NEWTONIAN 634 SECT. I.-DEFINITIONS AND HISTORY. The NEWTONIAN PHILOSOPHY as the true doctrine of the universe, and particularly of the heavenly bodies, their laws, affections, &c., deserves distinct notice in every compendium of general science. The term Newtonian philosophy is applied very differently; and various confused notions have hence arisen. Some authors under this term include all the corpuscular philosophy, considered as it now stands corrected and reformed by the discoveries and improvements made by Sir Isaac Newton. In this sense Gravesande 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 Corpuscular. Others, by the Newtonian philosophy, mean the method or order which Sir Isaac Newton observes in philosophising; viz. the reasoning and the conclusions drawn 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 corpuscular. Others, by the Newtonian philosophy, intend that wherein physical bodies are considered mathematically, and where geometry and mechanics are applied to the soIn this lution of the appearances of nature. sense the Newtonian is the same with the mechanical and mathematical philosophy. Others, again, understand by it that part of physical knowledge which Sir Isaac Newton has handled, improved, and demonstrated, in his Principia; while, lastly, others mean by this phrase the new principles which Sir Isaac Newton has brought into philosophy, the new system founded thereon, and the new solutions of phenomena thence deduced; or that which characterises and distinguishes his philosophy from all others. This is the sense wherein we shall chiefly consider it. The origin and history of this system of philosophy has been given under the article NEW TON. It was first made public in 1687 by its author, then a fellow of Trinity College, Cambridge; and in 1713 republished with considerable improvements. Several authors have since attempted to make it plainer, by setting aside many of the more sublime mathematical researches, and substituting either more obvious reasonings or experiments in lieu thereof; particularly Whiston in his Prælect. Phys. Mathemat.; Gravesande in Element. et Instit. ; and Dr. Pemberton in his View. PHILOSOPHY Philosophy. He founds his system on the fol- 6 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 remain at rest,' says Young, in his Examination of the third and fourth Definition of the first book of the Principia, 'is unnecessary, whilst nothing attempts to disturb the rest. It is likewise impossible to be conceived, as it implies a contradiction. A man, by opposing force to force, may endeavour not to be moved; but this opposition is an endeavour to move, not with a design to move, but by counteracting another force to prevent being moved. An endeavour not to move, therefore, cannot exist in bodies, because SECT. II. DEFINITIONS ON WHICH THE NEWTO- it is absurd; and if we appeal to fact, we shall NIAN PHILOSOPHY IS FOUNDED. find every body in an actual and constant endeavour 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 inertiæ, why is the body ever stopped? If, in the beginning of the motion, the body, by its innate force, overcomes a certain resistance of friction 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 passive; that they endeavour nothing; and that they continue in motion, not by any innate force or vis insita, 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 opposite 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 produced it. Now there are two grounds on which the truth of this doctrine may be supposed to rest. 1. 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. 2. 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 motion, though necessary for its production, is superfluous 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 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 there fore 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.' 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, or 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. SECT. III.-OF TIME, SPACE, PLACE, AND MO TION. Scholium 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, and 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 perpetuably 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 translatious 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 10,010 parts; while the ship itself with a fresh gale is carried towards the west, with a velocity expressed by ten 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 1001 parts; and relatively on the earth, towards the west, with a velocity of nine 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 the more accurate deducing of the celestial motions. It may be that there is no such thing as an equable motion whereby time may be accurately measured. All motions may be accelerated or retarded; but the true or equable 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. T necessity of which equation for determin times of a phenomenon is evinced, a the experiments of the pendulum eclipses of the satellites of Jur As the order of the parts of so also is the order of the pose those parts to be mo and they will be moved the expression) out o and spaces are, as it selves as of all other things. All the placed in time as to order of succession, space as to order of situation. It is fr essence or nature that they are places; a the primary places of things should be is absurd. These are therefore the places; and translations out of those plas the only absolute motions. But becas parts of space cannot be seen, or dis from one another by the senses, therei stead we use sensible measures of the from the positions and distances of th any body, considered as immoveable, all places; and then, with respect to s we estimate all motions, considering transferred from some of those places i And so, instead of absolute places and we use relative ones; and that withor convenience in common affairs: but ap phical disquisitions we ought to abs our senses, and consider things themere tinct from what are only sensible meas them. For it may be that there s really at rest, to which the places and others may be referred. But we may distinguish rest and m solute and relative, one from the other. properties, causes and effects. It is of rest, that bodies really at rest do spect of each other. And therefore, a sible that in the remote regions of the or perhaps far beyond them, there may body absolutely at rest, though it be to know from the position of bodies. ther in our regions whether any of the the same position to that remote bod lows that absolute rest cannot be d from the position of bodies in our regi a property of motion, that the parts wi given positions to their wholes do para motion of their wholes. For all parts ing bodies endeavour to recede from de motion; and the impetus of bodies wards arises from the joint impetus parts. Therefore, if surrounding moved, those that are relatively at them will partake of their motion. account the true and absolute motion cannot be determined by the tra from those only which seem to rest; ternal bodies ought not only to appr but to be really at rest. For others cluded bodies, beside their transiti the surrounding ones, partake likeries true motions; and, though h not made, they only seem dies star 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 immoveable place, as in the above-mentioned example of the sailor. Wherefore entire and absolute motions can be no otherwise determined than by immoveable places. Now no other places are immoveable 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 immoveable 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. SECT. IV. OF THE DIFFERENCE BETWEEN ABSOLUTE AND RELATIVE MOTION. 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 to recede from the axis; the water showed no tendency to the circumference, nor any ascent towards the sides of the ves sel, 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 quan-tities 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 these 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, 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 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 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 de crease 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 auginented; 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. SFCT. V. OF THE LAWS OF MOTION. Having thus explained himself Sir Isaac Newton 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. 1. 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. A top, whose parts, by their cohesion, are perpetually drawn aside from rectilinear motions, does not cease its rotation otherwise than as it is retarded by the air. The greater bodies of the planets and comets, meeting with less resistance in more free spaces, preserve their motions, both progressive and circular, for a much longer time.' Notwithstanding this demonstration, however, the axiom has been violently disputed. It has been argued, that bodies continue in their state of motion because they are subjected to the continual impulse of an invisible and subtile fluid, which always pours in from behind, and of which all places are full. It has been affirmed that motion is as natural to this fluid as rest is to all other matter; that it is impossible we can know in what manner a body would be influenced by moving forces if it were entirely destitute of gravity. According to what we can observe, the mometum 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 has a tendency to change from a state of motion to a state of rest, and from a state of rest to a state of motion. A paper appeared on this subject in the first volume of the Edinburgh Physical and Literary Essays; but the hypothesis never gained any ground. 2. The alteration of motion is ever proportional to the motive force impressed; and is made in the direction of the right line in which that force is impressed.—Thus, if any force generates a certain quantity of motion, a double force will generate a double quantity, whether that force be impressed all at once, or in successive moments. To this law no objection of consequence has ever been made. It is founded on this self-evident truth that every effect must be proportional to its cause. Mr. Young, who seems fond of detecting the errors of Newton, finds fault indeed with the expressions in which the law is stated; but he owns, that if thus expressed, The alteration of motion is proportional to the actions or resistances which produce it, and is in the direction in which the actions or resistances are made, it would be unexceptionable. 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 directed to contrary parts.-This axiom is also disputed by many. In the above-mentioned paper in the Physical Essays the author endeavours to make a distinction 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 certain that its effects have been destroyed by a contrary and equal action. When an action generates two contrary 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 is 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 reacts 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 react 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 |