Seven philosophical problems and two propositions of geometry by Thomas Hobbes of Malmesbury ; with an apology for himself and his writings.

CHAP. VII. Problems of Motion Perpendicular, Ob∣lique; of Pression and Percussion; Re∣flection and Refraction; Attraction and Repulsion. (Book 7)

IF a Bullet from a certain point given, be shot against a wall Perpendicularly and again from the same Point Oblique, What will be the proportion of the Forces wherewith they urge the wall?

For Example, let the wall be A B, a point given E, a Gun C E that carries the Bullet Perpendicularly to F, and another Gun D E that carries the like Bullet with the same swiftness Oblique to G; In what proportion will their Forces be upon the Wall?

B.

The force of the stroke Perpendi∣cular from E to F will be greater then

the Oblique force from E to G, in the proportion of the line E G to the line E F.

A.

How can the difference be so much? Can the Bullet lose so much of its force in the way from E to G?

B.

No we will suppose it loseth no∣thing of its swiftness. But the cause is, That their swiftness being equal, the one is longer in coming to the wall then the other, in Proportion of Time, as E G to E F. For though their swiftness be the same▪ considered in themselves, yet the swiftness of their approach to the wall is greater in E F then in E G, in proportion of the lines themselves.

A.

When a Bullet enters not, but re∣bounds from the wall, does it make the same Angle going off, which it did falling on, as the Sun-beams do?

B.

If you measure the Angles close by the wall there difference will not be ensible; otherwise it will be great e∣nough, For the Motion of the Bullet grows continually weaker. But it is not so with the Sun-beams which press con∣tinually and equally.

A.

What is the cause of Reflection? When a body can go no further on, it has lost its Motion. Whence then comes the Motion by which it reboundeth?

B.

This Motion of rebounding or re∣flecting proceedeth from the resistance. There is a difference to be considered between the Reflection of Light, and of a Bullet, answerable to their different Motions, pressing and striking. For the action which makes Reflection of Light, is the Pressure of the Air upon the Re∣flecting Body, caused by the Sun, or o∣ther shining body, and is but a contra∣ry endeavour; as if two men should press with their breasts upon the two ends of a Staff, though they did not remove one another, yet they would find in themselves a great disposition to press backward upon whatsoever is behind them, though not a total going out of their places. Such is the way of Reflect∣ing Light. Now, when the falling on of the Sun-beams is Oblique, the action of them is nevertheless Perpendicular to the Superficies it falls on. And therefore the Reflecting Body, by resisting, turneth back that Motion Perpendicularly, as from F to E, but taketh nothing from the force that goes on parallel in the line of E H; because the Motion never presses. And thus of the two Motions from F to E, and from E to H is a com∣pounded Motion in the line F H, which maketh an Angle in B G, equal to the Angle F G E.

But in Percussion (which is the Mo∣tion of the Bullet against a wall,) the Bullet no sooner goeth off then it loseth of its swiftness, and inclineth to the Earth by its weight. So that the Angles made in falling on and going off, cannot be equal, unless they be measured close to the point where the stroke is made.

A.

If a man set a Board upright upon its edge, though it may very easily be cast down with a little Pressure of ones finger, yet a Bullet from a Musquet shall not throw it down but go through it. What is the cause of that?

B.

In pressing with your finger you spend time to throw it down. For the Motion you give to the part you touch is communicated to every other part before it fall. For the whole cannot fall till every part be moved. But the stroke of a Bullet is so swift, as it breaks through before the Motion of the part it hits can be communicated to all the other parts that must fall with it.

A.

The stroke of a Hammer will drive a Nail a great way into a piece of Wood on a sudden. What weight laid upon the head of a Nail, and in how much time will do the same? It is a question I have heard propounded amonst Naturalists,

B.

The different manner of the ope∣ration

of weight from the operation of a stroke, makes it uncalculable. The suddenness of the stroke upon one point of the wood takes away the time of re∣sistance from the rest. Therefore the Nail enters so far as it does. But the weight not only gives them time, but also aug∣ments the resistance; but how much, and in how much time, is (I think) im∣possible to determine.

A.

What is tbe difference between Re∣flection and Recoiling?

B.

Any Reflection may (and not un∣properly) be called recoiling; but not contrariwise every Recoiling Reflection. Reflection is always made by the Re-acti∣on of a Body prest or stricken; but Re∣coiling not always. The Recoiling of a Gun is not caused by its own pressing up∣on the Gun-powder, but by the force of the Powder it self, inflamed and moved every way alike:

A.

I had thought it had been by the sudden re-entring of the Air after the flame and Bullet were gone out. For it is impossible that so much room as is left empty by the discharging of the Gun, should be so sud∣denly filled with the Air that entereth at the Touch-hole.

B.

The flame is nothing but the Pow∣der it self, which scattered into its smal∣lest

parts seems, of greater bulk by much, then in truth it is, because they shine. And as the parts scatter more and more, so still more Air gets between them, en∣tring not only at the Touch-hole, but al∣so at the mouh of the Gun. which two ways being opposite, it will be much too weak to make the Gun Recoil.

A.

I have heard that a great Gun char∣ged too much or too little, will Shoot (not above, nor below but) besides the mark; and charged with one certain charge be∣tween both will hit it.

B.

How that should be I cannot ima∣gine. For when all things in the cause are equal, the effects cannot be unnequal. As soon as Fire is given, and before the Bul∣let be out, the Gun begins to Recoil. If then there be any unevenness or rub in the ground more on one side then on the other, it shall shoot besides the mark, whether too much, or too little, or justly charged; because if the line wherein the Gun Recoileth decline, the way of the Bullet will also decline to the contrary side of the mark. Therefore I can ima∣gine no cause of this event, but either in the ground it Recoils on, or in the une∣qual weight of the parts of the Breech.

A.

How comes Refractin?

B.

When the action is in a line Per∣pendicular

to the superficies of the Body wrought upon, there will be no Refracti∣on at all. The action will proceed still in the same straight Line, whether it be Pres∣sion as in Light, or in Percussion as in the shooting of a Bullet. But when the Pression is Oblique, then will the Refraction be that way which the Na∣ture of the Bodies through which the Action proceeds shall determin.

H.

How is light Refracted?

B.

If is pass through a Body of less, into a Body of greater resistance, and to the Point of the Superficies it falleth on, you draw a Line Perpen∣dicular to the same superficies, the Action will proceed not in the same Line by which it fell on, but in another Line bending toward that Perpen∣diculare.

A.

What is the reason of that?

B.

I told you before, that the falling on worketh only in the Perpendicular; But as soon as the Action proceedeth fur∣ther inward then a meer touch, it worketh partly in the Perpendicular, and partly forward, and would proceed in the same line in which it fell on, but for for the greater resistance which now weakneth the Motion forward, and makes it to incline towards the Perpen∣dicular.

A.

In transparent Bodies it may be so; but there be Bodies through which the Light cannot pass at all.

B.

But the Action by which Light is made, passeth through all Bodies. For this Action is Pression; and whatsoever is prest, presseth that which is next be∣hind, and so continually. But the cause why there is no Light seen through it, is the uneveness of the parts within, whereby the Action is by an infinite number of Reflections so diverted and weakned, that before it hath proceeded through, it hath not strength left towork upon the Eye strongly enough to produce sight.

A.

If the Body being transparent the Acti∣on proceed quite through, into a Body again of less resistance, as out of Glass into the Air, which way shall it then proceed in the Air?

B.

From the Point where it goeth forth, draw a Perpendicular to the su∣perficies of the Glass, the Action now freed from the resistance it suffered, will go from that Perpendicular, as much as it did before come towards it.

A.

When a Bullet from out of the Air entreth into a Wall of Earth, will that al∣so be Refracted towards the Perpendicu∣lar?

B.

If the Earth be all of one kind, it will. For the parallel Motion, will there also at the first entrance be resisted, which it was not before it entred.

A.

How then comes a Bullet, when shot very Obliquely into any broad Water, and having entred, yet to rise, again into the Air?

B.

When a Bullet is shot very Ob∣liquely, though the Motion be never so swift, yet approach downwards to the Water is very slow, and when it cometh to it, it casteth up much Wa∣ter before it, which with its weight presseth downwards again, and maketh the Water to rise under the Bullet with force enough to master the weak Moti∣on of the Bullet downwards, and to make it rise in such manner as Bodies use to rise by Reflection.

A.

By what Motion (seeing you ascribe all Effects to Motion) can a Load-stone draw Iron to it?

B.

By the same Motion hitherto sup∣posed. But though all the smallest parts of the Earth have this Motion, yet it is not supposed that their Motions are in equal Circles; nor that they keep just time with one another; nor that they have all the same Poles. If they had, all Bodies would draw one another

alike. For such an agreement of Moti∣on, of Way, of Swiftness, of Poles, cannot be maintained without the con∣junction of the Bodies themselves in the Center of their common Motion, but by violence.

If therefore the Iron have but so much of the Nature of the Load-stone as re∣dily to receive from it the like Motion, as one String of a Lute doth from another String strained to the same Note (as it is like enough it hath, the Load-stone being but one kind of Iron Ore) it must needs after that Motion received from it, (unless the greatness of the weight hinder) come nearer to it, be∣cause at distance their Motions will differ in time, and oppose each other where∣by they will be forced to a common Cen∣ter. If the Iron be lifted up from the Earth, the Motion of the Load-stone must be stronger, or the Body of it near∣er, to overcome the Weight; and then the Iron will leap up to the Load-stone as as Swiftly as from the same distance, it would fall down to the Earth; but if both the Stone and the Iron be set float∣ing upon the Water, the attraction will begin to be manifest at a greater distance, because the hindrance of the weight is in part removed.

A.

But why does the Load-stone if it float on a Calm Water, never fail to place it self at last in the Meridian just North and South.

B.

Not so, just in the Meridian, but almost in all places with some variations. But the cause I think is, that the Axis of this Magnetical Motion is parallel to the Axis of the Ecliptique, which is the Ax∣is of the like Motion in the Earth, and consequently that it cannot freely exercise its Natural Motion in any other Scituation.

A.

Whence may this consent of Motion in the Load-stone and the Earth proceed? Do you think (as some have written) that the Earth is a great Load-stone?

B.

Dr. Gilbert that was the first that wrote any thing of this Subject ration∣ally, inclines to that opinion. Decartes thought the Earth (excepting this upper crust of a few Miles depth) to be of the same Nature with all other Stars, and bright. For my part I am content to be ignorant; but I believe the Load stone hath given its virtue by a long habitude in the Mine, the Vein of it lying in the plain of some of the Meridians, or ra∣ther of some of the great Circles that pass through the Poles of the Ecliptique, which are the same with the Poles of

the like Motion supposed in the Earth.

A.

If that be true▪ I need not ask why the filings of Iron laid on a Load-stone equally distant from its Poles will lie paral∣lel to the Axis, but one each side incline to the Pole that is next it. Nor why by drawing a Load-ston all a long a Needle of Iron, the Needle will receive the same Poles Nor why when the Load-stone and Iron (or two Load-stones) are put together floating upon Water, will fall one of them a Stern of the other, that their like parts may look the same way, and their unlike touch, in which Action they are commonly said to Repel one another. For all this may be deriv'd from the union of their Motions. One thing more I desire to know, and that is; What are those things they call Spirits? I mean Ghosts, Fairies, Hobgoblins, and the like Apparitions.

B.

They are no part of the Subject of Natural Philosophy.

A.

That which in all Ages, and all places is commonly seen (as those have been, un∣less a great part of Mankind by Lyers) cannot, I think, be supernatural.

B.

All this that I have hitherto said, though upon better ground than can be had for a discourse of Ghosts, you ought to take but for a Dream.

A.

I do so. But there be some Dreams more like sense then others. And that which is like sense pleases me as well (in natural Philosophy) as if it were the very truth.

B.

I was Dreaming also once of these things; but was weakened by their noise. And they never came into any Dream of mine since, unless Apparitionrs in Dreams and Ghoasts be all one.