1.ANY Thing is said to be Extended, or Extension is an Essential Property of that Thing, when we cannot conceive it with­out Limits, or Bounds, or Shape; or when we cannot form any Conception of it, without perceiving at the same Time, that it is capable of being greater or smaller; capable of Addition or Division, as consisting of Parts, or as being divisible into Parts: For that Property is Essential to any Thing, without which we cannot form any Conception of that Thing. Therefore,

2. Every Thing conceived as Quantity, is Extended.

3. A Thing is said to be Impenetrable, when it excludes every Thing else from the Space which it occupies. Every Thing, which we conceive as distinct from another, necessarily includes this Property: For the Moment that we suppose, that two Things absolutely occupy the same Space, all Distinction ceases in our Conception of them; and therefore the one or other, as to us, becomes a Non-entity, or That of which we have no Conception.

4. Every Thing which is conceived as Extended and Impenetrable, I call Matter.

5. Then if Matter be taken in this large Sense of the Word, which, I think, is the common Acceptation of it, we must allow that there are different Kinds or Species of Matter, distinguish'd by manifest Essential Properties, peculiar to each Sort, and inconsistent with the Essential Properties of the others; which I propose to show more particularly by what follows.

[Page 2]6. There is some Thing endowed with a certain kind of Force or Power, by which it resists every Alteration of its present State, whether it be in Motion or at Rest: This is commonly called, the Power of Resistance, and by Sir ISAAC NEWTON, Vis Inertiae. There can be no Doubt of something possessing this Property, or that is endowed with this Power or Force; for it is so generally observed in every Thing, which is the Object of our Sensations, that this Power is generally attributed to all Matter: But how truely this is done, will better appear after we have considered the Nature of this Power; which however will not be found easy for us to do, separately from other Species of Matter; because all the Ideas we form of Power, or Force, or of Action, are generally taken from Matter in Motion; and therefore we cannot easily conceive any Action without Motion: Yet it is evident, that Motion ought by no Means to enter into our Conception of this Power of Resisting, for it exerts its Force at Rest as well as in Motion.

7. In order to form an adaequate Notion of this Power or Force, I shall observe. 1. That this Power or Force cannot proceed from a meer Want of Action; for the Power of Re­sisting is sometimes greater, at other times less; sometimes it is able to resist a greater Force, at other times only a less; but a meer Want can never be greater or less; it is a Non-entity, and cannot be of any Quantity either great or small; it can have no Power or Force; for it is a Negation of all Power or Force. 2. No kind of Motion can enter into the Conception of the Manner of Action in the Power; for in the Idea of Motion we must conceive some kind of Tendency or Direction from one Place or Point, towards another Place or Point; If then the Idea of Resisting has any thing in common with Motion, it must oppose Motion more in one Direction than in another, more when the Motion which it opposes is in an opposite Direction to the Di­rection of Resistance, than when both Directions tend the same Way: But Resistance opposes Motion equally in all Directions; therefore nothing of Motion can properly enter into the Con­ception of it. 3. This Power equally exerts its Force whether it be in Motion or at Rest; for when two Quantities of this Resisting Power are different while at Rest, the one greater than [Page 3] the other, if they be put in Motion, that Quantity which resisted most while at Rest, will likewise resist most while in Motion. 4. The Effects of this Power appear in a Kind of Obstinacy, by which it opposes all other Power or Force; it does not destroy the opposite Power, but only opposes its Action, and in some Cases (as will be shown afterwards) continues the Effect of Action of the other Powers, which would otherwise cease: Neither can the Power or Force of Resisting be destroyed by an opposite Power; for if this Power be essential to any Thing, (as we shall afterwards prove) it cannot be destroy'd without annihilating the Thing it self. 5. This Power, and every Part of it or Particle, exerts its Force or Action in all Directions; for it, and every Part of it, equally opposes, resists or lessens the Action of other Powers, in whatever Direction they be applied. 6. The Thing or Being which exerts this Power or Force, is truely an Agent; it is a Principle which acts of itself, without the Force, Power or Agency of any other Thing; for, since its whole Power or Force is exerted in opposing the Actions of all other Power or Force, it cannot receive its Power or Force from that which it opposes. Therefore,

8. The Thing endowed with the Power of Resistance, or Vis Inertiae, is an Agent, or active Substance, Subsistence, Exi­stence, or Being, endowed with a certain Power or Force, whereby it persists in its present State, and opposes or resists all other Power that would change that State, whether it be in Motion or at Rest; and thereby weakens, or renders more or less ineffectual, the Action of all other Power or Force; which Force it exerts in a Manner peculiar to it self, and different from all other natural Agents. Force without Action, is a Contra­diction in Terms; yet we are so accustomed to join Motion with all Action, that I find it very difficult to convey any Notion of Action or Agency in the Power of resisting, tho' it demonstrably be an Agent or acting Principle.

9. This Power of Resisting, or Vis Inertiae, may be considered as Quantity, for it is every Day, and in all Places, observed to be greater or less; it is capable of being augmented or lessened; of Consequence it is contained within some Bounds or Limits, it is of some Shape, Parts may be taken from it, or added to it, [Page 4] that is, it is Extended. Indeed [...] of it, without conceiving it as existing within some Bo [...] or other; and therefore Extension is Essential to the Agent ex­erting this Power.

10. Again, it is impossible to conceive this Power of Re­sisting, without supposing at the same Time, that this Agent is Impenetrable; that no other Power can at the same Time possess the same Place; for as this Agent acts by resisting other Power or Force; the Thing which it resists must occupy a different Place, otherwise we cannot conceive the one as resisting the other; therefore Impenetrability is an Essential Property of the resisting Agent: And of Consequence,

11. The Agent endowed with, or exerting the Power or Force of Resisting, is a Species of Matter. There is no great Difficulty of forming a Conception of this Agent, as a Species of Matter, or as being extended and impenetrable; every Object of our Senses round us, raises this Idea in our Mind; but I have taken this Method of proving it, the more easily to apply this Reasoning to some other Agents, which we are not ac­customed to consider in this Manner.

12. It is generally concluded, that the Force of Resistance is in Proportion to the Quantity of Matter resisting; because a greater Quantity of resisting Matter, requires a greater Force to move it. But it must be observed, that in considering this resisting Matter, there are two different Ways of considering it as Quantity; either the Quantity of Extension (its Bulk) or the Quantity of its Force; when we say two Powers producing the same Effect are equal, we then mean only as to the Quantity of Force; but two different Quantities in Bulk may have the same Force: There may therefore be different Species of this resisting Matter, in which the Proportions of their Force to their Bulk may be different; and, as these different Proportions may be infinite in Number, the different Species of resisting Matter may be infinitely different. No Experiment, which only determines the Force of two different Agents to be equal, does, for that Reason, determine that their Bulk is so likewise. From Sir ISAAC NEWTON's Discovery of the infinitely different Species of Light, it is possible there may be as many different Species of [Page 5] resisting Matter; and if there be, we may hope that a Method may be discovered to demonstrate this. Before Sir Isaac's Discovery. Light was universally thought to be Homogeneous; and yet he has so clearly demonstrated the Contrary, that none can doubt of its being the very Reverse, that it consists of an infinite Variety of Species. Could any Man have imagined, that this Discovery, which had avoided all the curious Researches of Philosophers to his Day, was made by so simple and common a Contrivance, as a triangular Glass-Prism? Glass and Prisms had been known and in Use many Ages, and in all that Time it was never imagined that any such Discovery could be made; who then can say what Discoveries may be made, when such another Genius as Sir Isaac Newton's shall appear in the World?

13. We daily observe, that some Things move, or pass from one Place to another: The Power of Resisting is so very different from that of Moving, that they can in no Manner be conceived as the Effects of the same Agent, or of the same Cause. We every Day observe, that some Things in Motion, lose their Motion; that the same Things again, or other Things at Rest acquire Motion, and Things moving with small Velocity acquire greater Velocity; this Motion then must either be by some Power, Force or Agency in the moving Thing it self, or it must be the Effect of some other Power without it: This other Thing must be of itself an Agent, and has the Power of moving essential to it, or it must be put in Motion by a third Thing, and so on; we must then at last rest in something to which the Power of Moving is essential, or we must allow, that an Effect can be produced without a Cause: This Thing then to which Motion is essential, which moves by its own natural Force, must be an Agent which has its active Principle in it self.

14. We every Day perceive different Quantities of Motion, [...] its Force or Power sometimes greater, sometimes less, and we perceive it in different Places: We cannot then otherwise con­ceive it than as bounded, or of some Shape, and as consisting of Parts and therefore Extension is essential to the Idea thereof. We every Day likewise see Resisting Matter put in Motion by this Agent; therefore they must be impenetrable to each other; [Page 6] for otherwise [...] cannot conceive the one as Moving, the other as Resisting, [...] her can we otherwise conceive them as distinct Beings, without distinct Places: This moving Agent, or this Thing endowed with the Power of Moving, is a Species of Matter. When we [...] a small Spark gradually set a large City all in a Blaze; can any Man imagine that there is no more Motion in all the Parts of the City, thus on Fire together, than there was in the first little Spark that began the Fire? That there is no more Power or Force in this prodigious Fire, than there was in the scarce distinguishable Spark which began it? But if there be not supposed something mixed in the Materials of the City thus on Fire, which has a Power of moving of it self; all the prodigious Force of Motion in the City thus on Fire, must be supposed in the first little Spark which began the Fire; for Nothing can give what it has not. There are innu­merable other Phaenomena, which evidently show, that some Parts of Matter are self-moving Agents, and which ever move, unless hindered by the superior Force of resisting Matter; and that as soon as the resisting Power is by any Means removed, the self-moving Matter immediately recovers its Motion.

15. Since the resisting and moving Agents, are so very con­trary to each other in their Nature, resisting Motion and self-moving, that it is impossible to conceive them as existing in the same Thing, or that any one Thing can have both Powers essential to it; we must then be very careful not to attribute these different Powers, and inconsistent Modes of Action to the same Agent; which however, from what follows, it will appear, is not easy for us to avoid.

16. Suppose that two Quantities of the moving Agent, or two Particles of moving Matter (for both these Expressions signify the same thing) move towards each other with the same Force, in opposite Directions, what will happen after their Meeting? If you say, that they will stop each other, and remain at Rest; I deny it; because Motion never destroys Motion, or lessens it: It is the Property of resisting Matter only to stop, lessen or render ineffectual the Force of the moving Matter. I shall ask, what is it in the opposite Motions which destroys Motion? If you say, that it is their mutual Resistance; [Page 7] I answer, they have no Resistance. I have proved (7, 8, 13, 14, 15) that the Power of Resisting and Moving, can never exist in the same Agent; and therefore, two Particles of moving Matter, cannot, in the proper Sense of the Word, resist each other's Motion: What then, you'll say, must happen after the Meeting of these two opposite Movers? They must either return back, or go off together, or from each other in some Direction or other: I don't at present enquire which of these will happen; all that I assert is, that Motion will not be lessened in this Case, in either one or the other, or in both taken together, the Change of Direction only seems a necessary Consequence of their Impenetrability. The Truth of this appears in the Meeting of two Quantities of Elastic Matter; the Motion in this Case is no way lessened by the opposite Motions; it must then be something else than Motion which lessens or destroys it, for Nothing destroys itself, or its own Force. We must care­fully distinguish the Effects which are necessary Consequences of Impenetrability, from those which are the Consequences or Effects of the resisting Agent; without this Care, we shall often run ourselves into Confusion, because of a faulty Habit, which every one acquires of confounding these very distinct Properties in Matter, Impenetrability and Resistance; the Reason of this is, that all our Ideas of Motion, are taken from resisting Matter in Motion, which is endowed with both these Properties.

17. Suppose next, that two Quantities of Matter meet, the one of the Moving Agent, the other of the Resisting, what will happen? If the resisting Power be greater, or equal to the moving Power, it will stop the Action of the moving Power, and both remain at rest, tho' the Force, or Endeavour, or Power to move still remain in the moving Power; but if the moving Power be greater or stronger than the resisting, then the moving Power will only lose Part of its Motion, and both will move together with the remaining Force of Motion: This becomes a compound Quantity, endowed with both Motion and Resistance. It is not my present Business to prosecute this more particularly, but only to give general Notions of these two different Agents, and of their Manner of acting.

[Page 8]18. Again, Suppose that this united Quantity of the Moving and Resisting Agents, be by some Means separated; I say, that the moving Matter will, the Moment after it is seperated from the resisting Matter, recover its first and original Action of moving, or its whole Motion: And the resisting Matter will continue its Motion in the same Manner, or with the same Velocity, it did while joined with the moving Matter; and this by its Power of Resistance; for this Power or Force consists in persisting in whatever State it is at any Time in, and in opposing all Change of that State. As the Degree of Velocity with which it moves, is the State in which every Part of that Quan­tity of resisting Matter is in at the Time; the Force of resisting all Change, or persisting in that State, in two different Quantities so moving, will be as the Quantities themselves; and in different Quantities moving with different Velocities, as the Velocities multiplied into the respective Quantities of Resistance. This Force is called Momentum, by Sir ISAAC NEWTON, and is by him rightly distinguished from Motion; for it is plain, they arise from the Actions of Agents essentially different in their Nature and Manner of acting. It is likewise evident, that any Quantity of resisting Matter, moving thus by Motion commu­nicated to it, loses the Whole or some Part of its Motion every Time it meets with any other Quantity of resisting Matter, and never of itself recovers that Motion again. The Laws of this communicated Motion (Momentum) being most common to our Observation, are well described by Philosophers: But the Laws by which the Primary Agents act, are little understood, tho' they be truly the Cause of all the Phaenomena in Nature, and there­fore deserve the Trouble of further Enquiry.

19. But besides these two Powers, the one resisting, opposing or suppressing Motion, or any Alteration of its present State, the other a self-moving Power, always changing or endeavour­ing to change its Place, by moving in some one Direction or other, there is a third Kind of Force or Power observed, by which the Parts of this Thing, receive any Impression or Action from any other Agent, either the moving or resisting Agent; and by a kind of reacting Force communicates this Action to all Things round it, as by a Kind of Expansion of Action, or such [Page 9] Kind of Action as seems to proceed from a Center of every Part, in straight Lines to the Surface; and this Reaction is always observed to be equal to the Force impressed. As we take our Idea of this Power from elastic Bodies, whose Parts, if by any Force be compressed nearer, endeavour to recede and restore themselves with a Force equal to that which compressed them, and thereby equally press every Thing round them which opposes the restoring of them to their first Situation, it is usually called Elastic Force.

20. Now it is plain, that this Elastic or Expansive Force cannot be the Effect of the Resisting Agent: For the whole Power of the resisting Agent is exerted in preserving its present State, and opposing all Change; but the very Idea of this, includes a perpetual Endeavour of Change by Expansion. Again, the Resisting Power is exerted in opposing, lessening and rendering ineffectual all Motion; but this Power, by its Reaction, preserves the Motion impress'd upon it in its full Force, and only alters the Direction. Neither can it be the Effect of the Moving Power; for the moving Power exerts its Force only in one Direction; but this Power exerts its Force in all Directions from every Point. This then must be the Force or Power of an Agent essentially different from both the Resisting and Moving Agents; for the Effect of this Power cannot be produced by either of those Agents singly, or by both jointly. The whole Manner of Action in this Agent is singular and peculiar to itself. This Power neither resists nor moves, and exerts no Kind of Action of itself, without the Concurrence of some other Power; so that in the Absence of other Powers, it must be conceived as in perfect Inaction. Its Power consists in this, that every Part of it receives the Impression or Action of any other contiguous Power, and by a Kind of Expansion, or Elasticity, or Reaction, every Part reflects or expands that Action which it received, in every Direction, in an opposite Direction as well as in the direct, and thereby communicates it to the adjacent Parts. It must be conceived as existing alternately in two different States; the one of receiving, the other of reflecting, expanding or reacting: It receives in one Direction, and reflects in every Direction: It has no Manner of acting peculiar to itself, independantly of the [Page 10] other Powers; but receives any Manner of Action, either that of the Resisting or Moving Power; and then, if this Elastic Matter be supposed to fill the Space between any other Species of Matter, by a Power peculiar to itself, communicates the Action of the One to the Other at a Distance, which otherwise could not be done; so that it is the general Medium by which all Action is communicated to any Distance from the acting Power. This Power of Reaction and Reflecting any Force impressed upon it, is the Power peculiar to this Species of Matter, and it exerts this Power in a Manner similar to the Manner of acting of any other Power, from which it receives its Action.

21. The Resisting Power is negative to every other Power, to the Elastic Power as well as the Moving: For Resistance must lessen every other Action; and whatever lessens or weakens any Action, is negative to that Action. Therefore, in whatever Degree the Action of the Resisting Power is communicated to any Part or Particle of the Elastic Power, in the same Degree the Action of Reacting or Reflecting (which is the proper and peculiar Action of Elastic Matter) is lessened: But the Moving and Elastic Power being no Way negative to each other, in no Manner lessen or weaken each others Action. For the same Reason, the Action of several Quantities of the same Power, acting in opposite Directions, are in their Directions negative to each other; because it is impossible they both can at the same Time take their full Effect: But the Reaction of the Elastic Power, in the Direction opposite to the Direction of the Action which it reflects, is not negative to that Action, because perfor­med at different Times; as is evident from the Idea of receiving and reflecting. Hence the Action of every Power must not be conceived as one continued Act, but as a great many repeated Acts or momentaneous Vibrations; and that the Reaction of the Elastic Power is in the Interval of these Acts or Vibrations. This alternate Action and Reaction, or alternate Systole and Diastole, or undulating Vibration is particularly observed by Sir ISAAC NEWTON, in the Passage of Light through any Medium.

22. This Expansive or Elastic Force has been usually attri­buted to the Shape of the Parts which compose the Elastic Body. [Page 11] They are supposed to be Spiral Springs, like Watch-Springs: But why a spiral Shape, or any Shape, or any Manner of ar­ranging the Parts of any Thing, should give that Thing any Power which it had not before, is to me inconceivable. It is plain from common Observation, that no Shape can give an elastic Force to Lead; a Spiral of Lead is as little Elastic as a straight Line of Lead.

23. As we cannot conceive this Expansive or Elastic Power, otherwise than as consisting of Parts, every one of which exerts its reactive Force, as it were in Lines from the Center of every Part to its Surface, and every Part as acting upon all the sur­rounding Parts, and acted upon by them; the Agent exerting this Force cannot be conceived otherwise than as extended and impenetrable; and therefore, that it is a Species of Matter.

24. It follows then, from the Whole of what has been said, that these Species of Matter above described, are Agents or acting Principles; that each have a Power or Force peculiar to itself, differing from the others in its Essence and Manner of acting. Whether there be any more Species of Matter, is not easy to determine, though most of the Ancients agree in this Number. That these three are essentially distinct, I can make no Doubt: If there be any other distinct Species of Matter, it must likewise be an active Principle; for we can have no Idea of any Thing but what arises from Action, and there can be no Property without some Power or Force: For this Reason some of the antient Philosophers said, all Nature is alive; that is, all Nature is active. Try to describe Matter without Action, Power or Force, the whole Description must consist of Negatives, that is, it must be the Description of No Thing; and then it very certainly follows, that No Thing or No Being, exists No Where. The Word Matter, defined to be a Thing without Action, without Power or Force or Property, is synonimous to the Word No-Thing; and then I think it requires no great Penetration to demonstrate, that it exists No Where, or is not; and yet this is the Sum of some late learned and elaborate Discourses.

25. The Quantity of Power, or the Quantity of Matter, are similar Expressions; that is, a cubic Inch, for Example, of [Page 12] Resisting, Moving or Elastic Matter, has half the Quantity of Resistance, Motion or Elasticity, that two cubic Inches of the same Power or Species of Matter have: But the Manner of exerting that Power, or Degree of Action, or of Force, is as great in the cubic Inch as in the two Inches. Or more generally, every Part of any Species of Matter has the Power of acting in as great a Degree as the Whole has: For where any Power is essential, there can be Nothing in the Thing itself to obstruct the Exertion of that Power, and any external Obstruction is not supposed. It is necessary therefore, to distinguish carefully between the Quantity of Power, and the Degree or Force, or of Action, or of the Manner of exerting that Power: For Velocity, for Example, from the highest or quickest that can be conceived, to the slowest, may be divided into infinite Degrees; and all these Degrees are different Manners of exerting the Moving Power. Since Power is the Essence or Substance of the Thing, Nothing can communicate its Power; for that would be to transubstantiate or to create; but every Power can communicate a different Degree of Action or Manner of acting, to another; and therefore it cannot properly be said, that any Power com­municates any Quantity of Power to another, but only some certain Degree of Force or Manner of acting. And the only Effects or Alterations, which any Power or Agent can produce on another, is to communicate to this other, some Degree of its Action, or Manner of acting.

26. The Degree of Action communicated, is always in the Ratio of the Quantity of the Acting to the Receiving Power. Thus, if any Quantity of Moving Power communicate any Degree of Motion to a cubic Inch of the Resisting Power, or of the Elastic, it will communicate but half that Degree to two cubic Inches: So that the Degree communicated does not consist in the absolute Quantity of the acting Power, but in the Ratio is has to the receiving Power.

27. This communicated Action, or the Effects of different Powers, must be different according to the Nature or different Manner of acting. Thus, if any Degree of Motion be com­municated, it cannot be augmented by the Addition of a less Degree, in the same Direction; as the Velocity of a Ball [Page 13] moving at the Rate of 10 Miles in an Hour, cannot be aug­mented by the Action of a Ball moving at the Rate of 9 Miles in the same Time: Indeed the first can receive no Impulse or Action from the latter; and therefore there can be no Addition of different Degrees of Motion in the same Direction; but it is otherwise in the Resisting Power.

28. Tho' the Degree of Resistance communicated, be always in the Ratio of the Resisting Power to the Receiving, as in the Moving, the Effects arising from it are different from what they are in the Moving; because it exerts its Action not in one single Direction, as the moving Power, but in every Direction; for Example, if any Quantity of resisting Matter communicate to a Quantity of elastic Matter, a Degree of Resistance, as 10, and another Quantity of resisting Matter communicate to another Quantity of elastic Matter, a Degree of Resistance, as 5; and whenever these two Quantities of elastic Matter are contiguous, their several Degrees of Actions must be united in the Reaction; which is exerted or expanded in all Directions; and therefore, in the Reaction, the Degree of Action between these two, will be equal to 15 Degrees of Resistance: For since the Action of Resistance is negative to the other Action: and thereby lessens it; it is evident, that, tho' the moving Power be lessened in any Degree by a strong Action, it may be still further lessened by the Application of a weaker Action.

29. However, there still remains a Distinction to be observed between the Effects of the Power itself, and of the Action communicated to another Thing; for Example, any Quantity of elastic Matter, having any Degree of Resistance, or of Motion, communicated to it, cannot communicate a greater Degree than what it has received; if it communicate the whole Degree to another Inch of elastic Matter, it cannot communicate a greater Degree to half an Inch. It is otherwise as to the Power itself; for if it communicate a Degree, as 10, to any Quantity, it will communicate a Degree, as 20, to half that Quantity. And it is likewise to be observed, that tho' the Degree of communicated Action cannot, by being communi­cated to a less Quantity, be encreased; yet it may be lessened by being communicated to a greater.

[Page 14]30. If upon further Enquiry into the Nature and Manner of acting of these several Agents, some of the most general Phae­nomena in Nature become plain and easy to our Conception, and which have hitherto puzzled the greatest Philosophers; it will be a strong additional Proof of what has been advanced. My next Attempt shall be, to shew this in some Instances; and before I proceed, I shall only observe, that perhaps the Chymists aim at the same Thing I do, in the three Principles which they establish, viz. Salt, Sulphur, and Mercury: By Salt, they may intend the Resisting Matter or Power; by the Action of which chiefly the Parts of Matter (as will be afterwards shewn) attract each other, or are kept in Union: By Sulphur the Moving Matter, by which, Motion, or that kind of Action which is most evident to our Senses, is produced; and by Mercury, the Elastic Matter, by which (like a Messenger) the Action of one is carried thro' any Distance to another, and like Mercury or Proteus, takes or imitates the Action of either of the others: But the Enquiring into the Opinions of Philosophers on this Subject, is beside my present Purpose.

31. SIR ISAAC NEWTON, with wonderful Sagacity, has discovered, that Gravitation is an Effect of some Cause or Agent, which operates in every Part of the Universe of which we have any Knowledge; and he has de­scribed its Manner of acting, so far as can be concluded from the Effects: But what that Cause is, whether it acts by Attraction or Pulsion, he has no where determined. And tho' in several parts of his Writings (in the last Editions) he has more expressly declared his Opinion, that the Agent which makes all Bodies gravitate towards each other, acts by Pulsion; yet the Manner he has taken to explain this Pulsion, has not given that general Satisfaction which the other Parts of his Writings have; and he having at first explained himself, as done by Attraction, his Followers have frequently been puzzled, and Foreigners have [Page 18] received a Prejudice to the Whole of that Doctrine. Suppose that Gravitation be by Attraction, how can two Bodies be supposed mutually to draw each other, without something like Strings passing between them? but the free Motion of any other Body between these two, shews, that there can be Nothing of that Kind between them. Again, the Force of Gravitation towards any Body, being at every Distance reciprocally, as the Squares of the Distances, seems to shew, that Gravitation is the Effect of some Emanation from the attracting Body, for the Force of the Emanation of any Vertue, proceeding from any Body, as a Center in straight Lines, is at every Distance reciprocally, as the Squares of the Distances; which is demonstrated by Dr. Gregory, in the 48th Prop. of the 1st Book, and 57th Prop. of the 3d Book of his Astronomy. But this no Way lessens the Difficulty; for how can we conceive, that an Emanation or Motion from any Body, can make another move towards it. These Difficulties, and some others, have prevented the general Reception of a Doctrine which evidently agrees with all Phaenomena. If I can show then, how Gravi­tation is performed, so as one may be able to form a clear Con­ception of the same, consistently with all Manner of acting, of which we have any certain Knowledge, and founded on the Principles before explained, I hope to do Something that will be acceptable to the Curious.

32. Sir ISAAC supposes, that there is a fine subtle Fluid, or Medium, expanded thro' the Universe, which he calls Aether. This occupies all the Space not filled with other Matter, and permeats all the Interstices or Passages which are in or between Bodies, He brings several Proofs of the Existence of such a Medium, in the 18th and 21st Quest. at the End of his Opticks, and in several other places of that Book. Every Philosopher almost has supposed the Existence of some such Thing; all agreeing, that it is impossible to account for the general and constant Phaenomena, without the Existence of such a Medium. We have no Way of discovering the Existence of any physical Agent, Thing or Being, but by the mediate or immediate Impression it makes on our Senses. We only discover the Agent by the Effects, and the Manner of its acting, by a continued [Page 19] Observation of Effects. If then from a general Observation of many perpetual Phaenomena, and of the Particularities in them, they appear to be the Effects or Action of an Elastic Agent, (19, 20,) and necessarily follow, if such an Elastic Agent exist; we thereby have the same Proof of the Existence of such an Agent, that we have of the Existence of Resisting Matter, or of Moving Matter; for neither our Senses nor our Ideas reach to the Things or Substances themselves: We have no Idea or Conception of any Thing other than of its Power or Force, or of the Action or Manner of its exerting that Power or Force. By the Effects of the resisting or moving Matter, either mediately or immediately on our Senses, we conclude that such Powers exist; and no otherwise have we any Proof of their Existence: So that I presume to give the same Proof of the Existence of Aether (or of an elastic Medium) that can be given of the Existence of any Thing whatsoever, which does not immediately strike our Senses.

33. Suppose then a Line of elastic Matter, a, b, c, d, e, f, g, consisting of any Number of Particles or Parts; then if any Impression be made, or Action communicated on a, it will communicate the whole of the Impression or Action, and the whole Force it received, to b, and b in like Manner will communicate the whole Force to c, and c to d, and so on, thro' the whole Length of the Line, however long it be; and with whatever Force a presses b, with the same Force b in its Reaction will press a, and so c will press b, &c. the Reaction will every where be equal. If you say, that a communicates less to b, than it received, and b less to c; the communicated Force continually decreasing, by Reason of the Resistance of the several Parts: I say, that you have not sufficient Attention to the Caution given before (16, 20.) for elastic Matter has no Power of resisting in itself.

34. Suppose again, any triangular Surface,

filled with Particles of elastic Matter, or of Aether, in such Manner, that the Number of Particles in each Rank or Line continually encrease equally: Then whatever Degree of Action be communicated, by any Power whatsoever, to the single Particle at the Top, it [Page 20] will communicate one half of that Degree, to each of the two Particles in the next Rank, and one third of that Force or De­gree of Action, to each Particle in the third Rank, and one fourth to each Particle in the fourth Rank, &c. For, since the single Particle communicates the whole Force or Degree of Action which it received, to two Particles, it cannot communi­cate more than one half to each, otherwise it must give what it has not received; nor does it communicate less, because there is no Resistance to lessen it. Then the Force or Degree of Action, in this Case communicated to each Particle in each Rank, will be as the Distance of the Rank applied to the Force or Degree of Action of the first Particle; that is, as 1, ½, ⅓, ¼, ⅕, &c. Now it is plain, that the Difference between 1 and ½, is greater than ½ and ⅓, and the Difference between ½ and ⅓, is greater than between ⅓ and ¼, and so on; likewise, 1 : ½: 2 : 1, and ½ : ⅓: : 3 : 2, and ⅓ : ¼ : : 4 : 3. Therefore, these continually decrease reciprocally, to an encreasing Arith­metical Progression. Then the Degree of Force communicated to each Particle of the several Ranks, will, in the several Ranks be in the Ratio of Numbers decreasing reciprocally to arithme­tical encreasing Proportionals. Then by the Reaction of the Aether, in this triangular Surface of it, each Particle of the outermost or farthest Line or Rank, from the Summit or Point, will communicate the Degree of Force or of Action which [...] received, to the Particles in the next Line or Rank within it, to which the Direction of its Reaction can go: This second Rank, having its communicated Degree of Action thus augmented, will, by its Reaction, communicate its Degree of Action to the Particles of the Line or next Rank within it, in like Manner; and thereby this third Line or Rank of Aether, will have its Degree of Action augmented in the Ratio of the first and second Lines or Ranks; and in like Manner the fourth will be augmented by the Addition of the first or outermost, second and third; and the fifth by that of the first, second, third and fourth, [...] the Force or Degree of Action of the several Ranks or Lines [...] this triangular Surface of Aether, being thus changed by a con­tinued Addition of their Ratios, in an Order reciprocal or con­trary to the natural or direct Order of increasing Ratios, the [Page 21] Ratio of Force communicated to the single Particle at the Sum­mit, will become 15; the Ratio or Degree of Force communi­cated to each of the two Particles in the next will be 10; to each of the three next 6; to each of the four next, 3; and that of each of the five outermost will be 1: And the Differences of Degrees of Action communicated by the Reaction to the Par­ticles in each Line, from the Summit or single Particle, will be 5, 4, 3, 2, 1, or decreasing arithmetical Proportionals.

35. In order to understand the Nature of reciprocal Ratios, it is to be observed, That as the Direct are the Ratios of Quan­tities greater than Unity; so the Reciprocal are the Ratios of Quantities less than Unity; and that Unity is the common Measure to which both are referred. Therefore the Ratios of aequidistant Terms from Unity of similar Series's, the one increasing, and the other decreasing, are always the same. So likewise, if any Addition, Substraction, Multiplication, or Division, of any Number of Terms of the direct or increasing Series be made; and a like Addition, Substraction, Multiplica­tion or Division of the correspondent aequidistant Terms from Unity, of the decreasing or reciprocal Ratio; the Ratio arising from such Addition, Substraction, Multiplication or Division, will in both Series be the same. These two Series then are properly thus expressed, (&c. 4/1, 3/1, 2/1, 1, ½, ⅓, ¼, &c.) that is, 2 : 1 : : 1 : ½, 3 : 1 : : 1 : ⅓, and 4 : 1 : : 1 : ¼, &c. Then 2+3 : 1 : : 1 : ½+⅓, or 5 : 1 : : 1 : ⅕, and the Sum of all, 10 : 1 : : 1 : 1/10, For the Denominators in the Reciprocal, are Indexes of the same Ratios, that the Integers or Numerators are in the Direct. Therefore the reciprocal Ratios may be as well expressed by negative Numbers, thus, −2, −3, −4, &c. as by the Fractions; they both equally showing the Ratio to Unity. Therefore, whatever be the Product of two or more Serieses of increasing Ratios from Unity, how­ever combined, the same Product will arise from the similar Combination of similarly decreasing Serieses from Unity; and the one may be substituted in the Place of the other. But to avoid Mistakes, it must be carefully observed, that what is here affirmed, is not of the Quantities themselves, but of their [Page 22] Ratios only; and this Distinction between the Ratios of Quan­tities and the Quantities themselves, is constantly to be kept in Mind; for otherwise many Difficulties may arise, or Objections be made to what follows, only from not observing this Di­stinction: For generally, I treat of only the Ratios of Quan­tities, and not of the Quantities themselves.

36. But in the Case of the triangular Surface of Aether here put, the Aether is supposed to be bounded; which Case really never happens, because the Aether is expanded thro' the Uni­verse: Therefore, though I put it for the more easy Concep­tion of the Ratio of Action communicated, this Supposition is in several Respects defective in giving a true Conception of the Reaction of the Aether: And, as the Action of resisting Matter is negative to all other Power; the general Supposition of any Action cannot so clearly show that of the resisting Power. Let us suppose then, an unbounded Surface of Aether; then if any Point be taken in this Surface, and the Action of the resisting Power be communicated from this Point in all Directions; these Directions become so many Radii from this Point: From the same Point divide the Surface into any Number of Circles, so that their Radii be encreasing arithmetical Proportionals; the Circumferences of these Circles must likewise be encreasing arithmetical Proportionals. Now, by the same Reasoning used in the Case of the triangular Surface of Aether, the Ratio of Action communicated to the Particles of Aether in each Cir­cumference, must be in the reciprocal Ratio of the Radii, or of the Circumferences themselves; and the Reaction in the same Direction or Radius, must be reciprocal to encreasing Numbers, whose Differences are arithmetical Proportionals. But as this Ratio of Increase of the Reaction is fundamental in the Idea of the Manner of acting of the Aether; it may be necessary to explain this more fully, in order to give an adequate Conception of it▪ The Reaction or Reflection of Action of every Particle of Aether (20) is equal in every Direction; then if any Particle b, in any of these Circumferences be taken, and two other contiguous Particles, a and c, in the same Circum­ference, one on each Side; the Action communicated to these three Particles being in each equal, the Reaction of b, in the [Page 23] Direction of the Circumference, must be made null (21) to­wards a, by the equal and opposite Reaction of a; and its Reaction towards c, be made null by the Reaction of c: Therefore the Particles of Aether can have no Reaction in the Directions of these Circumferences. Again, take any Number of contiguous Particles, a, b, c, d, &c. all in the same Radius or Direction to the Center, but each in different Circumferences; since the Action of the resisting Power communicated to their several Particles, is reciprocal to their Distance from the Center, or is less in the Ratio of their Distance; and, as the resisting Power is negative (21) to every other Power; the Power of reacting or reflecting any Action, must be less in the Particles nearer to the Center, than in those further from it; and conse­quently the Particles further from the Center, must have a stronger Reaction, or Force of reflecting, than those that are nearer: Then there can be no Reaction in the Direction from the Center; for the stronger and contrary Action must annul the weaker in contrary Directions. (21) Therefore all Reaction in the Direction of every Radius must be towards the Center; and being in all instantaneous, (21) the Action of the farthest distant Particles must strengthen or increase the Action of the nearer to the Center. For the Action must in one Instant be communicated to the outmost Extent, and the Reaction made through the Parts in the next Instant.

37. Suppose in the third Place, a Cone of such elastic Particles or of Aether, and that this Cone is divided transversely to its Axis, into any Number of parallel Segments or circular Sur­faces: In this Case the Content of each Segment or circular Surface is as the Squares of their Distances from the Summit of the Core. Then any Force or Degree of Action communi­cated from the Summit, or single Particle at the Top, to each Particle in each circular Surface, will be as the Force impressed upon the first Particle applied to the Squares of the Distances, or reciprocally as the Squares of the Distances. And the Force communicated to each Particle in one Circle, and to each Particle in the next contiguous Circle, is reciprocally as the Squares of their Distances from the Top of the Cone: That is, as 1, ¼, 1/9, 1/16, 1/25, &c. Therefore by a similar Reasoning [Page 24] to that in the preceeding Paragraphs, the Force or Degree of Reaction of the Aether in the several Surfaces, will be reciprocal to a Series of encreasing Numbers, whose Differences encrease as the Squares of arithmetical Proportionals, or reciprocal to these Numbers 1, 5, 14, 30, 55, &c.

38. In the fourth Place, suppose a Particle of this elastic Matter placed in the Center of a Sphere of the same Matter, and that this Sphere be divided into any Number of concentrick spherical Surfaces. Now, since the Contents of these spherical Surfaces are as the Squares of their Distances from the Center, any Force communicated from the Center to every Particle in each respective spherical Surface, is as the Force at the Center applied to the Squares of their Distances, or reciprocally as the Squares of increasing arithmetical Proportionals; and the Re­action will be reciprocal to an increasing Series, whose Differences increase as the Squares of arithmetical Proportionals▪ For the Reasoning in this and the preceding Case is entirely the same.

39. Now, since elastic Matter communicates any Impression or Force made upon it, in the Manner above described; let there be any Quantity of resisting Matter placed any where in the Aether, which is supposed to extend all over the Universe▪ This resisting Matter is an Agent continually and necessarily acting and exerting Force, (8) and must therefore communicate its Action or Manner of acting, to the Parts of the Aether contiguous to it, and they to others next to them. (20) There­fore calling any Quantity of resisting Matter a Body; and sup­posing a spherical Body placed in the Aether, and the Aether round it divided into any Number of spherical Surfaces, con­centric with the Sphere of resisting Matter: Then the Force impressed by the resisting Agent, which is here supposed a spherical Body, will be communicated to the Particles in each spherical Surface of Aether, in a Ratio reciprocal to the Squares of their Distances. (38) And therefore by the Reaction as above described, the elastic Force of every Particle of Aether surrounding the resisting Body in its Action of reflecting the Action of any Motion, will be lessened in a Ratio reciprocal to increasing Numbers, whose Differences are increasing Squares of arithmetical Proportionals; for the Action or Force of resisting [Page 25] Matter, is to obstruct or lessen, or is negative to the Action of all other Power or Force,

40. Then if any moving Thing or Power or Agent, be placed within this Sphere of Aether, surrounding the resisting Body; it will by the Reaction in the Aether of its own Action be pressed on all Sides by the elastic Particles of Aether, whose Force of Reaction increases reciprocally, as in the preceeding Paragraph. Therefore, that Thing will be more pressed on the Side which is from that Body, than on the Side towards it, and must therefore approach towards the Body, every where with a Force equal to the Difference of Force of the elastic Particles of Aether, on the opposite Sides of the Thing. But these Differences are every where (39) reciprocally as the Squares of the Distances: Therefore every Body will seem to attract another in Motion, with a Force every where reciprocal to the Squares of the Distances from that Body; tho' more properly speaking this Thing is repelled towards the Body, by the elastic Force of the Aether before described; or if the Aether be put in Motion from any Cause (as it must constantly be by the continued Transmission of Light from the Sun, Planets and Stars) the Reaction of this Motion will be stronger on one Side of a Body at rest, within the Sphere to which the Action of the resisting Body is communicated, than on the other Side; and thereby this Body will be repelled towards the other Body, within whose Sphere of Aether the Action of the resisting Body is communicated.

41. Here again, before I proceed further, I must take Notice of an Objection which probably will arise from the commonly received Idea of Resistance, and which I observe is apt to return notwithstanding of what has been already wrote to prevent it. One is apt to think, that Resistance is one single Act which only happens when two Bodies in Motion, and in opposite Directions, meet each other; or when a small Body in Motion meets a greater One at rest, where after the first Shock they both remain at rest, and all Action is supposed to cease. Since then (it may be said) Resistance is only a single Act, whatever Impression be made by it on the Aether, it can only be momen­tary; and all Action between the resisting Body and the Aether [Page 26] must afterwards cease; I have already endeavoured to explain this (16, 17, 24, 25.) and I shall only now repeat, that the Mistake proceeds from thinking that there is no Action, but what consists in Motion; but as Resistance is a Power essential to one Species of Matter (24, 25.) this Species can never cease in exerting this Power, or must be continually in Action; and as this Action of Resistance is contrary to or negative of Motion, nothing of Motion can enter the proper Conception of it. Suppose that any Quantity of resisting Matter meet a Quantity of moving Matter, and by its Action of resisting, stop the Motion or Action of the moving Matter; and that immediately after this momentary Stop, the resisting Matter ceases to act or to resist, must not then the moving Matter recover its Action or Motion, since there is Nothing to resist or hinder it? Power [...] Force, and consequently Action, is essential to both these Species of Matter; and in this Case, while both remain at [...], they both exert their Force or power; but their Actions being con­trary and equal, and negative of each other, the Degree of Action in each becomes = 0. But as there is nothing [...] the elastic Power contrary to or negative to either the resisting or moving Powers, it equally receives the Action of both; [...] every Part of elastic Matter reflects the Actions of both, with the same Degree of Force with which they were impressed.

42. Now, supposing any spherical Quantity of resisting Matter to be placed in the Aether, the Action of the resisting Matter will be communicated in the Manner described (38.) If then any Body without Motion, be placed within the Sphere of Aether to which the Action of the resisting Matter is commu­nicated: this Body can have no Motion, either towards the resisting Matter, or from it, or in any Direction; for since the Action of resisting Matter is negative of Motion, and the Aether of itself has neither the Action of resisting nor of moving, and Motion is not supposed to be communicated to the Aether other­wise; this Body thus placed in the Aether, can acquire [...] Motion, but must remain in any Place in that Sphere where it shall happen to be placed. But if this Body move, or have the Action of moving, or if Motion be communicated to this Sphere of Aether from any other Cause; then the Reflection of the [Page 27] Action of Motion, from the several Particles of Aether, will be different; so that the Reflexion will be always less in the Par­ticles nearer to the resisting Matter; because the Reflexion of the Action of the resisting Matter, at the same Time commu­nicated to these Particles of Aether, is negative to the Action of Motion, and greater the nearer these Particles are to the resisting Matter; then any Thing or Body in this Case, placed within this Sphere of Aether, will have the Action of Motion more strongly impressed or reflected upon it, by the Aether on the Side furthest distant from the resisting Matter, than on the Side nearest to it: And the Difference of the Force of Reflexion on these two opposite Sides, being every where within that Sphere reciprocally, as the Squares of the Distance from the resisting Matter, that Body will be repelled towards the resisting Matter, by a Force or Degree of Velocity, every where reciprocal to the Squares of the Distance from the resisting Matter.

43. It follows then, that no Species of Matter has in it self a Power of attracting any other, or of gravitating towards any other; but that this apparent Attraction or Gravitation, is truly and really performed by Pulsion, or more properly is the Effect of the joint Actions of the moving, resisting and elastic Powers; however, as the Copernican Astronomers speak of the Motion of the Sun and Stars, tho' they know that they are ever at rest; so I think it may be allowed me, to treat of Attraction and Gravitation, and to consider this apparent Action as if it were real; tho' I be perswaded, that the Notion of Attraction and Gravitation arises from a false Conception of Things; and therefore I shall next show, how far this Theory agrees with the general Phaenomena of Attraction and Gravitation.

44. Every spherical Solid may be considered as composed of spherical Surfaces, and the Ratio of every outer Surface to the next contiguous Surface within, encreases as arithmetical Pro­portionals; for the Ratios between any Quantities encrease as the Differences of these Ratios of Quantities, and the Differences of the Ratios of these Sufaces are arithmetical Proportionals: Therefore the Ratios of the Degrees of Force, which every spherical Surface of the Body from the Center outwards, shall communicate to the Surface of Aether next within it, will [Page 28] encrease as arithmetical Proportionals, or as the Numbers 1, 2, 3, 4, 5, &c. Then the Force of Resistance communicated to the several Surfaces, by Reaction of the Aether, will become as 5, 5+4=9, 5+4+3=12. &c. or as these Numbers, 5, 9, 12, 14, 15. Therefore the Force of Attraction within any Body, will be as the Differences of these Numbers, or every where as the Distance from the Center of a spherical Body: Here it is to be observed, that since the Degree of Action communicated to the Aether within a spherical Body, encreases directly from the Center, and is not lessened reciprocally, as without the Body; the Degree of Action from the Reflexion of the Aether, is en­creased by a direct Addition of the Ratios, not by a reciprocal Addition, as without the Body.

45. This may be otherwise demonstrated thus; of all the Directions or Lines passing thro' any Particle of a Sphere, that is the longest within the Sphere which passes thro' the Center; therefore that Line in a spherical Quantity of resisting Matter, has more resisting Matter in it, than any other Line of the same Sphere not passing thro' the Center: consequently the Elasticity of all the Particles of Aether in that Line must be more lessened than of those in any other Line; and therefore the Reaction of every Particle of Aether must be in the Direction or Line passing thro' the Center. Likewise the Length of every Line within the Sphere, passing thro' any Particle of the Sphere and the Center, is longer on that Side of the Particle on which the Center is, than on the opposite Side towards the Surface, and consequently the Elasticity or Reaction is most lessened on that Side; the Re­action of every Particle must be towards the Center of the Sphere. Again, since every Line of a Sphere passing thro' the Center, is equally divided at the Center, the opposite Directions of Reaction in every Line must be equal at the Center; and therefore the Reaction of the Aether at the Center must be=o. And since the Differences of the Lengths of the Lines passing thro' every Particle and the Center, on the one Side, and the opposite Side of that Particle, encrease as the Distance of the Particle from the Center, the Differences of the Ratio of Force or Degree of Reaction in every Particle, must be as its Distance from the Center: The same Kind of Reasoning, may easily [Page 29] be applied to the Sphere of Aether surrounding a Body of resisting Matter, and to which the Action of the resisting Body is communicated.

46. Then if any spherical Body be placed any where in an unlimited Quantity of Aether, and the Aether be supposed to be divided, as well within the Body as without it, into any Num­ber of spherical Surfaces, concentric with the spherical Body; the elastic Force of the Aether will be least at the Center, and will continually encrease from the Center, but in different Ratios within the Body and without it: Within the Body it encreases as the Squares of the Distance from the Center, so that the Differences between each two spherical Surfaces within the Body, are directly as their Distance from the Center; but with­out the Sphere the elastic Force encreases reciprocally, as Numbers whose Differences are Squares of the Distance from the Surface of the spherical Body; and the Difference of Force of Elasticity, between each two elastic Particles is reciprocally, as the Squares of the Distance from the spherical Body.

47. Gravitation towards any spherical Body, is directed in Lines tending to the Center of that Body, and may be represented by two different decreasing Progressions, the greatest Term of both which is common to both, and at the Surface of the spherical Body; one of which Progressions decreases towards the Center reciprocally, as the Distance from the Surface, and the other decreases from the Surface outwards reciprocally, as the Squares of the Distance from the Surface: Thus if C be put for the Center, of any Sphere, S its Surface, and A the Limit of or Extremity to which the Action

of the Sphere is communicated in any Line passing thro' the Center: Then if C S and S A be each equally divided at a and b, the Ratio or Degree of Gravitation will be twice as great from S to a as from a to C, and four Times as great from b to S as from A to b, or in the reciprocal Ratio a C ½ of a S and A b ¼ of S b. Again, if C S and S A be each divided into three Parts, C c, c d, d S and S e, e f, f A1; then the Force of Gravitation will be three Times greater from S to d, than from C to c, and twice greater from d to c, than from c to C, but the [Page 30] Gravitation from e to S, will be nine Times greater than from A to f, and four Times greater from f to e, than from A to f. Therefore,

48. Into what ever Number of Parts the Distance to which the Action of resisting Matter extends, or the Force of Attraction; the Ratio or Force of Gravitation in each of these Parts may be found; but if the Distance be divided infinitely, the Degree of Gravitation will become an infinite Series, encreasing reci­procally to the Squares of the Distances from the resisting Body.

49. Then an infinite Series of Proportionals encreasing reciprocally as the Distances, or directly as the Distances, or reciprocally as the Squares of the Distances may be in any finite Distance; and if the Ratios or Differences between any finite Parts of such infinite Series be finite, the Distance to which all the Series extends must be finite. Therefore, if the Ratio of the Attraction of the Sun or of the Planets can be determined in any finite Distances, the Distance to which the Attraction of the Sun and Planets extends, may be finite and may be deter­mined: Therefore it is not universally true that all Bodies mutually attract each other.

50. If the Velocity (or the Times being reciprocal to the Velocities) with which any Body passes by Gravitation, thro' three equal and continued Distances be given, the Distance to the Limit of Attraction, or to the extent of Action of the resisting Body (which is supposed to attract) on the Aether, may be found thus; suppose the Velocities be 36, 45, 55; then 55−45=10, and 45−36=9, since 10 and 9 differ only by Unity; it shows, that the Distance where the Velocity was 55, was the Tenth of such Distances from the Limit of Attraction; but if the three Velocities be 64▪ 81, 100, the Differences will be 19 and 17, and the Differences of these Numbers is 2, then [...], and [...]; which shows, that these Velo­cities were acquired in the 9th and 10th of such equal Distances from the Limit of Attraction; the same Result will be if the Volocities were 15, 32, 51, for the Velocities are as the Squares of the Distances, and the Differences of these Squares are as the Distances.

[Page 31]51. Here it may be observed, that since Lines are composed of Points; and Surfaces of Lines; so Solids of Surfaces: A triangular Surface may be conceived as composed of an infinite Number of Lines, encreasing in an arithmetical Progression: So likewise Cones may be conceived as compounded of an infi­nite Number of Surfaces continually encreasing, so that the Dif­ferences between them are encreasing arithmetical Proportionals: therefore instead of a Series produced by the continual addition of arithmetical Proportionals, or by the continual addition of the Squares of arithmetical Proportionals, we shall hereafter say, a Series of the Squares of arithmetical Proportionals, or a Series of their Cubes. It is true, that these infinite Numbers are not perfect Squares and Cubes of arithmetical Proportionals, but as the Number of Terms encrease, they come nearer and nearer to the Truth, and in infinite Serieses they are perfect Squares and Cubes; for if any triangular Surface, for Exam­ple, be supposed to be divided into any small Number of Lines, these Lines must have some Breadth; then the opposite Sides of the Triangle, in which the Lines terminate, will not be streight Lines, but like so many Steps of Stairs; but the more of these Steps, they must be the smaller, and the Differences of the Lines less; and therefore if the Number of Lines be infinite, the Steps must vanish, and the Sides become streight Lines: Now, if the Parts of the Aether be infinitely small (as we have Reason to think and may perhaps afterwards be proved) there must be an infinite Number of Surfaces of Aether in every finite Space; and therefore we may properly say, that these Series's composed of encreasing Squares are truly Solids or Cubes; for all similar Solids are as the Cubes of their homologous Sides: And if from Observation it shall appear, that the Series of Elasticity of the Aether (as above described) at several Distances, is perfectly as the Cubes of these Distances, the Particles of Aether must be infinitely small. See Wallis's Arithmetica Infinitorum.

52. Suppose any cubical Quantity of resisting Matter be divided into any Number of square Surfaces, all equal to the Side of the Cube; then the Action of each of these Surfaces communicated to the Surface of Aether, contiguous to the Side or Surface of the cubical Body, will be as follows: Calling each square Surface, into which it is divided, x, that of the outermost [Page 32] will be x/1, of the next x/4, of the third x/9, of the fourth x/16, &c. and the Action communicated to the Surface of Aether conti­guous to the cubical Body, by the cubical Body, will be equal to the Sum of the Actions of all the square Surfaces, which compose it. But, by 21 Prop. of Dr. Wallis's Arithmetica Infinitorum, the Sum of an infinite Series of the Squares of arithmetical decreasing Proportionals is equal to one Third of the Sum of as many Surfaces, all equal to the greatest; that is, in this Case of so many all equal to the square Surface of the cubical Body: Consequently the Force of Attraction of every Quantity of Resisting Matter, is equal to one Third of the Quantity of Matter. (35, 38, 39, 47, 48, 49.) Therefore,

53. In several Quantities of Matter encreasing, as the Cubes of arthmetical Proportionals, the Differences between the Quan­tity of Matter, and Force of Attraction encrease continually, as the Cubes of arthmetical Proportionals: For supposing three Cones or Pyramids, A, B, C, of equal Height, but the Bases to be of A as 1, of B as 2, and of C as 3; then A will represent the Force of Attraction, C the Quantity of Matter, and B the Difference between the Force of Attraction and Quantity of Matter. Now at the Points in their Summits, all these three Cones or Pyramids are equal, or their Differences are = 0; and if the Axis's of these Cones or Pyramids be equally divided from the Points in their Summits, and they be likewise infinitely continued; each will be from their Summits Cubes of Arith­metical Proportionals increasing infinitely: Therefore, in several Quantities of Matter increasing, &c. Sir ISAAC NEWTON, and several after him, have observed, that the Force of Attrac­tion in little Bodies, at the Point of Contact, is prodigeously greater, in proportion to their Bulk, than that of great Bodies at their Surfaces; but I know not that any have assigned the Reason of this, or have given a Rule for discovering these Differences.

54. If then three homogeneous Bodies, encreasing as the Cubes of arithmetical Proportionals, be taken, and the Force of Attraction of each of these at their Surfaces, or at any equal Distance from their Surface, be discovered; the Force of Attraction of all other Bodies homogeneous to them, may be [Page 33] discovered by a similar Method to that in Par. 50. Experiments perhaps may be contrived on these Principles, to discover whether Bodies be homogeneous or not, and whether there be different Species of resisting Matter, (12) differing in their Force of Attraction, as the Rays of Light in their Refrangibility.

55. The Distance, Extent or Radius of the Sphere of Aether, to which the Action of any Body or Quantity of resisting Matter is communicated, is much longer in little Bodies, in Pro­portion to their Bulk, than in great Bodies; for the Extent or Number of Terms of any Series decreasing, as the Cubes or as the Squares of decreasing arithmetical Proportionals, is as the Cube Root or Square Root of the highest or first Term of each Series; and this holds true in infinite Serieses as well as finite; for Example, suppose two Quantities, one as 100, the other as 300; their Force of Attraction at the Surface is as 33 ⅓ and 100, and the Extent of their Attraction nearly, as 6 and 10 Again, if the Quantities of resisting Matter be as 300 and 3000, their Force of Attraction will be as 100 and 1000, and the Extent of their Attraction as 10 and not quite 32.

56. Suppose any Body or Quantity of resisting Matter, or of moving Matter, or of both resisting and moving Matter, mixed in one Body, placed within the Sphere of Aether, to which the Action of Resistance of any other Body is communicated, and that Motion by any Means be communicated to the same Sphere (42); then the first Body will appear to be attracted, or to gravitate towards the Quantity of resisting Matter; and tho' these apparent Actions of the attracting and gravitating Bodies, really arise from the same Cause; yet the Force of Gravitation in different gravitating Bodies, may be very different from the Force of Attraction in the same Bodies; for Gravitation is caused by the Action of the Aether on every Particle or Part of the gravitating Body, on the Parts of the moving Matter con­tained in that Body as well as on the resisting; and tho' there be different Species's of resisting Matter, the Action of the Aether may be equal on all of them, and they may all equally gravitate; but the Force of Attraction in different Bodies, is only as the resisting Matter in these Bodies; neither is it as the Quantities themselves: Therefore, by observing the Differences of Attrac­tion [Page 34] and Gravitation in the same Bodies, and by contriving proper Experiments for that Purpose, or perhaps by observing the Phaenomena of the great heavenly Bodies; the Quantities of resisting Matter and moving Matter in these several Bodies, or in the great heavenly Bodies, may be discovered, and whether there be different Species's of resisting Matter: Here, I suppose, that the Aether acts upon every Part or Particle of Bodies, and freely permeats between and round all the Parts of every Body: It is beside my present Purpose to prove this, but perhaps it may be afterwards done, when it can be shown by what Power, Force or Action, the Parts of Bodies cohere.

57. I shall next proceed to show, the joint Action of two distinct Bodies or Quantities of resisting Matter, on the Aether round them, or on the Aether between them and on their outer Sides; but, to make this the more clear to Readers, who have not a distinct Notion of reciprocal Ratios, I shall first observe, that if there be any Force or Action of any Power decreasing in the Line A B reci­procally, [...] as the Distance from A, then if that Line be divided equally in 2, the Force in 2 B will be ½ of that in A 2; but if the Distance be taken from B, and B 2 be 1 or x, 2 A will be 2 or 2 x: If the Line be divided into three Parts, as A 3, 33, 3 B, then if the Distance be taken from A, and the Force in A 3 be 1, that of 33 will be ½, and that of 3 B will be ⅓, that is, reciprocal to the Distance from A; but if the Distance be com­puted from B, and the Force in 3 B be 1, that of 33 will be 2, and of 3 A will be 3, directly as the Distance from B; and so in like Manner into what ever Number of Parts the Line A B is divided: Therefore the direct Ratios may be well substituted in Place of the reciprocal; for it is evident, they are the same considered in a different Manner; this is true not only in Ratios directly or reciprocally as the Distances, but in Ratios likewise as the Cubes or Squares of the Distances, and in any Series of decreasing or encreasing Ratios; for the same are encreasing Ratios, if the smallest Term be the first and be made Unity, which are decreasing when the greatest Term is put first, or made Unity, and thereby becomes reciprocal to the former.

[Page 35]58. If two equal spherical Bodies be placed within the Distance to which the Actions of the resisting Matter in each extend, or within each other's Spheres of Attraction, the Aether will have its Elasticity lessened by both, in a Ratio reciprocal to the Cubes of the Distances from each, as in the Margin.

Let there be two Quantities of re­sisting Matter, whose Force or Action on the contiguous Surface of Aether in each, is equal to 1240, and that these two Bodies are placed at the Extremity of each other's Spheres of Attraction; then the Aether between these two Bodies must have its Elasti­city lessened, in a Ratio reciprocal to the Cubes of the Distances of each, or in the Order and Ratio of the Num­bers 1240, 1015, 819, &c. in the two first Lines of Numbers; and the Elasticity of the Aether is lessened by the Action of both these Bodies, as the Sums of the Terms of these two Lines of Numbers, or as the Numbers 1241, 1020, 833, &c. in the third Line of Numbers: But the Sums of the Terms of two equal opposite Pro­gressions, each encreasing the contrary Way, as the Cubes of the Distances, are as the Squares of the Distances from the middle Point, and the Dif­ferences between these Terms en­creasing as the Squares of the Distances are directly as the Distances, or as 221, 187 in the fifth Line, or are arithmetical Proportionals.

59. The greatest Force of the Elasticity of the Aether be­tween two equal Bodies, is in the middle Point between them; [Page 36] for the Sum of the Terms of two oppositely decreasing equal Progressions, continually decrease to that Point from the greatest Point of each Progression, and the Sum of the Terms in this Case, is the Ratio in which the Elasticity of the Aether is lessen'd: Therefore a third small Body, placed any where between this middle Point and either of the Bodies, must be repelled and gravitate towards that Body; but it is to be observed, that such third Body can only gravitate towards either of the other two, which have their absolute Force of Attraction less than that compound Force at the Distance at which the third Body is placed; for if the absolute Force be greater, they will likewise attract the other, and that a small Body placed exactly in the middle between two equal large Bodies, will remain at rest.

60. This middle Point between equal Bodies, is called the Limit of their several Attractions: And to find the Limit of Attraction between unequal Bodies, which by any Force are kept at the same Distance, first find the Distance from the greater Body, at which the Force of its Attraction is equal to the abso­lute Force of the less Body; then if the smaller Body be placed nearer to the greater, or at that Distance, there is no Attraction to the smaller Body; but if it be placed further from the greater Body than this Distance, then the middle Distance between the smaller Body and this Distance, is the Limit of Attraction between the two unequal Bodies; for from that Place where the Force of Attraction of the greater Body, is equal to the absolute Force of Attraction of the smaller Body, the Elasticity of the Aether in the Space between this Place and the smaller Body, is lessened in the same Manner as between equal Bodies.

61. If two Bodies, a greater and a smaller, be so placed, that the Attraction of the greater Body, at the Distance at which the smaller is placed, be greater than the absolute Force of the smaller, then this smaller Body cannot attract a third Body, placed any where between them; but if the smaller Body be removed to a greater Distance, then a third little Body may be so placed between them, as to be attracted by the smaller Body, and the Distance at which the smaller Body can attract a third, will always encrease as its Distance from the greater Body encreases: This may be of Use to explain many Phaenomena [Page 37] among small or little Bodies where the Distance between them is continually changing, or is by some Force or other changed.

62. If two spherical Bodies be retained by any Force within the Spheres of each other's Attraction, at the same Distance, such as that a third Body at some Distance or other may be attracted to either one of them; and that a Surface be so ex­tended from the Limit of their spherical Attractions, in the Line connecting their Centers, that the Ratio of the Distances of every Point in that Surface to the two Bodies be the same, as the Ratio of the Distance of the Limit of Attraction in the Line connecting their Centers to the same Bodies; then a third little Body placed any where from the Point of Limit in this Surface, will be attracted towards this Point of Limit: And if the little Body be placed any where out of this Surface on either Side of the Line connecting the Centers of the greater Bodies, the little Body will be attracted towards that of the two greater Bodies, between which and that Surface it is placed: But this little Body will not move in a streight Line to the Center of that Body, but in a curve Line, whose Curvature continually decreases as it approaches to that Body.

63. Therefore if two Bodies be kept at the same Distance, a little Body no where gravitates to the Center of Gravity of these two Bodies.

64. If two spherical Bodies be so far placed within the Sphere of the other's Attraction, that it extends beyond the other Body; then the Force of Gravitation of a third little Body to either one of them, while in the Line passing through the Centers of the two Bodies, is reciprocally as the Distance from that Body to which it gravitates, or directly as the Distance from the Limit while it is between the two Bodies, but reciprocally as the Squares of the Distances, when on the other Side of either of them: The Force of Attrac­tion of each of these two Bodies on the opposite Side to each other, is encreased in the same Manner, as if their Quantity were encreased by a Quantity of resisting Matter, equal to the Force of the other at the Distance at which the other is placed. Thus supposing the absolute Force of each of these two Bodies to be 1240, and that the Bodies were placed [Page 38] within the Sphere of each other's Attraction, as these Numbers are in the Example in the Mar­gin; where the first and second Lines of Numbers are as the separate Forces of these two Bo­dies, at the several Distances; the third Line is as their united Force at the same Distances; and the Lines under it show the Differences between the Terms of this united Force, and the Force wherewith a third Body gravitates to either of them

65. But in a Circle▪ drawn from one Body, as a Center thro' the Center of the other, the Force of the Aether encreases reciprocally, as the Cubes of the Distances from the Body thro' which the Circle passes, but is at all these Distances further lessened equally, by the Force of the central Body at that Distance. Thus in the Example in the Margin, the Force of the central Body on the Body thro' which the Circle passes, is 140. and therefore their united Force there is 1240+140=1380, and at several Distances from this Body aequidistant from the other, it is 1015+140=1155, 819+140=959, 650+140=790, &c. then the Force of Gravitation in this Circle to the Body thro' which it passes, is the same every where, that it would be to that Body were it placed singly by it self, because the [Page 39] Differences between the Terms, are in both Cases the same.

66. It is likewise evident from the Numbers in 58 and 64, that the Differences of the Elasticity of the Aether in the Line passing thro' the Centers of two Bodies, placed within the Sphere of each other's Attraction, are different from what they are when either of the Bodies are placed single; and if they remove from each other, decrease in the Space between these Bodies reciprocally, as the Cubes of the Distances of the other from that Body; for these Differences are made by a continual addi­tion of the Cubes of an arithmetical Progression; and therefore that the Differences of the Force of Attraction in the same Cases decrease reciprocally, as the Squares of the same Distances, for the Differences of Differences encreasing as the Cubes are as the Squares; but since the Differences of the Elasticity of the Aether [...] the same Line, but on the other Sides of these Bodies, encrease reciprocally, as the Cubes of the Distances in the same Case, the Difference of the Force of Attraction will be reci­procally, as the Squares of the Distances from either Body; therefore as two Bodies approach to each other, the Force of their Attraction in the Line passing thro' their Centers, decreases in the Space between them reciprocally, as the Squares of their Distances, but on the other Side of them encreases reciprocally as the Squares of their Distances.

67. Hence the Gravitation of the Moon in one Half of her Orbit, from the Quadratures to the Opposition, and from the Opposition to the opposite Quadrature is encreased every where reciprocally, as the Squares of the Earth's Distance from the Sun; but in the other Half of her Orbit, her Gravitation is decreased every where reciprocally, as the Squares of the Earth's Distance from the Sun; and the Moon gravitates in her Con­junctions, towards either the Sun or the Earth, not reciprocally to the Squares of the Distances, but reciprocally to the Distances themselves.

68. I shall, in the last Place, apply this Theory of the Aether and of Gravitation to a most remarkable Phaenomena, which puzzled all the Philosophers till Sir ISAAC NEWTON explained it; I mean the Tides of the Sea: Any Fluid on the Surface of [Page 40] the Earth will be less pressed in the Places (and near them) where the Surface is cut by a Line passing thro' the Centers of the Moon and Earth, than where the Surface is cut by a plain Perpendicular to that Line, and passing thro' the Centers of the Earth; for the Elasticity of the Aether being every where equally lessened, on the Surface of any spherical Body, by the resisting Matter of that Body, there can be no Difference occasioned by it in any Part of the Surface; but the Elasticity of the Aether at the Surface of the Earth next the Moon, is more lessened by the resisting Matter in the Moon, than at the Distance of the Earth's Center from the Moon, and more at the Center than at the Surface farthest from the Moon: But of any three Terms of a Pro­gression, encreasing as the Cubes of arithmetical Proportionals, twice the middle Term is less than the Sum of the first and third Term; therefore the two opposite Surfaces of the Earth, but by a Line passing thro' the Centers of the Earth and Moon will be less pressed than any two opposite Surfaces of the Earth, cut by a plain Perpendicular to that Line, and passing thro' the Center of the Earth; and if by any Means the Pressure of the Aether on the opposite Sides of a spherical Body be unequal, (47) it must become on each Side equal to half the Sum of the pressure of both the opposite Sides, by the Point of equal pressure in the Body when single, being moved in the Line connecting the Centers of the two Bodies towards the Side which is least pressed. This perhaps may appear more plainly, by observing the Ratios of Elasticity of the Aether, in Par. 64 and 65, thus,

where the first Line of Numbers shows the Ratio of Elasticity of the Aether on both Sides of one of the Bodies, and which at the Distance of its Center from the other Body is=1380, and at every two equal Distances from the Center, are 1219+1106=2325, 1104+874=1978, 1035+680=1715. The se­cond Line shows the Differences of the Elasticity of the Aether on each Side of the same Body, in equal Distances in that Line, or the Ratio of Gravitation, viz. 161+274=435, 115+ [Page 41] 232=347, 69+194=263. The third Line shows the Ratio of Elasticity at the same Distances in the spherical Surface, every where equally distant from the Center of the other Body, where 1155+1155=2310, 959+959=1918, 790+790=1580. And the last Line shows the Ratio of Gravitation in the same spherical Surface, and at the same Distances 225+225=450, 196+196=392, 169+169=338: Now 2325 is greater than 2310, 1978 is greater than 1918, and 1715 is greater than 1580; therefore the Elasticity of the Aether is more lessened in the Line connecting the Centers of two Bodies, than in the spherical Surface in Parts aequidistant from the other Body. Again, 435 is less than 450, 347 is less than 397, and 263 than 338, or the Ratio or Force of Gravitation is always greater at the same Distances in the spherical Sur­face, every where aequidistant from the other Body, than in the Line connecting the Centers of the two Bodies; and in Distances near the Center of the Body thro' which this spherical Surface passes, it concides with a plain Normal to the Line passing thro' the Centers of the two Bodies.

So far as I have now gone, I think sufficient to show the Agreement of this Theory with several general Phaenomena, and may serve to show the Method of applying it to others, and to the Peculiarities of particular Cases, when any shall think proper to take the Trouble of doing it. I am perswaded, it might have been put into a strictly mathematical demonstrative Method, by separating the Definitions, Axioms, and Lemmata from other Sciences into their proper Order, and by deducing the Theorems from thence; but I was of Opinion, that the Method which I have taken, is more proper for conveying new Conceptions, and such as have not been before received; neither could that Method have been pursued within the Com­pass I had set to my self. Besides, I believe, that the Evidence of the Truth of it is much stronger, by showing its Agreement with Nature in every Instance, than by the most pompous Demonstration; for how often have the greatest Men erred in their Deductions in this Method. For this Reason, I had a strong Inclination to have showed the Conformity of this Theory with the Motion of the Planets, by showing in the Phaenomnea [Page 42] of their Motion, the Force and Ratio of the moving Power; and likewise in many Phaenomena observed by Sir ISAAC NEWTON, in his Optics, by which, I think, I might have illustrated many Things not touched in Sir ISAAC's Theory; and more particularly to have given (if I be not much deceived) a new Theory of the Moon; but I have too good Reason to conclude, that in my pesent Circumstances I shall never be able to accom­plish it. I thought, however, it may be of some Use to give these Hints to the Learned, which I have been able in some Measure to digest, that thereby others, more capable than my self, may improve them to the Benefit of the Publick. Sir ISAAC has taken wonderful Pains, and many of his Followers since, have been indefatigable in applying his Theory of the Moon to Practice; but after all, I do not find that they have been able to form Tables so useful in Practice as was expected, and which in all Cases agree with Observation: I may there­fore be allowed to suspect, that his Theory is in some Measure defective.

Since these Sheets were sent to the Press, I obtain'd Mr. Flamsteed's Historia [...]a [...]lestis; and as one great Advantage of the Doctrine above delivered, is, that it gives an easy and certain Method of forming Equations for the Planets Motions and Or­bits; which by all other Methods, which I have seen, seems to be very difficult and perplexing: I form'd Equations for the Earth, so far as to assure my self, by several Calculations in different Parts of her Orbit, that this Theory agrees with the Phaenomena to as great an Exactness as I expected. If I be not much mistaken, this Theory and Mr. Flamsteed's Observa­tions, will mutually prove the Accuracy of each other. I have fallen (I think) on a Method in proving this, independant of Refractions and of the Latitude, different from that which Mr. Flamsteed takes in his Prolegomina, and which has one Advan­tage above his, that it is less complicated, requires server data or things to be known, and consequently is less subject to Error.

Some Thoughts may have occurred to my Imagination in thinking so long as I have already on this Subject, which may not readily to Men of more Skill and Knowledge. Si Deus nobis haec otia secerit, that I could be enabled to digest into [Page 43] Order, and demonstrate these Thoughts without Prejudice, or rather with some Advantage to those Cares which every Man ought to have near his Heart, and which speculative Studies are apt to make him neglect, I should think it the greatest Happiness that can befal me in the last Stage of my Life, to be thus useful with the greatest Pleasure to my self.