
obvious, and perfect; for one complex, unnatural, and
incomplete. However this may be determined, it will
be allowed, that the circumstances mentioned, afford
no ground for the inference, that action and re-action
are equal, since appearances may be explained in an-
other way" (A).

Others grant that Sir Isaac's axiom is very true in
respect to terrestrial substances; but they affirm, that,
in

(A) If there be a perfect reciprocity betwixt an impinging body and a body at rest sustaining its impulse,
may we not at our pleasure consider either body as the agent, and the other as the resistant? Let a moving
body, A, pass from north to south, an equal body B at rest, which receives the stroke of A, act upon A from
south to north, and A resist in a contrary direction, both inelastic: let the motion reciprocally communicated
be called fix. Then B at rest communicates to A six degrees of motion towards the north, and receives six
degrees towards the south. B having no other motion than the six degrees it communicated, will, by its
equal and contrary loss and gain, remain in equilibrio. Let the original motion of A have been twelve,
then A having received a contrary action equal to six, six degrees of its motion will be destroyed or in equi-
librio; consequently, a motive force as six will remain to A towards the south, and B will be in equilibrio,
or at rest. A will then endeavour to move with six degrees, or half its original motion, and B will remain
at rest as before. A and B being equal masses, by the laws of communication three degrees of motion will
be communicated to B, or A with its six degrees will act with three, and B will re-act also with three. B
then will act on A from south to north equal to three, while it is acted upon or resisted by A from north
to south, equal also to three, and B will remain at rest as before; A will also have its six degrees of motion
reduced to one half by the contrary action of B, and only three degrees of motion will remain to A, with
which it will yet endeavour to move; and finding B still at rest, the same process will be repeated till the
whole motion of A is reduced to an infinitely small quantity, B all the while remaining at rest, and there
will be no communication of motion from A to B, which is contrary to experience.

Let a body, A, whose mass is twelve, at rest, be impinged upon first by B, having a mass as twelve, and
a velocity as four, making a momentum of 48; and secondly by C, whose mass is six, and velocity eight,
making a momentum of 48 equal to B, the three bodies being inelastic. In the first case, A will become
possessed of a momentum of 24, and 24 will remain to B; and, in the second case, A will become possessed
of a momentum of 32, and 16 will remain to C, both bodies moving with equal velocities after the shock, in
both cases, by the laws of percussion. It is required to know, if in both cases A resists equally, and if B and
C act equally? If the actions and resistances are equal, how does A in one case destroy 24 parts of B's
motion, and in the other case 32 parts of C's motion, by an equal resistance? And how does B communicate
in one case 24 degrees of motion, and C 32, by equal actions? If the actions and resistances are unequal,
it is asked how the same mass can resist differently to bodies impinging upon it with equal momenta, and how
bodies

Newtonian in these, both action and re-action are the effects of Philosophy gravity. Substances void of gravity would have no momentum; and without this they could not act; they would be moved by the least force, and therefore could not resist or re-act. If therefore there is any fluid which is the cause of gravity, though such fluid could act upon terrestrial substances, yet these could not re-act upon it; because they have no force of their own, but depend entirely upon it for their momentum. In this manner, say they, we may conceive that the planets circulate, and all the operations of nature are carried on by means of a subtle fluid; which being perfectly active, and the rest of matter altogether passive, there is neither resistance nor loss of motion. See MOTION.

From the preceding axiom Sir Isaac draws 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 we may explain 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 direct one the diagonal.

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: and if we suppose friction and the resistance of the air to be absent, the motion of a number of bodies which mutually impelled one another would be perpetual, and its quantity always equal.

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 outward actions and impediments) 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 is at rest, or moves uniformly forward in a right line without any circular motion. The truth of this is evidently shown by the experiment of a ship; where all motions happen after the same manner, whether the ship is at rest, or proceeds uniformly forward in a straight line.

6. If bodies, any how moved among themselves, are 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 been urged by no such forces.

The whole of the mathematical part of the Newtonian philosophy depends on the following lemmas; of which the first is the principal.