Physiologia Epicuro-Gassendo-Charltoniana, or, A fabrick of science natural, upon the hypothesis of atoms founded by Epicurus repaired [by] Petrus Gassendus ; augmented [by] Walter Charleton ...

SECT. II.

* 1.1BEing thus praepared 〈◊〉〈◊〉 Considerations of the most Genuine Noti∣on▪ most adaequate Definition, and Primary Cause of Motion in all Concretions▪ and an 〈…〉〈…〉 assurance, that there is such a thing as Mo∣t••on in the world▪ the 〈◊〉〈◊〉 degree to which our Enquiry is to advance, ••s the 〈◊〉〈◊〉 Gener••l and 〈◊〉〈◊〉 KINDS thereof▪ among which, the First we meet with, 〈…〉〈…〉 common Distinction of motion into Natural and Violent.

A Natural motion, 〈◊〉〈◊〉 Aristotle ••8. physic. 4.) is that, whose Princi∣ple is Internal; and a 〈◊〉〈◊〉, that, whose Principle is External: so that, accordingly▪ that Bo•••• 〈◊〉〈◊〉 be said to be moved Naturally, which is mo∣ved 〈…〉〈…〉, which is moved by another. But, for as much as Aristotle 〈…〉〈…〉 much amuse us, while he ever and anon 〈…〉〈…〉 be moved by another, and yet not be moved 〈…〉〈…〉 may be said to be Natural or Violent, in 〈…〉〈…〉 that some more easie and familiar Notion is 〈…〉〈…〉 of those Contrary Terms, Natural and 〈…〉〈…〉 more convenient for us, to understand a 〈…〉〈…〉 which is made either of Natures own accord, or with∣•••••• 〈…〉〈…〉 Violent to be that, which is made either Prae∣•••••• 〈…〉〈…〉 Repugnancy. Thus, the Progressive motion of 〈…〉〈…〉 made of Natures own accord; and yet if 〈…〉〈…〉 a steep hill, leap, or run, the motion

is to be accounted Violent, because though it proceed from an Internal Principle, the Soul of the Animal, yet is it not performed without some Repugnancy, either internal or external. On the contrary; when a Bul∣let is shot through the aer, the motion thereof is violent, because against the nature of the Bullet, and not performed without some repugnancy, either in∣ternal or external: and yet if the same Bullet be rowled upon a smooth plane, the motion thereof is Natural; because though it be caused by an External Principle, yet is it performed without any Repugnancy either in∣ternal or External.

But, that we may take the matter in a higher key,* 1.2 reflecting upon that so often inculcated Epicurean Principle, That all the motive Virtue of Con∣cretions is originally derived from the mobility inhaerent in, and inseparable from Atoms, which compose them; let us observe, that forasmuch as that essential mobility of Atoms doth neither cease, but is only impeded, when Concretions themselves begin to obtain a sensible Quiet; nor is produced anew, but only acquires more liberty, when Concretions begin to be mo∣ved: we may thence justly infer, that just so much motive Force is now, and ever will be in the World, while it is a world, as was in the first moment of its Creation. Which really is the same with that Rule of Des Cartes princip. philosoph. part. 2. art. ••6) Deum esse Primariam omnis motus Caus∣sam; & candem semper motus quantitatem in universo perseverare. And Hence may we extract these notable Conclusions. (1) That, because look how much one Atom, being impacted ag••inst another, doth impel it, just so much is it reciprocally impelled by it; and so the Force of motion ••oth neither increase, nor decrease, but in respect of the Compensation made, remains always the very same, while it 〈◊〉〈◊〉 executed through a free space, or without resistence: therefore, when Con••retions, likewise mutually occurring, do reciprocally impel each other; they are to be conceived, to act upon, or suf∣fer from each other, so, as that, if they encounter with equal forces, they re∣tain equal motions on each side, and if they encounter with unequal forces, such a Compensation of the tardity of one, is made by the supervelocity of the o∣ther, as that accepting both their motions together, or conjunctly the motion still continues the same. Which also is the same with that Third Law of Nature, registred by Des Cartes (princip. philosoph. part. 2. art. 4••.) Quod unum Corpus, alteri fortiori occurrendo, nihil amittat de suo motu: occurren∣do, vero minus forti, tantum amittere: quantum in illud transfert. (2) That forasmuch as Atoms constantly retain their motive Virtue even in the most compact and hard Concretions; therefore can there be no Absolute Qui••t in Nature: the Atoms uncessant striving for liberty, causing perpetual Com∣motions in all things, though those Commotions be intestine and insensible as we have often said. Which considered, Heraclitus seems to have been more reasonable, in his Denial of all Quiet, but to the dead (apud plutarch▪ 1. placit. 23.) than most have hitherto allowed: He understanding by the Dead, not only Animals deprived of life, and consequently of motion; but also all other things Dissolved, since then, and only then, the intestine Commotions of their Component Particles, or Atoms▪ cease. (3) That Motion is not only much more Natural than Quiet, in the G••••eral▪ but also always Natural, in respect of its Original, forasmuch as it proceeds from A∣toms▪ which are moved by their own Nature, or essentia Gravi••••▪ and ••ome∣times Violent, but ever so only at second hand, or from the nature of Concre∣tions, as they moved with a certain Repugnancy. And this Rule hath al∣so

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is moved per Accidens, because it is an Accident to him; and likewise his soul is moved by Accident, because it is only a Part of him. Again, when He teacheth, that whatever is moved, is moved by Another; that ought to be understood of that thing, which is moved per se: for, from hence it is, that when in the series of particular movents, He would have us to come at length to one First Movent, which is Immoveable, or which is not moved by any other; we are to understand that Primum Movens to be Immove∣able per se, since it may be moved per Accidens. Thus, when a stone is mo∣ved by a staff, the staff by the hand of a man, the mans hand by his Soul; the soul, indeed, is the First movent and Immoveable: but, understand it to be so, per se, because it is at the same moment moved per Accidens, i. e. when the hand, arme, and whole body, which contains it, is moved. More∣o••er, He declares, that whatever is moved per se, is moved juxta Naturam, according to Nature; such as he affirms that only to be, which is endowed with a soul: yet will He not admit, that what is moved by Another, should always be moved Praeter Naturam, Praeternaturally; but sometimes Un∣naturally (as a stone, when it is thrown upward) and sometimes Naturally (as a stone, when it falls Down again.) Now, if you hereupon Demand of Him, What that is, which makes a stone fall Down again; He shall An∣swer, that what moves it Downward, per se, is the Generant it self, or that which first Produced the stone: and that which moves it downward, per Accidens, is that which removes the impediment or obstacle to its descent, as the hand of a man, or other thing supporting the stone. And, if you again enquire of him, What is the Difference betwixt the Upward and Downward motion of a stone, how one should be Violent, and the other Natural, since, according to his own Assertion, both are Caused by ano∣ther: His Return will be, that the Difference lies in this, that the stone is not carried upward, of its own Nature, but Downward; as having the Principle of its Descent, inhaerent in it self, but not that of its Ascent. If you urge Him yet farther; since the stone hath in it self the Principle of its Motion, why therefore is it not moved only by it self, but wants Ano∣ther, or External Motor? His Answer will be: that there is a Twofold principle of motion, the one Active, the other Passive; and in the stone is only the Principle Passive, but in the External Motor is the Active. When yet it may be farther pressed; that since according to his own Do∣ctrine, the Passive principle is the matter, and the Active the Forme: as to the matter, that cannot be the principle of its motion Downward, no more than of its motion upward; and as for the Forme, if that be neither the Active principle, nor the Passive (as he will by no means admit) certainly there can be none. Which for Him to allow, were plainly to destroy his own great Definition of Nature, wherein He acknowledgeth it to be the Principle of Motion. But, alas! these are but light and venial Mistakes, in comparison of those gross Incongruities that follow.

When Aristotle comes to handle the Species,* 1.3 or sorts of Natural Moti∣on, you may remember, that He first Distinguisheth Natural motion in Di∣rect and Circular; and then subdistinguisheth the Direct into (1) that which is from the Circumference toward the Centre, or from the Extrems toward the middle of the world, which He calls Downward; and (2) that which is from the Centre toward the Circumference, which He calls Up∣ward: assigning the former, or Downward motion, only to Heavy things, to the Earth simply, to Water and mixt things, Secundum quid; and the Upward

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be. What then, must that External Principle be, as Aristotle contends, the very Generant of the thing moved? Certainly, thats highly Absurd; since the Generant is absent, and perhaps, long since ceased to be in rerum natura: and nothing either Absent, or Nonexistent, can be the Efficient of a Natural Action, such as motion is. If you will have, that to be moved by the Generant, signifies no more than to receive a Virtue or Power of moving it self, from the Generant▪ then while you endeavour to save Aristotle from the former Absurdity, you praecipitate him into a gross Contradiction of his own Doctrine: for, since the Generant it self ought to be moved by its Generant, and that again to be moved by its Generant, and so upward along the whole series of Generants, till you arrive at length at some First Gene∣rant, from whence that Virtue was first derived; you bring Aristotle to allow a First Generant, which impugns his fundamental supposition of the Eternity of the World. Nay, if you admit God to be the Author of the First Generant, it will then follow, that God must be the Cause of this par∣ticular motion, and not the First Generant, no more than the Last. Final∣ly, is that the Cause, which only removes the Impediment to a Heavy bo∣dies Descent? Neither is that Reasonable; for, as Aristotle himself con∣fesseth, such a Cause is only a C••use by Accident.

Seeing, therefore,* 1.4 that the Downward motion of a Heavy Body doth not proceed from any Intern••l Principle, nor from either its Generant, or that Accidental one, which removes the Impediment to its Descent, in the supposed Capacity of an External: let us proceed to enquire, Whether there be not some other External Cause, whereupon we may reasonably charge that Effect. Which that we may do with the more both of or∣der and plainness; it is requisite, that we first remember, how Philosophers constitute dive••s sorts of Violent, or Externally-caused motion. Emperi∣cus (••. advers. physicos.) makes 4 distinct species thereof, viz. Pulsion, Traction, Elation, Depression. And Aristotle sometimes superads a fifth, namely Collision; sometimes disallowing Empericus his Division, affirms that the species of motion, made by an External principle, are Traction, Pul∣sion, Vection, and Volutation: upon good reason reducing Elation and De∣pression to either Traction or Pulsion; forasmuch as a body may be eleva∣ted, or depressed by either ••raction or Pulsion. But, yet He hath left us rather a Confusion, than logical Discrimination of the species of Violent motion; for, Collision and Pulsion are one and the same thing; and Ve∣ction may be performed either by Pulsion or Traction, insomuch as the thing movent doth not forsake the thing pulsed, or drawn, but constantly adhaereth unto it: and as for Volutation; it is both Pulsion and Traction at once, as may be easily conceived by any man, who seriously considers the manner thereof. Nay, Traction it self may be justly reduced to Pulsion; forasmuch as the movent, which is said to Draw a thing, doth, indeed, no∣thing but Impel it, by frequently reiterated small strokes, either directly to∣ward it self, or to a lateral region: and yet notwithstanding, for pla••nness sake, and the cleerer Demonstration of our praesent thesis, we judge it con∣venient, to conserve the Common Notion, and to determine, that all Mo∣tion impressed upon one body by another, is performed, in the General ei∣ther when the movent Propels the moveable from it self, or Attracts it to∣ward it self. For, albeit the movent sometimes propels the thing moved from another body, or attracts it to another▪ yet can it not possibly do that▪ but it must, at the same time, either Avert it, in some measure, from, or Ad∣duce it toward it self. Nevertheless, it is not to be denied, but Pulsion is

always the Chie•• Species▪ ••nd for that consideration alone is it, that Pro∣••ection (which is only Impul••••on, or, as Aristotle emphatically calls it, a more Violent motion) is generall•• a••cepted as synonymous to Violent motion; and that Philosophers seldo•• or never Exemplifie Violent motion, but in Projectills, whether they be projected upward, or downward, ••••anve••sly, ob∣liquely▪ or any way whateve••▪

* 1.5These things considered•• 〈◊〉〈◊〉 follows of pure necessity, that the Down∣ward motion of Heavy Bo••••es, being caused (not by any Inte••nal, but) b•• an ••xternal Force impressed upon them▪ must be effected either by Im∣pulsion, or by Traction. B•• Impulsion it cannot; because, in the case of a stone throwneUpward, ther•• 〈◊〉〈◊〉 nothing External, that can be imagined to im∣pel 〈◊〉〈◊〉 Down again▪ 〈…〉〈…〉 attained the highest point of its mountee, unless 〈◊〉〈◊〉 should be the 〈◊〉〈◊〉 and i•• its Descent did proceed from the im∣pul••••▪ 〈…〉〈…〉 from below upon the upper part of the stone•• 〈…〉〈…〉 projection of the stone upward, during its Ascent, the motion thereo•• ••ould, in every degree of its remove from the pro••••cient▪ be Accelerated 〈…〉〈…〉 same proportion, as its Downward moti∣on is Accelerated▪ in ever•• ••••gree of its descent; but Experience testifies, ••hat ••ts upward motion 〈…〉〈…〉 and more Retarded, in every degree of its remo•••• from the projici•••••• and therefore it cannot be, that the Downward motion thereof should be ••••used, nay not so much as advanced by the Aer. Which thing ••as••endus 〈◊〉〈◊〉 Epist. de proport. qua Gravia decidentia a••∣celerantu•• 〈…〉〈…〉 ••••monstrated; and we our selves, out of him, 〈◊〉〈◊〉 the 9 Article of our 2 〈◊〉〈◊〉 concerning Gravity and Levity, in the 3. Book. praecedent. Wha••▪ 〈◊〉〈◊〉, can remain, but that it must be by AT∣TRACTION? 〈◊〉〈◊〉▪ because no other Attractive Force, which might begin and continu•• 〈◊〉〈◊〉 Downward motion of a stone, can be imagi∣ned▪ unless it be that Mag••••••••que Virtue of the Earth, whereby it Draws all Terrene Bodies to an 〈…〉〈…〉 it self, in order to their, and its own bet∣ter Conservation▪ 〈…〉〈…〉 Conclude, that the Cause of the Down∣war•• motion o•• all 〈…〉〈…〉, is the Magnetique Attraction of the Earth. Nor need we adferr other ••••guments, in this place, to confirm this Positi∣on•• in respect we have 〈◊〉〈◊〉 made it the chief subject of the 2 Sect. of our Chap. of Gravity 〈…〉〈…〉; whether we, therefore, remit our unsa∣tisfied Reader.

* 1.6From the Cause of 〈◊〉〈◊〉 Downward motion of Heavy bodies, let us ad∣vance to the Acceleration 〈◊〉〈◊〉 them, in every degree of space, through which 〈…〉〈…〉 reason, why we should at all enquire 〈…〉〈…〉 upward mo••ion of Light bodies, in every de∣gree 〈…〉〈…〉 as we know of no man, but Aristotle, that 〈…〉〈…〉 motion of Fire, and Aer is slower in the begin∣ning▪ and gradually 〈◊〉〈◊〉 and swifter in the progress. And so short was 〈…〉〈…〉 proving that his s••••gular conception, by Experiment, as he ought; 〈…〉〈…〉 assumed ••t upon 〈◊〉〈◊〉 credit of only one poor Argument, which is 〈◊〉〈◊〉.

〈…〉〈…〉 and other things of the like light and aspiring 〈…〉〈…〉 Caelo. cap. 8.) were Extruded and Impelled 〈…〉〈…〉 descending and crouding toward the 〈…〉〈…〉 force, as some have contended; and we••e 〈…〉〈…〉 spontaneous tendency of their own inhaerent 〈…〉〈…〉 moved more swiftly in the beginning, and mo••e slowly 〈…〉〈…〉 their motion▪ but Fire, and Aer are more 〈…〉〈…〉 beginning 〈…〉〈…〉 more and more swift in the progress of their

Assent; therefore are they not moved upward by the Extrusion and Im∣pulsion, but spontaneously, or by their own Levity.

And to Confirm his Minor proposition, that Fire and Aer are Accelerated in every degree of their Assent; without the suffrage of any Experiment, He subjoyns only, that as a Greater quantity of Earth is moved downward more swiftly, than a less; so is a Greater quantity of Fire moved upward more swiftly than a less: which could not be, if either of them were Impelled, or mo∣ved by an External Force.

But, this is, as the Former, meerly Petition∣ary; for, why should not a Greater quantity of Earth, or Fire be moved more swiftly than a less, both being moved (as we suppose) by External force, in ••••se the External force be proportionate to the quantity of each? Doubtless, the force of the ambient Aer, extruding and impelling flame up∣ward, is alway•• so much the greater, or more sensible, by how much more Copious the ••••re is; as may be evinced even from the greater Impetus and waving motion of the flame of a great fire: though it cannot yet be discerned, whether that Undulous or waving motion in a Great flame be (as He praesume•••• more swift and rapid, than that more calm and equal one observed in the flame of a Candle. Tha•• (youl say) is enough to detect the incircumspection of Aristotle, in assuming, upon so weak grounds, that the motion of Light things Ascending, is accelerated in the progress, and that in the same proportion, as that of Heavy things Descending is accele∣rated: but not enough to refute the Position it self; and therefore we think it expedient, to superad a Demonstrative Reason or two, toward the ple∣nary Refutation thereof. Seeing it is evident from Experience, that a Bladder blown up is so much the more hardly depressed in deep water, by how much neerer it com••s to the bottom▪ and a natural Consequent thereupon, that the bladder, in respect of the Aer included therein, begin∣ning its upward motion at the bottom of the Water, is moved toward the region of Aer so much the more slow••y, by how much the higher it riseth toward the surface of the Water, or lower part of the re∣gion of Aer incumbent thereupon; and that the Cause thereof is th••s, that so much the fewer parts of Water are incumbent upon the bladder and aer contained therein, and consequently so much the less must that force of Extrusion be, whereby the parts of Water bearing downward impel them upward: we may well infer hereupon, that if we imagine that any Flame should ascend through the region of Aer; till it arrived at the region of Fire, feigned to be immediately above the region of Aer; that Flame would always be moved so much the slower, by how much the higher it should ascend, or by how much the neerer it should arive at the region of Fire. Because Fire and Aer are conceived to be of the same aspiring na∣ture: and because the same Reason holds good, in proportion, for the de∣crease of Velocity in the ascension of Flame through the Aer, as for that of the decrease of velocity in the ascension of Aer, included in a bladder, through Water. And, as for Aristotles other relat••ve Assertion, that a Greater quantity of Earth is moved more swiftly Downward, than a Less; manifest 〈…〉〈…〉 without▪ nay 〈…〉〈…〉 E••perience doth 〈…〉〈…〉

inhaerent in bodies account•••• Heavy, and that every body must therefore ••all down so much the mor•• swiftly and violently, by how much the more of Gravity 〈◊〉〈◊〉 possesseth. H••ving thus totally subverted Aristotle•• errone∣ous Tenent▪ that the 〈◊〉〈◊〉 of L••ght bodies Ascending, is Accele••a••••d in every degree of their A••••••ntion: it follows, that we apply our selves to the consideration of the 〈◊〉〈◊〉 of t••e motion of Heavy bodies 〈◊〉〈◊〉 in every degree 〈…〉〈…〉 Descention. Whe••ein the First obs••••v••∣abl•• o••••urring, i•• the 〈…〉〈…〉, or that it is so, which is easily proved from hence, that in all ages 〈…〉〈…〉 been observed, that the motion of 〈◊〉〈◊〉 things Descendent▪ 〈…〉〈…〉 the beginning, and grows swifter and swi•••••••• 〈◊〉〈◊〉 toward th•• end▪ 〈…〉〈…〉 that in fine 〈◊〉〈◊〉 becomes highly rapid▪ 〈…〉〈…〉 that the 〈…〉〈…〉 or impression made upon the Earth▪ 〈…〉〈…〉 down from 〈◊〉〈◊〉 high, is always so much the greater or strong∣•••• by h••w much the 〈◊〉〈◊〉 ••he place is from which it ••ell.

* 1.7The Second, 〈◊〉〈◊〉 the 〈◊〉〈◊〉 or Cause of that velocity Encreasing in 〈…〉〈…〉 which though enquired into by many of the Ancients, seem•• 〈…〉〈…〉 been 〈◊〉〈◊〉 by none of them. For (1) albeit Aristotle 〈◊〉〈◊〉 was so wary▪ as 〈…〉〈…〉 explicate his thoughts concerning it; y••t ••o••h hi•• great 〈◊〉〈◊〉 Simpli•••••••• tell us ••in Comment. 87.) that it was H••s opinion▪ that a 〈…〉〈…〉 other thing ••alling from on high, is Corrobo∣••••ted [〈 in non-Latin alphabet 〉〈 in non-Latin alphabet 〉] a Totalitate propria, and hath its spe∣cies ma•••• mor•• and mo•••• 〈◊〉〈◊〉▪ as it comes neerer and neerer to its pro∣per 〈◊〉〈◊〉▪ and so 〈…〉〈…〉 degree of Gravity acceding to it in every ••egree of its 〈◊〉〈◊〉 to the Earth, it is accordingly carried more and more sw••ftly. But, 〈◊〉〈◊〉 that Simplicius hath not expounded, how the 〈◊〉〈◊〉 ston•• can 〈…〉〈…〉▪ how it can be Corroborated, or acquire more and more 〈…〉〈…〉 its species; or how that additament of fresh ••ravity should 〈…〉〈…〉 judge you, whether He hath done Aristotle 〈…〉〈…〉 Author of that Opinion, which instead of 〈◊〉〈◊〉 ••he 〈…〉〈…〉 much more obscure than afore. Besides, we have the 〈…〉〈…〉, that a descending body is not carried the more ••w••ftly▪ by re••so•• 〈◊〉〈◊〉 ••ny access or additament of Gravity: a stone 〈…〉〈…〉 ounce 〈…〉〈…〉 as speedily down, as one of an hundred poun••▪

* 1.8(2) Others 〈…〉〈…〉 as the same Simplicius commemorates) who 〈…〉〈…〉 the Cause 〈…〉〈…〉 the Decrease of the quantity of the Aer 〈◊〉〈◊〉 the s••o••••▪ 〈◊〉〈◊〉 that by how much the higher a stone is, by so 〈…〉〈…〉 and so much the greater Resistence to the motion 〈…〉〈…〉 much the greater quantity of the Aer resist∣ing 〈…〉〈…〉 consequently the resistence of the Aer grow∣ing 〈…〉〈…〉 of the stones descent, the velocity of its 〈…〉〈…〉 proportion thereunto. And this after 〈…〉〈…〉, sinking in deep water▪ more slowly 〈…〉〈…〉 neer the bottom. But, though we adm••t, 〈…〉〈…〉 stone Descending▪ yet we 〈…〉〈…〉 to m••ke ••ny sensible difference of 〈…〉〈…〉 And, would you have an Argument to 〈…〉〈…〉 one fathom; 〈…〉〈…〉 fall the same 〈…〉〈…〉

fathoms, observe again with what velocity it passeth the last, or tenth f••∣thom. This done, consider, sin••e in the latter case, the velocity shall be incompa••ably greater, than in the former; whether it be not necessary, that th••t great au••mentation of velocity in the stone, while it pervadeth the t••nth fathom of space, must not arise from some other, and more potent C••use, th••n the resistence of the inferio•• 〈◊〉〈◊〉? For, in both case••, the stone carries the same proportion of weight▪ and in the lowest f••thom there is the same quantity of Aer, and consequently the same measure o•• resistence. And, if you weigh the stone, fi••st in some very high place, ••n•• afterward in a low, or very neer the Earth; surely, you cannot expect to find•• ••t heavier in the low place in respect of the lesser quantity of A••r ••ub••ja••ent, than in the high, in respect of the greater quantity of Aer there 〈◊〉〈◊〉 it. Lastly, as for their Argument desumed from the slower sink••ing of weights in deep, than in sh••llow 〈…〉〈…〉 thereof 〈…〉〈…〉 same with th••t of the more diffi••ult depression of a 〈…〉〈…〉 Aer, neer the bottom, th••n neer the top of the 〈…〉〈…〉 explained.

(3) A third ••onceipt there 〈◊〉〈◊〉 (imputed to Hipparchu••,* 1.9 by the 〈◊〉〈◊〉 Simplicius) which comparing the Downward motion of a stone, 〈◊〉〈◊〉 by its own proper Gr••vity, with the Upward motion of the 〈…〉〈…〉, caused by an External ••orce impressed upon it by the 〈…〉〈…〉 infers, that as long as the force imprest praevails over the stones Gravity, 〈◊〉〈◊〉 long is the stone carried upward, and that more swiftly in the beginning, because the ••orce is then strongest, but afterward less and less swiftly, be∣cause the same f••rce imprest is gradually debilitated, until the stones pro∣per Gravity at length getting the upper hand of the force imprest, the stone begins it motion Downward; which is slower in the beginning, because the Gravity doth not y••t much praevail, but afterwards grows more and more sw••ft, because the Gravity more and more praevails. But this leaves us more than half way short of the Difficulty; for, though it be reasonable to assume, that a certain Compensation of Velocity is made in both 〈…〉〈…〉. that the Decrease of Velocity toward the end of the Upward motion, is made up again by the Encrease of Velocity toward the end of the Down∣ward, and that in proportion to the degrees of space: yet forasmuch as the motion of a stone falling down is constantly Accelerated, not only after it hath been projected Upward, but also when it is only dropt down from some high place, to which perhaps it was never elevated, but remained there from the beginning of the world, as it often happens in deep mines, the earth ••••∣derneath the stones neer the surface of it being 〈…〉〈…〉 cannot the stones Gravity, gradually praevailing over the Imprest Force, be, as Hipparchus concludes, the Cause of it•• 〈…〉〈…〉 of its Descent.

These Reasons thus deluding our Curiosity,* 1.10 let us have 〈…〉〈…〉 formerly asserted Position, that All terrene 〈…〉〈…〉 are Attracted by the magnetique Virtue of the Earth. 〈…〉〈…〉 that the magnetique Virtue of the Earth is 〈…〉〈…〉 afar off: and thereupon infer, that the 〈…〉〈…〉 therefore more rapid neer the earth, than far from 〈…〉〈…〉 took Virtue seems to be greater, and so the 〈…〉〈…〉 truth neerer the stone 〈…〉〈…〉

and plausible to our first thought: but insatisfactory to our second. For, if it were so, then ought the Celerity of the stones motion, in one fa∣thom neer the Earth, to be the same whether the stone be let fall from the altitude of only one fathom, or from that of 10, 20, an 100 fathoms, when we exactly measure the spa•••• of time, in which it pervades the one fathom neer the earth, in the former case, and compare it with that space of time, in which it pervades the same lowest fathom, in the latter. It may be farther observed, that, whether a stone be let fall from a small, or a great altitude, the motion thereof for the first fathom of its descent, is always of equal velocity, i. e. it is not more nor less swift for the first fathom of its descent from the altitude of an 1•••• fathoms, than from the altitude of only two fa∣thoms: when yet it ought to be more swift for the first fathom of the two, than for the first of the hundred, if the Attraction of the Earth be more vehement neer at hand, than far off; in a sensible proportion. We say, in a sensible proportion; because, forasmuch as the magnetique rays emit∣ted from it, are diffused in ••ound from all parts of the superfice thereof, and so must be so much the more dense, and consequently more potent, by how much less they are removed from it: therefore must the Attraction be some∣what more potent at little than at very great distance; but yet there is no tower or praecipice so high, as to accommodate us with convenience to ex∣periment, whether the power of the Earths magnetique rayes is Grea∣ter, to a sensible proportion, in a very low place, than in a very high.

And yet notwithstanding, nothing seems more reasonable than to con∣ceive, that since the magnetique Attraction of the Earth is the true Cause of a stones Downward motion, therefore it should be also the true Cause of the continual Increment of its Velocity, during that motion. But how it should be so; there's the Knot. Which that we may undo, let us first re∣sume our former supposition (in the 2. Sect. of our chap. of Gravity and Levity.) that a stone were situate in any of the Imaginary spaces; consi∣dering that in that case it could not of it self be moved at all: because, hold∣ing no Communion with the World (which you may suppose also to be Annihilated) there could be, in respect thereof, no inferior place or region, whereto it might be imagined to tend or fall; nor could it have any Re∣pugnancy to motion, because there would be no superior region, to which it might be conceived to aspire or mount. Then let us suppose it to be moved by simple Impulsion, or Attraction, toward any other part of the Empty, or Imaginary spaces; and without all doubt, it would be moved thitherward, with a motion altogether Equal or Uniform in all its parts: because there could be no Reason, why it should be more slow in some parts of its motion and more swift in others, there being no Centre, to which it might approach, or from which it might be removed. Suppose farther, that, as the stone is in th••t motion, another Impulse, equal in force to the former, whereby it was first moved, were impressed upon it; then, assured∣ly, would the stone be moved forward more swiftly than before, not by rea∣son of any Affection to tend to any Centre, but because the force of the 〈◊〉〈◊〉 impulse persevering▪ the force of the second impulse is superadded un∣to it, and the accession of that force must so corroborate the former, as to augment the Velocity of the stones motion. And hence comes it, that to move forward a bo•••• already in motion, doth not only prolong, but ac∣celerate the motion the••••of. Imagine moreover, that a third impulse were ••••••••ntinent••y superadded to the second▪ and then would the motion be yet

more swift than before; the Encrease of Velocity of necessity still respon∣ding to the multiplicity of Impulses made upon the body moved. This may be familiar to our conceptions, from the Example of a Globe set upon a plane; which may be emoved from its place with a very gentle impulse, and if many of those Impulses be repeated thickly upon it, as it moves, the motion thereof will be so accelerated, as at length to become superlatively rapid. Which also seems to be the Reason, why a clay Bullet is discharged by the breath of a man, from a Trunck, with so great force, as to kill a Pidgeon at 20, or 30 yards distance: the Impetus or force impelling the bullet, growing still greater and greater, because in the whole length of the trunck there is no one point, in which some of the particles of the mans breath successively flowing, do not impress fresh strokes, or impulses upon the hinder part of the bullet. The same also may be given, as the most probable Cause, why Long Guns carry or shot, or bullet farther than short; though yet there be a certain determinate proportion to be observed be∣twixt the diametre of the bore, and the length of the barrel or tube, as well in Truncks, as Guns: experience assuring, that a Gun of five foot, musket bore, will do as good execution upon Fowl, with shot, and kill as far, as one of ten foot, and the same bore; and consequently that those Gunners are mistaken, who desire to use Fowling pieces of above 5, or 6 foot long; These considerations premised, we may conceive, that when a stone first begins to move downward, it then hath newly received the first impulse of the magnetique rays emitted from the Earth: and that if after the impres∣sion of that first impulse, the Attraction of the Earth should instantly cease, and no nevv force be superadded thereunto from any Cause vvhate∣ver; in all probability, the stone vvould be carried on tovvard the Earth vvith a very slovv, but constantly equal and Uniform pace. But, because the Attraction of the Earth ceaseth not, but is renevved in the second mo∣ment by an impulse of equal force to that first, vvhich began the stones mo∣tion, and is again renevved in the third moment, in the 4, 5, 6, &c. as it vvas in the second, therefore is it necessary, that because the former impul∣ses, impressed are not destroyed by the subsequent, but so united as still to corroborate the first, and all combining together to make one great force; vve say, therefore is it necessary, that the motion of the stone, from the repeated impulses, and so continually multiplied Impetus or Force, should be more swift in the second moment, than in the first; in the third, than in the second; in the fourth, than the third, and so in the rest succes∣sively; and consequently, that the Celerity should be Augmented in one and the same tenour, or rate, from the beginning to the end of the mo∣tion.* 1.11

The Third thing considerable in this Downward motion of Bodies, is the PROPORTION, or Rate, in which their Celerity is encreased. Concerning this, we know of no Enquiry at all made by any one of the Ancients; only Hipparchus, as hath been said, thought that in the General, the increment of Velocity in things falling down, was made in the same re∣ciprocal proportion, as the Velocity of the same things projected upward. But, about 90 yeers past, one Michael Varro, an eminent Mathematician (in tract. de motu.) depending meerly upon Reason; would have the Problem to be thus solved. What is the Ration, or Proportion of space to space, the same is the Ration of Celerity to Celerity; so that if a stone falling down from the heigth of four fathoms, shall in the end of the first fathom acquire

one degree of Velocity, 〈…〉〈…〉 ••nd of the second two, in the end of the third three, in the end of 〈◊〉〈◊〉 fourth four: it will be moved twice as swift∣ly in the end of the second ••athom, as in the end of the first, thrice as swiftly in the end of the 〈◊〉〈◊〉, and four times as swiftly in the end of the fourth•• as of the first. 〈◊〉〈◊〉 this Proportion is deficient, first in this; that though the increment of ••••lerity, or of its equal degrees, may be com∣pared with the equal mo••••nts or parts of space: yet can it not be com∣pared also with the equal ••••ments o•• parts of Time, without which the myst••ry can never be 〈◊〉〈◊〉. And therefore Aristotle did excel∣lently well, in Defining 〈◊〉〈◊〉▪ and Slow, by Time▪ determining that to be swift, which 〈…〉〈…〉 deal of space in a little time; and on the contrary▪ that to be 〈…〉〈…〉 pervading a little of space in a great deal of time. Again, 〈…〉〈…〉 suppose the theorem to be explicable by e∣qual moments of times 〈…〉〈…〉 such as are the respites or intervals betwixt the pulses of our 〈…〉〈…〉 and that a stone falling down doth pervade the first fathom of 〈…〉〈…〉 the first moment: then, if it pervade the se∣cond fathom twice as 〈◊〉〈◊〉 as the first (as Varro conceives) it must ne∣cessarily follow, that 〈◊〉〈◊〉 second fathom must be pervaded in the half of a moment; if the 〈◊〉〈◊〉 ••hom he percurred thrice as swiftly as the first, it must be pervaded in 〈◊〉〈◊〉 third part of a moment; and if the fourth fathom be percurred four times 〈◊〉〈◊〉 swiftly as the first, it must be pervaded in the fourth part of a 〈◊〉〈◊〉 And, because, if you conjoyn the half, third, and fourth part of a mome•••• ••ou shall have a whole moment with one twelfth part of a moment; it 〈◊〉〈◊〉 necessary, that in the second moment, three fa∣thoms (very neer) must 〈◊〉〈◊〉 percurred: which indeed is very far from truth. For▪ because, if we 〈◊〉〈◊〉 after the same method, so that the fifth fathom be percurred in the 〈◊〉〈◊〉 part of a moment; the sixth in the sixth part of a moment, 〈◊〉〈◊〉 so successively; out of these fragments of time we shall not be 〈◊〉〈◊〉 to make up another whole moment, until it be after the stone hath 〈◊〉〈◊〉 the eleventh fathom, or thereabout; and so in the third moment 〈◊〉〈◊〉 fathoms shall be pervaded, nor shall we again be able to make up 〈…〉〈…〉 whole moment, until after the stone hath per∣vaded the 31 fathom 〈…〉〈…〉 so in the fourth moment, it shall pervade 20 fathoms, nor shall 〈◊〉〈◊〉 able to make up another complete moment, un∣t•••• after the stone 〈…〉〈…〉, neer upon, the 84 fathom, and so in the fifth moment, 53 fath••••s shall be percurred, &c. so that proceeding 〈…〉〈…〉, neer upon; you shall consequently, in a very short time, 〈…〉〈…〉 it up to Immensity: as is manifest from the short progress 〈…〉〈…〉 numbers, 1.2, 4, 11, 31, 84, &c. Which is impugned by easie 〈…〉〈…〉, and not defensible by any Reason whatever.

* 1.12This the brave 〈◊〉〈◊〉 well considering, and long labouring his subtle and active 〈…〉〈…〉 explore a fully satisfactory Solution of this dark 〈…〉〈…〉 most happily to set up his rest in this. First, He defines Motion 〈◊〉〈◊〉 Accelerated to be that, which receding from qui∣et, doth acqu•••••• 〈…〉〈…〉 of Celerity, not in equal spaces, but equal 〈…〉〈…〉 upon Grounds partly Experimental, partly 〈…〉〈…〉 that the moments, or equal Degrees of Ce∣le••••ty 〈…〉〈…〉 or equal degrees of Time, or (more plain∣•••• 〈…〉〈…〉 the same proportions as the Times; so that 〈…〉〈…〉 of time pass during the motion, so many de∣grees 〈…〉〈…〉 by the thing moved. That the equal 〈…〉〈…〉 continently in single moments of time, do

encrease in each single moment, according to the progression not of U∣nities, but of Numbers unequal from an Unity: so that if in the first moment of time, the stone fall down one fathom, in the second moment, it must fall down three fathom, in the third five, in the fourth seven, in the fifth nine, in the sixth eleven, and so forward. And, because those Numbers, which they ••••ll Quadrate (viz. One is the quadrate of an U∣nity, Fower the quadrate of a Binary, Nine the quadrate of a Ternary, Sixteen of a Quaternary, and) are made up by the continual addition of unequal number•• (for, three added to one, make four; five added to four, make nine; seven, to nine▪ make sixteen▪ nine to sixteen, make twenty five; eleven to twenty five, make thirty six, &c.) thereupon He infers▪ that the Aggregates of the spaces percurred from the beginning to the end of the motion, are as the Quadrates of the times: i. e. assu∣ming any one particular moment of time, so many spaces are found per∣vaded in the end of that moment, as are indicated in the quadrate num∣ber of the same moment. For Example, when in the end of the first moment, one fathom of space is pervaded; in the end of the second mo∣ment, four fathom shall be pervaded▪ (viz. three being added to one) in the end of the third moment, nine fathom (five being added to four) in the end of the fourth moment, sixteen fathom (seven being added to nine) and so forward: so that, accordingly, the spaces pervaded from the beginning to the end of the motion, are among themselves in a Duplicate Ration of moments (as Geometricians speak) or equ••l Divisions of Time; or, all one as the Quadrates of moments are one to another.

Galilaeus, we said, herein relyed partly upon Experience,* 1.13 partly upon Reason. First, therefore, for his Experience; He affirms, that letting fall a Bullet, from the altitude of 100 Florentine Cubits (i. e. ac∣cording to exact comparation, 180 feet, Par••s measure, and thirty fathom of ours) He observed it to pervade the whole space, and arrive at the ground, in the space of five seconds, or ten sem••seconds▪ and accor∣ding to such a ration, as that in the first semisecond, it fell down one cubi••, in the second semisecond, four cubits; in the third semisecond, nine cubits, in the fourth sixteen; in the fifth twenty five; in the sixth 36; in the seventh, forty nine; in the eighth, sixty four; in the ninth, eighty and one; in the tenth the whole hundred. And though the good Mer∣sennus afterward found a bullet to pervade the same altitude in a much shorter time; nay, that in the space of five seconds, a bullet fell down through the space not onely of one hundred and eighty foot, but even of three hundred▪ i. e. of fifty fathom: yet doth He fully consent, that the Acceleration of its motion ariseth exactly according to Galilaeos progres∣sion by the Quadrates of unequal numbers. So as that if in the first se∣misecond, it descend one semi-fathom▪ in the second semisecond, it shall descend four semifathoms, in the third sem••second, nine semifathoms, &c. And Gassendu•• likewise, though he wanted the opportunity of experi∣menting the thing•• from a Tower of the like altitude; found notwith∣standing, from different heights, that the proportion was always the same; as Himself at large declares 〈…〉〈…〉 qua gravia decident. accelerantu•••• 〈…〉〈…〉 you doubt to find it so your self, if in a Glass Tube, neer upon two 〈◊〉〈◊〉 ••••ng, divided into an hundred degrees, or equal parts, 〈…〉〈…〉 either cut in, or inscribed

upon papers (after the manner of those usually starcht on to Weather-glasses, to denote the several degrees) and not perpendicularly erected, but somewhat inclining, you let fall a bullet, and exactly observe the manner of its descent, and rate of Acceleration. For, Heavy bodies are, indeed, moved more slowly in Tubes inclined, than in such as are perpendicularly erected; but yet still with the same proportion of Acce∣leration.

Secondly, for His Reason, it consists in this; that, if the Increment of Velocity be supposed to be Uniforme (and there is no reason, which can persuade to the contrary) certainly, no other proportion can be found out, but that newly exposed: since, with what Celerity, or Tardity soever you shall suppose the first fathom to be pervaded it is necessary that in the same proportion of time following, three fathoms should be pervaded; and in the same proportion of time following, five fathoms should be pervaded; &c. according to the progression of Quadrate Numbers. This, that Great man Ioh. Baptista Ballianus (whom Ricciolus often mentions (in Almagesto novo) but never without some honourable attribute) hath de∣monstrated divers ways in lib. 2. de Gravium motu.): but the most plain Demonstration of the verity thereof, yet excogitated, we conceive to be this, invented by Gassendus.

* 1.14

[illustration]

Understand the Lines LAB and ACI making a rectangular Trian∣gle, by their meeting at the point A, to be so divided, on each side, into equal parts, at the points DEFGHIKL: (being continued, they may be divided into many more) as that the Lines drawn both betwixt those points, and from them to the points MNO, divide the whole space KAL into Triangles perfect∣ly alike and equal each to other. This done, Assume the point o•• A∣pex A, for the beginning of Time, the beginning of space, and the be∣ginning of Velocity: All which are to be here considered in the motion, as beginning together with it. First, then we may account the equal parts of each Line, AB, AC. for the parts or equal moments of Time, flowing on from the beginning: so that AE may represent the first moment, EG the second, GI the third, IL the fourth. Secondly, we may account those equal Triangles, for the equal parts of the space, which are pervaded from the beginning: so that A∣nother perpendicular Line PQ. being drawn apart, and representing the fall of a stone, thro••gh sixteen fathom, the triangle ADE, may refer the first fathom P••, which is percurred in the first moment; the three next triangles may refer the three fathoms RS, which are percurred in the second moment; the five following triangles, the five fathoms ST, which are pervade•• in the third moment: and the seven following, the seven fathoms, which are pervaded in the fourth moment. Now from

hence it is manifest, that the Aggregate spaces carry the same pro∣portions,

[illustration]

as the Quadrates of Times: when, the Triangle ADE (or space PR.) is one, as the Quadrate of AE, that is of one Time, is one: and the Aggregate AFG (or PS) is four: as the Quadrate AG, of two, is fower: and the Aggregate AHI (or PT) is nine: as the Quadrate AI of three, is nine; and the Aggregate AKL (or PQ.) is sixteen, as the Qua∣drate AL of four, is sixteen.

Thirdly, we may account the Line DE for the first degree of Velocity acquired in the end of the first time; insomuch, as the first time AE is not individual, but may be divided into so many instants, or shorter times, as there are points, or particles in the line AE (or AD) so neither is the degree of Velocity indivi∣dual, or wholly acquired in one instant; but from the beginning encreaseth through the whole first time, and may be repraesented by so many Lines, as may be drawn parallel to the Line DE, be∣twixt the points of the Lines AD and AE: so that, as those Lines do continually encrease from the point A to the Line DE; so likewise doth the Velocity continually encrease from the begin∣ning of the motion, and being represented what it is in the inter∣cepted instants of the first time, by the intercepted Lines, it may be represented what it is in the last instant of the same first time, by the Line DE drawn betwixt the two last points of the Trian∣gle ADE. And because the Velocity, thenceforward conti∣nuing its Encrease, may be again signified, by Greater and Greater Lines continently drawn betwixt all the succeeding points of the remaining Lines, DB and EC; hence comes it, that the Line FG, doth represent the degree of Velocity acquired, in the end of the second moment: the Line HI. the Velocity acquired in the end of the third moment; and the Line KL. the velocity acquired in the end of the fourth moment. And evident it is from hence, how the velocities respond in proportions to the Times; since, by reason of the Triangles of a common angle, and parallel bases, it is well known, that as DE are to EA, so FG to GA: HI to IA, and KL to LA. Thus, keeping your eye upon the Figure, and your mind upon the Analogy; you shall fully comprehend, that in the first moment of Time, the falling stone doth ac∣quire one degree of Velocity, and pervades one degree of space; that in the second moment of Time, it acquires another degree of Velocity, which being conjoynd to the former, makes two, and in the mean while three spaces are pervaded; that in the third moment, it acquires another degree of Velocity, which conjoyned to the two former makes three, and in the mean while seven parts of space are pervaded; and so forward. You shall fully comprehend also, that the Celerities obtain the same Ra∣tion, as the moments of Time: and that the spaces pervaded from the beginning to the end of the motion, have the same Ration, as the Qua∣drates of the moments of Time; which we assumed to Demonstrate, out of Gassendus. But still it concerns you to remember, that we here dis∣course of that Motion, which is Equally, or Uniformly Accelerated; or whose velocity doth continually and uniformly encrease, nor is there any moment of the consequent time, in which the motion is not more swift, than it was in every antecedent moment, and in which it is not accelerated

according to the same Reason. For, the want of this Advertisement in chief, seems to have been the unhappy occasion of that great trouble the Learned Jesuit Petrus Cazraeus put Gassendus to, in his two Epistles, De Proportione, qua Gravia decidentia accelerantur.

* 1.15And this kindly conducts us to the Physical Reason of this Proportion, in which the velocity of bodies Descending is observed to encrease. For wholly excluding the supposition of the Aers assistance of the Downward motion of a stone, by recurring above, and so impelling it downward; and admitting the Magnetick Attraction of the Earth to be the sole Cause of its Descent; unto both which the considerations formerly alleadged seem to oblige us: it is familiar for us to conceive, that the Increment of its Celerity, according to the proportion assigned, ariseth from hence. While in the first moment, the earth attracts the stone, one degree of Ce∣lerity is acquired, and one degree of space is pervaded. In the second moment, the attraction of the Earth continuing, another degree of ce∣lerity is acquired, and three equal spaces are pervaded: one by reason of the degree of celerity in the mean while acquired, and two by reason of the degree of celerity formerly acquired, and still persevering, as that which is doubly ••equivalent to the new degree in the mean while ac∣quired; because it is Complete and entire from the very beginning of the 2^d moment, but the other is only acquiring, or in fieri, and so not complete till the end of the second moment. Then, according to the same Ration, in the third moment another degree of celerity is acquired, and five spaces (equal) are pervaded; one by reason of the new degree of celerity in the mean while acquired, and fower by reason of the two former persever∣ing, i. e. two in each moment praecedent, or one of a duplicate aequivalen∣cy to the new one not yet complete. Then, in the fourth moment another degree of celerity is acquired, and seven spaces are pervaded; one by reason of the fresh degree in the interim acquired, and six by reason of the three former per••••vering, i. e. two in each praecedent moment. And so of the rest through the whole motion, computing the degrees of en∣creasing Celerity, by the ration of Quadrate Numbers.

Now, many are the Physical Theorems, and of considerable impor∣tance,* 1.16 which might be genuinely deduced from this excellent and fruitful Physicomathematical speculation; and as many the admired Apparen∣ces in nature, that offer themselves to be solved by Reasons more than hinted in the same: but, such is the strictness of our method, and weari∣ness of our Pen, that we can, in the praesent, make no farther advantage of it, than only to infer from thence the most probable Reason of that so famous Phaenomenon, The equal velocity of two stones, or bullets, the one of 100 pound, the other of only one ounce weight, descending from the same altitude; experience constantly attesting, that being dropt down together, or turned off, in the same instant, from the top of a tower; the Lesser shall arrive at the ground, as soon as the Greater. For, this admirable Effect seems to have no other Cause but this; that the Lesser body, as it containeth fewer parts, so doth it require the Impulses or strokes of fewer Magnetical rays, by which the attraction is made: and such is the pro∣portion of the two forces, as that each moveable being considered with what Resistence you please, still is the force in the movent equally suffici∣ent to overcome that resistence, and a few magnetique rays suffice to the

attraction of a few parts, as well as many to the attraction of many parts. So that the space being equal, which both are to pervade; it fol∣lows, that it must be pervaded by both, in equal or the same time. Pro∣vided always, that the two bodies assumed, be of the same matter; for, in case they be of divers matters, as the one of Wood, the other of Iron or Lead, that may cause some small Difference in their Velocity. We say, some small Difference; because, if we take two Globes of different materials and weights, but of the same or equal diameters, as (V. G.) one of Lead, the other of Wax: we shall be very far from finding, that the Heavier will be carried down more swiftly than the Lighter, in a pro∣portion to the excess of its Gravity. For, if one be ten times heavier than the other; yet shall not the Heavier therefore, both being turned off, in the same instant, arrive at the ground ten times sooner than the Lighter: but, at the same time as the heavier, arrives at the ground, from the alti∣tude of 10 Fathoms; the lighter shall come within a foot of the earth; so far short doth the lighter come of being nine fathoms behind the Heavier. And the Cause, why the Lighter Globe of Wax, is carried so swiftly, is the same with that, why a bullet of Lead of only an ounce weight, is carried down as swiftly as another bullet of 100 pound. And, what though the Globe of Wax be as great in circumference, as the o∣ther of Lead, and somewhat greater; yet seeing still it hath fewer parts to be attracted, it therefore requires fewer magnetical rays to its attracti∣on with equal velocity to the heavier. But, the Cause why it is carried som∣what, though very little, slower than the heavier; is to be derived chiefly from the Aer resisting it underneath, the Aer being more copious in pro∣portion to the virtue Attrahent, in respect of the greatness of its Ambite, or Circumference: and thence is it, that Cork, Pith of Elder, straws, feathers, and the like less compact, and so more light bodies, fall down much more slowly.

From this Experiment, and the Reason of it,* 1.17 we have an opportuni∣ty of observing and easily understanding the Distinction of Gravity in∣to Simple and Adjectitious: the Former being that, which is competent to a body though unmoved, and whose quantity may be exactly determi∣ned by the balance suspending the body in the aer; the Latter being proper only to a body moved, and vanisheth as soon as the body attaineth quiet, and whose measure is to be explored both from the quantity of the simple gravity which the body bears during its quiet, and the Altitude from which it falls. Thus, assuming two Bullets, the one of an ounce, the o∣ther of 100 pound, Simple Gravity, according to the Scales; the Ad∣jectitious Gravity of the Lesser bullet, acquired by the increment of its velocity during its descent, must be less proportionably to its simple gra∣vity, than the Adjectitious gravity of the Greater bullet, acquired by the increment of its Velocity during its Descent, in the same time, and from the same altitude: because, the space and time of the descent of both being equal, the proportion of the acquired gravity of each must be respondent to the proportion of the simple gravity of each. So that if in the end of the fall of the Lesser bullet of an ounce weight, the Ad∣jectitious Gravity of it shall amount to 10 ounces: the Adjectitious gra∣vity of the Greater of 100 pound weight, shall, in the end of its fall, amount to a thousand pound; nor can the Acquired Gravity of the Les∣ser ever equal that of the Greater, unless it fall from a far greater Alti∣tude.

* 1.18Here, perhaps, you'l Demand our opinion, concerning that admirable because superlative Velocity, which Galilaeo and other Mathematicians conceive that a bullet would acquire in case it should fall to the ••arth from those vast (we might have said Immense) heights of the Moon, Sun, and region of the Fixed starrs. Of this, therefore, we say in short; (1) That, in this case, Mathematicians are wont to suppose, that there are the same Causes of Gravity and Velocity in those sublime places, as are observed here with us below, or neer the surface of the Earth: and if they be not, certainly our Description and Computation must be altoge∣ther vain and fruitless. For, if the Cause of Gravity, and consequent∣ly of the Velocity be the Attraction made by the magnetique rays trans∣mitted from the Earth; forasmuch as those magnetique rays must become more Rare, and fewer of them arrive at a body, by how much farther it is removed from the Earth: though, perchance, a bullet might be attra∣cted down from the region of the Moon (and if so, the motion of the bullet would be very slow, for a good while, in respect of the very few magnetique rays, that could arrive to that great height) yet from that far greater height of th•• region of the Fixt stars, a bullet could not be attra∣cted at all, it being impossible that any magnetique ray should be transmit∣ted so far as half way thither. (2) But, supposing that the magnetique Virtue of the Earth did extend thither; and that a bullet, from whence soever falling, should begin its motion with that speed, and proceed ac∣cording to the same degrees of Acceleration, which we observe in a stone, or bullet falling from a very high tower: then must it of necessity acquire that incredible Velocity, which our Mathematicians describe. To Par∣ticular; conceding the Distances or Intervals betwixt the Earth and each of those Caelestial Orbs, which our modern and best Astronomers gene∣rally assign; a bullet would fall from the body, or rather the Limbus of the Moon, to the Earth, in two hours and an half; from the Limbus of the Sun, in eleven hours and a quarter: from the region of the Fixt stars, in 39 hours and a quarter. And so, if we imagine the Earth to be per∣forated to the Centre, since a bullet would fall from the superfice thereof down to the Centre, in 20 minutes, or the third part of an hour: the same bullet coming from the moon, would pervade the same space from the su∣perfice of the Earth to the Centre of it, in one minute and twenty se∣conds, or the third part of a minute: coming from the Sun, it would per∣vade the same semidiametral space of the Earth, in seventeen seconds: and coming from the region of the Fixt stars, it would percur the same semi∣diametral space of the Earth, in five seconds. So incredibly great would be the Velocity of a bullet falling from such vast Altitudes. And this we think sufficient▪ concerning the Downward motion of Bodies, accoun∣ted Heavy.

Notes

• * 1.1

  Art. 1. 〈…〉〈…〉
• * 1.2

  Art. 2 The 〈◊〉〈◊〉 de∣duced from the 〈◊〉〈◊〉 Epi∣curean P••••••ci∣p••e of mo••••on, 〈◊〉〈◊〉▪ and 〈◊〉〈◊〉 consid••∣ra••le Conclusi∣ons extracted from the••ce.
• * 1.3

  Art. 4. 〈◊〉〈◊〉 or Aequanility, ••he 〈◊〉〈◊〉 ••haracter of a Natural moti∣on•• and 〈◊〉〈◊〉 want of uni∣••ormity, of a 〈◊〉〈◊〉.
• * 1.4

  Art. 5. ••he D••wn∣w••rd motion 〈◊〉〈◊〉 Inanimates, derived from ••n External Principle, contrary to A¦ristotle
• * 1.5

  〈1 paragraph〉〈1 paragraph〉
• * 1.6

  〈1 paragraph〉〈1 paragraph〉
• * 1.7

  〈1 paragraph〉〈1 paragraph〉
• * 1.8

  〈1 paragraph〉〈1 paragraph〉
• * 1.9

  Art. 〈1 paragraph〉〈1 paragraph〉
• * 1.10

  〈1 paragraph〉〈1 paragraph〉
• * 1.11

  Art. 12. That the Pro∣portion, or Ration of Ce∣lerity to Cele∣rity, encreasing in the descent of Heavy things; is not the same as the Proporti∣on, or Ration of Space to Space, which they pervade contrary to Michael Var•• the Mathema∣tician▪
• * 1.12

  〈1 paragraph〉〈1 paragraph〉
• * 1.13

  Art. 14 〈…〉〈…〉
• * 1.14

  Art. 15. The same De∣monstrated.
• * 1.15

  Art. 16. The Physical Reason of that Proportion.
• * 1.16

  Art. 17. The Reason of the E••ual Veloc••ty of B••∣dies of very d••ffe••••n•• weig••ts, fal∣ling from the same altitude; inferred from the same The∣••••y.
• * 1.17

  Art. 18. Gravity Di∣stinguish't in∣to Simple, and Adjectitious.
• * 1.18

  Art. 19. The R••••e of that superla∣tive velocity, with which a Bullet would be carried, in case it should fall from the Moon, Sun, or region of the ••ixed stars, to the Earth: and 〈◊〉〈◊〉 each of those vast heights, to the 〈◊〉〈◊〉 of the 〈◊〉〈◊〉.