CHAPTER I.

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THE

ENGLISH WORKS

OF

THOMAS HOBBES

OF MALMESBURY;

NOW FIRST COLLECTED AND EDITED

BY

SIR WILLIAM MOLESWORTH, BART.

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VOL. VII.

-------

LONDON:

LONGMAN, BROWN, GREEN, AND LONGMANS,

PATERNOSTER-ROW.

--

MDCCCXLV.

LONDON:

RICHARDS, PRINTER, 100, ST. MARTIN’S LANE.

CONTENTS.

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PAGE

SEVEN PHILOSOPHICAL PROBLEMS 1

DECAMERON PHYSIOLOGICUM 69

PROPORTION OF A STRAIGHT LINE TO HALF THE ARC OF A QUADRANT 178

SIX LESSONS TO THE SAVILIAN PROFESSORS OF THE MATHEMATICS 181

ΣΤΙΓΜΑΙ, OR MARKS OF THE ABSURD GEOMETRY ETC. OF DR. WALLIS 357

EXTRACT OF A LETTER FROM HENRY STUBBE 401

THREE PAPERS PRESENTED TO THE ROYAL SOCIETY AGAINST DR. WALLIS 429

CONSIDERATIONS ON THE ANSWER OF DR. WALLIS 443

LETTERS AND OTHER PIECES 449

SEVEN

PHILOSOPHICAL PROBLEMS

AND

TWO PROPOSITIONS OF GEOMETRY.

BY

THOMAS HOBBES

OF MALMESBURY.

WITH

AN APOLOGY FOR HIMSELF AND HIS WRITINGS.

DEDICATED TO THE KING IN THE YEAR 1662.

TO THE KING.

That which I do here most humbly present to your sacred Majesty, is the

best part of my meditations upon the natural causes of events, both of

such as are commonly known, and of such as have been of late

artificially exhibited by the curious.

They are ranged under seven heads. 1. Problems of gravity. 2. Problems

of tides. 3. Problems of vacuum. 4. Problems of heat. 5. Problems of

hard and soft. 6. Problems of wind and weather. 7. Problems of motion

perpendicular and oblique, &c. To which I have added two propositions of

Geometry: one is, the duplication of the cube, hitherto sought in vain;

the other, a detection of the absurd use of arithmetic, as it is now

applied to geometry.

The doctrine of natural causes hath not infallible and evident

principles. For there is no effect which the power of God cannot produce

by many several ways.

But seeing all effects are produced by motion, he that supposing some

one or more motions, can derive from them the necessity of that effect

whose cause is required, has done all that is to be expected from

natural reason. And though he prove not that the thing was thus

produced, yet he proves that thus it may be produced when the materials

and the power of moving are in our hands: which is as useful as if the

causes themselves were known. And notwithstanding the absence of

rigorous demonstration, this contemplation of nature (if not rendered

obscure by empty terms) is the most noble employment of the mind that

can be, to such as are at leisure from their necessary business.

This that I have done I know is an unworthy present to be offered to a

king: though considered, as God considers offerings, together with the

mind and fortune of the offerer, I hope will not be to your Majesty

unacceptable.

But that which I chiefly consider in it is, that my writing should be

tried by your Majesty’s excellent reason, untainted with the language

that has been invented or made use of by men when they were puzzled; and

who is acquainted with all the experiments of the time; and whose

approbation, if I have the good fortune to obtain it, will protect my

reasoning from the contempt of my adversaries.

I will not break the custom of joining to my offering a prayer; and it

is, that your Majesty will be pleased to pardon this following short

apology for my _Leviathan_ . Not that I rely upon apologies, but upon

your Majesty’s most gracious general pardon.

That which is in it of theology, contrary to the general current of

divines, is not put there as my opinion, but propounded with submission

to those that have the power ecclesiastical.

I did never after, either in writing or discourse, maintain it.

There is nothing in it against episcopacy; I cannot therefore imagine

what reason any episcopal man can have to speak of me, as I hear some of

them do, as of an atheist, or man of no religion, unless it be for

making the authority of the Church wholly upon the regal power; which I

hope your Majesty will think is neither atheism nor heresy.

But what had I to do to meddle with matters of that nature, seeing

religion is not philosophy, but law?

It was written in a time when the pretence of Christ’s kingdom was made

use of for the most horrid actions that can be imagined; and it was in

just indignation of that, that I desired to see the bottom of that

doctrine of the kingdom of Christ, which divers ministers then preached

for a pretence to their rebellion: which may reasonably extenuate,

though not excuse the writing of it.

There is therefore no ground for so great a calumny in my writing. There

is no sign of it in my life; and for my religion, when I was at the

point of death at St. Germain’s, the Bishop of Durham can bear witness

of it, if he be asked. Therefore I most humbly beseech your sacred

Majesty not to believe so ill of me upon reports, that proceed often,

and may do so now, from the displeasure which commonly ariseth from

difference in opinion; nor to think the worse of me, if snatching up all

the weapons to fight against your enemies, I lighted upon one that had a

double edge.

Your Majesty’s poor and

most loyal subject,

THOMAS HOBBES.

==========

[Illustration: _Seven Philosophical Problems. English Works, Vol. 7._]

PHILOSOPHICAL PROBLEMS.

---

CHAPTER I.

PROBLEMS OF GRAVITY.

_A._ What may be the cause, think you, that stones and other bodies

thrown upward, or carried up and left to their liberty, fall down again,

for aught a man can see, of their own accord? I do not think with the

old philosophers, that they have any love to the earth; or are sullen,

that they will neither go nor stay. And yet I cannot imagine, what body

there is above that should drive them back.

_B._ For my part, I believe the cause of their descending is not in any

natural appetite of the bodies that descend; but rather that the globe

of the earth hath some special motion, by which it more easily casteth

off the air than it doth other bodies. And then this descent of those we

call heavy bodies must of necessity follow, unless there be some empty

spaces in the world to receive them. For when the air is thrown off from

the earth, somewhat must come into the place of it, in case the world be

full: and it must be those things which are hardliest cast off, that is,

those things which we say are heavy.

_A._ But suppose there be no place empty, (for I will defer the question

till anon), how can the earth cast off either the air or anything else?

_B._ I shall show you how, and that by a familiar example. If you lay

both your hands upon a basin with water in it, how little soever, and

move it circularly, and continue that motion for a while; and you shall

see the water rise upon the sides, and fly over. By which you may be

assured that there is a kind of circulating motion, which would cast off

such bodies as are contiguous to the body so moved.

_A._ I know very well there is; and it is the same motion which country

people use to purge their corn; for the chaff and straws, by casting the

grain to the sides of the sieve, will come towards the middle. But I

would see the figure.

_B._ Here it is. There is a circle pricked out, whose centre is A, and

three less circles, whose centres are B, C, D. Let every one of them

represent the earth, as it goeth from B to C, and from C to D, always

touching the uttermost circle and throwing off the air, as is marked at

E and F. And if the world were not full, there would follow by this

scattering of the air, a great deal of space left empty. But supposing

the world full, there must be a perpetual shifting of the air, one part

into the place of another.

_A._ But what makes a stone come down, suppose from G?

_B._ If the air be thrown up beyond G, it will follow that at the last,

if the motion be continued, all the air will be above G, that is, above

the stone; which cannot be, till the stone be at the earth.

_A._ But why comes it down still with increasing swiftness?

_B._ Because as it descends and is already in motion, it receiveth a new

impression from the same cause, which is the air, whereof as part

mounteth, part also must descend, supposing as we have done the

plentitude of the world. For, as you may observe by the figure, the

motion of the earth, according to the diameter of the uttermost circle,

is progressive; and so the whole motion is compounded of two motions,

one circular and the other progressive; and consequently the air ascends

and circulates at once. And because the stone descending receiveth a new

pressure in every point of its way, the motion thereof must needs be

accelerated.

_A._ It is true; for it will be accelerated equally in equal times; and

the way it makes will increase in a double proportion to the times, as

hath heretofore been demonstrated by Galileo. I see the solution now of

an experiment, which before did not a little puzzle me. You know that if

two plummets hang by two strings of equal length, and you remove them

from the perpendicular equally, I mean in equal angles, and then let

them go, they will make their turns and returns together and in equal

times; and though the arches they describe grow continually less and

less, yet the times they spend in the greater arches will still be equal

to the time they spend in the lesser.

_B._ It is true. Do you find any experiment to the contrary?

_A._ Yes; for if you remove one of the plummets from the perpendicular,

so as, for example, to make an angle with the perpendicular of eighty

degrees, and the other so as to make an angle of sixty degrees; they

will not make their turns and returns in equal times.

_B._ And what say you is the cause of this?

_A._ Because the arches are the spaces which these two motions describe,

they must be in double proportion to their own times: which cannot be,

unless they be let go from equal altitudes, that is, from equal angles.

_B._ It is right; and the experiment does not cross, but confirm the

equality of the times in all the arches they describe, even from ninety

degrees to the least part of one degree.

_A._ But is it not too bold, if not extravagant an assertion, to say the

earth is moved as a man shakes a basin or a sieve? Does not the earth

move from west to east every day once, upon its own centre; and in the

ecliptic circle once a year? And now you give it another odd motion. How

can all these consist in one and the same body?

_B._ Well enough. If you be a shipboard under sail, do not you go with

the ship? Cannot you also walk upon the deck? Cannot every drop of blood

move at the same time in your veins? How many motions now do you assign

to one and the same drop of blood? Nor is it so extravagant a thing to

attribute to the earth this kind of motion; but that I believe, if we

certainly knew what motion it is that causeth the descent of bodies, we

should find it either the same, or more extravagant. But seeing it can

be nothing above that worketh this effect, it must be the earth itself

that does it; and if the earth, then you can imagine no other motion to

do it withal but this. And you will wonder more, when by the same motion

I shall give you a probable account of the causes of very many other

works of nature.

_A._ But what part of the heaven do you suppose the poles of your

pricked circle point to?

_B._ I suppose them to be the same with the poles of the ecliptic. For,

seeing the axis of the earth in this motion and in the annual motion,

keeps parallel to itself, the axis must in both motions be parallel as

to sense. For the circle which the earth describes, is not of visible

magnitude at the distance it is from the sun.

_A._ Though I understand well enough how the earth may make a stone

descend very swiftly under the ecliptic, or not far from it, where it

throws off the air perpendicularly; yet about the poles of the circle

methinks, it should cast off the air very weakly. I hope you will not

say, that bodies descend faster in places remote from the poles, than

nearer to them.

_B._ No; but I ascribe it to the like motion in the sun and moon. For

such motions meeting, must needs cast the stream of the air towards the

poles; and then there will be the same necessity for the descent there,

that there is in other places, though perhaps a little more slowly. For

you may have observed, that when it snows in the south parts, the flakes

of snow are not so great as in the north: which is a probable sign they

fall in the south from a greater height, and consequently disperse

themselves more, as water does that falls down from a high and steep

rock.

_A._ It is not improbable.

_B._ In natural causes all you are to expect, is but probability; which

is better yet, than making gravity the cause, when the cause of gravity

is that which you desire to know; and better than saying the earth draws

it, when the question is, how it draws.

_A._ Why does the earth cast off air more easily than it does water, or

any other heavy bodies?

_B._ It is indeed the earth that casteth off that air which is next unto

it; but it is that air which casteth off the next air; and so

continually, air moveth air; which it can more easily do than any other

thing, because like bodies are more susceptible of one another’s

motions: as you may see in two lute-strings equally strained, what

motion one string being stricken communicates to the air, the same will

the other receive from the air; but strained to a differing note, will

be less or not at all moved. For there is no body but air, that hath not

some internal, though invisible, motion of its parts: and it is that

internal motion which distinguisheth all natural bodies one from

another.

_A._ What is the cause why certain squibs, though their substance be

either wood or other heavy matter, made hollow and filled with

gunpowder, which is also heavy; do nevertheless, when the gunpowder is

kindled, fly upwards?

_B._ The same that keeps a man that swims from sinking, though he be

heavier than so much water. He keeps himself up, and goes forward, by

beating back the water with his feet; and so does a squib, by beating

down the air with the stream of fired gunpowder, that proceeding from

its tail makes it recoil.

_A._ Why does any brass or iron vessel, if it be hollow, float upon the

water, being so very heavy?

_B._ Because the vessel and the air in it, taken as one body, is more

easily cast off than a body of water equal to it.

_A._ How comes it to pass, that a fish, (especially such a broad fish as

a turbot or a plaice, which are broad and thin), in the bottom of the

sea, perhaps a mile deep, is not pressed to death with the weight of

water that lies upon the back of it?

_B._ Because all heavy bodies descend towards one point, which is the

centre of the earth: and consequently the whole sea, descending at once,

does arch itself so, as that the upper parts cannot press the parts next

below them.

_A._ It is evident; nor can there possibly be any weight, as some

suppose there is, of a cylinder of air or water or any other liquid

thing, while it remains in its own element, or is sustained and inclosed

in a vessel by which one part cannot press the other.

==========

CHAPTER II.

PROBLEMS OF TIDES.

_A._ What makes the flux and reflux of the sea, twice in a natural day?

_B._ We must come again to our basin of water; wherein you have seen,

whilst it was moved, how the water mounteth up by the sides, and withal

goes circling round about. Now if you should fasten to the inside of the

basin some bar from the bottom to the top, you would see the water,

instead of going on, go back again from that bar ebbing, and the water

on the other side of the bar to do the same, but in counter-time; and

consequently to be highest where the contrary streams meet together; and

then return again, marking out four quarters of the vessel; two by their

meeting, which are the high waters; and two by their retiring, which are

the low waters.

_A._ What bar is that you find in the ocean that stops the current of

the water, like that you make in the basin?

_B._ You know that the main ocean lies east and west, between India and

the coast of America; and again on the other side, between America and

India. If therefore the earth have such a motion as I have supposed, it

must needs carry the current of the sea east and west: in which course,

the bar that stoppeth it, is the south part of America, which leaves no

passage for the water but the narrow strait of Magellan. The tide rises

therefore upon the coast of America; and the rising of the same in this

part of the world, proceedeth from the swelling chiefly of the water

there, and partly also from the North Sea; which lieth also east and

west, and has a passage out of the South Sea by the strait of Anian,

between America and Asia.

_A._ Does not the Mediterranean Sea lie also east and west? Why are

there not the like tides there?

_B._ So there are, proportionable to their lengths and quantity of

water.

_A._ At Genoa, at Ancona, there are none at all, or not sensible.

_B._ At Venice there are, and in the bottom of the straits, and a

current all along both the Mediterranean Sea and the Gulf of Venice: and

it is the current that makes the tides insensible at the sides; but the

check makes them visible at the bottom.

_A._ How comes it about that the moon hath such a stroke in the

business, as so sensibly to increase the tides at full and change?

_B._ The motion I have hitherto supposed but in the earth, I suppose

also in the moon, and in all those great bodies that hang in the air

constantly, I mean the stars, both fixed and errant. And for the sun and

moon, I suppose the poles of their motion to be the poles of the

equinoxial. Which supposed, it will follow (because the sun, the earth,

and the moon, at every full and change are almost in one straight line)

that this motion of the earth will then be made swifter than in the

quarters. For this motion of the sun and moon being communicated to the

earth, that hath already the like motion, maketh the same greater; and

much greater when they are all three in one straight line, which is only

at the full and change, whose tides are therefore called spring tides.

_A._ But what then is the cause that the spring tides themselves are

twice a-year, namely, when the sun is in the equinoxial, greater than at

any other times?

_B._ At other times of the year, the earth being out of the equinoxial,

the motion thereof, by which the tides are made, will be less augmented,

by so much as a motion in the obliquity of twenty-three degrees, or

thereabout, which is the distance between the equinoxial and ecliptic

circles, is weaker than the motion which is without obliquity.

_A._ All this is reasonable enough, if it be possible that such motions

as you suppose in these bodies, be really there. But that is a thing I

have some reason to doubt of. For the throwing off of air, consequent to

these motions, is the cause, you say, that other things come to the

earth; and therefore the like motions in the sun and moon and stars,

casting off the air, should also cause all other things to come to every

one of them. From whence it will follow, that the sun, moon, and earth,

and all other bodies but air, should presently come together into one

heap.

_B._ That does not follow. For if two bodies cast off the air, the

motion of that air will be repressed both ways, and diverted into a

course towards the poles on both sides; and then the two bodies cannot

possibly come together.

_A._ It is true. And besides, this driving of the air on both sides,

north and south, makes the like motion of air there also. And this may

answer the question, how a stone could fall to the earth under the poles

of the ecliptic, by the only casting off of air?

_B._ It follows from hence, that there is a certain and determinate

distance of one of these bodies, the stars, from another, without any

very sensible variation.

_A._ All this is probable enough, if it be true that there is no vacuum,

no place empty in all the world. And supposing this motion of the sun

and moon to be in the plain of the equinoxial, methinks that this should

be the cause of the diurnal motion of the earth; and because this motion

of the earth is, you say, in the plain of the equinoxial, the same

should cause also a motion in the moon on her own centre, answerable to

the diurnal motion of the earth.

_B._ Why not? What else can you think makes the diurnal motion of the

earth but the sun? And for the moon, if it did not turn upon its own

centre, we should see sometimes one, sometimes another face of the moon,

which we do not.

==========

CHAPTER III.

PROBLEMS OF VACUUM.

_A._ What convincing argument is there to prove, that in all the world

there is no empty place?

_B._ Many; but I will name but one; and that is, the difficulty of

separating two bodies hard and flat laid one upon another. I say the

difficulty, not the impossibility. It is possible, without introducing

vacuum, to pull asunder any two bodies, how hard and flat soever they

be, if the force used be greater than the resistance of the hardness.

And in case there be any greater difficulty to part them, besides what

proceeds from their hardness, than there is to pull them further asunder

when they are parted, that difficulty is argument enough to prove there

is no vacuum.

_A._ These assertions need demonstration. And first, how does the

difficulty of separation argue the plenitude of all the rest of the

world?

_B._ If two flat polished marbles lie one upon another, you see they are

hardly separated in all points at one and the same instant; and yet the

weight of either of them is enough to make them slide off one from the

other. Is not the cause of this, that the air succeeds the marble that

so slides, and fills up the place it leaves?

_A._ Yes, certainly. What then?

_B._ But when you pull the whole superficies asunder, not without great

difficulty, what is the cause of that difficulty?

_A._ I think, as most men do, that the air cannot fill up the space

between in an instant; for the parting is in an instant.

_B._ Suppose there be vacuum in that air into which the marble you pull

off is to succeed, shall there be no vacuum in the air that was round

about the two marbles when they touched? Why cannot that vacuum come

into the place between? Air cannot succeed in an instant, because a

body, and consequently cannot be moved through the least space in an

instant. But emptiness is not a body, nor is moved, but is made by the

act itself of separation. There is therefore, if you admit vacuum, no

necessity at all for the air to fill the space left in an instant. And

therefore, with what ease the marble coming off presseth out the vacuum

of the air behind it, with the same ease will the marbles be pulled

asunder. Seeing then, if there were vacuum, there would be no difficulty

of separation, it follows, because there is difficulty of separation,

that there is no vacuum.

_A._ Well, now, supposing the world full, how do you prove it possible

to pull those marbles asunder?

_B._ Take a piece of soft wax; do not you think the one half touches the

other half as close as the smoothest marbles? Yet you can pull them

asunder. But how? Still as you pull, the wax grows continually more and

more slender; there being a perpetual parting or discession of the

outermost part of the wax one from another, which the air presently

fills; and so there is a continual lessening of the wax, till it be no

bigger than a hair, and at last separation. If you can do the same to a

pillar of marble, till the outside give way, the effect will be the

same, but much quicker, after it once begins to break in the

superficies; because the force that can master the first resistance of

the hardness, will quickly dispatch the rest.

_A._ It seems so by the brittleness of some hard bodies. But I shall

afterward put some questions to you, touching the nature of hardness.

But now to return to our subject. What reason can you render (without

supposing vacuum) of the effects produced in the engine they use at

Gresham college?

_B._ That engine produceth the same effects that a strong wind would

produce in a narrow room.

_A._ How comes the wind in? You know the engine is a hollow round pipe

of brass, into which is thrust a cylinder of wood covered with leather,

and fitted to the cylinder so exactly as no air can possibly pass

between the leather and the brass?

_B._ I know it; and that they may thrust it up, there is a hole left in

the cylinder to let the air out before it, which they can stop when they

please. There is also in the bottom of the cylinder a passage into a

hollow globe of glass, which passage they can also open and shut at

pleasure. And at the top of that globe there is a wide mouth to put in

what they please to try conclusions on, and that also to be opened and

shut as shall be needful. It is of the nature of a pop-gun which

children use, but great, costly, and more ingenious. They thrust forward

and pull back the wooden cylinder (because it requires much strength)

with an iron screw. What is there in all this to prove the possibility

of vacuum.

_A._ When this wooden cylinder covered with leather, fit and close, is

thrust home to the bottom, and the holes in the hollow cylinder of brass

close stopped, how can it be drawn back, as with the screw they draw it,

but that the space it leaves must needs be empty: for it is impossible

that any air can pass into the place to fill it?

_B._ Truly I think it close enough to keep out straw and feathers, but

not to keep out air, nor yet matter. For suppose they were not so

exactly close but that there were round about a difference for a small

hair to lie between; then will the pulling back of the cylinder of wood

force so much air in, as in retiring it forces back, and that without

any sensible difficulty. And the air will so much more swiftly enter as

the passage is left more narrow. Or if they touch, and the contact be in

some points and not in all, the air will enter as before, in case the

force be augmented accordingly. Lastly, though they touch exactly, if

either the leather yield, or the brass, which it may do, to the force of

a strong screw, the air will again enter. Do you think it possible to

make two superficies so exquisitely touch in all points as you suppose,

or leather so hard as not to yield to the force of a screw? The body of

leather will give passage both to air and water, as you will confess

when you ride in rainy and windy weather. You may therefore be assured

that in drawing out their wooden leather cylinder, they force in as much

air as will fill the place it leaves, and that with as much swiftness as

is answerable to the strength that drives it in. The effect therefore of

their pumping is nothing else but a vehement wind, a very vehement wind,

coming in on all sides of the cylinder at once into the hollow of the

brass pipe, and into the hollow of the glass globe joined to it.

_A._ I see the reason already of one of their wonders, which is, that

the cylinder they pump with, if it be left to itself, after it is pulled

back, will swiftly go up again. You will say the air comes out again

with the same violence by reflection, and I believe it.

_B._ This is argument enough that the place was not empty. For what can

fetch or drive up the sucker, as they call it, if the place within were

empty? For that there is any weight in the air to do it, I have already

demonstrated to be impossible. Besides, you know, when they have sucked

out, as they think, all the air from the glass globe, they can

nevertheless both see through it what is done, and hear a sound from

within when there is any made; which, if there were no other, but there

are many other, is argument enough that the place is still full of air.

_A._ What say you to the swelling of a bladder even to bursting, if it

be a little blown when it is put into the receiver, for so they call the

globe of glass?

_B._ The streams of air that from every side meeting together, and

turning in an infinite number of small points, do pierce the bladder in

innumerable places with great violence at once, like so many invisible

small wimbles, especially if the bladder be a little blown before it be

put in, that it may make a little resistance. And when the air has once

pierced it, it is easy to conceive, that it must afterward by the same

violent motion be extended till it break. If before it break you let in

fresh air upon it, the violence of the motion will thereby be tempered,

and the bladder be less extended; for that also they have observed. Can

you imagine how a bladder should be extended and broken by being too

full of emptiness?

_A._ How come living creatures to be killed in this receiver, in so

little a time as three or four minutes of an hour?

_B._ If they suck into their lungs so violent a wind thus made, you must

needs think it will presently stop the passage of their blood; and that

is death; though they may recover if taken out before they be too cold.

And so likewise will it put out fire; but the coals taken out whilst

they are hot will revive again. It is an ordinary thing in many

coal-pits, whereof I have seen the experience, that a wind proceeding

from the sides of the pit every way, will extinguish any fire let down

into it, and kill the workmen, unless they be quickly taken out.

_A._ If you put a vessel of water into the receiver, and then suck out

the air, the water will boil; what say you to that?

_B._ It is like enough it will dance in so great a bustling of the air;

but I never heard it would be hot. Nor can I imagine how vacuum should

make anything dance. I hope you are by this time satisfied, that no

experiment made with the engine at Gresham College, is sufficient to

prove that there is, or that there may be vacuum.

_A._ The world you know is finite, and consequently, all that infinite

space without it is empty. Why may not some of that vacuum be brought

in, and mingled with the air here?

_B._ I know nothing in matters without the world.

_A._ What say you to Torricellio’s experiment in quicksilver, which is

this: there is a basin at A filled with quicksilver, suppose to B, and C

D a hollow glass pipe filled with the same, which if you stop with your

finger at B, and so set it upright, and then if you take away your

finger, the quicksilver will fall from C downwards but not to the

bottom, for it will stop by the way, suppose at D. Is it not therefore

necessary that that space between C and D be left empty? Or will you say

the quicksilver does not exactly touch the sides of the glass pipe?

_B._ I will say neither. If a man thrust down into a vessel of

quicksilver a blown bladder, will not that bladder come up to the top?

_A._ Yes, certainly, or a bladder of iron, or anything else but gold.

_B._ You see then that air can pierce quicksilver.

_A._ Yes, with so much force as the weight of quicksilver comes to.

_B._ When the quicksilver is fallen to D, there is so much the more in

the basin, and that takes up the place which so much air took up before.

Whither can this air go if all the world without that glass pipe B C

were full? There must needs be the same or as much air come into that

space, which only is empty, between C and D: by what force? By the

weight of the quicksilver between D and B. Which quicksilver weigheth

now upward, or else it could never have raised that part higher, which

was at first in the basin. So you see the weight of quicksilver can

press the air through quicksilver up into the pipe, till it come to an

equality of force as in D, where the weight of the quicksilver is equal

to the force which is required in air to go through it.

_A._ If a man suck a phial that has nothing in it but air, and presently

dip the mouth of it into water, the water will ascend into the phial. Is

not that an argument that part of the air had been sucked out, and part

of the room within the phial left empty?

_B._ No. If there were empty space in the world, why should not there be

also some empty space in the phial before it was sucked? And then why

does not the water rise to fill that? When a man sucks the phial he

draws nothing out, neither into his belly, nor into his lungs, nor into

his mouth; only he sets the air within the glass into a circular motion,

giving it at once an endeavour to go forth by the sucking, and an

endeavour to go back by not receiving it into his mouth; and so with a

great deal of labour glues his lips to the neck of the phial. Then

taking it off, and dipping the neck of the phial into the water before

the circulation ceases, the air, with the endeavour it hath now gotten,

pierces the water and goes out: and so much air as goes out, so much

matter comes up into the room of it.

==========

CHAPTER IV.

PROBLEMS OF HEAT AND LIGHT.

_A._ What is the cause of heat?

_B._ How know you, that any thing is hot but yourself?

_A._ Because I perceive by sense it heats me.

_B._ It is no good argument, the thing heats me; therefore it is hot.

But what alteration do you find in your body at any time by being hot?

_A._ I find my skin more extended in summer than in winter; and am

sometimes fainter and weaker then ordinary, as if my spirits were

exhaled; and I sweat.

_B._ Then that is it you would know the cause of. I have told you before

that by the motion I suppose both in the sun, and in the earth, the air

is dissipated, and consequently that there would be an infinite number

of small empty places, but that the world being full, there comes from

the next parts other air into the spaces they would else make empty.

When therefore this motion of the sun is exercised upon the superficies

of the earth, if there do not come out of the earth itself some corporal

substance to supply that tearing of the air, we must return again to the

admission of vacuum. If there do, then you see how by this motion fluid

bodies are made to exhale out of the earth. The like happens to a man’s

body or hand, which when he perceives, he says he is hot. And so of the

earth when it sendeth forth water and earth together in plants, we say

it does it by heat from the sun.

_A._ It is very probable, and no less probable, that the same action of

the sun is that which from the sea and moist places of the earth, but

especially from the sea, fetcheth up the water into the clouds. But

there be many ways of heating besides the action of the sun or of fire.

Two pieces of wood will take fire if in turning they be pressed

together.

_B._ Here again you have a manifest laceration of the air by the

reciprocal and contrary motions of the two pieces of wood, which

necessarily causeth a coming forth of whatsoever is aereal or fluid

within them, and (the motion pursued) a dissipation also of the other

more solid parts into ashes.

_A._ How comes it to pass that a man is warmed even to sweating, almost

with every extraordinary labour of his body?

_B._ It is easy to understand, how by that labour all that is liquid in

his body is tossed up and down, and thereby part of it also cast forth.

_A._ There be some things that make a man hot without sweat or other

evaporation, as caustics, nettles, and other things.

_B._ No doubt. But they touch the part they so heat, and cannot work

that effect at any distance.

_A._ How does heat cause light, and that partially, in some bodies more,

in some less, though the heat be equal?

_B._ Heat does not cause light at all. But in many bodies, the same

cause, that is to say, the same motion, causeth both together; so that

they are not to one another as cause and effect, but are concomitant

effects sometimes of one and the same motion.

_A._ How?

_B._ You know the rubbing or hard pressing of the eye, or a stroke upon

it, makes an apparition of light without and before it, which way soever

you look. This can proceed from nothing else but from the restitution of

the organ pressed or stricken, unto its former ordinary situation of

parts. Does not the sun by his thrusting back the air upon your eyes

press them? Or do not those bodies whereon the sun shines, though by

reflection, do the same, though not so strongly? And do not the organs

of sight, the eye, the heart, and brains, resist that pressure by an

endeavour of restitution outwards? Why then should there not be without

and before the eye, an apparition of light in this case as well as in

the other?

_A._ I grant there must. But what is that which appears after the

pressing of the eye? For there is nothing without that was not there

before; or if there were, methinks another should see it better, or as

well as he; or if in the dark, methinks it should enlighten the place.

_B._ It is a fancy, such as is the appearance of your face in a

looking-glass; such as is a dream; such as is a ghost; such as is a spot

before the eye that hath stared upon the sun or fire. For all these are

of the regiment of fancy, without any body concealed under them, or

behind them, by which they are produced.

_A._ And when you look towards the sun or moon, why is not that also

which appears before your eyes at that time a fancy?

_B._ So it is. Though the sun itself be a real body, yet that bright

circle of about a foot diameter cannot be the sun, unless there be two

suns, a greater and a lesser. And because you may see that which you

call the sun, both above you in the sky, and before you in the water,

and two suns, by distorting your eye, in two places in the sky, one of

them must needs be fancy. And if one, both. All sense is fancy, though

the cause be always in a real body.

_A._ I see by this that those things which the learned call the

accidents of bodies, are indeed nothing else but diversity of fancy, and

are inherent in the sentient, and not in the objects, except motion and

quantity. And I perceive by your doctrine you have been tampering with

_Leviathan_ . But how comes wood with a certain degree of heat to shine,

and iron also with a greater degree; but no heat at all to be able to

make water shine?

_B._ That which shineth hath the same motion in its parts that I have

all this while supposed in the sun and earth. In which motion there must

needs be a competent degree of swiftness to move the sense, that is, to

make it visible. All bodies that are not fluid will shine with heat, if

the heat be very great. Iron will shine and gold will shine; but water

will not, because the parts are carried away before they attain to that

degree of swiftness which is requisite.

_A._ There are many fluid bodies whose parts evaporate, and yet they

make a flame, as oil, and wine, and other strong drinks.

_B._ As for oil I never saw any inflamed by itself, how much soever

heated, therefore I do not think they are the parts of the oil, but of

the combustible body oiled that shine; but the parts of wine and strong

drinks have partly a strong motion of themselves, and may be made to

shine, but not with boiling, but by adding to them as they rise the

flame of some other body.

_A._ How can it be known that the particles of wine have such a motion

as you suppose?

_B._ Have you ever been so much distempered with drinking wine, as to

think the windows and table move?

_A._ I confess, though you be not my confessor, I have; but very seldom;

and I remember the window seemed to go and come in a kind of circling

motion, such as you have described. But what of that?

_B._ Nothing, but that it was the wine that caused it; which having a

good degree of that motion before, did, when it was heated in the veins,

give that concussion, which you thought was in the window, to the veins

themselves, and, by the continuation of the parts of man’s body, to the

brain; and that was it which made the window seem to move.

_A._ What is flame? For I have often thought the flame that comes out of

a small heap of straw to be more, before it hath done flaming, than a

hundred times the straw itself.

_B._ It was but your fancy. If you take a stick in your hand by one end,

the other end burning, and move it swiftly, the burning end, if the

motion be circular, shall seem a circle; if straight, a straight line of

fire, longer or shorter, according to the swiftness of the motion, or

the space it moves in. You know the cause of that.

_A._ I think it is, because the impression of that visible object, which

was made at the first instant of the motion, did last till it was ended.

For then it will follow that it must be visible all the way, the

impressions in all points of the time being equal.

_B._ The cause can be no other. The smallest spark of fire flying up

seems a line drawn upward; and again by that swift circular motion which

we have supposed for the cause of light, seems also broader than it is.

And consequently the flame of every thing must needs seem much greater

than it is.

_A._ What are those sparks that fly out of the fire?

_B._ They are small pieces of the wood or coals, or other fuel loosened

and carried away with the air that cometh up with them. And being

extinguished before their parts be quite dissipated into others, are so

much soot, and black, and may be fired again.

_A._ A spark of fire may be stricken out of a cold stone. It is not

therefore heat that makes this shining.

_B._ No it is the motion that makes both the heat and shining; and the

stroke makes the motion. For every of those sparks, is a little parcel

of the stone, which swiftly moved, imprinteth the same motion into the

matter prepared, or fit to receive it.

_A._ How comes the light of the sun to burn almost any combustible

matter by refraction through a convex glass, and by reflection from a

concave?

_B._ The air moved by the sun presseth the convex glass in such manner

as the action continued through it, proceedeth not in the same straight

line by which it proceeded from the sun, but tendeth more toward the

centre of the body it enters. Also when the action is continued through

the convex body, it bendeth again the same way. By which means the whole

action of the sun-beams are enclosed within a very small compass: in

which place therefore there must be a very vehement motion; and

consequently, if there be in that place combustible matter, such as is

not very hard to kindle, the parts of it will be dissipated, and receive

that motion which worketh on the eye as other fire does.

The same reason is to be given for burning by reflection. For there also

the beams are collected into almost a point.

_A._ Why may not the sun-beams be such a body as we call fire, and pass

through the pores of the glass so disposed as to carry them to a point,

or very near?

_B._ Can there be a glass that is all pores? if there cannot, then

cannot this effect be produced by the passing of fire through the pores.

You have seen men light their tobacco at the sun with a burning glass,

or with a ball of crystal, held which way they will indifferently. Which

must be impossible, unless the ball were all pores. Again, neither you

nor I can conceive any other fire than we have seen, nor than such as

water will put out. But not only a solid globe of glass or crystal will

serve for a burning-glass, but also a hollow one filled with water. How

then does the fire from the sun pass through the glass of water without

being put out before it come to the matter they would have it burn?

_A._ I know not. There comes nothing from the sun. If there did, there

is come so much from it already, that at this day we had had no sun.

==========

CHAPTER V.

PROBLEMS OF HARD AND SOFT.

_A._ What call you hard, and what soft?

_B._ That body whereof no one part is easily put out of its place,

without removing the whole, is that which I and all men call hard; and

the contrary soft. So that they are but degrees one of another.

_A._ What is the cause that makes one body harder than another, or,

seeing you say they are but degrees of one another, what makes one body

softer than another, and the same body sometimes harder, sometimes

softer?

_B._ The same motion which we have supposed from the beginning for the

cause of so many other effects. Which motion not being upon the centre

of the part moved, but the part itself going in another circle to and

again, it is not necessary that the motion be perfectly circular. For it

is not circulation, but the reciprocation, I mean the to and again, that

does cast off, and lacerate the air, and consequently produce the

fore-mentioned effects.

For the cause therefore of hardness, I suppose the reciprocation of

motion in those things which are hard, to be very swift, and in very

small circles.

_A._ This is somewhat hard to believe. I would you could supply it with

some visible experience.

_B._ When you see, for example, a cross-bow bent, do you think the parts

of it stir?

_A._ No. I am sure they do not.

_B._ How are you sure? You have no argument for it, but that you do not

see the motion. When I see you sitting still, must I believe there is no

motion in your parts within, when there are so many arguments to

convince me there is.

_A._ What argument have you to convince me that there is motion in a

cross-bow when it stands bent?

_B._ If you cut the string, or any way set the bow at liberty, it will

have then a very visible motion. What can be the cause of that?

_A._ Why the setting of the bow at liberty.

_B._ If the bow had been crooked before it was bent, and the string tied

to both ends, and then cut asunder, the bow would not have stirred.

Where lies the difference?

_A._ The bow bent has a spring; unbent it has none, how crooked soever.

_B._ What mean you by spring?

_A._ An endeavour of restitution to its former posture.

_B._ I understand spring as well as I do endeavour.

_A._ I mean a principle or beginning of motion in a contrary way to that

of the force which bent it.

_B._ But the beginning of motion is also motion, how insensible soever

it be. And you know that nothing can give a beginning of motion to

itself. What is it therefore that gives the bow (which you say you are

sure was at rest when it stood bent) its first endeavour to return to

its former posture?

_A._ It was he that bent it.

_B._ That cannot be. For he gave it an endeavour to come forward, and

the bow endeavours to go backward.

_A._ Well, grant that endeavour be motion, and motion in the bow unbent,

how do you derive from thence, that being set at liberty it must return

to its former posture?

_B._ Thus there being within the bow a swift (though invisible) motion

of all the parts, and consequently of the whole; the bending causeth

that motion, which was along the bow (that was beaten out when it was

hot into that length) to operate across the length in every part of it,

and the more by how much it is more bent; and consequently endeavours to

unbend it all the while it stands bent. And therefore when the force

which kept it bent is removed, it must of necessity return to the

posture it had before.

_A._ But has that endeavour no effect at all before the impediment be

removed? For if endeavour be motion, and every motion have some effect

more or less, methinks this endeavour should in time produce something.

_B._ So it does. For in time (in a long time) the course of this

internal motion will lie along the bow, not according to the former, but

to the new acquired posture. And then it well be as uneasy to return it

to its former posture, as it was before to bend it.

_A._ That is true. For bows long bent lose their appetite to

restitution, long custom becoming nature. But from this internal

reciprocation of the parts, how do you infer the hardness of the whole

body?

_B._ If you apply force to any single part of such a body, you must

needs disorder the motion of the next parts to it before it yield, and

there disordered, the motion of the next again must also be disordered;

and consequently no one part can yield without force sufficient to

disorder all: but then the whole body must also yield. Now when a body

is of such a nature as no single part can be removed without removing

the whole, men say that body is hard.

_A._ Why does the fire melt divers hard bodies, and yet not all?

_B._ The hardest bodies are those wherein the motion of the parts are

the most swift, and yet in the least circles. Wherefore if the fire, the

motion of whose parts are swift, and in greater circles, be made so

swift, as to be strong enough to master the motion of the parts of the

hard body, it will make those parts to move in a greater compass, and

thereby weaken their resistance, that is to say, soften them, which is a

degree of liquefaction. And when the motion is so weakened, as that the

parts lose their coherence by the force of their own weight, then we

count the body melted.

_A._ Why are the hardest things the most brittle, insomuch that what

force soever is enough to bend them, is enough also to break them?

_B._ In bending a hard body, as (for example) a rod of iron, you do not

enlarge the space of the internal motion of the parts of iron, as the

fire does; but you master and interrupt the motion, and that chiefly in

one place. In which place the motion that makes the iron hard being once

overcome, the prosecution of that bending must needs suddenly master the

motions of the parts next unto it, being almost mastered before.

_A._ I have seen a small piece of glass, the figure whereof is this, A A

B C. Which piece of glass if you bend toward the top, as in C, the whole

body will shatter asunder into a million of pieces, and be like to so

much dust. I would fain see you give a probable reason of that.

_B._ I have seen the experiment. The making of the glass is thus: they

dip an iron rod into the molten glass that stands in a vessel within the

furnace. Upon which iron rod taken out, there will hang a drop of molten

but tough metal of the figure you have described, which they let fall

into the water. So that the main drop comes first to the water, and

after it the tail, which though straight whilst it hung on the end of

the rod, yet by falling into the water becomes crooked. Now you know the

making of it, you may consider what must be the consequence of it.

Because the main drop A comes first to the water, it is therefore first

quenched, and consequently the motion of the parts of that drop, which

by the fire were made to be moved in a larger compass, is by the water

made to shrink into lesser circles towards the other end B, but with the

same or not much less swiftness.

_A._ Why so?

_B._ If you take any long piece of iron, glass, or other uniform and

continued body; and having heated one end thereof, you hold the other

end in your hand, and so quench it suddenly, though before you held it

easily enough, yet now it will burn your fingers.

_A._ It will so.

_B._ You see then how the motion of the parts from A toward C is made

more violent and in less compass by quenching the other parts first.

Besides, the whole motion that was in all the parts of the main drop A,

is now united in the small end B C. And this I take to be the cause why

that small part B C is so exceeding stiff. Seeing also this motion in

every small part of the glass, is not only circular, but proceeds also

all along the glass from A to B, the whole motion compounded will be

such as the motion of spinning any soft matter into thread, and will

dispose the whole body of the glass in threads, which in other hard

bodies are called the grain. Therefore if you bend this body (for

example) in C (which to do will require more force than a man would

think that has not tried) those threads of glass must needs be all bent

at the same time, and stand so, till by the breaking of the glass at C,

they be all at once set at liberty; and then all at once being suddenly

unbent, like so many brittle and overbent bows, their strings breaking,

be shivered in pieces.

_A._ It is like enough to be so. And if nature have betrayed herself in

any thing, I think it is in this, and in that other experience of the

crossbow; which strongly and evidently demonstrates the internal

reciprocation of the motion, which you suppose to be in the internal

parts of every hard body. And I have observed somewhat in

looking-glasses which much confirms that there is some such motion in

the internal parts of glass, as you have supposed for the cause of

hardness. For let the glass be A B, and let the object at C be a candle,

and the eye at D. Now by divers reflections and refractions in the two

superficies of the glass, if the lines of vision be very oblique, you

shall see many images of the candle, as E, F, G, in such order and

position as is here described. But if you remove your eye to C, and the

candle to D, they will appear in a situation manifestly different from

this. Which you will yet more plainly perceive if the looking-glass be

coloured, as I have observed in red and blue glasses; and could never

conceive any probable cause of it, till now you tell me of this secret

motion of the parts across the grain of the glass, acquired by cooling

it this or that way.

_B._ There be very many kinds of hard bodies, metals, stones, and other

kinds, in the bowels of the earth, that have been there ever since the

beginning of the world; and I believe also many different sorts of

juices that may be made hard. But for one general cause of hardness it

can be no other than such an internal motion of parts as I have already

described, whatsoever may be the cause of the several concomitant

qualities of their hardness in particular.

_A._ We see water hardened every frosty day. It is likely therefore you

may give a probable cause of ice. What is the cause of freezing of the

ocean towards the poles of the earth?

_B._ You know the sun being always between the tropics, and (as we have

supposed) always casting off the air; and the earth likewise casting it

off from itself, there must needs on both sides be a great stream of air

towards the poles, shaving the superficies of the earth and sea, in the

northern and southern climates. This shaving of the earth and sea by the

stream of air must needs contract and make to shrink those little

circles of the internal parts of earth and water, and consequently

harden them, first at the superficies, into a thin skin, which is the

first ice; and afterwards the same motion continuing, and the first ice

co-operating, the ice becomes thicker. And this I conceive to be the

cause of the freezing of the ocean.

_A._ If that be the cause, I need not ask how a bottle of water is made

to freeze in warm weather with snow, or ice mingled with salt. For when

the bottle is in the midst of it, the wind that goeth out both of the

salt and of the ice as they dissolve, must needs shave the superficies

of the bottle, and the bottle work accordingly on the water without it,

and so give it first a thin skin, and at last thicken it into a solid

piece of ice. But how comes it to pass that water does not use to freeze

in a deep pit?

_B._ A deep pit is a very thick bottle, and such as the air cannot come

at but only at the top, or where the earth is very loose and spungy.

_A._ Why will not wine freeze as well as water?

_B._ So it will when the frost is great enough. But the internal motion

of the parts of wine and other heating liquors is in greater circles and

stronger than the motion of the parts of water; and therefore less

easily to be frozen, especially quite through, because those parts that

have the strongest motion retire to the centre of the vessel.

==========

CHAPTER VI.

PROBLEMS OF RAIN, WIND, AND OTHER WEATHER.

_A._ What is the original cause of rain? And how is it generated?

_B._ The motion of the air (such as I have described to you already)

tending to the disunion of the parts of the air, must needs cause a

continual endeavour (there being no possibility of vacuum) of whatsoever

fluid parts there are upon the face of the earth and sea, to supply the

place which would else be empty. This makes the water, and also very

small and loose parts of the earth and sea to rise, and mingle

themselves with the air, and to become mist and clouds. Of which the

greatest quantity arise there, where there is most water, namely, from

the large parts of the ocean; which are the South Sea, the Indian Sea,

and the sea that divided Europe and Africa from America; over which the

sun for the greatest part of the year is perpendicular, and consequently

raiseth a greater quantity of water; which afterwards gathered into

clouds, falls down in rain.

_A._ If the sun can thus draw up the water, though but in small drops,

why can it not as easily hold it up?

_B._ It is likely it would also hold them up, if they did not grow

greater by meeting together, nor were carried away by the air towards

the poles.

_A._ What makes them gather together?

_B._ It is not improbable that they are carried against hills, and there

stopt till more overtake them. And when they are carried towards the

North or South where the force of the sun is more oblique and thereby

weaker, they descend gently by their own weight. And because they tend

all to the centre of the earth, they must needs be united in their way

for want of room, and so grow bigger. And then it rains.

_A._ What is the reason it rains so seldom, but snows so often upon very

high mountains?

_B._ Because, perhaps, when the water is drawn up higher than the

highest mountains, where the course of the air between the equator and

the poles is free from stoppage, the stream of the air freezeth it into

snow. And it is in those places only where the hills shelter it from

that stream, that it falls in rain.

_A._ Why is there so little rain in Egypt, and yet so much in other

parts nearer the equinoxial, as to make the Nile overflow the country?

_B._ The cause of the falling of rain I told you was the stopping, and

consequently the collection of clouds about great mountains, especially

when the sun is near the equinoxial, and thereby draws up the water more

potently, and from greater seas. If you consider therefore that the

mountains in which are the springs of Nile, lie near the equinoxial and

are exceedingly great, and near the Indian Sea, you will not think it

strange there should be great store of snow. This as it melts makes the

rain of Nile to rise, which in April and May going on toward Egypt

arrive there about the time of the solstice, and overflow the country.

_A._ Why should not the Nile then overflow that country twice a year,

for it comes twice a-year to the equinoxial.

_B._ From the autumnal equinox, the sun goeth on toward the southern

tropic, and therefore cannot dissolve the snow on that side of the hills

that looks towards Egypt.

_A._ But then there ought to be such another inundation southward.

_B._ No doubt but there is a greater descent of water there in their

summer than at other times, as there must be wheresoever there is much

snow melted. But what should that inundate, unless it should overflow

the sea that comes close to the foot of those mountains? And for the

cause why it seldom rains in Egypt, it may be this, that there are no

very high hills near it to collect the clouds. The mountains whence Nile

riseth being near two thousand miles off. The nearest on one side are

the mountains of Nubia, and on the other side Sina and the mountains of

Arabia.

_A._ Whence think you proceed the winds?

_B._ From the motion, I think, especially of the clouds, partly also

from whatsoever is moved in the air.

_A._ It is manifest that the clouds are moved by the winds; so that

there were winds before any clouds could be moved. Therefore I think you

make the effect before the cause.

_B._ If nothing could move a cloud but wind, your objection were good.

But you allow a cloud to descend by its own weight. But when it so

descends, it must needs move the air before it, even to the earth, and

the earth again repel it, and so make lateral winds every way, which

will carry forward other clouds if there be any in their way, but not

the cloud that made them. The vapour of the water rising into clouds,

must needs also, as they rise, raise a wind.

_A._ I grant it. But how can the slow motion of a cloud make so swift a

wind as it does?

_B._ It is not one or two little clouds, but many and great ones that do

it. Besides, when the air is driven into places already covered, it

cannot but be much the swifter for the narrowness of the passage.

_A._ Why does the south wind more often than any other bring rain with

it?

_B._ Where the sun hath most power, and where the seas are greatest,

that is in the south, there is most water in the air; which a south wind

can only bring to us. But I have seen great showers of rain sometimes

also when the wind hath been north, but it was in summer, and came

first, I think, from the south or west, and was brought back from the

north.

_A._ I have seen at sea very great waves when there was no wind at all.

What was it then that troubled the water?

_B._ But had you not wind enough presently after?

_A._ We had a storm within a little more than a quarter of an hour

after.

_B._ That storm was then coming and had moved the water before it. But

the wind you could not perceive, for it came downwards with the

descending of the clouds, and pressing the water bounded above your sail

till it came very near. And that was it that made you think there was no

wind at all.

_A._ How comes it to pass that a ship should go against the wind which

moves it, even almost point blank, as if it were not driven but drawn?

_B._ You are to know first, that what body soever is carried against

another body, whether perpendicularly or obliquely, it drives it in a

perpendicular to the superficies it lighteth on. As for example, a

bullet shot against a flat wall, maketh the stone, or other matter it

hits, to retire in a perpendicular to that flat; or, if the wall be

round, towards the centre, that is to say, perpendicularly. For if the

way of the motion be oblique to the wall, the motion is compounded of

two motions, one parallel to the wall, and the other perpendicular. By

the former whereof the bullet is carried along the wall side, by the

other it approacheth to it. Now the former of these motions can have no

effect upon it; all the battery is from the motion perpendicular, in

which it approacheth, and therefore the part it hits must also retire

perpendicularly. If it were not so, a bullet with the same swiftness

would execute as much obliquely shot, as perpendicularly, which you know

it does not.

_A._ How do you apply this to a ship?

_B._ Let A B be the ship, the head of it A. If the wind blow just from A

towards B, it is true the ship cannot go forward howsoever the sail be

set. Let C D be perpendicular to the ship, and let the sail E C be never

so little oblique to it, and F C perpendicular to E C, and then you see

the ship will gain the space D F to the headward.

_A._ It will so; but when it is very near to the wind it will go forward

very slowly, and make more way with her side to the leeward.

_B._ It will indeed go slower in the proportion of the line A E to the

line C E. But the ship will not go so fast as you think sideward: one

cause is the force of that wind which lights on the side of the ship

itself; the other is the bellying of the sail; for the former, it is not

much, because the ship does not easily put from her the water with her

side; and bellying of the sail gives some little hold for the wind to

drive the ship astern.

_A._ For the motion sideward I agree with you; but I had thought the

bellying of the sail had made the ship go faster.

_B._ But it does not; only in a fore wind it hinders least.

_A._ By this reason a broad thin board should make the best sail.

_B._ You may easily foresee the great incommodities of such a sail. But

I have seen tried in little what such a wind can do in such a case. For

I have seen a board set upon four truckles, with a staff set up in the

midst of it for a mast, and another very thin and broad board fastened

to that staff in the stead of a sail, and so set as to receive the wind

very obliquely, I mean so as to be within a point of the compass

directly opposite to it, and so placed upon a reasonable smooth pavement

where the wind blew somewhat strongly. The event was first, that it

stood doubting whether it should stir at all or no, but that was not

long, and then it ran a-head extreme swiftly, till it was overthrown by

a rub.

_A._ Before you leave the ship, tell me how it comes about that so small

a thing as a rudder can so easily turn the greatest ship.

_B._ It is not the rudder only, there must also be a stream to do it;

you shall never turn a ship with a rudder in a standing pool, nor in a

natural current. You must make a stream from head to stern, either with

oars or with sails; when you have made such a stream, the turning of the

rudder obliquely holds the water from passing freely, and the ship or

boat cannot go on directly, but as the rudder inclines to the stern, so

will the ship turn; but this is too well known to insist upon. You have

observed that the rudders of the greatest ships are not very broad, but

go deep into the water, whereas western barges, though but small

vessels, have their rudders much broader, which argues that the holding

of water from passing is the true office of a rudder; and therefore to a

ship that draws much water the rudder is made deep accordingly; and in

barges that draw little water, the rudders being less deep, must so much

the more be extended in breadth.

_A._ What makes snow?

_B._ The same cause which, speaking of hardness, I supposed for the

cause of ice. For the stream of air proceeding from that both the earth

and the sun cast off the air, consequently maketh a stream of air from

the equinoxial towards the poles, passing amongst the clouds, shaving

those small drops of water whereof the clouds consist, and congeals them

as they do the water of the sea, or of a river. And these small frozen

drops are that which we call snow.

_A._ But then how are great drops frozen into hailstones, and that

especially (as we see they are) in summer?

_B._ It is especially in summer, and hot weather, that the drops of

water which make the clouds, are great enough; but it is then also that

clouds are sooner and more plentifully carried up. And therefore the

current of the air strengthened between the earth and the clouds,

becomes more swift; and thereby freezeth the drops of water, not in the

cloud itself, but as they are falling. Nor does it freeze them

thoroughly, the time of their falling not permitting it, but gives them

only a thin coat of ice; as is manifest by their sudden dissolving.

_A._ Why are not sometimes also whole clouds when pregnant and ready to

drop, frozen into one piece of ice?

_B._ I believe they are so whensoever it thunders.

_A._ But upon what ground do you believe it?

_B._ From the manner or kind of noise they make, namely a crack; which I

see not how it can possibly be made by water or any other soft bodies

whatsoever.

_A._ Yes, the powder they call _aurum fulminans_, when thoroughly warm,

gives just such another crack as thunder.

_B._ But why may not every small grain of that _aurum fulminans_ by

itself be heard, though a heap of them together be soft, as is any heap

of sand. Salts of all sorts are of the nature of ice. But gold is

dissolved into _aurum fulminans_ by nitre and other salts. And the least

grain of it gives a little crack in the fire by itself. And therefore

when they are so warmed by degrees, the crack cannot choose but be very

great.

_A._ But before it be _aurum fulminans_ they use to wash away the salt

(which they call dulcifying it), and then they dry it gently by degrees.

_B._ That is, they exhale the pure water that is left in the powder, and

leave the salt behind to harden with drying. Other powder made of salts

without any gold in them will give a crack as great as _aurum

fulminans_. A very great chemist of our times hath written, that salt of

tartar, saltpetre, and a little brimstone ground together into a powder,

and dried, a few grains of that powder will be made by the fire to give

as great a clap as a musket.

_A._ Methinks it were worth your trial to see what effect a quart or a

pint of _aurum fulminans_ would produce, being put into a great gun made

strong enough on purpose, and the breech of the gun set in hot cinders,

so as to heat by degrees, till the powder fly.

_B._ I pray you try it yourself; I cannot spare so much money.

_A._ What is it that breaketh the clouds when they are frozen?

_B._ In very hot weather the sun raiseth from the sea and all moist

places abundance of water, and to a great height. And whilst this water

hangs over us in clouds, or is again descending, it raiseth other

clouds, and it happens very often that they press the air between them,

and squeeze it through the clouds themselves very violently; which as it

passes shaves and hardens them in the manner declared.

_A._ That has already been granted; my question is what breaks them?

_B._ I must here take in one supposition more.

_A._ Then your basin, it seems, holds not all you have need of.

_B._ It may for all this, for the supposition I add is no more but this;

that what internal motion I ascribe to the earth, and the other concrete

parts of the world, is to be supposed also in every of their parts how

small soever; for what reason is there to think, in case the whole earth

have in truth the motion I have ascribed to it, that one part of it

taken away, the remaining part should lose that motion. If you break a

loadstone, both parts will retain their virtue, though weakened

according to the diminution of their quantity; I suppose therefore in

every small part of the earth the same kind of motion, which I have

supposed in the whole: and so I recede not yet from my basin.

_A._ Let it be supposed, and withal, that abundance of earth, (which I

see you aim at), be drawn up together with the water. What then?

_B._ Then if many pregnant clouds, some ascending and some descending

meet together, and make concavities between, and by the pressing out of

the air, as I have said before, become ice; those atoms, as I may call

them, of earth will, by the straining of the air through the water of

the clouds, be left behind, and remain in the cavities of the clouds,

and be more in number than for the proportion of the air therein.

Therefore for want of liberty they must needs justle one another, and

become, as they are more and more straightened of room, more and more

swift, and consequently at last break the ice suddenly and violently,

now in one place, and by and by in another; and make thereby so many

claps of thunder, and so many flashes of lightning. For the air

recoiling upon our eyes, is that which maketh those flashes to our

fancy.

_A._ But I have seen lightning in a very clear evening, when there has

been neither thunder nor clouds.

_B._ Yes, in a clear evening; because the clouds and the rain were below

the horizon, perhaps forty or fifty miles off; so that you could not see

the clouds nor hear the thunder.

_A._ If the clouds be indeed frozen into ice, I shall not wonder if they

be sometimes also so situated, as, like looking-glasses, to make us see

sometimes three or more suns by refraction and reflection.

==========

CHAPTER VII.

PROBLEMS OF MOTION PERPENDICULAR, AND OBLIQUE;

OF PRESSION AND PERCUSSION; REFLECTION AND

REFRACTION; ATTRACTION AND REPULSION.

_A._ If a bullet from a certain point given, be shot against a wall

perpendicularly, and again from the same point obliquely, 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 obliquely to G; in what proportion will their

forces be upon the wall?

_B._ The force of the stroke perpendicular 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 nothing of its swiftness. But the

cause is, that their swiftness being equal, the one is longer in coming

to the wall than 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 than in E G,

in proportion of the lines themselves.

_A._ When a bullet enters not, but rebounds 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 their difference will

not be sensible; otherwise it will be great enough, for the motion of

the bullet grows continually weaker. But it is not so with the sun-beams

which press continually 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 reflecting 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 reflecting body, caused by

the sun, or other shining body, and is but a contrary 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 reflecting 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 compounded 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 motion of the bullet against a wall,)

the bullet no sooner goeth off than 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 one’s finger, yet a bullet

from a musket 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

amongst naturalists.

_B._ The different manner of the operation of weight from the operation

of a stroke, makes it incalculable. The suddenness of the stroke upon

one point of the wood takes away the time of resistance from the rest.

Therefore the nail enters so far as it does. But the weight not only

gives them time, but also augments the resistance; but how much, and in

how much time, is, I think, impossible to determine.

_A._ What is the difference between reflection and recoiling?

_B._ Any reflection may, and not unproperly, be called recoiling; but

not contrariwise every recoiling reflection. Reflection is always made

by the reaction of a body pressed or stricken; but recoiling not always.

The recoiling of a gun is not caused by its own pressing upon the

gunpowder, but by the force of the powder itself, inflamed and moved

every way alike.

_A._ I had thought it had been by the sudden re-entering 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

suddenly filled with the air that entereth at the touchhole.

_B._ The flame is nothing but the powder itself, which scattered into

its smallest parts, seems of greater bulk by much, than in truth it is,

because they shine. And as the parts scatter more and more, so still

more air gets between them, entering not only at the touchhole, but also

at the mouth 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 charged too much or too little, will

shoot, not above, nor below, but beside the mark; and charged with one

certain charge between both, will hit it.

_B._ How that should be I cannot imagine. For when all things in the

cause are equal, the effects cannot be unequal. As soon as fire is

given, and before the bullet be out, the gun begins to recoil. If then

there be any unevenness or rub in the ground more on one side than on

the other, it shall shoot beside 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 imagine no cause of this event, but either in

the ground it recoils on, or in the unequal weight of the parts of the

breech.

_A._ How comes refraction?

_B._ When the action is in a line perpendicular to the superficies of

the body wrought upon, there will be no refraction at all. The action

will proceed still in the same straight line, whether it be pression as

in light, or percussion as in the shooting of a bullet. But when the

pression is oblique, then will the refraction be that way which the

nature of the bodies through which the action proceeds shall determine.

_A._ How is light refracted?

_B._ If it 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 perpendicular 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 perpendicular.

_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 farther inward than

a mere touch, it worketh partly in the perpendicular, and partly

forward, and would proceed in the same line in which it fell on, but for

the greater resistance which now weakeneth the motion forward, and makes

it to incline towards the perpendicular.

_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 pressed, presseth that

which is next behind, and so continually. But the cause why there is no

light seen through it, is the unevenness of the parts within, whereby

the action is by an infinite number of reflections so diverted and

weakened, that before it hath proceeded through, it hath not strength

left to work upon the eye strongly enough to produce sight.

_A._ If the body being transparent, the action 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

superficies 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 entereth into a wall of earth,

will that also be refracted towards the perpendicular.

_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 entered.

_A._ How then comes a bullet, when shot very obliquely into any broad

water, and having entered, yet to rise again into the air?

_B._ When a bullet is shot very obliquely, though the motion be never so

swift, yet the approach downwards to the water is very slow, and when it

cometh to it, it casteth up much water 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 motion 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

loadstone draw iron to it?

_B._ By the same motion hitherto supposed. 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 motion, of way,

of swiftness, and of poles, cannot be maintained, without the

conjunction of the bodies themselves in the centre of their common

motion, but by violence. If therefore the iron have but so much of the

nature of the loadstone as readily 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 loadstone 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, because at distance

their motions will differ in time, and oppose each other, whereby they

will be forced to a common centre. If the iron be lifted up from the

earth, the motion of the loadstone must be stronger, or the body of it

nearer, to overcome the weight; and then the iron will leap up to the

loadstone as swiftly, as from the same distance it would fall down to

the earth; but if both the stone and the iron be set floating 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 loadstone, if it float on a calm water, never fail

to place itself 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 ecliptic, which is the axis of the

like motion in the earth, and consequently that it cannot freely

exercise its natural motion in any other situation.

_A._ Whence may this consent of motion in the loadstone and the earth

proceed? Do you think, as some have written, that the earth is a great

loadstone?

_B._ Dr. Gilbert, that was the first that wrote anything of this subject

rationally, inclines to that opinion. Descartes 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 loadstone hath been given its virtue by a

long habitude in the mine, the vein of it lying in the plane of some of

the meridians, or rather of some of the great circles that pass through

the poles of the ecliptic, 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

loadstone equally distant from its poles will lie parallel to the axis,

but on each side will incline to the pole that is next. Nor why by

drawing a loadstone all along a needle of iron, the needle will receive

the same poles. Nor why when the loadstone and iron, or two loadstones,

are put together floating upon water, will fall one of them astern 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 derived 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, unless a great part of mankind be liars) 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 wakened by their

noise. And they never came into any dream of mine since, unless

apparitions in dreams and ghost be all one.

==========

CHAPTER VIII.

THE DELPHIC PROBLEM, OR DUPLICATION OF THE

CUBE.

_A._ Have you seen a printed paper sent from Paris, containing the

duplication of the cube, written in French?

_B._ Yes. It was I that writ it, and sent it thither to be printed, on

purpose to see what objections would be made to it by our professors of

algebra here.

_A._ Then you have also seen the confutations of it by algebra.

_B._ I have seen some of them; and have one by me. For there was but one

that was rightly calculated, and that is it which I have kept.

_A._ Your demonstration then is confuted though but by one.

_B._ That does not follow. For though an arithmetical calculation be

true in numbers, yet the same may be, or rather must be false, if the

units be not constantly the same.

_A._ Is their calculation so inconstant, or rather so foolish as you

make it?

_B._ Yes. For the same number is sometimes so many lines, sometimes so

many planes, and sometimes so many solids; as you shall plainly see, if

you will take the pains to examine first a demonstration I have to prove

the said duplication, and after that, the algebraic calculation which is

pretended to confute it. And not only that this one is false, but also

any other arithmetical account used in geometry, unless the numbers be

always so many lines, or always so many superficies, or always so many

solids.

_A._ Let me see the geometrical demonstration.

_B._ There it is. Read it.

TO FIND A CUBE DOUBLE TO A CUBE GIVEN:

Let the side of the cube given be V D. Produce V D to A, till A D be

double to D V. Then make the square of A D, namely A B C D. Divide A B

and C D in the middle at E and F. Draw E F. Draw also A C cutting E F in

I. Then in the sides B C and A D take B R and A S, each of them equal to

A I or I C.

Lastly, divide S D in the middle at T, and upon the centre T, with the

distance T V, describe a semi-circle cutting A D in Y, and D C in X.

I say the cube of D X is double to the cube of D V. For the three lines

D Y, D X, D V are in continual proportion. And continuing the

semi-circle V X Y till it cut the line R S, drawn and produced in Z, the

line S Z will be equal to D X. And drawing X Z it will pass through T.

And the four lines T V, T X, T Y and T Z will be equal. And therefore

joining Y X and Y Z, the figure V X Y Z will be a rectangle.

[Illustration:

_Delphic Problem.

Vol. VII. Eng. p. 60._

]

Produce C D to P so as D P be equal to A D. Now if Y Z produced fall on

P, there will be three rectangle equiangled triangles, D P Y, D Y X, and

D X V; and consequently four continual proportionals, D P, D Y, D X, and

D V, whereof D X is the least of the means. And therefore the cube of D

X will be double to the cube of D V.

_A._ That is true; and the cube of D Y will be double to the cube of D

X; and the cube of D P double to the cube of D Y. But that Y Z produced,

falls upon P, is the thing they deny, and which you ought to

demonstrate.

_B._ If Y Z produced fall not on P, then draw P Y, and from V let fall a

perpendicular upon P Y, suppose at _u._. Divide P V in the midst at

_a._, and join _a u._; which done _a u._ will be equal to _a._ V or _a._

P. For because V _u._ P is a right angle, the point _u._ will be in the

semi-circle whereof P V is the diameter.

Therefore drawing V R, the angle _u._ V R will be a right angle.

_A._ Why so?

_B._ Because T V and T Y are equal; and T D, T S equal; S Y will also be

equal to D V. And because D P and R S are equal and parallel, R Y will

be equal and parallel to P V. And therefore V R and P Y that join them

will be equal and parallel. And the angles P _u._ V, R V _u._ will be

alternate, and consequently equal. But P _u._ V is a right angle;

therefore also R V _u._ will be a right angle.

_A._ Hitherto all is evident. Proceed.

_B._ From the point Y raise a perpendicular cutting V R wheresoever in

_t._, and then (because P Y and V R are parallel) the angle Y _t_ V will

be a right angle. And the figure _u_ Y _t_ V a rectangle, and _u t_

equal to Y V. But Y V is equal to Z X; and therefore Z X is equal to _u

t_. And _u t_ must pass through the point T (for the diameters of any

rectangle divide each other in the middle), therefore Z and _u_ are the

same point, and X and _t_ the same point. Therefore Y Z produced falls

upon P. And D X is the lesser of the two means between A D and D V. And

the cube of D X double to the cube of D V, which was to be demonstated

_A._ I cannot imagine what fault there can be in this demonstration, and

yet there is one thing which seems a little strange to me. And it is

this. You take B R, which is half the diagonal, and which is the sine of

forty-five degrees, and which is also the mean proportional between the

two extremes; and yet you bring none of these proprieties into your

demonstration. So that though you argue from the construction, yet you

do not argue from the cause. And this perhaps your adversaries will

object, at least, against the art of your demonstration, or enquire by

what luck you pitched upon half the diagonal for your foundation.

_B._ I see you let nothing pass. But for answer you must know, that if a

man argue from the negative of the truth, though he know not that it is

the truth which is denied, yet he will fall at last, after many

consequences, into one absurdity or another. For though false do often

produce truth, yet it produces also absurdity, as it hath done here. But

truth produceth nothing but truth. Therefore in demonstrations that tend

to absurdity, it is no good logic to require all along the operation of

the cause.

_A._ Have you drawn from hence no corollaries?

_B._ No. I leave that for others that will; unless you take this for a

corollary, that, what arithmetical calculation soever contradicts it, is

false.

_A._ Let me see now the algebraical demonstration against it.

_B._ Here it is:

Let A B or A D be equal to 2

Then D F or D V is equal to 1

And B R or A S is equal to the square root of 2

And D Y equal to 3

want the square root of 2

The cube of A B is equal to 8

The cube of D Y is equal to 45

want the square root of 1682 that is almost equal to 4

For 45 want the square root of 1681 is equal to 4

Therefore D Y is a little less then the greater of the two means between

A D and D V.

_A._ There is I see some little difference between this arithmetical and

your geometrical demonstration. And though it be insensible, yet if his

calculation be true, yours must needs be false, which I am sure cannot

be.

_B._ His calculation is so true, that there is never a proposition in it

false, till he come to the conclusion, that the cube of D Y is equal to

45, want the square root of 1682. But that, and the rest, is false.

_A._ I shall easily see that A D is certainly 2, whereof D V is 1, and A

V is certainly 3, whereof D V is 1.

_B._ Right.

_A._ And B R is without doubt the square root of 2.

_B._ Why, what is 2?

_A._ 2 is the line A D as being double to D V which is 1.

_B._ And so, the line B R is the square root of the line A D.

_A._ Out upon it, it is absurd. Why do you grant it to be true in

arithmetic?

_B._ In arithmetic the numbers consist of so many units, and are never

considered there as nothings. And therefore every one line has some

latitude, and if you allow to B I, the semi-diagonal, the same latitude

you do to A B, or to B R, you will quickly see the square of half the

diagonal to be equal to twice the square of half A B.

_A._ Well, but then your demonstration is not confuted; for the point Y

will have latitude enough to take in that little difference which is

between the root of 1681 and the root of 1682. This putting off an unit

sometimes for one line, sometimes for one square, must needs mar the

reckoning. Again he says, the cube of A B is equal to 8; but seeing A B

is 2, the cube of A B must be just equal to four of its own sides; so

that the unit which was before sometimes a line, sometimes a square, is

now a cube.

_B._ It can be no otherwise when you so apply arithmetic to geometry, as

to number the lines of a plane, or the planes of a cube.

_A._ In the next place, I find that the cube of D Y is equal to 45, want

the square root of 1682. What is that 45? Lines, or squares, or cubes?

_B._ Cubes; cubes of D V.

_A._ Then if you add to 45 cubes of D V the square root of 1682, the sum

will be 45 cubes of D V; and if you add to the cube of D Y the same root

of 1682, the sum will be the cube of D Y, plus the square root of 1682,

and these two sums must be equal.

_B._ They must so.

_A._ But the square root of 1682, being a line, adds nothing to a cube;

therefore the cube alone of D Y, which he says is equal almost to 4

cubes of D V, is equal to 45 cubes of the same D V.

_B._ All these impossibilities do necessarily follow the confounding of

arithmetic and geometry.

_A._ I pray you let me see the operation by which the cube of D Y (that

is, the cube of 3, want the root of 2) is found equal to 45, want the

square root of 1682.

_B._ Here it is.

A DETECTION OF THE ABSURD USE OF ARITHMETIC AS IT IS NOW APPLIED TO

GEOMETRY.

3————√2

3————√2

———————

—√18 + 2

9—√18

—————————

9—√72 + 2

3——√2

——————————————

——√162 + 12——√8

27——√648 + 6

———————————————————

27—√658—√162 + 18—√8

======================

_A._ Why for two roots of 18 do you put the root of 72.

_B._ Because 2 roots of 18 are equal to one root of four times 18, which

is 72.

_A._ Next we have, that the root of 2 multiplied into 2 makes the root

of 8. How is that true?

_B._ Does it not make 2 roots of two? And is not B R the root of 2, and

2 B R equal to the diagonal? And is not the square of the diagonal equal

to 8 squares of D V?

_A._ It is true. But here the root of 8 is put for the cube of the root

of 2. Can a line be equal to a cube?

_B._ No. But here we are in arithmetic again, and 8 is a cubic number.

_A._ How does the root of 2 multiplied into the root of 72 make 12?

_B._ Because it makes the root of 2 times 72, that is to say the root of

144 which is 12.

_A._ How does 9 roots of 2 make the root of 162?

_B._ Because it makes the root of 2 squares of 9, that is the root of

162.

_A._ How does 3 roots of 72 make the root of 648?

_B._ Because it makes the root of 9 times 72, that is of 648.

_A._ For the total sum I see 27 and 18, which make 45. Therefore the

root of 648 together with the root of 162 and of 8, which are to be

deducted from 45, ought to be equal to the root of 1682.

_B._ So they are. For 648 multiplied by 162 makes 104976, of

which the double root is 648

and 648 and 162 added together make 810

Therefore the root of 648, added to the root of 162, makes

the root of 1458

Again 1458 into 8 is 11664. The double root whereof is 216

The sum of 1458 and 8 added together 1466

The sum of 1466 and 216 is 1682, and the root, the root of 1682

_A._ I see the calculation in numbers is right, though false in lines.

The reason whereof can be no other than some difference between

multiplying numbers into lines or planes, and multiplying lines into the

same lines or planes.

_B._ The difference is manifest. For when you multiply a number into

lines, the product is lines; as the number 2 multiplied into 3 lines is

no more than 3 lines 2 times told. But if you multiply lines into lines

you make planes, and if you multiply lines into planes you make solid

bodies. In geometry there are but three dimensions, lengths,

superficies, and body. In arithmetic there is but one, and that is

number or length which you will. And though there be some numbers called

plane, other solids, others plano-solid, others square, others cubic,

others square-square, others quadrato-cubic, others cubi-cubic, &c., yet

are all these but one dimension, namely number, or a file of things

numbered.

_A._ But seeing this way of calculation by numbers is so apparently

false, what is the reason this calculation came so near the truth?

_B._ It is because in arithmetic units are not nothings, and therefore

have breadth. And therefore many lines set together make a superficies

though their breadth be insensible. And the greater the number is into

which you divide your line, the less sensible will be your error.

_A._ Archimedes, to find a straight line equal to the circumference of a

circle, used this way of extracting roots. And it is the way also by

which the table of sines, secants, and tangents have been calculated.

Are they all out?

_B._ As for Archimedes, there is no man that does more admire him than I

do: but there is no man that cannot err. His reasoning is good. But he,

as all other geometricians before and after him, have had two principles

that cross one another when they are applied to one and the same

science. One is, that a point is no part of a line, which is true in

geometry, where a part of a line when it is called a point, is not

reckoned; another is, that a unit is part of a number; which is also

true; but when they reckon by arithmetic in geometry, there a unit is

sometimes part of a line, sometimes a part of a square, and sometimes

part of a cube. As for the table of sines, secants, and tangents, I am

not the first that find fault with them. Yet I deny not but they are

true enough for the reckoning of acres in a map of land.

_A._ What a deal of labour has been lost by them that being professors

of geometry have read nothing else to their auditors but such stuff as

this you have here seen. And some of them have written great books of it

in strange characters, such as in troublesome times, a man would suspect

to be a cypher.

_B._ I think you have seen enough to satisfy you, that what I have

written heretofore concerning the quadrature of the circle, and of other

figures made in imitation of the parabola, has not been yet confuted.

_A._ I see you have wrested out of the hands of our antagonists this

weapon of algebra, so as they can never make use of it again. Which I

consider as a thing of much more consequence to the science of geometry,

than either of the duplication of the cube, or the finding of two mean

proportionals, or the quadrature of a circle, or all these problems put

together.

FINIS.

DECAMERON PHYSIOLOGICUM;

OR,

TEN DIALOGUES OF NATURAL PHILOSOPHY.

BY

THOMAS HOBBES

OF MALMESBURY.

TO WHICH IS ADDED

THE PROPORTION OF A STRAIGHT LINE TO

HALF THE ARC OF A QUADRANT,

BY THE SAME AUTHOR.

[Illustration]

DECAMERON PHYSIOLOGICUM.

CHAPTER I.

OF THE ORIGINAL OF NATURAL PHILOSOPHY.

_A._ I have heard exceeding highly commended a kind of thing which I do

not well understand, though it be much talked of, by such as have not

otherwise much to do, by the name of philosophy; and the same again by

others as much despised and derided: so that I cannot tell whether it be

good or ill, nor what to make of it, though I see many other men that

thrive by it.

_B._ I doubt not, but what so many do so highly praise must be very

admirable, and what is derided and scorned by many, foolish and

ridiculous. The honour and scorn falleth finally not upon philosophy,

but upon the professors. Philosophy is _the knowledge of natural

causes_. And there is no knowledge but of truth. And to know the true

causes of things, was never in contempt, but in admiration. Scorn can

never fasten upon truth. But the difference is all in the writers and

teachers. Whereof some have neither studied, nor care for it, otherwise

than as a trade to maintain themselves or gain preferment; and some for

fashion, and to make themselves fit for ingenious company: and their

study hath not been meditation, but acquiescence in the authority of

those authors whom they have heard commended. And some, but few, there

be, that have studied it for curiosity, and the delight which commonly

men have in the acquisition of science, and in the mastery of difficult

and subtil doctrines. Of this last sort I count Aristotle, and a few

others of the ancients, and some few moderns: and to these it is that

properly belong the praises which are given to philosophy.

_A._ If I have a mind to study, for example natural philosophy, must I

then needs read Aristotle, or some of those that now are in request?

_B._ There is no necessity of it. But if in your own meditation you

light upon a difficulty, I think it is no loss of time, to enquire what

other men say of it, but to rely only upon reason. For though there be

some few effects of nature, especially concerning the heavens, whereof

the philosophers of old time have assigned very rational causes, such as

any man may acquiesce in, as of eclipses of the sun and moon by long

observation, and by the calculation of their visible motions; yet what

is that to the numberless and quotidian phenomena of nature? Who is

there amongst them or their successors, that has satisfied you with the

causes of gravity, heat, cold, light, sense, colour, noise, rain, snow,

frost, winds, tides of the sea, and a thousand other things which a few

men’s lives are too short to go through, and which you and other curious

spirits admire (as quotidian as they are), and fain would know the

causes of them, but shall not find them in the books of naturalists; and

when you ask what are the causes of any of them, of a philosopher now,

he will put you off with mere words; which words, examined to the

bottom, signify not a jot more than I cannot tell, or because it is:

such as are intrinsical quality, occult quality, sympathy, antipathy,

antiperistasis, and the like. Which pass well enough with those that

care not much for such wisdom, though wise enough in their own ways; but

will not pass with you that ask not simply what is the cause, but in

what manner it comes about that such effects are produced.

_A._ That is cozening. What need had they of that? When began they thus

to play the charlatans?

_B._ Need had they none. But know you not that men from their very

birth, and naturally, scramble for every thing they covet, and would

have all the world, if they could, to fear and obey them? If by fortune

or industry one light upon a secret in nature, and thereby obtain the

credit of an extraordinary knowing man, should he not make use of it to

his own benefit? There is scarce one of a thousand but would live upon

the charges of the people as far as he dares. What poor geometrician is

there, but takes pride to be thought a conjurer? What mountebank would

not make a living out of a false opinion that he were a great physician?

And when many of them are once engaged in the maintenance of an error,

they will join together for the saving of their authority to decry the

truth.

_A._ I pray, tell me, if you can, how and where the study of philosophy

first began.

_B._ If we may give credit to old histories, the first that studied any

of the natural sciences were the astronomers of Ethiopia. My author is

Diodorus Siculus, accounted a very faithful writer, who begins his

history as high as is possible, and tells us that in Ethiopia were the

first astronomers; and that for their predictions of eclipses, and other

conjunctions and aspects of the planets, they obtained of their king not

only towns and fields to a third part of the whole land, but were also

in such veneration with the people, that they were thought to have

discourse with their gods, which were the stars; and made their kings

thereby to stand in awe of them, that they durst not either eat or drink

but what and when they prescribed; no nor live, if they said the gods

commanded them to die. And thus they continued in subjection to their

false prophets, till by one of their kings, called Ergamenes, (about the

time of the Ptolemies), they were put to the sword. But long before the

time of Ergamenes, the race of these astrologers (for they had no

disciples but their own children) was so numerous, that abundance of

them (whether sent for or no I cannot tell) transplanted themselves into

Egypt, and there also had their cities and lands allowed them, and were

in request not only for astronomy and astrology, but also for geometry.

And Egypt was then as it were an university to all the world, and

thither went the curious Greeks, as Pythagoras, Plato, Thales, and

others, to fetch philosophy into Greece. But long before that time,

abundance of them went into Assyria, and had their towns and lands

assigned them also there; and were by the Hebrews called Chaldees.

_A._ Why so?

_B._ I cannot tell; but I find in Martinius’s Lexicon they are called

Chasdim, and Chesdim, and (as he saith) from one Chesed the son of

Nachor; but I find no such man as Chesed amongst the issue of Noah in

the scripture. Nor do I find that there was any certain country called

Chaldæa; though a town where any of them inhabited were called a town of

the Chaldees. Martinius saith farther, that the same word Chasdim did

signify also Demons.

_A._ By this reckoning I should conjecture they were called Chusdim, as

being a race of Ethiopians. For the land of Chus is Ethiopia; and so the

name degenerated first into Chuldim, and then into Chaldim; so that they

were such another kind of people as we call gipsies; saving that they

were admired and feared for their knavery, and the gipsies counted

rogues.

_B._ Nay pray, except Claudius Ptolomæus, author of that great work of

astronomy, the Almegest.

_A._ I grant he was excellent both in astronomy and geometry, and to be

commended for his _Almegest_ ; but then for his _Judiciar Astrologie_

annexed to it, he is again a gipsy. But the Greeks that travelled, you

say, into Egypt, what philosophy did they carry home?

_B._ The mathematics and astronomy. But for that sublunary physics,

which is commonly called natural philosophy, I have not read of any

nation that studied it earlier than the Greeks, from whom it proceeded

to the Romans. Yet both Greeks and Romans were more addicted to moral

than to natural philosophy; in which kind we have their writings, but

loosely and incoherently, written upon no other principles than their

own passions and presumptions, without any respect to the laws of

commonwealth, which are the ground and measure of all true morality. So

that their books tend rather to teach men to censure than to obey the

laws; which has been a great hindrance to the peace of the western world

ever since. But they that seriously applied themselves to natural

philosophy were but few, as Plato and Aristotle, whose works we have;

and Epicurus whose doctrine we have in Lucretius. The writings of

Philolaus and many other curious students being by fire or negligence

now lost: though the doctrines of Philolaus concerning the motion of the

earth have been revived by Copernicus, and explained and confirmed by

Galileo now of late.

_A._ But methinks the natural philosophy of Plato, and Aristotle, and

the rest, should have been cultivated and made to flourish by their

disciples.

_B._ Whom do you mean, the successors of Plato, Epicurus, Aristotle, and

the other first philosophers? It may be some of them may have been

learned and worthy men. But not long after, and down to the time of our

Saviour and his Apostles, they were for the most part a sort of needy,

ignorant, impudent, cheating fellows, who by the profession of the

doctrine of those first philosophers got their living. For at that time,

the name of philosophy was so much in fashion and honour amongst great

persons, that every rich man had a philosopher of one sect or another to

be a schoolmaster to his children. And these were they that feigning

Christianity, with their disputing and readiness of talking got

themselves into Christian commons, and brought so many heresies into the

primitive Church, every one retaining still a tang of what they had been

used to teach.

_A._ But those heresies were all condemned in the first Council of Nice.

_B._ Yes. But the Arian heresy for a long time flourished no less than

the Roman, and was upheld by divers Emperors, and never fully

extinguished as long as there were Vandals in Christendom. Besides,

there arose daily other sects, opposing their philosophy to the doctrine

of the Councils concerning the divinity of our Saviour; as how many

persons he was, how many natures he had. And thus it continued till the

time of Charlemagne, when he and Pope Leo the third divided the power of

the empire into temporal and spiritual.

_A._ A very unequal division.

_B._ Why? Which of them think you had the greater share?

_A._ No doubt, the Emperor: for he only had the sword.

_B._ When the swords are in the hands of men, whether had you rather

command the men or the swords?

_A._ I understand you. For he that hath the hands of the men, has also

the use both of their swords and strength.

_B._ The empire thus divided into spiritual and temporal, the freedom of

philosophy was to the power spiritual very dangerous. And for that cause

it behoved the Pope to get schools set up not only for divinity, but

also for other sciences, especially for natural philosophy. Which when

by the power of the Emperor he had effected, out of the mixture of

Aristotle’s metaphysics with the Scripture, there arose a new science

called School-divinity; which has been the principal learning of these

western parts from the time of Charlemagne till of very late.

_A._ But I find not in any of the writings of the Schoolmen in what

manner, from the causes they assign, the effect is naturally and

necessarily produced.

_B._ You must not wonder at that. For you enquire not so much, when you

see a change of anything, what may be said to be the cause of it, as how

the same is generated; which generation is the entire progress of nature

from the efficient cause to the effect produced. Which is always a hard

question, and for the most part impossible for a man to answer to. For

the alterations of the things we perceive by our five senses are made by

the motion of bodies, for the most part, either for distance, smallness,

or transparence, invisible.

_A._ But what need had they then to assign any cause at all, seeing that

they could not show the effect was to follow from it?

_B._ The Schools, as I said, were erected by the Pope and Emperor, but

directed by the Pope only, to answer and confute the heresies of the

philosophers. Would you have them then betray their profession and

authority, that is to say, their livelihood, by confessing their

ignorance? Or rather uphold the same, by putting for causes, strange and

unintelligible words; which might serve well enough not only to satisfy

the people whom they relied on, but also to trouble the philosophers

themselves to find a fault in.

_A._ Seeing you say that alteration is wrought by the motion of bodies,

pray tell me first what I am to understand by the word body.

_B._ It is a hard question, though most men think they can easily answer

it, as that it is whatsoever they can see, feel, or take notice of by

their senses. But if you will know indeed what is body, we must enquire

first what there is that is not body. You have seen, I suppose, the

effects of glasses, how they multiply and magnify the object of our

sight; as when a glass of a certain figure will make a counter or a

shilling seem twenty, though you be well assured there is but one. And

if you set a mark upon it, you will find the mark upon them all. The

counter is certainly one of those things we call bodies: are not the

others so too?

_A._ No, without doubt. For looking through a glass cannot make them

really more than they are.

_B._ What then be they but fancies, so many fancies of one and the same

thing in several places?

_A._ It is manifest they are so many idols, mere nothings.

_B._ When you have looked upon a star or candle with both your eyes, but

one of them a little turned awry with your finger, has not there

appeared two stars, or two candles? And though you call it a deception

of the sight, you cannot deny but there were two images of the object.

_A._ It is true, and observed by all men. And the same I say of our

faces seen in looking-glasses, and of all dreams, and of all apparitions

of dead men’s ghosts; and wonder, since it is so manifest, I never

thought upon it before, for it is a very happy encounter, and such as

being by everybody well understood, would utterly destroy both idolatry

and superstition, and defeat abundance of knaves that cheat and trouble

the world with their devices.

_B._ But you must not hence conclude that whosoever tells his dream, or

sometimes takes his direction from it, is therefore an idolater, or

superstitious, or a cheater. For God doth often admonish men by dreams

of what they ought to do; yet men must be wary in this case that they

trust not dreams with the conduct of their lives farther than by the

laws of their country is allowed: for you know what God says, Deut.

xiii: _If a prophet or a dreamer of dreams give thee a sign or a wonder,

and the sign come to pass, yet if he bid thee serve other Gods let him

be put to death_. Here by serving other Gods (since they have chosen God

for their King) we are to understand revolting from their King, or

disobeying of his laws. Otherwise I see no idolatry nor superstition in

following a dream, as many of the Patriarchs in the Old Testament, and

of the Saints in the New Testament did.

_A._ Yes: their own dreams. But when another man shall dream, or say

that he has dreamed, and require me to follow that, he must pardon me if

I ask him by what authority, especially if he look I should pay him for

it.

_B._ But if commanded by the laws you live under, you ought to follow

it. But when there proceed from one sound divers echoes, what are those

echoes? And when with fingers crossed you touch a small bullet, and

think it two; and when the same herb or flower smells well to one and

ill to another, and the same at several times, well and ill to yourself,

and the like of tastes, what are those echoes, feelings, odours, and

tastes?

_A._ It is manifest they are all but fancies. But certainly when the sun

seems to my eye no bigger than a dish, there is behind it somewhere

somewhat else, I suppose a real sun, which creates those fancies, by

working, one way or other, upon my eyes, and other organs of my senses,

to cause that diversity of fancy.

_B._ You say right; and that is it I mean by the word body, which

briefly I define to be any thing that hath a being in itself, without

the help of sense.

_A._ Aristotle, I think, meaneth by body, _substance_, or _subjectum_,

wherein colour, sound, and other fancies are, as he says, inherent. For

the word essence has no affinity with substance. And Seneca says, he

understands it not. And no wonder: for essence is no part of the

language of mankind, but a word devised by philosophers out of the

copulation of two names, as if a man having two hounds could make a

third, if it were need, of their couples.

_B._ It is just so. For having said in themselves, (for example): _a

tree is a plant_, and conceiving well enough what is the signification

of those names, knew not what to make of the word _is_, that couples

those names; nor daring to call it a body, they called it by a new name

(derived from the word _est_), _essentia_, and _substantia_, deceived by

the idiom of their own language. For in many other tongues, and namely

in the Hebrew, there is no such copulative. They thought the names of

things sufficiently connected, when they are placed in their natural

consequence; and were therefore never troubled with essences, nor other

fallacy from the copulative _est_.

==========