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. III.

THe Remnant of our praesent Province consists only in the conside∣ration of the Upward motion of Heavy Bodies PROJECTED: concerning which the principal Enquiries among Philosophers are (1) VVhat and whence is that Force, or Virtue motive, whereby bodies pro∣jected are carried on, after they are separated from the Projicient? (2) What are the Laws of their motion. Direct, and Reflex?

Concerning the FIRST, therefore, we observe,* 1.1 that Aristotle (in 8. physic. cap. ult.) and most of his Sectators confidently affirm, that a stone thrown out of a sling, an arrow shot from a bow, a bullet discharged from a Gun, &c. is moved only by the Aer, from the time of its separation from the sling, bow, or Gun: and the manner of that mo••ive activity of the Aer upon the thing projected, They thus explicate. The Aer (say they) which is first moved by the Projicient, together with the moveable, doth, at the same time, both propel the moveable, and impel the Aer im∣mediately beyond it, which being likewise moved, doth in the same man∣ner propel the moveable, and impel the aer immediately beyond it; and that aer being thus moved, doth again impel both the moveable and the aer next beyond it: and so consequently the next aer impels both the moveable and the next aer beyond it, until the propulsion and promo∣tion being gradually debilitated, and at length wholly overcome, partly by the Gravity of the thing moved, partly by the Resistence of the occurring Aer, the motion wholly ceaseth, and the thing projected attain∣eth quiet.

And that Others contend, that the Body Projected is carryed forward by a Force (as They call it) Imprest; which they account to be a Qua∣lity so communicated unto the body projected, from the Projicient, as that not being indelible, it must gradually decay in the progress thereof, and at length wholly perish, whereupon the motion also must by degrees remit its violence, and at length absolutely vanish, and the thing project∣ed again recover its native quiet. But, lest we trifle away our praecious moments, in confutin•• each of these weak Opinions, against which the Reason of every man is ready to object many great absurdities, especially such as the praecedent theory will soon advertise him of: let us praesently recur to the more solid speculations of our master Gassendus in his Epi∣stles (de motu impresso a motore translato) and praesenting you the sum∣mary thereof, without further delay satisfie your Curiosity, and our own Debt of assisting it.

First we are to determine, that nothing, remaining it self unmoved, can move another. For, since our Discourse concerns not the First Cause of all motion, God, whose Power is infinite, who is in all places, who can, on∣ly by the force of his Will, create, move, and destroy all things; mani∣fest it is, that nothing Finite, especially Corporeal (and such only hath

an interest in our praesent consideration) can move another thing, unless it self be also moved at the same time: as Plato well observed in his say∣ing, Neque est Dissicile modo, sed etiam plane impossibile, ut quidpiam mo∣tum imprimere, sine quapiam sui commotione, valeat: (in Timaeo.) And the Reason is this; whatever doth move, doth act; and e converso, what∣ever doth act, doth move; Action and Passion (as Aristotle, 3. physic. 3) being the same with motion. Again, the movent and Moveable ought to be together, or to touch each other, because, whether the movent im∣pel, attract, carry, or ••owle the moveable: necessary it is, that still it should impress some certain Force upon it: and force it can impress none there∣upon, unless by touching it. And though it doth touch it, yet if it dis∣charge no force of motion upon it, i. e. remain unmoved it self: there shall be only a meer Contact reciprocal, but no motion, and as the one, so shall the other remain unmoved. Therefore, that the one may move the other: it ought to have that vigour or motion first in it self, which it doth impress upon the other: since if it have none, it can give none. Even sense demonstrates, that by how much more vehement motion the mo∣vent it self is in, at the instant it toucheth the moveable, by so much the farther doth it always propel the same: and thence our Reason may ne∣cessarily infer, that the movent must it self be in some small motion, in the same instant it gives a small motion to another. Moreover, though Aristotle (in 8. Physic cap 5.) subtly Distinguisheth three Things in mo∣tion, viz. the 〈◊〉〈◊〉 ut quod, as (V. G.) a man, the Movens ut quo, as a staff: and the Mobile, as a stone: and thereupon magisterially teach∣eth, that the stone is moved, and doth not move; that the staff is mo∣ved, and doth move: that the man doth move, and is not mo∣ved: yet is it not ••••ident, how far short He comes, of thereby De∣monstrating the immobility of the First Movent, to which He praetended. For whereas He urgeth, that otherwise we must proceed to In∣finity; that binds not at all: because the movens ut quod, the man is mo∣ved by Himself: and sense declares, that the man must move his Arm, or Hand together with the staff, which if you suppose not to be the movens ut quo, (the stone b••••ng not moved thereby) but the mobile it self: is not the movent it self ••••so moved? Suppose also, that the mans Arme, or Hand is the move•••• 〈◊〉〈◊〉 quo, nay if you please, that his whole Body, or the Muscles, or Nerve, or Spirits, are the movens ut quo, and deriving the motion from his very Soul, suppose that to be the movens ut quod: yet truely can you not ••••••ceive, that the Soul, it self remaining Immote, doth move the Arm, o•• ••and. Nor is the Soul it self then moved onely by Accident (as whe•• •• marriner is carried by the motion of his ship) but also per se, as w•••••• the mariner moves himself, that he may move the Oar, that it may move the ship, in which himself is carried. For, as a ship, in a calm sea, ••ould not be moved it self, nor the mariner be moved with it, by Accid••••••▪ in case the mariner himself wanted motion, where∣by to impel his ship•• so neither would the body be moved, nor the Soul be moved therew•••••• by Accident, unless the soul be first agitated within, with a motion wh••••••by the body is moved. Conclude, therefore that nothing can be 〈◊〉〈◊〉, but the Projicient must not only Touch it, ei∣ther immediately, ••••mediately by some Instrument; but also Propel it with the same 〈◊〉〈◊〉, wh••••••with it self is, in the same instant, moved.

It is moreover ••••••••ssary, that the movent be moved, not only in a point,

or so far as that point of space, in which it first toucheth the moveable: but also that a while cohaering unto the moveable, it be moved along with it: so as we may well conceive them to be made, by that Cohaesion, as it were one and the same body, or one entire moveable, pro tempore; and consequently, that the motion of both the movent and moveable is one intire motion. For, what motion is in the moveable, so long as it remains conjoyned to the movent, is in a manner a certain Tyrocinium, in which the moveable is as it were taught to progress foreward in that way, which the movent hath begun, upward, downward, transverse, ob∣lique, circular, and that either slowly, or swiftly, and according as the mo∣vent shall guide and direct it, before its manumission or dismission.

Thus, when a man throws a stone with his hand, you may plainly per∣ceive, how the motion thereof begins together with that of his hand: and after it is discharged from his hand, you cannot say, that a new moti∣on is impressed upon the stone, but only that the same motion begun in the hand is continued. And, therefore, it seems also very unnecessary to require the impression of any new and distinct Force upon the stone projected, by the projicient, which should be the Cause of its motion af∣ter its Dismission: seeing nothing else is impressed, but the very motion to be continued through a certain space; so that we are not to enquire, what motive Virtue that is, which makes the Persevering motion, but what hath made the motion, that is to persever. In the moveable, cer∣tainly, there is none but a Passive Force to motion; nor can the Active Force be required in any thing but the movent: and should we, with the Vulgar, say, that there is an Imprest Force remaining, for some time, in the thing moved, or projected; we could thereby understand no other than the Impetus, or motion it self.

Here might we opportunely insist upon this,* 1.2 that motion is impressed upon a thing moved, only in respect, that the thing moved hath less force of Resistence, than the movent hath of Impulsion: so that the movent, forcing it self into the place of the moveable, compels it to recede, or give way, and go into another place. But it is more material for us to observe; that when a thing projected is impelled, it is first touch∣ed by the projicient only in those parts, which are in its superfice or outside and that those outward parts, being pressed by the impulse, do drive in∣ward or press upon the parts next to them; and those again impel the parts next to them, and those again the next to them; till the impulse be by succession propagated quite through the body of the thing projected, to the superficial parts in the opposite side, and then begins the motion of the whole, the parts reciprocally cohaering: as hath been formerly explain∣ed, in the example of a long pole, or beam of wood. Which being per∣cussed, but with a very gentle or softly stroke, that one end hath all its parts so commoved successively, as that the stroke may be plainly percei∣ved by a man, that lays his ear close to the other end: which could not be if the impulse were not propagated from parts to parts successively, through the whole substance of the beam. To which it is requisite, that we superad this observable also; that by reason of the force made by Contact, and that short Cohaesion of the moveable to the movent, there is created a certain Tension, or stress of all the parts of it, towards the opposite region: and of that by that means, all the parts of the thing

projected, are disposed or conformed as it were into certain Fibers, or di∣rect Files; of all which the most strong and powerful is that, which being trajected through the Centre of Gravity in the thing projected, becomes as it were the Axis to all the circumstant ones. Our eys ascertain, that unless the Centre of Gravity be in the middle of the thing projected, or directly obverted to the mark, at which the thing is thrown; the thing instantly turns it self about, and that part, wherein the Centre of Gravi∣ty is, always goes foremost, and as it were carries the rest of the parts, as that which is the most Direct and most Tense of all the Fibres. And this cannot be effected, but with some (more or less) Deflection from the mark, at which the force, according to the Centre and Axis of Gravity, was directed; forasmuch as the Centre of Gravity, wherein many Fibres concur, makes some Resistence, and detorting the Fibres, inflecteth them another way, and so a new Axis is made pro tempore, according to which the Direction of all the parts in their motion afterward is determined. Hence is it, that, if you would hit a mark, either with a sling, or stone∣bow, you must choose a stone, or bullet of an uniform matter and com∣position: or, at least, turn the heavier part of the body to be thrown, for∣ward; because otherwise, it will Deflect more or less, to one side or other according to the position and inclination of its Centre of Gravity. More∣over, whether soever the thing projected doth tend, all the Fibers constant∣ly follow the Direction of the Axis, or are made parallels thereunto; so that as often as the Centre is changed, so often doth the Axis, so often do all the Fibres change their position, and follow the Centre. Which we insert chiefly in respect of the motion of Convolution, or Turning of a thing projected immediately after its Dismission; and of the Curvity of that Line, which is thereby described, whether ascending, or descending. But these are onely Transient Touches, or Hints; that we might easily intimate, why a motion once imprest, is continued rather this way, than that: and why Feathers, Sponges, and the like Light and Porous bodies, are incapable of having quick and vehement motions imprest upon them; because they consist of interrupted Fibres, and such as are not Dirigi∣ble with the Centre of Gravity.

* 1.3Here we ask leave, once more to have recourse to that useful suppositi∣on of a stone situate in the immensity of the Imaginary spaces. We lately said, as you may remember, that if a stone placed in the empty Ex∣tramundane spaces, should be impelled any way, the motion there∣of would be continued the same way, and that uniformly or equally, and with tardity or celerity proportionate to the smartness or gentleness of the Impulse, and perpetually in the same line; because in those empty spaces it could meet with no cause, which by Diversion might either accelerate, or retard its motion. Nor ought it to be Objected, that nothing Violent can be Perpetual; because, in this case, there could be no Repugnancy or Resistence, but a pure indifferency in the stone to all regions, there being no Centre, in relation whereunto it may be conceived to be Heavy or Light. And, therefore, the condition of the stone would be the very same, as to Uniformity and Perpetuity of motion, with that of the Cae∣lestial Orbs; which being obnoxious to no Retardation, or Acceleration, but free from all Repugnancy internal, and Resistence External, constant∣ly and inde••inently maintain that Circular motion, which was, in the first moment of their Creation, imprest uopon them, by the Will of the Cre∣ator;

and that toward one part, rather than any other. Let us now far∣ther consider; seeing that if upon some large horizontal plane you should place a smooth Globe, and then gently impel it; you would observe it to be moved therupon equally and indefinently, till it came to the end there∣of: why may you not lawfully conjecture, that if the Terrestrial Globe were of a superfice exquisitely polite, or smooth as the finest Venice Glass; and another small Globe as polite were placed in any part of its superfice, and but gently impelled any way, it would be moved with constant Uni∣formity quite round the Earth, according to the line of its first direction; and having rowled once round the Earth, it would, without intermission again begin, or rather continue another Circuit, and so maintain a perpe∣tual Circulation upon the surface of the Earth? Especially, since there is no Difficulty 〈◊〉〈◊〉 discourage that conjecture; forasmuch as look how many parts of the small Globe, during the motion thereof, tend toward the Centre of the Earth, just so many are, at the same time, elevated from it: so that a full Compensation being made in all points of the motion, the same cannot but perpetually continue, and in the same equal tenour, there being no Declivity, whereby it should be Accelerated, no Acclivity, wher∣by it should be Retarded, no Cavity, whereby after many accurses and recurses, or reciprocations, it should be brought at length to acquiesce. Moreover, in order to our grand scope, let us suppose, that the space, through which a stone should be Projected, were absolute Inane, or such as the Imaginary spaces; and then we must acknowledge, that it would be carried in a direct and invariate line, through the same space, and with an Uniforme and Perpetual motion, until it should meet with some other space, full of magnetique rayes, Aer, or some other resisting sub∣stance. But, here with us, in the Atmosphere, because no space is Inane (sensibly) but replete as well with Aer, as with millions of mag∣netique rayes transmitted from the Earth; and so a stone Projected must encounter them in every point of space through which it moves: therefore is it, that it cannot be moved either in a direct Line, or equally, or long. For, since multitudes of magnetique Rayes must necessarily invade and attach it, as soon as it is discharged from the Projicient; though at first setting forth it break through them, and so is scarce at all Deflected: yet because more and more magnetique rayes freshly lay hold of it in every part of space, renew the Attra∣ction, and so more and more infringe and weaken the force of its motion; hence comes it, that in the progress it doth by little and little Deflect from the Line of Direction, moves slower and slower, and at length sinking down to the Earth, thereon attains its quiet. Hereupon, when men shall Demand, what is that Cause, which weakens and at last quite destroys the Virtue Impressed upon a thing Pro∣jected; rightly understanding, by the Virtue Imprest, the motion be∣gun by the Projicient, and continued by the Projectum: the Answer is manifest; viz. That it is the Attraction of the Earth, which first op∣poseth, after gradually refracteth, and in fine wholly overcometh the motion imprest, and so determineth the Projectum to Quiet. Hence also may we learn, that All motion once impressed, is of it self Indelible, and cannot be Diminished, or Determined, but by some External Cause, that is of power to repress it.

* 1.4This considered, you may please to observe, that through the Atmo∣sphere, or spaces circumvironing the Terrestrial Globe, being so pos∣sessed by the Aer and swarms of Magnetique Rayes, no body can be pro∣jected in an absolute Direct: or perfectly streight Line, unless perpendi∣cularly upward or downward. For, if the projection be made either obliquely, or parallel to the Horizon; the projectum suddain∣ly begins to Deflect from the mark at which it was aimed, and so describes not a streight, but crooked line. Not that the Deflection or Curvity is sensible, at a small distance, especially if the motion be vehement, such as that of an Arrow shot from a Bowe, or Bullet discharged from a Gun: but, that in every point of space, and time, the thing Proje∣cted is attracted somewhat Downward; and there is the same Reason for its Deflection in the first, as there is for its Deflection in the second, third, fourth, or any following point of space, and instant of time, though the greater opposition of the Force imprest makes that Deflection less at the first. Nor ought it to incline us to the contrary, that Archers and Gunners frequently hit the mark, at which they levelled, to some certain distance: because, that Distance is commonly such, as that the Deflecti∣on therein is not sensible, though it be sometimes an hairs-breadth, two, three, or four, sometimes an inch below the mark.

* 1.5Further you may observe, that when a stone is projected, or a bullet shot upward, yet not p••••pendicularly, but obliquely; the motion there∣of is to be considered, not as simply perpendicular, or simply Horizontal, but as mixed, or composed of an Horizontal and Perpendicular toge∣ther: of a Perpendicular, forasmuch as the Altitude thereof may be measured by a Perpendicular line; of an Horizontal, forasmuch as it is made according to the Horizon, and the Latitude thereof may be taken by the plane of the Horizon. But, because by how much the more it hath of the perpendicular, so much the less it hath of the Horizontal; so that the Altitude of it may amount to fifty feet, and the Latitude not exceed one foot: therefore is it manifest, that the crooked Line described by this Compass motion, cannot be Circular; and Galilaeo (Dialog. 4.) hath demonstrated that the Line is Parabolical, or such as Geometricians describe in the ambite of a Cone, when they so intersect it obliquely from one side at the base, that the motion of the intersection is made parallel to the other side left whole, for the Area of each resegment is the Geometricians Para∣bola: and the crooked ambite of the Area, is a Parabolical Line, and frequently taken for the Parabola it self. We remember also, how Galilaeo, upon consequence, and among other remarkables doth observe; that of all Projections, made by the same force, the Longest, and in that respect the most Efficacious, is that, which is made to an half-right Angle, or by aiming at the forty fifth de∣gree of Altitude; in respect of the more prolix Parabola which is described by the Pr••jectum, aimed at that altitude: since at all other altitudes the Parabola must be shorter; the superior Altitudes being less, and the inferior more open than is requisite.

Now this Composition of a Perpendicular and Horizontal moti∣on may be most conveniently Demonstrated unto you, thus.* 1.6 Be∣ing in a ship, under sayl, if you hold a Ball in your hand; the mo∣tion of the ball will be onely Horizontal, viz. That, whereby the ship doth carry you, your hand, and the ball in it. If the ship stand still, and you throw the ball directly upward; the motion of the ball will be onely Perpendicular: but if the ship be moved, at the same instant you throw the ball upward; then will the moti∣on thereof be Compound, partly Perpendicular, partly Horizon∣tal. For, the ball shall be carried obliquely, and describe a Para∣bolical line, in which it ascends and again falls down again; and in the mean time, it shall be promoved Horizontally. The Per∣pendicular alone, your self may discern with your own eye: because, the horizontal is common both to the ball and your eye, and when as well the ball, as your eye is promoved, therefore doth it always appear imminent over your eye, and in the same perpendicular: but, for the Horizontal, He onely can deprehend it, who stands still on the shoare, or another ship not carryed on at the same rate, as that where∣in you are.

Herein there occur Two things, not unworthy our admiration.* 1.7 The One is, that though there be two divers Forces or motions impressed upon the Ball, at the same time: the one from the Vibration of your Arm, the other from the horizontal Translation of the ship: yet doth neither destroy the other, but each attains its proper scope as fully, as if they were impressed apart. For, the Ball ascends as high, when the ship is moved forward, as when it stands still: and whether it describe a Direct, or a semiparabolical: and again, it is as much promoved Horizontally, when you divert it upward by projection, as when you hold it still in your hand and so it be carried onely by the motion of the ship: and consequently whether the motion there∣of describe a Direct line, or a whole Parabola. Onely this you are to note: that a greater Force is required to the projection of a Ball from the foot to the top of the Mast, when the ship moves for∣ward, than when it lies at anchor: because that semiparabolical line, which the Ball must describe in the former case, is shorter than that perpendicular one, which it must describe in the latter: and how∣ever the vibration or swing of your arme may seem to you to be e∣qual in both cases, yet is that vibration or force, whereby the ball is carried upward to the top of the Mast, when the ship is in motion, really greater than that, whereby the same ball is carried to the same height, when the ship lies quiet: because, in the former case, there is superadded to the force of your arme, the force which is impressed both upon you and your arme (without your apprehension) by the motion of the ship. This you shall plainly perceive, if you onely drop down a ball from the top of the Mast, without any swing or motion of your arme at all. For, seeing that the ball doth always fall at the foot of the mast, in the same distance from it, as it was in the instant of its dimission from the top; whether the ship be mo∣ved, or quiet: necessary it is, that some force be imprest upon

the ball by the motion of the ship, or the the same motion, where∣by both the Mast it self, and your hand are affected, at the instant of its dimission; since it must describe a semiparabolical line, longer than that Direct one, which it would describe, if it fell down the ship being quiet. And hence comes it, that if you project a ball from the Poop to the Fore Castle of a ship, under sayl, and back again from the Fore-Castl•• to the Poop; you shall impress a greater force upon it, in throwing it from the Poop to the Fore-Castle, than back again from the Fore-Castle to the Poop: because, in the former case, the force or seconding impulse of the ship must be superadded to the force of your arme in projection, and so make it the stronger; and, in the latter case, the contrary force of the ship doth as much detract from the force of your arme, and so make it the weaker. And though the ball be carried over equal spaces of the Deck of the ship, in both cases: yet shall it not be carried through equal spaces in the Aer.

* 1.8Hence may it be Demonstrated, that the space of Time which the ball is Ascending from the foot to the top of the Mast, is Equal to that in which it is Descending again from the top to the foot. For, were it not so, when the ball is projected in a line perpendicular and parallel to the Mast, the ball would not ascend and descend always at the same distance from the Mast, but would either desert it, or be deserted by it, the ship being in motion. Whence it follows also, that in what proportion the velocity of the ball Ascending doth de∣crease; in the same proportion doth the velocity of the ball again Descending encrease•• so that the motion of the ball must be of equal velocity, when it is removed from the plane of the ship, one fathom ascending, or descending, and likewise at the altitude of one foot, ascending or descending. Again, forasmuch as the force of your arme, projecting the ball, is still equal; but the force superadded thereunto by the motion of the ship, may be more or less vehement, according as the s••••p is carried with greater or less speed: thence it follows, that the ••arabolical lines described by the ball, are respe∣ctively Greater or Less, and the motions of it through the Aer more or less swift. 〈◊〉〈◊〉, yet all are performed in Equal Time; be∣cause the times of them all are equal to the same time, which is due to the simple Assent and Descent, and with the same proportion of parts.

* 1.9The Other, which deserves our admiration, is this; that not∣withstanding, of the twofold motion composing the Oblique one, that which is Perpendicular, is Unequal, the Velocity there∣of being as well diminished in the assent, as augmented in the de∣scent, so that; in equal moments of time, less spaces are pervaded in the assent, and greater in the descent: yet is that motion, which is Horizontal, plainly Equal in all its parts, or of equal velocity throughout; so that equal spaces of the Horizon are pervaded in e∣qual times. The truth of this is constant from hence; that if (the ship being equally moved on, and the ball being projected in a line parallel to the Mast) the foot of the Mast shall pervade twenty

paces, or an hundred foot of horizontal space: the ball shall be horizontally (i. e. toward that region, to which the ship tends) pro∣moved, not more swiftly or slowly in one pace or foot, than in a∣nother, but equally in all: for, otherwise, it could not be al∣ways imminent over the same part of the ship neer the Mast: nor therefore consist in the same line, or distance from the Mast: which yet it constantly observes. But this easily deceives, that at the end of the balls ascent, or beginning of its descent, the motion is slowest: but then are we to observe, that the Devexity, or Con∣formity of it to the Horizon is the Greater, as when it comes low∣er, where the motion is more rapid, the Devexity is less, and its conformity to the Perpendicular greater: so that the whole Inaequa∣bility doth consist in the Assent and Descent, or Perpendicular moti∣on of the ball: while in the mean time there is a perfect Aequability in its Horizontal advance, or promotion. From hence we collect: that since a thing Projected is moved unequally, insomuch as it tends upward or downward: and not as it progresseth parallel to the Hori∣zon, or Ambite of the Earth: therefore is it, that the upward and downward motions are both to be accounted Violent: but the Hori∣zontal, or Circular, Natural: Equality, or Uniformity being the inseparable Character of Natural, and Inequality of Violent motion.

Thus far have we treated of that Returning or Reflex motion of Bodies, whereby, being violently projected upward,* 1.10 they re∣vert or fall down again, by reason of the magnetique Attraction of the Earth: and it now remains onely, that we consider the Rea∣sons of that other species of motion Reflex or Rebounding, whereby Bodies, being also violently moved or projected any way, are im∣peded in their course and Diverted from the line of their Direction, by other bodies encountring them. Concerning this Theorem, therefore, be pleased to know, that among all Reflexions, by way of Rebound or Resilition, that is the Chiefest, when a body projected, and impinged against another body, is returned from thence directly, or in the same line toward the place, from whence it was projected: which always happens, when the Projection is made to right Angles, or in regular line, such as that in which a Heavy body descends upon an horizontal plane. And all other Reflections are in dignity inferior thereunto, as such whereby the thing projected doth not rebound in a direct line toward the same point from whence it was projected, but to some other region by o∣ther lines: according as it is projected in lines more or less oblique. Because, with what inclination a body falls upon a plane, with the very same inclination doth it rebound from the plane (especially a Globe, and such as is of an uniform matter, and consequently hath the Centre of magnitude and that of Gravity coincident in the same point) so that by how much the more oblique the projection is, and how much the less is the Angle made of its line with the line of the plane, (called the Angle of Incidence) so much the more ob∣lique is the reflexion made, and so much the less the Angle made of its line, with the line of the plane continued (called the Angle of Re∣flexion)

and that so long, as till the line of projection shall become pa∣rallel to the plane, and so, no body occurring to or encountring the pro∣jectum, no reflexion at all be made.

* 1.11Know moreover, that betwixt No Reflexion at all, and the Least Reflexion that is possible, there may be assigned as it were a certain Medium; and that is the Emersion or Rising up again of a weight appensed to a thread or Lutestring, when performing a vibration or swing from one side to the other, it ascends from the perpen∣dicular Line, to which by descending it had reduced it self. For, in that case, no ••••••lecting body doth occur, a simple Arch is described; and y•••• ••here is as a certain Procidence or falling down to the lowest point of the Arch, so also a certain Resilition or ri∣sing up again from ••he lowest point of the Arch, toward the con∣trary side. Again▪ having conceived a direct line touching the lowest point of the Arch, so as that the weight suspended by a string, may, in its vibration, glance upon it with its lowest extreme, and onely in a point touch the horizontal line; you shall have on each side an Angle mad•• from the Arch and the line touching it, which is therefore called the Angle of Contingence: and because Geome∣tricians demonstrate•• that the Angle of Contingence, which truly differs from a right line, is less than any Rectilinear Angle, how∣ever acute; therefore may each of those Angles be said to be Medi∣an betwixt the right line, and the Angle either of Incidence•• or of Reflexion, how small soever it be; and consequently, the E∣mersion of the weight in Vibration may as justly be said to be Me∣dian betwixt the smallest Reflexion and none at all. However, this Emersion seems to 〈◊〉〈◊〉 the Rule of all Reflection whatever; for, as in the Vibration of a weight appensed to a string, and describing a simple Arch, the A••gle of its Emersion is always equal to the An∣gle of its Prociden••••: so in Projection describing an Angular line, the Angle of Reflection is always (quantum ex se est) equal to the Angle of Incidence▪ We say, quantum ex se est; for otherwise, whether it be sensible, or not, because so long as the Projectum is transferred, it is a••ways somewhat depressed toward the earth, for the reason formerly alleadged; thence comes it, that the Refle∣xion can neither be so strong or smart as the Incidence, nor make as great an angle, 〈◊〉〈◊〉 arise to as great an altitude. Which we in∣sinuate, that we might not insist upon this advertisement; that the Aequality of the Angle of the Reflexion to that of the Incidence, may be so much th•• less, by how much the less the projected body comes to a spherical figure, or doth consist of matter the less uniform.

* 1.12For, to attain to that Aequality of the Angels of Incidence and Reflexion, necessary it is, that the body projected be exactly sphe∣rical, and of Uni••orm matter, and so having the Centre of Gra∣vity, and the Centre of magnitude coincident in one and the same point; as we have formerly intimated: it being as well against Reason, as Experience, that bodies wanting those conditions should arise to that aequali•••• which that we may the better understan••, let us consider, that 〈◊〉〈◊〉 in a Globe, or Ball Falling down, we regard onely that Gravity▪ which it acquires in its descent, from the mag∣netique

Attraction of the Earth: so in a Globe, or Ball Projected, we are to regard onely that Impetus or Force, which being imprest upon it by the Projicient, supplies the place of Gravity, and in re∣spect whereof the Centre of its Gravity may be conceived to be one with that of its magnitude. Let a Ball, therefore, be projected Directly or to right Angles, upon a plane; and, because, in that case, that Fibre must be the Axis of its Gravity, whose extreme going foremost is impinged against the plane: thence is it mani∣fest, that the Repression must be made, in a direct line, along that Axis; the parallel Fibres in equal number on each part invi∣roning that Axis, and so not swaying or diverting the ball more to one part than to another, by reason of any the least dispro∣portion of quantity on either side. Then, l••t the same Ball be projected Obliquely against the same plane; and because, in this case, not that middle Fibre, which constituteth the Axis of Gravity, but some one or other of the Fibres circumstant about it, must with one of its extreams strike against the plane: there∣fore is it necessary, that that same Fibre be repressed by that im∣pulse, and by that repression compelled to give backward toward its contrary extream, and thereby in some measure to oppose the motion begun, which it wholly overcome, and so the ball would rebound from the plane, the same way it came, if the Fibres on that side the Axis of Gravity, which is neerest to the plane, were equal in number to that are on the farther, or contrary side of it: but, because those Fibres, that are on the farther side, or on the part of the Centre and Axis, are far more in number, and so the••e is a greater quantity of matter, and consequently a greater force imprest, than on the side neerer to the plane; therefore doth the begun motion persever, as praevailing upon the repression and renitency of the Fibre impinged against the plane, and since it can∣not be continued in a direct line, because of the impediment arise∣ing from the parts cohaerent, it is continued by that way it can, i. e. by the open and free obliquity of the plane. But, this, of necessity, must be done with some certain Evolution of the Ball, and with the contact of the Fibres posited in order both toward the Axis and beyond it; and while this is in doing, every Fibre strives to give back, but, because the farther part doth yet praevail over the neerer, therefore doth the neerer part still follow the sway, and conform to the inclination and conduct of the farther, and all the toucht Fibres change their situation, nor are they any longer capa∣ble of returning by the same way they came, because they no long∣er respect that part from whence they came. We say, with the Contact of the plane by the Fibres posited toward the Axis and be∣yond it; because, since in that Evolution or Turn of the Ball, the extream of the Axis toucheth the plane, yet nevertheless no Resi∣lition, or Rebound is therefore caused, in that instant; and if there were a resilition, at that time, it would be to a perpendicu∣lar, as well the Axis, as all the circumstant Fibres being erected perpendicularly upon the face of the plane: but the Resilition there must be beyond it, because the force of the farther part of the Fi∣bres doth yet praevail over that of the neerer. For, the Force of

the farther part doth yet continue direct and intire; but, that of the neerer is reflected, and by the repression somewhat debilitated: and therefore, the Resilition cannot be made, until so much of Repression and Debilitation be made in the further part, as was made at first in the neerer. And that must of necessity be done, so soon as ever the plane is touched by some one Fibre, which is distant from the Axis as much beyond, as that Fibre, which first touched the plane, is distant from the Axis on this side: for, then do the two forces become equal, and so one part of the Fibres having no reason any longer to praevail over the other, by counter inclination, the Ball instantly ceaseth to touch the plane, and flies off from it, toward that region, to which the Axis and all the cir∣cumstant Fibres are then, i. e. after the Evolution, directed. Now, because the Ball is, after this manner, reflected from the plane, with the same inclination, or obliquity, with which it was impin∣ged against it; it is an evident consequence, that the Angle of its Reflexion must be commensurable by the Angle of its Incidence: and that each of them must be so much the more Obtuse, by how much less the line of projection doth recede from a perpendicular; and contrariwise, so much the more Acute, by how much more the line of projection doth recede from a perpendicular, or how much neerer it approacheth to a parallel with the plane.

* 1.13From these Considerations we may infer Two Observables. The One, that the oblique projection of a Globe against a plane, is com∣posed of a double Parallel, the one with the Perpendicular, the other with the plane: for, the Globe at one and the same time, tends both to the plane, and to that part toward which the plane runs out for∣ward. The Other, that Nature loseth nothing of her right, by the Reflexion of bodies; forasmuch as she may nevertheless be allowed still to affect and pursue the shortest, or neerest way: for, because the Angle of Reflexion above the plane, is equal to that Angle, which would have been below the plane, in case the plane had not hinderd the progress of the line of projection beyond it, by reason of the Angles Equal at the Vertex, as Geometricians speak; therefore, is the Reflex way equal to the Direct, and consequently to the shortest, in which the ball projected could have tended from this to that place.

* 1.14Here, to bring up the rear of this Section, we might advance, a discourse, concerning the Aptitude and Ineptitude of Bodies to Reflexion; but, the dulness of our Pen with long writing, as well as the Confidence we have of our Readers Collective Abili∣ties, inclining us to all possible brevity, we judge it sufficient onely to advertise, that what we have formerly said, concerning the Aptitude and Ineptitude of Bodies to Projection, hath anticipated that Disquisition. For, certain it is, in the General, that such Bodies, which are More Compact, Cohaerent, and Hard, as they may be, with more vehemence, and to greater distance, Projected: so may they, with more vehemence, and to greater distance Rebound, or be Reflected; provided, they be impinged against other bodies

of requisite Compactness, Cohaerence, and Hardness. And, the Reason, why a Tennis-ball doth make a far greater Rebound, than a Globe of Brass, of the same magnitude, and thrown with equal force; is onely this, that there is not a proportion be∣twixt the Force imprest by the Projicient, and the Gravity of each of them; or betwixt the Gravity of each, and the Resistence of the Plane. Which holds true also concerning other bodies, of dif∣ferent Contextures.

Notes

• * 1.1

  Art. 1. What, and whence is that Force, or Vir∣tue Motive, whereby Bo∣dies Projected are carried on after their Dismission from the Pro∣jicient.
• * 1.2

  Art. 2. The Manner of the Impression of that Force▪
• * 1.3

  Art. 3. That all Moti∣on, in a free or Empty space, must be Vniform, and Perpetual: and that the chief Cause of the Inequality and Brevity of the motion of things project∣ed through the Atmosphere, is the magne∣tique Attracti∣on of the Earth.
• * 1.4

  Art. 4. That, in the Atmosphere, no body can be projected in a Direct line; unless perpendicu∣larly Upward, o•• Downward: and why.
• * 1.5

  Art. 5. That the Mo∣tion of a stone pro••ected up∣wards ob∣liquely, is Composed of an H••••iz••••tal and Perpendi∣••ular together.
• * 1.6

  Art. 6. Demonstrati∣on of that Composition.
• * 1.7

  Art. 7. That of the two different Forces, impres∣sed upon a ball, thrown upward from the hand of a man standing in a ship, that is under sayl; the one doth not destroy the other▪ but each attain•• its proper scope.
• * 1.8

  Art. 8. T••at the space of time, in w••i••h the ••all is A••cending f••om the F 〈…〉〈…〉 the Top of the M••st; is equal to that, in which it is again Descend∣ing from the top to the ••oot.
• * 1.9

  Art. 9. 〈…〉〈…〉.
• * 1.10

  Art. 10. The Reason and Manner of the Reflexion or Rebounding motion of Bo∣dies, diverted from the line of their di∣rection by o∣thers encoun∣tring them.
• * 1.11

  Art. 11. That the ••mer∣si••n of a weight appen••••d to a 〈…〉〈…〉 the perpendicular, 〈◊〉〈◊〉 which it had ••••duced it self, in Vibration; 〈◊〉〈◊〉 a R••flexion 〈◊〉〈◊〉 betwixt 〈◊〉〈◊〉 Reflexion at all, and the Least Reflexion assignable; and the R••le of all other Reflexion whatever.
• * 1.12

  Art. 12. ••he ••ea••••n of the Ae••ualit•• of the Angles of In••iden••e and R••••l••xi••n.
• * 1.13

  Art. 13. Two Inferen∣ces from the praea••ses▪ viz. (1) That the oblique Proje∣ction of a Globe against a plane, is composed of a double Paral∣lel: and (2) That Nature suffers no di∣minution of her right to the shortest way, by Refle∣xion.
• * 1.14

  Art. 14. Wherein the Aptitude or In∣e••••itude of bo∣dies to Re∣fle••ion doth consist.