Oeuvres complètes. Tome VI. Correspondance 1666-1669

N^o 1747.
W. Neile à Christiaan Huygens.
Appendice au No. 1746.
Juin 1669.

La pièce se trouve à Leiden, coll. Huygens.

Theory concerning Motion proposed by William Neile Esq.

Let there be 2. Equal Cubes, A and B, (which I instance in only for better Explanation). Let these Cubes be without any Interstices of vacuity, and without any Intestine Motion in their particles. Suppose, ye 2 Cubes to move one against ye other with Equal Velocity, so as one whole Square side of ye noe may be fully apply'd to one whole Square side of ye other at ye same Instant of time. At their Concourse they shall both cease to move (suppose A to come from ye right hand, and B. from ye left.) Either they must cease to move, or both be reflected, as is manifest enough. Now if A. giue a motion to B, A must at ye same time move a litle towards ye left hand, yt is to say, must goe along with B a litle yt way: For if we should suppose A. to stopp, when it comes to touch B. and not

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to proceed forward, there would be no reason, why it should give a motion



¹⁾ to B, for, why should B. goe out of its place, when nothing presses vpon it. Now if A. at ye time of Concourse be allow'd to move a litle to ye left hand, it follows, because ye Case is alike between both Cubes, that B must at ye same time move a litle to ye right hand for the like reason. But B. was before suppos'd to move at yt time to ye left hand, which two things are inconsistent. Therefore ye motion of both the Cubes will cease at ye time of their Concourse.

1) Ces ronds désignent les cubes du texte.

2.

Now suppose A. to move with ye greater Velocity and B. with the lesse, yet both their motions will cease at their Concourse. For B. shall either haue some effect towards ye stopping of A, or else no velocity whatsoeuer shall be able to stopp it, because ye greatest velocity is but ye velocity of B. severall times multiply'd. But if B. leave off moving towards ye right hand at ye time when it comes to touch A, there will be no reason, why B. should haue any effect upon A; Jt follows therefore, yt B. at ye time of Concourse must move a litle towards ye right hand. But for ye like reason A. shall at ye same time driue B. a little towards ye left hand; consequently B. must move two ways at once; which is impossible. Therefore both the motions will stopp at ye time of Concourse.

For ye like reasons it will follow, that any different motions meeting together will stopp one another, though they were not directly opposite.

3.

Now suppose A to move against B. quiscent, after ye appulse of A to B; both A and B will move to ye left hand with ye same velocity as A. had before (supposing no other Body to act vpon ym). For if A doe not move B. a litle, no velocity will be able to move it. Now if B. can giue no hindrance to ye motion of A, the motion of A will continue; but B being at rest hath no power of acting upon A; for, if it haue any power of acting upon A, this power is not motion, because B is quiscent; it can at ye most be but said to be propensity to motion: But B. being quiescent, there is no reason why it should haue a propensity to mo-

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tion one way more than to motion another way; and it can't haue a propensity to motion every way at once. Therefore B hath no power of acting upon A; consequently ye motion of A will continue (there being no reason, why it should stop itself,) and consequently B. will be driuen before it with ye same velocity, which A had before, yt is to say, A will propagate its motion to B. or generate ye like in B, without transmission of any thing into it.

If A ouertake B. being already in motion, ye same way it cannot be suppos d to haue lesse power to driue A before it, than in ye former case; but A hath no power to giue B a greater velocity than A had itself before, nor hath B. any power to augment its owne velocity.

4.

From the preceding Principles it follows, That whereuer there is resistance or reaction, there is motion; for if ye matter were quiescent, there would be no resistance to motion, but it would be driuen along with ye impellent matter. Now because all Bodies, which we haue knowledge of, haue resistance more or lesse, and haue resistance alike every way, yt is, have their parts every where alike dispos'd to make a resistance: As one part of Air is alike dispos'd to make resistance as another part of Air, and one part of wood as another part of ye same wood (it being generally so as to appearance;) which is all I require; it will follow from hence, yt there is an innumerable variety of motions in ye small particles of all Bodies, which is ready to oppose any External impulse, yt shall happen to ym, wheresoeuer they are struck, they haue a resistance; which inferrs a different motion in ym from ye motion of ye Impellent; And this resistance working every way, inferrs almost an insinite variety of motion in ye particles, which in firme Bodies are so close sett to one another, as they cannot extricate ymselues from one another by this variety of motion, which hinders ye dissolution of ye Body and also hinders ye transferring of it any way by this intestine motion of ye particles without an external cause.

5.

The Intestin motion of ye Particles must by ye preceding Rules be perform'd with intervals of rest; for where different motions meet, they will stopp one another, and where motion meets with quiescent matter, it will beget new motion in it: suppose the Body A to consist of innumerable litle particles variously moving according to ye foremention'd Rules; these particles are not invariably ye same, but grow sometimes bigger by accretion one to another, and sometimes lesse by

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separation of parts, according as motion sometimes unites and sometimes divides ym. Neverthelesse for better Explication, I will call ye particles litle a's: Now take any assignable litle a, in ye whole Body A, and it will follow from this, almost infinite, variety of motion in ye particles, yt ye litle a assigned will in an inconsiderable space of time be mov'd to ye right hand, and left, upwards and downwards, and every way imaginable, and yet haue intervals of quiet, and yet neuer stir considerably all ye while from ye first place. This I concieue to be ye manner of ye motion of ye litle a's, when the whole body A seems quiescent; which neuerthelesse may loose something by effluvia, and admit something from extraneous bodies in ye mean time.

6.

Now if we shall suppose, yt these litle a's are carried considerably oftner forward than any other way, or with greater velocity forward, than any other way, and with fewer or lesse during intervals of quiet than they had before; it will follow, yt in a short space of time ye whole body A will be transferr'd forwards, according to ye Rules of ye preceding Principles, with intervals of Rest in its particles: And as it may be mov'd forwards, so it may in like manner be turn'd backwards or any way, and yet no such thing really in ye world as Reflexion, but only perpetual Pulsion of Bodies, with Intervals of Rest.

I think it is not to be exspected, that one should make a Microscope so as to be able to see ye motions and stopps of these litle a's without which ye verity of this doctrine is not to be exhibited to sense.

7.

Now suppose A and B to be Cubes, yt haue intestin motion in their particles, and yt (all things alike) A strike against B. quiescent: ye foremost parts of A, which come to touch B, communicate as much motion to ye outermost parts of B, as ye hinder parts in ye Body A. had before communicated to ym, and this pressure made by ye outermost parts of A is seconded and backed by ye succeeding hinder parts of A; and as ye motion was thus communicated through ye parts of A, so it shall be communicated through ye parts of B, and being seconded by ye motion of as many parts as equal ye Bulk of B, there is no reafon but A. shall move B with ye same velocity, with which A itselfe mov'd, because ye foremost parts of B will haue as much reason to move; as ye foremost parts of A: And there being suppos'd nothing before B. to stopp it, it will follow, yt B. will be driuen out of its place with ye same velocity as A had before, but ye hindermost parts of

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B. will be repelled mto ye place, they held afore in respect of ye Body B; and the swifter they are impell'd ye sooner they meet with sufficient opposition: Therefore they must be repell'd with ye same velocity as they are impell'd, and consequently ye particles of B. react upon A. with ye same velocity, as A hath.

8.

And this Reaction being of ye same velocity, which A hath, and being seconded by a Bulk equal to A; A. hath no more reason to move forwards than backwards, and consequently must stand still; ye reacting and restitutive motion in ye parts of B. being oppos'd by ye like power of Reaction in A. But if B. were suppos'd to be in ye like motion to ye right hand, as A. was in, to ye left hand, then there will be a new cause to overcome ye restitutive or reacting power of A, and consequently A will return back with ye same velocity, as it had before. But for ye like reason, as A will return back, for ye like reason B will return back with the same velocity, the Case being alike between both Cubes. So yt the Case stands thus; A looseth its velocity by ye Elastick power of B, and gaines it again from ye velocity of B, and B does also ye like from the velocity of A.

In like manner it will happen, and for the like reasons, what euer the velocity's of A and B were, yt is, in all Cases, where A and B. are equall, they will make an Exchange of their velocity's, yt is to say, A. will return with ye velocity, which B had before; and B. will return with ye same velocity, as A had before.

9.

Jf the Bulk of ye Body A. were suppos'd to be doubled, and the velocity, with which it moues ye same as before, it will follow, that twice the Quantity of particles are mou'd forward together at ye same time in ye double A, as were before in ye simple A; otherwise the whole double Body would not be transferr'd in ye same time with ye whole single Body, because they are both suppos'd to move with the same swiftnesse. And if ye single Body A. move with double ye velocity to what it had before, the particles will move with double ye swiftnesse. But double ye swiftnesse and double ye quantity of particles haue equall power of impulsion upon one another. Therefore velocity and Body Bulke are equivalent one to another; because what ye swiftnesse of motion does in ye one, ye number of particles moving together forward at ye same time does in ye other; therefore it is all one, whether ye velocity or bulk be increased, as to ye power of moving,

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unlesse it be, yt ye figure of ye Bodys makes an alteration, which may cause a difference in ye Communication of motion to ye small particles, as when a Bullet or Arrow pierces a Body of a very broad superficies, and ye more velocity it hath, ye more it will pierce it.

10.

If ye power of single A moving be 1.; ye power of double A moving with double ye velocity, will be 2. because there is double the swiftnesse back'd by double ye number of particles. Therefore ye cause being doubled, ye Effect will be doubled. But ye power of double A moving with double ye velocity is equal to ye power of quadruple A. moving with single velocity. Therefore ye power of quadruple A. moving with single velocity is 2, and ye power of single A moving with single ye velocity is 1; which is but sub-duplicate to ye proportion of ye Magnitudes. Therefore ye moving power increaseth only in sub-duplicate proportion to ye proportion of ye increase of the magnitudes. The like may be said, if ye velocity only were increased and not ye magnitudes. For ye like reason the Resisting or Elastick power of a Body quiescent will increase in sub-duplicate ye proportion to ye increase of ye magnitudes, because ye cause of resistance comes from ye intestine motion of ye particles, and from the number of ye particles. Therefore double A. quiescent, if it had also double the swiftnesse in ye intestine motion of ye particles, would haue double ye power of resisting: But quadruple A. quiescent hath ye same power without increasing ye swiftnesse of ye intestine motion: therefore the power of quadruple A quiescent, is to ye power of single A quiescent, as 2. to 1.