Mathematical principles of natural philosophy pdf

 
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  1. The mathematical principles of natural philosophy
  2. The Mathematical Principles of Natural Philosophy - Sir Isaac Newton, John Machin - Google книги
  3. The Mathematical Principles of Natural Philosophy
  4. Newton’s Philosophy

branches of philosophy. But has not the Analytical encroached upon the Synthetical, and Algorithmic Formulae been employed when not requisite, either for the. reproduced here, translated into English by Andrew Motte. Motte's translation of Newton's. Principia, entitled The Mathematical Principles of Natural Philosophy. Text and images from Newton's Principia: The Mathematical Principles of Natural Philosophy; to which is added, Newton's System of the World.

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Mathematical Principles Of Natural Philosophy Pdf

One or more conditions of the original document may affect the quality of the image, such as: Discolored pages. Faded or light ink. Binding. Isaac Newton'sPrincipiawas published in The full title isPhilosophiae Naturalis Principia Mathematica,orMathematical Principles of Natural Philosophy. MATHEMATICAL PRINCIPLES. OF. NATURAL PHILOSOPHY,. BY SIR ISAAC NEWTON;. TRANSLATED INTO ENGLISH BY ANDREW MOTTE.

Even after more than three centuries and the revolutions of Einsteinian relativity and quantum mechanics, Newtonian physics continues to account for many of the phenomena of the observed world, and Newtonian celestial dynamics is used to determine the orbits of our space vehicles. This authoritative, modern translation by I. Bernard Cohen and Anne Whitman, the first in more than years, is based on the edition, the final revised version approved by Newton; it includes extracts from the earlier editions, corrects errors found in earlier versions, and replaces archaic English with contemporary prose and up-to-date mathematical forms. Newton's principles describe acceleration, deceleration, and inertial movement; fluid dynamics; and the motions of the earth, moon, planets, and comets. It set forth the fundamental three laws of motion and the law of universal gravity, the physical principles that account for the Copernican system of the world as emended by Kepler, thus effectively ending controversy concerning the Copernican planetary system.

Public domain Public domain false false. Retrieved from " https: Namespaces Page Discussion. Views Read Edit View history. Display Options. This page was last edited on 8 January , at By using this site, you agree to the Terms of Use and Privacy Policy. Introduction to the American Edition. Life of Sir Isaac Newton. The Author's Preface. Axioms, or Laws of Motion.

Section I: Of the method of first and last ratios of quantities, by the help whereof we demonstrate the propositions that follow. Section II: Of the Invention of Centripetal Forces. Section III: Of the motion of bodies in eccentric conic sections. Section IV: Of the finding of elliptic, parabolic, and hyperbolic orbits, from the focus given. If one fixes Descartes's two basic mistakes, one obtains what More regarded as a proper philosophical view: space is distinct from matter because it is extended but penetrable, whereas matter is extended but impenetrable; and, in tandem, all substances are extended, but whereas some, such as tables and chairs, are impenetrable, others, such as the mind and even God, are penetrable and therefore not material.

In a number of texts, including De Gravitatione, the famous discussion of space and time in the Scholium to the Principia, and the discussion of God in the General Scholium, Newton made his generally Morean attitudes perfectly clear. He rejected the Cartesian identification of extension and matter, arguing that space itself exists independently of material objects and their relations , and he contended that all entities, including the human mind and even the divine being, are extended in the sense that they have spatial location, even if they are extended in ways that distinguish them from ordinary material bodies.

As Newton puts it in a famous passage from De Gravitatione: Space is an affection of a being just as a being. No being exists or can exist which is not related to space in some way. God is every where, created minds are somewhere, and body is in the space that it occupies; and whatever is neither everywhere nor anywhere does not exist.

And hence it follows that space is an emanative effect of the first existing being, for if any being whatsoever is posited, space is posited. Newton 25 Space is a fundamental concept in part because Newton not only conceives of it as independent of objects and their relations, but because he argues that every entity must somehow connect with space in some way.

Newton does not shy away from making this conception of the divine explicit in his public writings, despite the fact that it was anathema to his Cartesian and Leibnizian contemporaries. In the General Scholium to the Principia, which was added to the second edition of the text in , for instance, he famously writes of God: He endures always and is present everywhere, and by existing always and everywhere he constitutes duration and space.

Since each and every particle of space is always, and each and every indivisible moment of duration is everywhere, certainly the maker and lord of all things will not be never or nowhere … God is one and the same God always and everywhere.

He is omnipresent not only virtually but also substantially; for active power cannot subsist without substance. Newton For Newton, just as bodies are present in some spatial location, God, an infinite being, is present throughout all of space throughout all of time.

There could not be a clearer expression of agreement with More in his debate with the Cartesians concerning the substantial presence of the divine within space. Newton also took issue with Cartesian ideas about motion. His rejection of Cartesian views of space, and his embrace of space as a fundamental concept in philosophy following More's influence, aligns with his famous discussion of space and time in the Scholium that follows the opening definitions in the Principia.

This text influenced nearly every subsequent philosophical discussion of space and time for the next three centuries, so its contours are well known see DiSalle ch. Newton contends in De Gravitatione that this idea of proper motion, according to which the motion of a body is at least partially a function of its relations to other bodies, is in tension with Descartes's own laws of nature, also presented in the Principles.

For according to the conception of what we now call inertia that Descartes presents as his first two laws, a body moving rectilinearly will continue to do so unless caused to deviate from its path—hence a body's motion is not a function of its spatial relations to other bodies, but rather of its causal relations.

That is, according to the first two laws, changing a body's spatial relations to others bodies will not alter its rectilinear motion unless a causal interaction occurs. This tension runs deep in the Cartesian system. Newton's Scholium reflects his idea that the concept of motion in the Principia ought to cohere with the laws of motion he endorses.

He distinguishes between absolute and relative motion, true and apparent motion, and mathematical and common motion the same distinctions hold for time, space and place , and the former item in each of these three pairings is a concept that coheres with the laws of motion.

Newton's first law reflects Descartes's laws: it is a new version of the principle of inertia, one incorporating the concept of an impressed force. Since this law indicates that a body's motion is not a function of its spatial relations to other bodies, but rather of whether forces are impressed on it—which replaces the Cartesian concept of causal interactions that involve only impact see below —Newton cannot rely on a body's motion relative to other bodies if he is to avoid the kind of tension he found in the Cartesian view.

Hence he indicates that a body's true motion—rather than its apparent motion, which depends on our perceptions, or its relative motion, which depends on its spatial relations—is a body's change of position within space itself. That is, true motion should be understood as absolute motion. This means, in turn, that we must distinguish between the common idea of space, according to which space is conceived of as involving relations among various objects like the space of our air , and the mathematical idea, one presumably obtained from geometry or geometrical reasoning, that space is independent of any objects or their relations.

Newton was perfectly well aware that the notion of absolute space is not unproblematic. Indeed, how would we detect any body's true motion on this view? We might be able to detect a body's changing spatial relations with its neighbors, but not its changing relationship with space itself! Newton's solution to this problem is ingenious. Under certain circumstances, we can detect a body's true motion by detecting its acceleration.

We can do so when the body is rotating or has a circular motion, for such motions often have detectable effects. This is one way of understanding what has become one of the most famous, if not infamous, gedankenexperimenten of the early modern period, Newton's bucket. If one takes an ordinary bucket and fills it with water, and then attaches a rope to the top of the bucket, one can then twist the rope and let it go in order to make the bucket spin.

When the bucket full of water spins around, we can detect the water's acceleration by its changing surface. As Newton puts it, using some concepts from his laws of motion, the water endeavors to recede from the axis of its motion hence its changing surface.

In this way, despite the fact that Newton wishes to conceive of the water's true motion as its absolute motion within space itself, which cannot be perceived, he shows his readers how they might detect the water's true motion through its effects.

The mathematical principles of natural philosophy

Newton provides another gedankenexperiment to illustrate a similar point. If two balls are joined together by a rope and then spun around, say over one's head, then the changing tension in the rope will indicate that the balls are accelerated. Since any acceleration is a true motion—although not all true motions are accelerations, since a so-called inertial motion is not—this case indicates that we can detect a body's true motion even though space itself is imperceptible.

In this way, Newton did not merely develop an alternative to the Cartesian view of motion, along with its allied conception of space; he presented a view that could be employed to pick out some of the true motions of objects within nature. Once one has found a true motion, one can then ask what caused that motion for Newton, as we will see, it is forces that are understood to cause motions.

As the last line of the Scholium in the Principia indicates, that is one reason that Newton wrote his magnum opus in the first place. Newton's idea of space, then, fulfilled at least two roles. First, it enabled him to avoid the tension between the concept of true motion and the laws of motion of the kind found in Descartes.

The Mathematical Principles of Natural Philosophy - Sir Isaac Newton, John Machin - Google книги

Second, it also enabled him to articulate what he took to be God's relation to the natural world. Many regarded his achievements as an important advance over the Cartesian system.

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However, it would be a mistake to think that Newton vanquished Cartesian ideas within his lifetime: even in England, and certainly on the Continent, Cartesianism remained a powerful philosophical force for several decades after Newton published his primary works. In that arena, Newton's views were especially prominent, and came in for significant criticism from Leibniz. Methodology II: the Principia Many legends concerning momentous events in history are apocryphal, but the legend of Halley's visit to Newton in is true, and explains what prompted Newton to write his magnum opus.

In August of , Edmond Halley—for whom the comet is named—came to visit Newton in Cambridge in order to discover his opinion about a subject of much dispute in celestial mechanics. At this time, many in the Royal Society and elsewhere were at work on a cluster of problems that might be described as follows: how can one take Kepler's Laws, which were then considered among the very best descriptions of the planetary orbits, and understand them in the context of dynamical or causal principles?

What kind of cause would lead to planetary orbits of the kind described by Kepler? In particular, Halley asked Newton the following question: what kind of curve would a planet describe in its orbit around the Sun if it were acted upon by an attractive force that was inversely proportional to the square of its distance from the Sun?

Newton immediately replied that the curve would be an ellipse rather than, say, a circle.

But Newton also said that he had mislaid the paper on which the relevant calculations had been made, so Halley left empty handed whether there was any such paper is a subject of dispute.

But he would not be disappointed for long. In November of that year, Newton sent Halley a nine-page paper, entitled De Motu on motion , that presented the sought-after demonstration, along with several other advances in celestial mechanics. Halley was delighted, and immediately returned to Cambridge for further discussion. It was these events that precipitated the many drafts of De Motu that eventually became Principia mathematica by Several aspects of the Principia have been central to philosophical discussions since its first publication, including Newton's novel methodology in the book, his conception of space and time, and his attitude toward the dominant orientation within natural philosophy in his day, the so-called mechanical philosophy, which had important methodological consequences.

When Newton wrote the Principia between and , he was not contributing to a preexisting field of study called mathematical physics; he was attempting to show how philosophers could employ various mathematical and experimental methods in order to reach conclusions about nature, especially about the motions of material bodies.

In his lectures presented as the Lucasian Professor at Cambridge, Newton had been arguing since at least that natural philosophers had to employ geometrical methods in order to understand various phenomena in nature. He did not immediately convince many of them of the benefits of his approach. Just as his first publication in optics in sparked an intense debate about the proper methods for investigating the nature of light—and much else besides—his Principia sparked an even longer lasting discussion about the methodology that philosophers should adopt when studying the natural world.

This discussion began immediately with the publication of the Principia, despite the fact that its first edition contained few explicit methodological remarks Smith —39 and it intensified considerably with the publication of its second edition in , which contained many more remarks about methodology, including many attempts at defending the Newtonian method. Indeed, many of Newton's alterations in that edition changed the presentation of his methods.

Discussions of methodology would eventually involve nearly all of the leading philosophers in England and on the Continent during Newton's lifetime. In Cartesian natural philosophy, all natural change is due to the impacts that material bodies make upon one another's surfaces this is reflected in Descartes's first two laws of nature.

The concept of a force plays little if any role.

Unlike Descartes, Newton placed the concept of a force at the very center of his thinking about motion and its causes within nature. But Newton's attitude toward understanding the forces of nature involved an especially intricate method that generated intense scrutiny and debate amongst many philosophers and mathematicians, including Leibniz Garber This was a confusing notion at the time.

Perhaps it is not difficult to see why that should be so. To take one of Newton's own examples: suppose I hit a tennis ball with my racquet—according to Newton, I have impressed a force on the tennis ball, for I have changed its state of motion hopefully!

We have a reasonably good idea of what the tennis ball is, of what the racquet is, and even of what I am, and a Cartesian might wish to stop her analysis there. The ball, the racquet and I are physical things of one sort or another, but is the force physical? Is it not physical? It does not seem likely that a force is itself a physical thing in the sense of being a substance, to use a philosophical notion popular in Newton's day as we saw above in his first optics paper.

So when I hit the tennis ball over the net, the force I impressed on it was the action of hitting the ball, or an action associated with hitting the ball, and not a property of me or of the ball after the action had ceased. This idea confused many of Newton's readers. By the mid-eighteenth century, the time of Hume's analysis of causation in the Treatise and the Enquiry, many philosophers started to think that actions and other kinds of event are important items to have in one's ontology, and they often contended in particular that causal relations hold between events.

But in Newton's day, philosophers typically regarded objects or substances as the causal relata one finds an equivocation between thinking of events and thinking of objects as the relevant causal relata even in Hume. So actions were difficult to analyze or often left out of analyses. As a result, Newton's conception of force proved confusing. Moreover, it was unclear to many of Newton's mechanist readers how his forces fit into their rather austere ontological view that material bodies consist solely of properties such as size, shape, mobility and solidity.

Newton did try to clarify his method of characterizing forces.

The Mathematical Principles of Natural Philosophy

If one brackets the question of how to understand forces as ephemeral actions that do not persist after causal interactions have ceased, one can make progress by conceiving of forces as quantities.

In particular, since Newton's eight definitions and three laws indicate that forces are proportional to mass and to acceleration, and since mass—or the quantity of matter, a concept Newton transformed from its Cartesian origins, where it was understood as a measure of a body's volume—and acceleration are both quantities that can be measured, Newton gives us a means of measuring forces. This is crucial to his method. If one thinks of forces as measurable quantities, moreover, then one can attempt to identify two seemingly disparate forces as in fact the same force through thinking about measuring them.

For instance, in Book III of the Principia, Newton famously argues in proposition five and its scholium that the centripetal force maintaining the planetary orbits is in fact the same as the force of gravity, viz. This was a revolutionary idea at the time, one rendered possible in the first place by Newton's way of thinking about forces as quantities.

This idea then led Newton to the even more revolutionary view in proposition seven of Book III that all bodies gravitate toward one another in proportion to their quantity of matter.

That is, it led him to the idea of universal gravity, a view that shocked many of his Continental readers in its boldness. This helped to unify what were once called superlunary and sublunary phenomena, a unification that was obviously crucial for later research in physics.

Again, the idea was enabled by Newton's abstract way of understanding forces—without conceiving of a force as involving any specific mechanism or type of physical interaction, Newton thought of forces as quantities that are proportional to other features of nature. Despite his evident success in obtaining what we now call the law of universal gravitation, Newton admits that he lacks another kind of knowledge about gravity; this lack of knowledge directly reflects an aspect of his abstract characterization of forces.

This interpretation is sometimes coupled with the view that some British philosophers in the late seventeenth century regarded Cartesianism as overly reliant on hypotheses in reaching conclusions about phenomena. But this interpretation may be hard to square with Newton's texts.

Newton’s Philosophy

For instance, in the Scholium to Proposition 96 of Book I of the Principia, Newton discusses hypotheses concerning light rays. Similarly, in query 21 of the Opticks, he proposes that there might be an aether whose differential density accounts for the gravitational force acting between bodies. Hence Newton thinks that he has established the fact that gravity acts on all material bodies in proportion to their quantity of matter, but he has not established the existence of the aether.

By the time of the General Scholium, Newton was increasingly embroiled in philosophical disputes with Leibniz. In order to account for the motions of the planetary bodies in his Tentamen of , Leibniz introduces ex hypothesi the premise that some kind of fluid surrounds, and is contiguous to, the various planetary bodies, and then argues that this fluid must be in motion to account for their orbits. A debate between the two philosophers on this score would bring them to the question of the mechanical philosophy: whereas Newton would object to Leibniz's reasoning on methodological grounds, Leibniz would reply that Newton's theory of gravity involves action at a distance, which his vortex hypothesis avoids see below for more details.

Once the Principia was published, Newton had a vexed relationship with the mechanical philosophy, an orientation within natural philosophy that is associated strongly with nearly every significant early modern philosopher, including Descartes, Boyle, Huygens, Leibniz, and Locke.

His second law indicates that a body moving rectilinearly will continue to do so unless a force is impressed on it. This is not equivalent to claiming that a body moving rectilinearly will continue to do so unless another body impacts upon it.

A vis impressa—an impressed force—in Newton's system is not the same as a body, nor even a quality of a body, as we have seen; but what is more, some impressed forces need not involve contact between bodies at all. For instance, gravity is a kind of centripetal force, and the latter, in turn, is a species of impressed force.

As to respiration in a man and in a beast; the descent of stones in Europe and in America; the light of our culinary fire and of the sun; the reflection of light in the earth, and in the planets. RULE III The qualities of bodies, which admit neither intensification nor remission of degrees, and which are found to belong to all bodies within the reach of our experiments, are to be esteemed the universal qualities of all bodies whatsoever.

For since the qualities of bodies are only known to us by experiments, we are to hold for universal all such as universally agree with experiments; and such as are not liable to diminution can never be quite taken away. We are certainly not to relinquish the evidence of experiments for the sake of dreams and vain fictions of our own devising; nor are we to recede from the analogy of Nature, which is wont to be simple, and always consonant to itself.

We no other way know the extension of bodies than by our senses, nor do these reach it in all bodies; but because we perceive extension in all tht are sensible, therefore we ascribe it universally to all others also. That abundance of bodies are hard, we learn by experience; and because the hardness of the whole arises from the hardness of the parts, we therefore justly infer the hardness of the undivided particles not only of the bodies we feel but of all others.

That all bodies are impenetrable, we gather not from reason, but from sensation. The bodies which we handle we find impenetrable, and thence conclude impenetrability to be an universal property of all bodies whatsoever.

That all bodies are movable, and endowed with certain powers which we call the inertia of persevering in their motion, or in their rest, we only infer from the like properties observed in the bodies which we have seen. The extension, hardness, impenetrability, mobility, and inertia of the whole, result from the extension, hardness, impenetrability, mobility, and inertia of the parts; and hence we conclude the least particles of all bodies to be also all extended, and hard and impenetrable, and movable, and endowed with their proper inertia.

And this is the foundation of all philosophy. Moreover, that the divided but contiguous particles of bodies may be separated from one another, is matter of observation; and, in the particles that remain undivided, our minds are able to distinguish yet lesser parts, as is mathematically demonstrated. But whether the parts so distinguished, and not yet divided, may, by the powers of Nature, be actually divided and separated from one another, we cannot certainly determine.

Yet, had we the proof of but one experiment that any undivided particle, in breaking a hard and solid body, suffered a division, we might by virtue of this rule conclude that the undivided as well as the divided particles may be divided and actually separated to infinity.

Lastly, if it universally appears, by experiments and astronomical observations, that all bodies about the earth gravitate towards the earth, and that in proportion to the quantity of matter which they severally contain; that the moon likewise, according to the quantity of its matter, gravitates towards the earth; that, on the other hand, our sea gravitates towards the moon; and, all the planets one towards another; and the comets in like manner towards- the sun; we must, in consequence of this rule, universally allow that all bodies whatsoever are endowed with a principle of mutual gravitation.

For the argument from the appearances concludes with more force for the universal gravitation of all bodies than for their impenetrability; of which, among those in the celestial regions, we have no experiments, nor any manner of observation. Not that I affirm gravity to be essential to bodies: by their vis insita I mean nothing but their inertia. This is immutable. Their gravity is diminished as they recede from the earth. RULE IV In experimental philosophy we are to look, upon propositions inferred by general induction from phenomena as accurately or very nearly true, notwithstanding any contrary hypotheses that may be imagined, till such time as other phenomena occur, by which they may cither be made more accurate, or liable to exceptions.

This rule we must follow, that the argument of induction may not be evaded by hypotheses. Phenomena Propositions and Theorems That the smaller vortices may maintain their lesser revolutions about Saturn, Jupiter, and other planets, and swim quietly and undisturbed in the greater vortex of the sun, the periodic times of the parts of the sun's vortex should be equal; but the rotation of the sun and planets about their axes, which ought to correspond with the motions of their vortices, recede far from all these proportions.

The motions of the comets are exceedingly regular, are governed by the same laws with the motions of the planets, and can by no means be accounted for by the hypothesis of vortices; for comets are carried with very eccentric motions through all parts of the heavens indifferently, with a freedom that is incompatible with the notion of a vortex.

Bodies projected in our air suffer no resistance but from the air. Withdraw the air, as is done in Mr. Boyle's vacuum, and the resistance ceases; for in this void a bit of fine down and a piece of solid gold descend with equal velocity. And the same argument must apply to the celestial spaces above the earth's atmosphere; in these spaces, where there is no air to resist their motions, all bodies will move with the greatest freedom; and the planets and comets will constantly pursue their revolutions in orbits given in kind and position, according to the laws above explained; but though these bodies may, indeed, continue in their orbits by the mere laws of gravity, yet they could by no means have at first derived the regular position of the orbits themselves from those laws.

The six primary planets are revolved about the sun in circles concentric with the sun, and with motions directed towards the same parts, and almost in the same plane. Ten moons are revolved about the earth, Jupiter, and Saturn, in circles concentric with them, with the same direction of motion, and nearly in the planes of the orbits of those planets; but it is not to be conceived that mere mechanical causes could give birth to so many regular motions, since the comets range over all parts of the heavens in very eccentric orbits; for by that kind of motion they pass easily through the orbs of the planets, and with great rapidity; and in their aphelions, where they move the slowest, and are detained the longest, they recede to the greatest distances from each other, and hence suffer the least disturbance from their mutual attractions.

This most beautiful system of the sun, planets, and comets, could only proceed from the counsel and dominion of an intelligent and powerful Being. And if the fixed stars are the centres of other like systems, these, being formed by the like wise counsel, must be all subject to the dominion of One; especially since the light of the fixed stars is of the same nature with the light of the sun, and from every system light passes into all the other systems: and lest the systems of the fixed stars should, by their gravity, fall on each other, he hath placed those systems at immense distances from one another.

This Being governs all things, not as the soul of the world, but as Lord over all; and on account of his dominion he is wont to be called Lord God pantokrator, or Universal Ruler; for God is a relative word, and has a respect to servants; and Deity is the dominion of God not over his own body, as those imagine who fancy God to be the soul of the world, but over servants.

The Supreme God is a Being eternal, infinite, absolutely perfect; but a being, however perfect, without dominion, cannot be said to be Lord God; for we say, my God, your God, the God of Israel, the God of Gods, and Lord of Lords; but we do not say, my Eternal, your Eternal, the Eternal of Israel, the Eternal of Gods; we do not say, my Infinite, or my Perfect: these are titles which have no respect to servants.

The word God' usually signifies Lord; but every lord is not a God. It is the dominion of a spiritual being which constitutes a God: a true, supreme, or imaginary dominion makes a true, supreme, or imaginary God.

And from his true dominion it follows that the true God is a living, intelligent, and powerful Being; and, from his other perfections, that he is supreme, or most perfect. He is eternal and infinite, omnipotent and omniscient; that is, his duration reaches from eternity to eternity; his presence from infinity to infinity; he governs all things, and knows all things that are or can be done.

He is not eternity and infinity, but eternal and infinite; he is not duration or space, but he endures and is present. He endures forever, and is everywhere present- and, by existing always and everywhere, he constitutes duration and space. Since every particle of space is always, and every indivisible moment of duration is everywhere, certainly the Maker and Lord of all things cannot be never and nowhere. Every soul that has perception is, though in different times and in different organs of sense and motion, still the same indivisible person.

There are given successive parts in duration, coexistent parts in space, but neither the one nor the other in the person of a man, or his thinking principle; and much less can they be found in the thinking substance of God.

Every man, so far as he is a thing that has perception, is one and the same man during his whole life, in all and each of his organs of sense. God is the same God, always and everywhere.

He is omnipresent not virtually only, but also substantially; for virtue cannot subsist without substance. In him are all things contained and moved; yet neither affects the other: God suffers nothing from the motion of bodies; bodies find no resistance from the omnipresence of God. It is allowed by all that the Supreme God exists necessarily; and by the same necessity he exists always and everywhere.

Whence also he is all similar, all eye, all ear, all brain, all arm, all power to perceive, to understand, and to act; but in a manner not at all human, in a manner not at all corporeal, in a manner utterly unknown to us. As a blind man has no idea of colours, so have we no idea of the manner by which the all-wise God perceives and understands all things.

He is utterly void of all body and bodily figure, and can therefore neither be seen, nor heard, nor touched; nor ought he to be worshiped under the representation of any corporeal thing. We have ideas of his attributes, but what the real substance of anything is we know not. In bodies, we see only their figures and colours, we hear only the sounds, we touch only their outward surfaces, we smell only the smells, and taste the savours; but their inward substances are not to be known either by our senses, or by any reflex act of our minds: much less, then, have we any idea of the substance of God.

We know him only by his most wise and excellent contrivances of things, and final causes; we admire him for his perfections; but we reverence and adore him on account of his dominion: for we adore him as his servants; and a god without dominion, providence, and final causes, is nothing else but Fate and Nature.

Blind metaphysical necessity, which is certainly the same always and everywhere, could produce no variety of things. All that diversity of natural things which we find suited to different times and places could arise from nothing but the ideas and will of a Being necessarily existing.

But, by way of allegory, God is said to see, to speak, to laugh, to love, to hate, to desire, to give, to receive, to rejoice, to be angry, to fight, to frame, to work, to build; for all our notions of God are taken from the ways of mankind by a certain similitude, which, though not perfect, has some likeness, however. And thus much concerning God; to discourse of whom from the appearances of things, does certainly belong to Natural Philosophy.

Hitherto we have explained the phenomena of the heavens and of our sea by the power of gravity, but have not yet assigned the cause of this power.

This is certain, that it must proceed from a cause that penetrates to the very centres of the sun and planets, without suffering the least diminution of its force; that operates not according to the quantity of the surfaces of the particles upon which it acts as mechanical causes used to do , but according to the quantity of the solid matter which they contain, and propagates its virtue on all sides to immense distances, decreasing always as the inverse square of the distances.

Gravitation towards the sun is made up out of the gravitations towards the several particles of which the body of the sun is composed; and in receding from the sun decreases accurately as the inverse square of the distances as far as the orbit of Saturn, as evidently appears from the quiescence of the aphelion of the planets; nay, and even to the remotest aphelion of the comets, if those aphelions are also quiescent.

But hitherto I have not been able to discover the cause of those properties of gravity from phenomena, and I frame no hypotheses; for whatever is not deduced from the phenomena is to be called an hypothesis; and hypotheses, whether metaphysical or physical, whether of occult qualities or mechanical, have no place in experimental philosophy.

In this philosophy particular propositions are inferred from the phenomena, and afterwards rendered general by induction. Thus it was that the impenetrability, the mobility, and the impulsive force of bodies, and the laws of motion and of gravitation, were discovered. And to us it is enough that gravity does really exist, and act according to the laws which we have explained, and abundantly serves to account for all the motions of the celestial bodies, and of our sea.

And now we might add something concerning a certain most subtle spirit which pervades and lies hid in all gross bodies; by the force and action of which spirit the particles of bodies attract one another at near distances, and cohere, if contiguous; and electric bodies operate to greater distances, as well repelling as attracting the neighbouring corpuscles; and light is emitted, reflected, refracted, inflected, and heats bodies; and all sensation is excited, and the members of animal bodies move at the command of the will, namely, by the vibrations of this spirit, mutually propagated along the solid filaments of the nerves, from the outward organs of sense to the brain, and from the brain into the muscles.

But these are things that cannot be explained in few words, nor are we furnished with that sufficiency of experiments which is required to an accurate determination and demonstration of the laws by which this electric and elastic spirit operates.