The Mathematical Principles of Natural Philosophy (1729)/Preface

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Mr. Roger Cotes,

To the Second Edition of this Work, so far as it relates to the Inventions and Discoveries herein contained.

THOSE who have treated of natural pilosophy, may be nearly reduced to three classes. Of these some have been attributed to the several species of things, specific and occult qualities; on which, in a manner unknown, they make the operations of the several bodies to depend. The sum of the doctrine of the Schools derived from Aristotle and the Peripatetics is herein contained. They affirm that the several effects of the bodies arise from the particular natures of those bodies arise from the particular natures of those bodies. But whence it is that bodies derive those natures they don't tell us; and therefore they tell us nothing. And being entirely employed in giving names to things, and not in searching into things themselves, we may say that they have invented a philosophical way of speaking, but not that they have made known to us true philosophy.

Others therefore by laying aside that useless heap of words, thought to employ their pains to better purpose. These supposed all matter homogeneous, and that the variety of forms which is seen in bodies arises from some very plain and simple affections of the component particles. And by going on from simple things to those which are more compounded they certainly proceed right; if they attribute no other properties to those primary affections of the particles than Nature has done. But when they take a liberty of imagining at pleasure unknown figures and magnitudes, and uncertain situations and motion of the parts; and moreover of supposing occult fluids, freely pervading the pores of bodies, endued with an all-performing subtilty, and agitated, with occult motions; they now run out into dreams and chimera's, and neglect the true constitution of things; which certainly is not to be expected from fallacious conjectures, when we can scarce reach it by the most certain observations. Those who fetch from by hypotheses the foundation on which they build their speculations, may form indeed an ingenious romance, but a romance it will still be.

There is left then the third class, which prosess experimental philosophy. These indeed derive the causes of all things from the most simple principles possible; but then they assume nothing as a principle, that is not proved by phænomena. They frame no hypotheses, nor receive them into philosophy otherwise than as questions whose truth may be disputed. They proceed therefore in a two-fold method, synthetical and analytical. From some select phænomena they deduce by analysis the forces of nature, and the more simple laws of forces; and from thence by synthesis shew the constitution of the rest. This is that incomparably best way of philosophizing, which our renowned author most justly embraced before the rest; and thought alone worthy to be cultivated and adorned by his excellent labours. Of this he has given us a most illustrious example by the explication of the System of the World, most happily deduced from the Theory of Gravity. That the virtue of gravity was found in all bodies, others suspected, or imagined before him; but he was the only and the first philosopher that could demonstrate it from appearances, and make it a solid foundation to the most noble speculations.

I know indeed that some persons and those of great name, too much prepossessed with certain prejudices, are unwilling to assent to this new principle, and are ready to prefer uncertain notions to certain. It is not my intention to detract from the reputation of these eminent men; I shall only lay before the reader such considerations as will enable him to pass an equitable sentence in this dispute.

Therefore that we may begin our reasoning from what is most simple and nearest to us; let us consider a little what is the nature of gravity with us on Earth, that we may proceed the more safely when we come to consider it in the heavenly bodies, that lie at so vast a distance from us. It is now agreed by all philosophers that all circumterrestrial bodies gravitate towards the Earth. That no bodies really light are to be found, is now confirmed by manifold experience. That which is relative levity, is not true levity, but apparent only; and arises from the preponderating gravity of the contiguous bodies.

Moreover, as all bodies gravitate towards the Earth, so does the Earth again towards bodies. That the action of gravity is mutual, and equal on both sides, is thus proved. Let the mass of the Earth be distinguished into any two parts whatever, either equal, or any how unequal; now if the weights of the parts towards each other were not mutually equal, the lesser weight would give way to the greater, and the two parts joined together would move on ad infinitum in a right line towards that part to which the greater weight tends; altogether against experience. Therefore we must say that the weights of the parts are constituted in equilibrio; that is, that the action of gravity is mutual and equal on both sides.

The weights of bodies, at equal distances from the centre of the Earth, are as the quantities of matter in the bodies. This is collected from the equal acceleration of all bodies that fall from a state of rest by the force of their weights; for the forces by which unequal bodies are equally accelerated must be proportional to the quantities of the matter to be moved. Now that all bodies are in falling equally accelerated appears from hence, that when the resistance of the air is taken away, as it is under an exhausted receiver, bodies falling describe equal spaces in equal times; and this is yet more accurately proved by the experiments of pendulums.

The attractive forces of bodies at equal distances, are as the quantities of matter in the bodies. For since bodies gravitate towards the Earth, and the Earth again towards bodies with equal moments; the weight of the Earth towards every body, or the force with which the body attracts the Earth, will be equal to the weight of the same body towards the Earth. But this weight was shewn to be as the quantity of matter in the body; and therefore the force with which every body attracts the Earth, or the absolute force of the body, will be as the same quantity of matter.

Thefore the attractive force of the entire bodies arises from, and is compounded of, the attractive forces of the parts, because as was just shewn, if the bulk of the matter be augmented or diminished, its virtue is proportionably augmented or diminished. We must therefore conclude that the action of the Earth is compounded of the united actions of its parts; and therefore that all terrestrial bodies must attract each other mutually, with absolute forces that are as the matter attracting. This is the nature of gravity upon Earth; let us now see what it is in the Heavens.

That every body perseveres in its state either of rest, or of moving uniformly in a right line, unless in so far as it is compelled to change that state by forces impressed, is a law of nature universally received by all philosophers. But from thence it follows that bodies which move in curve lines, and are therefore continually going off from the right lines that are tangents to their orbits, are by some continued force retained in those curvilinear paths. Since then the Planets move in curvilinear orbits there must be some force operating, by whose repeated actions they are perpetually made to deflect from the tangents.

Now it is collected by mathematical reasoning, and evidently demonstrated, that all bodies that move in any curve line described in a plane, and which, by a radius drawn to any point, whether quiescent, or any how moved, describe areas about that point proportional to the times, are urged by forces directed towards that point. This must therefore be granted. Since then all astronomers agree that the primary Planets describe about the Sun, and the secondary about the primary, areas proportional to the times; it follows that the forces by which they are perpetually turned aside from the rectilinear tangents, and made to revolve in curvilinear orbits, are directed towards the bodies that are situate in the centres of the orbits. This force may therefore not improperly be called centripetal in respect of the revolving body, and in respect of the central body attractive; whatever cause it may be imagined to arise from.

But besides, these things must be also granted, as being mathematically demonstrated: If several bodies revolve with an equable motion in concentric circles, and the squares of the periodic times are as the cubes of the distances from the common centre; the centripetal forces will be reciprocally as the squares of the distances. Or, if bodies revolve in orbits that are very near to circles, and the apsides of the orbits rest; the centripetal forces of the revolving bodies will be reciprocally as the squares of distances. That both these cases hold in all the Planets all astronomers consent. Therefore the centripetal forces of all the Planets are reciprocally as the squares of the distances from the centres of their orbits. If any should object, that the apsides of the Planets, and especially of the Moon, are not perfectly at rest; but are carried with a slow kind of motion in consequentia; one may give this answer, that though we should grant this very slow motion to arise from hence, that the proportion of the centripetal force is a little different from the duplicate, yet that we are able to compute mathematically the quantity of that aberration, and find it perfectly insensible. For the ratio of the Lunar centripetal force it self, which must be the most irregular of them all, will be indeed a little greater than the duplicate, but will be near sixty times nearer to that than it is to the triplicate. But we may give a truer answer, by saying that this progresion of the apsides arises not from an aberration from the duplicate proportion, but from a quite different cause, as is most admirably shewn in this philosophy. It is certain then that the centripetal forces with which the primary Planets tend to the Sun, and the secondary to their primary, are accurately as the squares of the distances reciprocally.

From what has been hitherto said, it is plain that the Planets are retained in their orbits by some force perpetually acting upon them; it is plain that that force is always directed towards the centres of their orbits; it is plain that its efficacy is augmented with the nearness to the centre, and diminished with the same; and that it is augmented in the same proportion with which the square of the distance is diminished, and diminished in the same proportion with which the square of the distance is augmented. Let us now see whether, by making a comparison between the centripetal forces of the Planets, and the force of gravity, we may not by chance find them to be of the same kind. Now they will be of the same kind if we find on both sides the same laws, and the same affections. Let us then first consider the centripetal force of the Moon which is nearest to us.

The rectilinear spaces, which bodies let fall from rest describe in a given time at the very beginning of the motion, when the bodies are urged by any forces whatsoever, are proportional to the forces. This appears from mathematical reasoning. Therefore the centripetal force of the Moon revolving in its orbit is to the force of gravity at the surface of the Earth, as the space, which in a very small particle of time the Moon, deprived of all its circular force and descending by its centripetal force towards the Earth, would describe, is to the space which a heavy body would describe, when falling by the force of its gravity near to the Earth, in the same given particle of time. The first of these spaces is equal to the versed sine of the arc described by the Moon in the same time, because that versed sine measures the translation of the Moon from the tangent, produced by the centripetal force; and therefore may be computed, if the periodic time of the Moon and its distance from the centre of the Earth are given. The last space is found by experiments of pendulums, as Mr. Huygens has shewn. Therefore by making a calculation we shall find that the first space is to the latter, or the centripetal force of the Moon revolving in its orbit will be to the force of gravity at the superficies of the Earth, as the square of the semi-diameter of the Earth to the square of the semi-diameter of the orbit. But by what was shewn before the very same ratio holds between the centripetal force of the Moon revolving in its orbit, and the centripetal force of the Moon near the surface of the Earth. Therefore the centripetal force near the surface of the Earth is equal to the force of gravity. Therefore these are not two different forces, but one and the same; for if they were different, these forces united would cause bodies to descend to the Earth with twice the velocity they would fall with by the force of gravity alone. Therefore it is plain that the centripetal force, by which the Moon is perpetually, either impelled or attracted out of the tangent and retained in its orbit, is the very force of terrestrial gravity reaching up to the Moon. And it is very reasonable to believe that virtue should extend it self to vast distances, since upon the tops of the highest mountains we find no sensible diminution of it. Therefore the Moon gravitates towards the Earth; but on the other hand, the Earth by a mutual action equally gravitates towards the Moon; which is also abundantly confirmed in this philosophy, where the Tides in the Sea and the Præcesson of the Æquinoxes are treated of; which arise from the action both of the Moon and of the Sun upon the Earth. Hence lastly, we discover by what law the force of gravity decreases at great distances from the Earth. For since gravity is no ways different from the Moon's centripetal force, and this is reciprocally proportional to the square of the distance; it follows that it is in that ratio that the force of gravity decreases.

Let us now go on to the rest of the Planets. Because the revolutions of the primary Planets about the Sun, and of the secondary about Jupiter and Saturn, are phænomena of the same kind with the revolution of the Moon about the Earth; and because it has been moreover demonstrated that the centripetal forces of the primary Planets are directed towards the centre of the Sun, and those of the secondary towards the centres of Jupiter and Saturn, in the same manner as the centripetal force of the Moon is directed towards the centre of the Earth; and since besides, all these forces are reciprocally as the squares of the distances from the centres, in the same manner as the centripetal force of the Moon is as the square of the distance from the Earth; we must of course conclude, that the nature of all is the same. Therefore as the Moon gravitates towards the Earth, and the Earth again towards the Moon; so also all the secondary Planets will gravitate towards their primary, and the primary Planets again towards their secondary; and so all the primary towards the Sun; and the Sun again towards the primary.

Therefore the Sun gravitates towards all the Planets, and all the Planets towards the Sun. For the secondary Planets, while they accompany the primary, revolve the mean while with the primary about the Sun. Therefore by the same argument, the Planets of both kinds gravitate towards the Sun, and the Sun towards them. That the secondary Planets gravitate towards the Sun is moreover abundantly clear from the inequalities of the Moon; a most accurate theory of which laid open with a most admirable sagacity, we find explained in the third book of this Work.

That the attractive virtue of the Sun is propagated on all sides to prodigious distances, and is diffused to every part of the wide space that surrounds it, is most evidently shewn by the motion of the Comets; which coming from places immensely distant from the Sun, approach very near to it; and sometimes so near, that in their perihelia they almost touch its body. The theory of these bodies was altogether unknown to astronomers, till in our own times our excellent author most happily discovered it, and demonstrated the truth of it by most certain observations. So that it is now apparent that the Comets move in conic sections having their foci in the Sun's centre, and by radii drawn to the Sun describe areas proportional to the times. But from these phænomena it is manifest, and mathematically demonstrated, that those forces, by which the Comets are retained in their orbits, respect the Sun, and are reciprocally proportional to the squares of the distances from its centre. Therefore the Comets gravitate towards the Sun; and therefore the attractive force of the Sun not only acts on the bodies of the Planets, placed at given distances and very nearly in the same plane, but reaches also to the Comets in the most different parts of the heavens, and at the most different distances. This therefore is the nature of gravitating bodies, to propagate their force at all distances to all other gravitating bodies. But from thence it follows that all the Planets and Comets attract each other mutually, and gravitate mutually towards each other; which is also confirmed by the perturbation of Jupiter and Saturn, observed by astronomers, which is caused by the mutual actions of these two Planets upon each other; as also from that very slow motion of the apsides, above taken notice of, and which arises from a like cause.

We have now proceeded so far as to shew that it must be acknowledged, that the Sun, and the Earth, and all the heavenly bodies attending the Sun, attract each other mutually. Therefore all the least particles of matter in every one must have their several attractive forces, whose effect is as their quantity of matter; as was shewn above of the terrestrial particles. At different distances these forces will be also in the duplicate ratio of the distances reciprocally; for it is mathematically demonstrated that particles attracting according to this law will compose globes attracting according to the same law.

The foregoing conclusions are grounded on this axiom, which is received by all philosophers; namely that effects of the same kind; that is, whose known properties are the same, take their rise from the same causes and have the same unknown properties also. For who doubts, if gravity be the cause of the descent of a stone in Europe, but that it is also the cause of the same descent in America? If there is a mutual gravitation between a stone and the Earth in Europe, who will deny the same to be mutual in America? If in Europe, the attractive force of a stone and the Earth is compounded of the attractive forces of the parts; who will deny the like composition in America? If in Europe, the attraction of the Earth be propagated to all kinds of bodies and to all distances; why may it not as well be propagated in like manner in America? All philosophy is founded on this rule; for if that be taken away we can affirm nothing of universals. the constitution of particular things is known by observations and experiments; and when that is done, it is by this rule that we judge universally of the nature of such things in general.

Since then all bodies, whether upon Earth or in the Heavens, are heavy, so far as we can make any experiments or observations concerning them; we must certainly allow that gravity is found in all bodies universally. And in like manner as we ought not to suppose that any bodies can be otherwise than extended, moveable or impenetrable; so we ought not to conceive that any bodies can be otherwise than heavy. The extension, mobility and impenetrability of bodies become known to us only by experiments; and in the very same manner their gravity becomes known to us. All bodies we can make any observations upon, are extended, moveable and impenetrable; and thence we conclude all bodies, and those we have no observations concerning, to be extended and moveable and impenetrable. So all bodies we can make observations on, we find to be heavy; and thence we conclude all bodies, and those we have no observations of; to be heavy also. If any one should say that the bodies of the fixed Stars are not heavy because their gravity is not yet observed; they may say for the same reason that they are neither extended, nor moveable nor impenetrable, because these affections of the fixed Stars are not yet observed. In short, either gravity must have a place among the primary qualities of all bodies, or extension, mobility and impenetrability must not. And if the nature of things is not rightly explained by the gravity of bodies, it will not be rightly explained by their extension, mobility and impenetrability.

Some I know disapprove this conclusion, and mutter something about occult qualities. They continually are cavilling with us, that gravity is an occult property; and occult causes are to be quite banished from philosophy. But to this the answer is easy; that those are indeed occult causes whose existence is occult; and imagined but not proved; but not those whose real existence is clearly demonstrated by observations. Therefore gravity can by no means be called an occult cause of the celestial motions; because it is plain from the phenomena that such a virtue does really exist. Those rather have recourse to occult causes; who set imaginary vortices, of a matter entirely fictious, and imperceptible by our senses, to direct those motions.

But shall gravity be therefore called an occult cause, and thrown out of philosophy, because the cause of gravity is occult and not yet discovered? Those who affirm this, should be careful not to fall into an absurdity that may overturn the foundations of all philosophy. For causes use to proceed in a continued chain from those that are more compounded to those that are more simple; when we are arrived at the most simple cause we can go no farther. Therefore no mechanical account or explanation of the most simple cause is to be expected or given; for if it could be given, the cause were not the most simple. These most simple causes will you then call occult, and reject them? Then you must reject those that immediately depend upon them, and those which depend upon these last, till philosophy is quite cleared and disencumbred of all causes.

Some there are who say that gravity is præternatural, and call it a perpetual miracle. Therefore they would have it rejected, because præternatural causes have no place in physics. It is hardly worth while to spend time in answering this ridiculous objection which overturns all philosophy. For either they will deny gravity to be in bodies; which cannot be said; or else, they will therefore call it præternatural because it is not produced by the other affections of bodies, and therefore not by mechanical causes. But certainly there are primary affections of bodies; and these, because they are primary, have no dependence on the others. Let them consider whether all these are not in like manner præternatural, and in like manner to be rejected; and then what kind of philosophy we are like to have.

Some there are who dislike this celestial physics because it contradicts the opinions of Des Cartes, and seems hardly to be reconciled with them. Let these enjoy their own opinion; but let them act fairly; and not deny the same liberty to us which they demand for themselves. Since the Newtonian Philosophy appears true to us, let us have the liberty to embrace and retain it, and to follow causes proved by phænomena, rather than causes only imagined, and not yet proved. The business of true philosophy is to derive the natures of things from causes truly existent; and to enquire after those laws on which the Great Creator actually chose to found this most beautiful Frame of the World; not those by which he might have done the same, had he so pleased. It is reasonable enough to suppose that from several causes, somewhat differing from each other, the same effect may arise; but the true cause will be that, from which it truly and actually does arise; the others have no place in true philosophy. The same motion of the hour-hand in a clock may be occasioned either by a weight hung, or a spring shut up within. But if a certain clock should be really moved with a weight; we should laugh at a man that would suppose it moved by a spring, and from that principle, suddenly taken up without farther examination, should go about to explain the motion of the index; for certainly the way he ought to have taken should have been, actually to look into the inward parts of the machine, that he might, find the true principle of the proposed motion. The like judgment ought to be made of those philosophers, who will have the heavens to be filled with a most subtile matter, which is perpetually carried round in vortices. For if they could explain the phænomena ever so accurately by their hypotheses, we could not yet say that they have discovered true philosophy and the true causes of the celestial motions, unless they cou'd either demonstrate that those causes do actually exist, or at least, that no others do exist. Therefore if it be made clear that the attraction of all bodies is a property actually existung in rerum natura; and if it be also shewn how the motions of the celestial bodies may be solved by that property; it would be very impertinent for any one to object, that their motions ought to be accounted for by vortices; even though we should never so much allow such an explication of those motions to be possible. But we allow no such thing; for the phænomen can by no means be accounted for by vortices; as our Author has abundantly proved from the clearest reasons. So that Men must be strangely fond of chimera's, who can spend their time so idly, as in patching up a ridiculous figment and setting it off with new comments of their own.

If the bodies of the Planets and Comets are carried round the Sun in vortices; the bodies so carried, and the parts of the vortices next surrounding them, must be carried with the same velocity and the same direction, and have the same density, and the same vis inertia answering to the bulk of the matter. But it is certain, the Planets and Comets, when in the very same parts of the Heavens, are carried with various velocities and various directions. Therefore it necessarily follows that those parts of the celestial fluid, which are at the same distances from the Sun, must revolve at the same time with different velocities in different directions; for one kind of velocity and direction is required for the motion of the Planets, and another for that of the Comets. But since this cannot be accounted for; we must either say that all the celestial bodies are not carried about by vortices; or else that their motions are derived, not from one and the same vortex, but from several distinct ones, which fill and pervade the spaces round about the Sun.

But if several vortices are contained in the same space, and are supposed to penetrate each other, and to revolve with different motions; then because these motions must agree with those of the bodies carried about by them, which are perfectly regular. and performed in conic sections which are sometimes very eccentric, and sometimes nearly circles; one may very reasonably ask, how it comes to pass that these vortices remain entire, and have suffered no manner of perturbation in so many ages from the actions of the conflicting matter. Certainly if these fictitious motions are more compounded and more hard to be accounted for than the true motions of the Planets and Comets, it seems to no purpose to admit them into philosophy; since every cause ought to be more simple than its effects. Allowing men to indulge their own fancies, suppose any man should affirm that the Planets and Comets are surrounded with atmospheres like our Earth; which hypothesis seems more reasonable than that of vortices. Let him then affirm that these atmospheres by their own nature move about the Sun and describe conic sections, which motion is much more easily conceived than that of the vortices penetrating each other. Lastly, that the Planets and Comets are carried about the Sun by these atmospheres of theirs; and then applaud his own sagacity in discovering the causes of the celestial motions. He that rejects this fable must also reject the other; for two drops of water are not more like than this hypothesis of atmospheres, and that of vortices.

Galileo has shewn, that when a stone projected moves in a parabola, its deflexion into that curve from its rectilinear path is occasioned by the gravity of the stone towards the Earth, that is, by an occult quality. But now some body, more cunning than he, may come to explain the cause after this manner. He will suppofe a certain subtile matter, not discernable by our sight, our touch or any other of our senses, which fills the spaces which are near and contiguous to the superficies of the Earth; and that this matter is carried with different directions, and various, and often contrary, motions, describing parabolic curves. Then see how easily he may account for the deflexion of the stone above spoken of. The stone, says he, floats in this subtile fluid, and following its motion, can't chuse but describe the same figure. But the fluid moves in parabolic curves; and therefore the stone must move in a parabola of course. Would not the acuteness of this philosopher be thought very extraordinary, who could deduce the appearances of nature from mechanical causes, matter and motion, so clearly that the meanest man may undestand it? Or indeed should not we smile to see this new Galileo taking so much mathematical pains to introduce occult qualities into philosophy, from whence they have been so happily excluded? But I am ashamed to dwell so long upon trifles.

The sum of the matter is this; the number of the Comets is certainly very great; their motions are perfectly regular; and observe the same laws with those of the Planets. The orbits in which they move are conic sections, and those very eccentric. They move every way towards all parts of the Heavens, and pass through the planetary regions with all possible freedom, and their motion is often contrary to the order of the signs. These phænomena are most evidently confirmed by astronomical observations, and cannot be accounted for by vortices. Nay indeed they are utterly irreconcilable with the vortices of the Planets. There can be no room for the motions of the Comets; unless the celestial spaces be entirely cleared of that fictitious matter.

For if the Planets are carried about the Sun in vortices; the parts of the vortices which immediately surround every Planet must be of the same density with the Planet, as was shewn above. Therefore in all the matter contiguous to the perimeter of the magnus orbis, must be of the same density as the Earth. But now that which lies between the magnus orbis and the orb of Satum must have either an equal or greater density. For to make the constitution of the vortex permanent, the parts of less density must he near the centre, and those of greater density must go farther from it. For since the periodic times of the Planets are in the sesquiplicate ratio of their distances from the Sun, the periods of the parts of the vortices must also preserve the same ratio. Thence it will follow that the centrifugal forces of the parts of the vortex must be reciprocally as the squares of their distances. Those parts therefore which are more remote from the centre endeavour to recede from it with less force; whence if their density be deficient, they must yield to the greater force with which the parts that lie nearer the centre endeavour to ascend. Therefore the denser parts will ascend; and those of less density will descend; and there will be a mutual change of places, till all the fluid matter in the whole vortex be so adjusted and disposed, that being reduced to an equilibrium its parts become quiescent. If two fluids of different density be contained in the same vessel; it will certainly come to pass that the fluid of greater density will sink the lowest; and by a like reasoning it follows that the denser parts of the vortex by their greater centrifugal force will ascend to the highest places. Therefore all that far greater part of the vortex which lies without the Earth's orb, will have a density, and by consequence a vis inertia answering to the bulk of the matter, which cannot be less than the density and vis inertia of the Earth. But from hence will arise a mighty resistance to the passage of the Comets, and such as can't but be very sensible; not to say, enough to put a stop to, and absorb, their motions entirely. But now it appears from the perfectly regular motion of the Comets, that they suffer no resistance that is in the least sensible; and therefore that they meet with no matter of any kind, that has any resisting force, or, by consequence, any density or vis inertia. For the resistance of mediums arises, either from the inertia of the matter of the fluid, or from its want of lubricity. That which arises from the want of lubricity is very small, and is scarce observable in the fluids commonly known, unless they be very tenacious like oil and honey. The resistance we find in air, water, quick-silver and the like fluids that are not tenacious, is almost all of the first kind; and cannot be diminished by a greater degree of subtilty, if the density and vis inertia, to which this resistance is proportional, remains; as is most evidently demonstrated by our Author in his noble theory of resistances in the second book.

Bodies in going on through a fluid communicate their motion to the ambient fluid by little and little, and by that communication lose their own motion. and by losing it are retarded. Therefore the retardation is proportional to the motion communicated; and the communicated motion, when the velocity of the moving body is given, is as the density of the fluid; and therefore the retardation or resistance will be as the same density of the fluid; nor can it be taken away, unless the fluid coming about to the hinder parts of the body restore the motion lost. Now this cannot be done unless the impression of the fluid on the hinder parts of the body be equal to the impression of the fore parts of the body on the fluid, that is unless the relative velocity with which the fluid pushes the body behind is equal to the velocity with which the body pushes the fluid; that is, unless the absolute velocity of the recurring fluid be twice as great as the absolute velocity with which the fluid is driven forwards by the body; which is impossible. Therefore the resistance of fluids arising from their vis inertia can by no means be taken away. So that we must conclude that the celestial fluid has no vis inertia, because it has no resisting force; that it has no force to communicate motion with, because it has no vis inertia; that it has no force to produce any change in one or more bodies, because it has no force wherewith to communicate motion; that it has no manner of efficacy, because it has no faculty wherewith to produce any change of any kind. Therefore certainly this hypothesis may be justly called ridiculous, and unworthy a philosopher; since it is altogether without foundation, and does not in the least serve to explain the nature of things. Those who would have the Heavens filled with a fluid matter, but suppose it void of any vis inertia; do indeed in words deny a vacuum, but allow it in fact. For, since a fluid matter of that kind can no ways be distinguished from empty space; the dispute is now about the names, and not the natures of things. If any are so fond of matter, that they will by no means admit of a space void of body; let us consider, where they must come at last.

For either they will say, that this constitution of a world every where full, was made so by the will of God to this end, that the operations of Nature might be assisted every where by a subtile æther pervading and filling all things; which cannot be said however, since we have shewn from the phænonena of the Comets, that this æther is of no efficacy at all; or they will say, that it became so by the same will of God for some unknown end; which ought not to be said, because for the same reason a different constitution may be as well supposed, or lastly, they will not say that it was caused by the will of God, but by some necessity of its nature. Therefore they will at last sink into the mire of that infamous herd; who dream that all things are governed by Fate, and not by Providence; and that matter exists by the necessity of its nature always and every where, being infinite and eternal. But supposing these things; it must be also every where uniform; for variety of forms is entirely inconsistent with necessity. It must be also unmoved; for if it be necessarily moved in any determinate direction, with any determinate velocity, it will by a like necessity be moved in a different direction with a different velocity; but it can never move in different directions with different velocities; therefore it must be unmoved. Without all doubt this World, so diversified with that variety of forms and motions we find in it, could arise from nothing but the perfectly free will of God directing and presiding over all.

From this fountain it is that those laws, which we call the laws of Nature, have flowed; in which there appear many traces indeed of the most wise contrivance, but not the least shadow of necessity. These therefore we must not seek from uncertain conjectures; but learn them from observations and experiments. He who thinks to find the true principles of physics and the laws of natural things by the force alone of his own mind, and the internal light of his reason must either suppose that the World exists by necessity, and by the same necessity follows the laws proposed; or if the order of Nature was established by the will of God, that himself, a miserable reptile, can tell what was fittest to be done. All found and true philosophy is founded on the appearances of things; which if they draw us never so much against our wills, to such principles as most clearly manifest to us the most excellent counsel and supreme dominion of the All-wise and Almighty Being; those principles are not therefore to be laid aside, because some men may perhaps dislike them. They may call them, if they please, miracles or occult qualities; but names maliciously given ought not to be a disadvantage to the things themselves; unless they will say at last, that all philosophy ought to be founded in atheism. Philosophy must not be corrupted in complaisance to these men; for the order of things will not be changed.

Fair and equal judges will therefore give sentence in favour of this most excellent method of philosophy. which is founded on experiments and observations. To this method it is hardly to be said or imagined, what light, what splendor, hath accrued from this admirable work of our illustrious author; whose happy and sublime genius, revolving the most difficult problems, and reaching to discoveries of which the mind of man was thought incapable before, is deservedly admired by all those who are somewhat more than superficially versed in thes matters. The gates are now set open; and by his means we may freely enter into the knowledge of the hidden secrets and wonders of natural things; He has so clearly laid open and set before our eyes the most beautiful frame of the System of the World, that if King Alphonsus were now alive, he would not complain for want of the graces either of simplicity or of harmony in it. Therefore we may now more nearly behold the beauties of Nature, and entertain our selves with the delightful contemplation; and, which is the best and most valuable fruit of philosophy, be thence incited the more profoundly to reverence and adore the great Maker and Lord of all. He must be blind who from the most wise and excellent contrivances of things cannot see the infinite Wisdom and Goodness of their Almighty Creator, and he must be mad and senseless who refuses to acknowledge them.