the Motion lasts also but when that ceaseth the Motion ceaseth likewise And 't is added That this Quality cannot last always being in its nature so imperfect that it cannot last long Besides it is Objected That Experience shews that all Motions do cease little by little as appeareth in a Wheel that hath been violently agitated in a Ball that hath been rolled on a Billiard-Table in a Ball suspended and vibrated and in other innumerable Bodies the Motions of which do by little and little diminish and at last are quite extinguish'd VII A Finite Cause may have an Effect that lasts always I Say it is very easie to Answer all these Objections and many such others If any one will maintain that Motion is an Infinite Effect because it lasts forever he must also say that Rest will be an Infinite Effect if it thus last eternally and that consequently a Finite Cause not being able to have an Infinite Effect it must be said that after a Man hath put a Body at Rest this Body cannot remain in that Rest forever but that Rest must at last cease and the Body begin to move which is not consonant to reason There is a great difference between an Infinite and an Ever-during Effect And if it be true that a Finite Cause cannot produce an Infinite Effect it is as true that a Cause how bounded soever it be may produce an Ever-subsisting Effect if it be not destroyed by some new Cause For if I make a square Figure upon Wax this Figure will last always if nothing survene to spoil it or to destroy the Wax it self So that 't is not incongruous at all to say that if Rest or Motion be once produced in a Body this Rest or Motion shall last without end if nothing come to destroy it VIII This Quality which is called Impetuosity lasts always AS to that Quality which is pretended to be produced in the Body by him that striketh it 't is all one to me whether it be believed to be so or not But this I say that if that Quality be necessary it will last forever after it hath been once produced and that it will never cease to be till some new Cause destroy it And herein the Sentiment of Vasquez 1. 2. d. 81. c. 2 3. is very remarkable when he teacheth generally of all Forms substantial and accidental and particularly of Motion and Impetuosity That if they can subsist one moment without needing the influence of their first Efficient Cause they will last always until they be destroyed by the production of a new contrary Form If Men will still persist in this Opinion and say That this Quality is so weak in its own nature that it destroys it self I do maintain that after this Quality shall have been destroy'd the Motion notwithstanding must continue for the reasons already deliver'd in regard that Motion cannot cease unless Rest be produced a new But there must always be a positive Cause to produce a new what Effect soever it be whereas there needs none such to make that subsist which is already in being And this is the true reason why a square Figure made in Wax would last eternally if God should keep all external Agents from destroying any thing in that Wax because this square Body of Wax could not lose this Figure unless another Figure were produced And as a Figure cannot begin to be a new unless there be some positive Cause to produce it and we also suppose that there is none such in this Case it must needs follow that this first Figure which is already produced keeps forever the possession of its existence 'T is the same thing with Motion And although this pretended Impetuosity ceaseth to be yet the Motion which is already produced is not therefore to cease also because there is no new Cause producing Rest and Motion cannot cease but Rest must be produced instead thereof IX The Bodies which we move do cease to move because they are impeded LAstly when we see that Bodies moved by us do in a little time cease to move that proveth nothing against us it being certain that those Bodies meet with impediments to their Motion Whence we see that the more or the less we remove of those impediments the more or less do those Motions continue Thus a Ball rolleth much longer over a very smooth Alley than in a rugged way A Wheel turns much better if its Axle-tree be slender and well turned than when 't is big and irregular A Stone is cast much farther in the Air than in Water But I shall endevour in the Sequel of this Discourse to explain how all these Impediments do by little and little make the Motion of Bodies to cease X. A Demand for the safety of the following Demonstrations ALl I have been just now deducing about the Nature and Perpetuity of Motion is in a manner necessary for the understanding what I pretend to demonstrate in this Discourse But as this Question can never be handled so clearly but that it will always be obnoxious to the Cavils of Disputants I foresee well enough that after all my reasonings it will doubtless so fall out that all will not be convinced of what I shall have undertaken to prove And besides not being willing to clash with any nor to leave ground to believe that I build my Discourse upon a doubtful Principle I declare that for the firmness of my Demonstrations I need not it should be thought that Motion would in effect be perpetual so it be but allow'd me which no Man can deny that Motion once begun lasts at least for some time and continues the more uniformly the less impediments there are to stop or diminish it Let this Continuance of Motion be explain'd by the production of an impressed Quality or by a simple Determination or by whatever you please 't is indifferent to me I only demand it may be allow'd me to take this as a Postulatum of Geometry That after a Body is once mov'd it continues to move for some time and that this time is considerable when there is nothing without able to stop or lessen the Motion By the means of which Demand I hope that all the following Demonstrations will be found of full force XI A Body receiving successively many Determinations remains only affected with the last A Body not only persevereth in Rest or Motion according as it hath once begun to be in either but it persists also in the same kind of Motion and with the same degree of Celerity in which it hath been put For Example If it have begun to move in a straight Line Eastward with one degree of Celerity it continues to move with the same degree without ever receding a jot from the same Line Which is evident from the same reasons I alledged to prove the Motion to last always But it is to be Noted that when a Body hath successively received many different Determinations it remains
are made in pleno as in vacuo pag. 56. XXXV When the Bodies are unequal the percussions are made in pleno otherwise than in vacuo pag. 57. XXXVI The Percussions of unequal Bodies cannot be reduced to one General Rule pag. 59. XXXVII Of Refraction pag. 61. XXXVIII The Conclusion pag. 62. An Appendix containing a Review of this Discourse made by the Author himself pag. 67. A DISCOURSE OF LOCAL MOTION I. A Body is in it self indifferent to Rest or Motion IF we should imagin that in the World there were nothing corporeal but one or two Balls and sever from the same whatever might cause any kind of secret Commerce whereby the one might attract or repel the other Or if we should consider such Balls free from all kind of particular Determination without Levity without Gravity in Vacuo or at least in a Space altogether uniform where nothing were that might carry them rather this than that way or hinder them to move freely if they should happen to be propelled towards a place Then should we conceive these Balls to be absolutely indifferent to touch one another or to be sever'd to be here or there forasmuch as they would find nothing more in one place than in another and consequently be equally indifferent for Rest or Motion II. If a Body be once at Rest it will ever remain therein ANd so if we further conceive that one of these Balls is at Rest having been put in that state by some Cause that hath power to stir or stop Bodies we at the same time conceive it will eternally remain at Rest if there be not some new Cause displacing it by putting it into Motion because this Ball being of it self indifferent to Rest or Motion and being once determined to Rest it is impossible it should of it self quit that Rest and fall to Motion Wherefore it must needs continue forever in that Rest if nothing happen to make it change that state III. And if it be once in Motion it continues also to move always BY the same Reason we must conceive that if one of these Balls be put in Motion by some Cause or other it will continue to move forever if no new Cause come to stop it Because this Ball being of it self indifferent to Motion and Rest and being once determined to Motion it is impossible it should determine it self to cease from that Motion to take Rest And so it must ever remain in this Motion if nothing else come to stop it IV. That Rest is not a meer Negation I Find that we are generally inclined to consider Rest as a Cessation of Action and to take Motion for a positive Action which we experiment in our selves when we move our selves or will move another Body Whereas we conceive a Body to be at Rest from the time that no Body touches it or that there is no other Cause which actually imprints in it this Quality or this Action necessary to Motion And so it seems that although a Body being once at Rest remains therein forever yet it should not follow that if it be once in Motion it should ever persist therein since that for to be mov'd there is required a positive Action but that Rest is nothing else but a Negation or a Ceasing from Action or Motion V. That there is as much positive Action in Rest as in Motion BUt if the Weight of our Bodies which we must bear the rigidness of our Limbs which we must bend the agitation of the Spirits which we must employ and many other things make us feel some resistance and oblige us to use some force to overcome these impediments We cannot draw from thence any Sequel against our Hypothesis in which we suppose there is no impediment neither of Gravity nor of particular Inclination nor of any Body resisting from without In this Case 't is manifest that there needs no more Action for Motion than for Rest and that for the Rest of a Body it is not less requisite it should be put at Rest than it is necessary for its Motion that it should be put into it And indeed if we consider well the nature of Rest and Motion we shall find that Motion may as well be called a Cessation of Rest as Rest a Cessation of Motion or rather we shall find that both are something positive in regard that Motion is a state by which a Body corresponds successively â—o many places or a passing Presence or a sequel of divers Presences in divers places As Rest is a state by which a Body always corresponds to one and the same place or one and the same Presence in one and the same place So that Rest as well as Motion is a State or a Presence but differing in this that Rest is a State of Consistency and a Constant Presence always kept to be the same whereas Motion is a Changing State and a Transitory Presence Now in what manner soever these constant or passing Presences be consider'd if there be any Action or any Power or any kind of Cause in the Body which is to produce this Consecution of divers Presences in Motion there is no less Action or Force necessary in Rest to preserve the same Presence in regard that to preserve a thing is to produce it continually It is therefore evident that after the Presence hath been produced by a Body in the first instant I speak in the sense of those who hold that there is a true production of these Presences it must needs be also produced a new in the instant following by the same Body to make it remain Quiescent But methinks there is in that as much Action and as much Power as there is for the producing in the second instant a new Presence instead of reproducing the first Nec minor est virtus quà m quaerere parta tueri So that whether there be to be produced every instant a new Presence for Motion or reproduced the same Presence for Rest it will always amount to the same and a Body will have no less work to preserve to it self this same Presence and to remain Quiescent than to produce new Presences and conserve it self in Motion Whence it is to be concluded that as a Body from the very time it hath been once determin'd to Rest is sufficiently determin'd always to keep it self in the same Presence so also from the very moment it hath been once determin'd to Motion it is sufficiently determin'd always to produce new Presences and so to move it self without ceasing VI. Objections I Shall not stay to answer all the cavilling Scruples that may be cast in upon this Subject seeing they are easie enough to resolve For instance 't is said That a Finite Cause cannot produce an Infinite Effect and that this Motion would be Infinite since it would last forever 'T is further alledged That whoever moveth a Body impresseth therein a certain Quality call'd Impetuosity and that as long as this Quality lasts
vacuo Whence it appears that those who will prove the necessity of a vacuum from Motion do not reason well XXXIII Motions diminish little by little in the Air. BUt if the hard Bodies are in a spongious Liquor capable of compression or if this Liquor be not so well bounded in but that the extrimeties will yield a little then the Motion will not be perpetual but diminish by degrees and be at last quite extinct For the hard Body will find more resistance by the anteriour parts of the Liquor than it will receive of impulse by the posteriour because the Liquor which is before being compressed or the extremities yielding the communication of the impression cannot be made perfectly and so the posteriour parts of the Liquor will not be so much thrust as the anteriour and consequently will not so much thrust the hard Body as the anteriour ones retard it And 't is for this reason that all the Motions cease in the Air and Water or in other Liquors because 't is certain that the Air is spongious and easily compressed And that the Liquors are not bounded but by the Air when they are abroad or at least by the sides of some Vessel that can yield and bend a little For we know by certain experience that Glass Vessels will stretch and even those of Iron and Brass will bend to the strokes made upon them XXXIV The Percussions of equal Bodies are made in pleno as in vacuo THe percussions that are made of Bodies thus moving in Liquors differ in something from those that are made in vacuo To understand the Cause thereof we are to note that when an hard Body is moved in a Liquor it also communicateth its Motion to the same Liquor in such a manner that it moveth also in following the hard Body so as to divide it self and to open before and to follow and close it self after the Body And if the Body by any accident should come to lose its Motion yet the Liquor being thus determined to move would give again to that Body its Motion and carry it away with it self in some such manner as Rivers carry away with them the floating Wood. If therefore a Body comes to hit another equal to it the phoenomena will happen as in vacuo because these two equal Bodies being encompassed with the same quantity of Liquor as much as the Liquor of the Body percussed hinders this same Body percussed from moving freely so much an equal quantity of Liquor which is about the Body percutient driveth also anew the percutient as well as the percussed Thus their Motion after the percussion will be made as in vacuo forasmuch as the resistance of the Liquor from the Body percussed is precisely recompensed by the impulsion of the Liquor from the Body percutient XXXV When the Bodies are unequal the percussions are made in pleno otherwise than in vacuo BUt if the Body percutient be greater it must needs receive not so great an effect from the percussion as the other because 't is carried away with more violence by the Liquor which environs it For we see that a Beam carried away by the Stream of a River hath much more effect when it comes to hit against a Bridge or a Mill than a stick would have being carried down by the same River although the Beam should not move swifter than the Stick And that because the Beam coming to hit is also carried by the great quantity of water surrounding it whereas the Stick is but little so by reason of the small space it taketh up and of the little water by which 't is carried away Thus therefore if the little Body be at Rest and the greater come to hit it this greater by communicating its motion to the smaller will not so be stopped as to become moveless as it would do in vacuo but it will continue to move and to follow though more slowly On the contrary if the great one be quiescent the smaller after it shall have hit the other and communicated to it a part of its Motion will be reflected losing a part of its velocity And from all this it appears that Aristotle is not so much to be blamed as some pretend when to explicate the causes of the continuation of the Motions we see he hath made use of the medium that is of the liquid substance wherein our Bodies are moved XXXVI The Percussions of unequal Bodies cannot be reduced to one General Rule TO determine the excess which there may be in the resistances or in the greatest impressions of these unequal Bodies I esteem a thing not to be undertaken at least if we consider the Bodies such as we have them among us because that depends from the resistance made by the liquid Bodies wherein the Hard Bodies we see are moved from the facility they have to be condensed or rarified and from many other things that cannot be known to us no more than an infinity of other impediments the combinations whereof may infinitely diversifie all the effects of the percussions Only I may say that making a certain Hypothesis which appears natural enough it may be shewed by the precedent Rules that the percussions of Bodies unequal shall be after the manner delivered by Monsieur Hugens in the late * Published March 18. 1669. in French and inserted also in the Philosophical Transactions Numb 46. pag. 927. Which Rules of Motion are conform to those of Dr. Christ Wren Printed in the Transactions Numb 43. pag. 867. Journal Des Scavans But I shall not stay longer upon that I may possibly meet with another opportunity to discourse more amply of it XXXVII Of Refraction THere appears also from what I have been explaining the reason of the Refractions that are made when an hard Body passeth out of one Liquor into another of different consistence For if the Hard Body passeth out of a more free Liquor into one that is less so it will lose somewhat of its velocity in the passage finding more resistance in the Liquor which is before than it feels it self thrust by that which follows and so the Refraction will be made by receding from the Perpendicular On the contrary if the Body passeth out of a more impeding Liquor into another more free the Refraction will be made by approaching to the Perpendicular and the Body will increase its velocity in the passage because it is thrust more by the Liquor which follows than 't is detained by that which is found before And 't is of this augmentation of velocity which I think no body hath as yet given the reason of I shall not note the measures of these Refractions because that hath been done by others and their Demonstrations may be very well accommodated to the things here by me advanced Nor do I speak in this place of the Refraction of Light because I believe that that is made quite otherwise that is by causes and means altogether different as