Chapter
16
Syringes, Siphons and Suckling Infants
t
It is just as natural for air to enter and drop down into the lungs when they open, as
for wine to drop into a bottle when it is poured in.
Dr
af
Introduction
—Blaise Pascal
In Chapter 5 of his Treatise on the Equilibrium of Liquids, Pascal observed that a submerged
body is pressed on all sides by the surrounding fluid. The forces on the top and bottom surfaces
of the body, however, are not equal because the fluid which is in contact with the bottom surface
is under greater pressure than the fluid which is in contact with the top surface. This gives rise
to an overall buoyant force acting on the submerged body which turns out to be exactly equal
to the weight of the displaced fluid—just as Archimedes said. But how does the force which acts
on a surface of a submerged body vary with its depth, h? This force per unit area is called the
hydrostatic pressure, p. It is given by
p = ⇢gh.
(16.1)
Here, ⇢ is the density of the ambient fluid and g is the acceleration of gravity, which acts as a
conversion factor between mass and weight. Essentially, the hydrostatic pressure at a particular
depth is equal to the weight of the fluid pressing down on it from above.
Thus far, Pascal has been dealing with fluids such as water and mercury. But what about air—
does it have weight? According to Aristotle, gravity is a quality possessed by the elements earth
and water; it causes them to fall toward the center of the world. Levity, on the other hand, is a
quality which is possessed by the elements fire and air; it causes them to rise towards the heavens.
Gravity and levity are thus opposing and absolute qualities of substances.1 Aware of Aristotle’s
theory, Pascal begins his Treatise on the Weight of the Mass of the Air by reminding the reader
of the experimental evidence which proves that air in fact possesses gravity, or heaviness, just like
rocks. He then proceeds to derive the consequences of this fact. In particular, he suggests that
1 See,
for instance, Aristotle’s Meteorology, Book I, Physics, Book IV, and especially On the Heavens, Book IV.
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CHAPTER 16. SYRINGES, SIPHONS AND SUCKLING INFANTS
many of the phenomena which had previously been attributed to nature’s apparent abhorrence of a
vacuum—a doctrine advanced by Aristotle and maintained by Galileo2 —could be understood more
readily by considering Earth’s atmosphere to be a vast sea of air whose weight presses down upon
bodies submerged in it.3
Reading
Pascal, B., Scientific treatises, in Pascal, Great Books of the Western World, vol. 33, edited by
R. M. Hutchins, Encyclopedia Britannica, Inc., Chicago, 1952. Treatise on the Weight of the Mass
of the Air.
Chapter 1
That the mass of the air has weight, and that it presses with its weight all the bodies
it surrounds.
Dr
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No one denies today that the air is heavy. We know that a balloon weighs more when inflated
than when empty, which is sufficient proof; for if the air were light, the more of it we put in the
balloon the more levity the whole would have, for the whole would have more than a part would
have; but since on the contrary the more air we put in the heavier the whole is, it follows that each
part is itself heavy and consequently that the air is heavy.
Those who want longer proofs have only to look them up in the authors who have expressly
dealt with this matter.
If it be objected that air is light when it is pure but that the air which surrounds us is not pure
air because it is mixed with vapors and gross bodies, and that it is only because of these foreign
bodies that it is heavy, I reply in a word that I do not know pure air and that it might be hard
to find; but I speak in this treatise only of the air as it exists in the state in which we breathe it,
without considering whether it be composite or not; and it is that body, simple or composite, which
I call air and of which I say that it is heavy: a fact which cannot be denied, and that is all I require
in what follows.
This principle laid down, I shall stop only to draw certain consequences.
1. Since each part of the air is heavy, it follows that the whole mass of the air (that is, the whole
sphere of the air) is heavy; and since the sphere of the air is not infinite in its extent, since it has
limits, so also the weight of the mass of all the air is not infinite.
2. Just as the mass of the water of the sea presses with its weight the earth beneath it, and just
as, if it covered the whole earth instead of a part of it only, it would press with its weight the whole
surface of the earth; so since the mass of the air covers the entire surface of the earth, this weight
presses its every part.
3. Just as the bottom of a bucket containing water is more pressed by the weight of the water
when the bucket is full than when it is half full, and is the more pressed the deeper the water; so
2 Albeit
in a limited form; see Galileo’s treatment of this subject in Ch. 2 of the present volume.
doctrine which Pascal here defends had been proposed a few years earlier by Galileo’s successor at the
Academy of Florence, Evangelista Torricelli; see, for instance, Torricelli, E., The Barometer, in A Source Book
in Physics, edited by W. F. Magie, Source Books in the History of Science, pp. 70–73, Harvard University Press,
Cambridge, Massachusetts, 1963.
3 The
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high places like mountain tops are not so pressed by the weight of the mass of the air as are low
places like valleys, because there is more air above the valleys than above the mountain tops; for
all the air alongside the mountain weighs on the valley and not on the summit, because it is above
the one and below the other.
4. Just as bodies in water are pressed on all sides by the weight of the water above, as I have
shown in the Treatise on the equilibrium of liquids, so bodies in the air are pressed on all sides by
the weight of the mass of the air above.
5. As animals in water do not feel its weight, so for the same reason we do not feel the weight
of the air; and as we could not conclude that water has no weight from our not feeling it when we
are immersed in it, so we cannot conclude that air is not heavy because we do not feel it to be so.
We have shown the reason for this in the Equilibrium of liquids.
6. Just as if we had got together a great heap of wool twenty or thirty fathoms high, this mass
would be compressed by its own weight, and the bottom part would be much more compressed
than the middle pact or the part near the top because it would be pressed by a greater amount of
wool; so the mass of the air, which like wool is a compressible and heavy body, is compressed by
its own weight; and the air on the bottom, that is, in low-lying places, is much more compressed
than that higher up, as on mountain tops, because it carries a greater weight of air.
Dr
af
t
7. Just as if we took a handful of that mass of wool from the bottom in its compressed state
and keeping it still compressed in the same way, put it in the middle of the mass, it would of
itself increase in size since it was nearer the top, because it would have to carry the weight of a
lesser amount of wool there; so if we contrived in some way to take air, as it is down here and
compressed as it is, to the top of a mountain, it would have to increase in size of itself and attain to
the condition of the air surrounding it on the mountain top, because it would carry a lesser weight
of air in this place than below. Consequently if we took a balloon only half filled with air, and not
entirely inflated as they usually are, and carried it up a mountain, it should be more inflated on the
mountain top and should increase in size in proportion to its being less pressed; and the di↵erence
should be perceptible if the weight of the quantity of air alongside the mountain from which it is
freed is considerable enough to cause a sensible e↵ect and di↵erence.
These consequences are so necessarily bound up with their principle that the one cannot be true
without the others being equally so; and since it is certain that the air reaching from the earth to
the top of its sphere has weight, all our conclusions therefrom are equally true.
But however certain we find these conclusions, it seems to me that everyone, even though
accepting them, would want to see the last consequence confirmed by experiment, because it contains
both all the rest and its own principle; for it is certain that if we saw a balloon, as described above,
expand as it is carried higher, we could not possibly doubt that this expansion came from the fact
that the air in the balloon was more pressed below than above, since there is nothing else that
could cause it to expand, it being even colder on the mountain tops than in the valleys; and this
compression of the air in the balloon could have no other cause than the weight of the mass of the
air, for the air was taken as it was in the low altitude and was not compressed, since the balloon
was even soft and only half filled. Consequently this would absolutely prove that the air is heavy;
that the mass of the air is heavy; that it presses with its weight all the bodies it surrounds; that it
presses low-lying places more than high places; that it is itself compressed by its own weight; that
the air is more compressed below than above. And since in physics experiments have much more
force of persuasion than arguments have, I do not doubt that everyone would want to see the latter
confirmed by the former.
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But if the experiment were made, I should have this advantage that in case there occurred no
di↵erence in the inflation of the balloon on the highest mountains, that would not invalidate my
conclusion, because I could say they are not yet sufficiently high to cause a perceptible di↵erence;
whereas if there should be a very considerable di↵erence, as of one-eighth or one-ninth, certainly
the experiment would be decisive in my favor, and there could no longer be any doubt of the truth
of everything I have established.
But I must say at once without further delay that the test has been made, and successfully, as
follows.
Experiment made in two places, di↵ering in altitude by about 500 fathoms.
Dr
af
t
If we take a balloon half filled with air, flaccid and soft, and carry it at the end of a string up
a mountain 500 fathoms high, it will expand of itself as we go up, and when we are at the top, it
will be entirely full and rounded out as if we had blown in more air; and as we go down again, it
will little by little lose its roundness, passing through the same degrees, so that when we reach the
bottom, the balloon will have returned to its original state.
This experiment proves conclusively everything I have said about the mass of the air; and it
was necessary to establish that firmly, since it is the foundation of the whole discourse.
It only remains to point out that the mass of the air is heavier at one time than at another,
namely, when it carries more vapor or is more compressed by cold.
Let us observe then, 1. that the mass of the air is heavy; 2. that its weight is limited; 3. that
it is heavier at one time than at another; 4. that it is heavier in certain places than in others, as
in valleys; 5. that it presses with its weight all the bodies it surrounds, and presses the more the
heavier it is.
Chapter 2
That the weight of the mass of the air produces all the e↵ects hitherto attributed to
the horror of a vacuum.
This chapter is divided into two sections: in the first is an account of the principal e↵ects
attributed to the horror of the vacuum; and in the second it is shown that they come from the
weight of the air.
First section Account of the e↵ects attributed to the horror of a vacuum.
There are certain e↵ects which it is claimed nature produces because of her horror of a vacuum.
The chief are:
1. It is hard to open a bellows whose apertures have been carefully stopped; and if we try to do
it, we feel resistance as if its sides were glued together. And the piston of a sealed syringe resists
when we try to pull it up, as if it were stuck to the bottom.
It is claimed that this resistance comes from nature’s horror of the vacuum which would be made
in the bellows if it could be opened up; which is confirmed by the fact that the resistance ceases as
soon as the stoppers are removed and the air can get in to fill the bellow; when it is opened.
2. Two polished bodies when placed together are hard to separate and seem to adhere.
Similarly a hat when put on a table is hard to snatch up.
Dr
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t
181
Figure 16.1: Figures for Pascal’s Treatise on the Weight of the Mass of the Air (image courtesy of
IIHR).—[K.K.]
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CHAPTER 16. SYRINGES, SIPHONS AND SUCKLING INFANTS
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Similarly a piece of leather when put on a paving stone and suddenly lifted, loosens and lifts up
the stone.
It is claimed that this adhesion comes from nature’s horror of the vacuum which would exist
during the time it would take the air to get from the edges to the center.
3. When a syringe is dipped in water, if the piston is pulled up, the water follows and rises as
if it adhered to the piston.
Similarly the water rises in a suction pump, which is actually nothing but a long syringe, and
follows the piston when it is lifted, as if it adhered to it.
It is claimed that the rising of the water comes from nature’s horror of the vacuum which would
be made in the place left by the piston if the water did not rise, because the air cannot get in; which
is confirmed by this, that if holes are made through which the air can get in, the water no longer
rises.
In the same way if we put the nozzle of a bellows in water and suddenly open the bellows, the
water rises to fill it because the air cannot get in, and especially if we stop the air holes in the wing.
Similarly when we put our mouth in water and suck, we draw up the water for the same reason;
for the lungs are like a bellows, of which the mouth would be the nozzle.
Similarly in breathing we draw in the air as a bellows in opening draws in the air to fill up its
capacity.
Similarly when we put lighted wicks in a saucer filled with water and a glass over them, as the
flame of the wicks dies down, the water rises in the glass because the air in the glass, which had
been rarefied by the flame, is now condensed by the cold and draws the water up and makes it rise
along with itself as it contracts, in order to fill the place it is leaving; just as the piston of a syringe
draws the water up with it when we lift it.
Similarly cupping glasses draw the flesh and cause a swelling, because the air inside the glass,
rarefied by the candle flame, is now condensed by rile cold when the flame is extinguished and
draws the flesh with it to fill the place it leaves, as it drew the water in the preceding example.
4. If we put a bottle filled with water mouth down in a vessel filled with water, the water in the
bottle remains suspended without falling.
It is claimed that the water does not fall because of nature’s horror of the vacuum which would
be made in the place left by the water if falling, for the air could not get in; this explanation is
confirmed by the fact that if a hole is made through which the air can get in, all the water falls
immediately.
We can make the same test with a tube, ten feet long say, stopped at the upper end and open
at the bottom; for if it is filled with water and the lower end is dipped in a vessel of water, all the
water in the tube remains suspended, whereas it would fall at once if the top of the rube had been
opened.
We can do the same thing with a like tube, stopped at the top and recurved at the bottom,
without putting it in a vessel of water as was done with the other one; for if it is filled with water,
this water too will remain suspended, whereas if the top were opened, the water would at once
spurt out with violence from the recurved end as from a fountain.
Finally the same thing can be done with a plain tube, without its being recurved, provided it be
very narrow at the bottom; for if it is stopped at the top, the water will remain suspended, whereas
it would fall with violence if we opened the upper end.
It is for the same reason that a cask filled with wine does not give up a drop of it, though the
spigot be open, unless we make an opening in the top to admit air.
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5. If we fill with water a tube in the shape of an inverted crescent (which is ordinarily called a
siphon), and let each leg dip in a vessel filled with water, then unless the two vessels are at exactly
the same level, all the water in the higher vessel will rise in the leg dipping in it to the top of
rhe siphon and will pass through the other leg into the lower vessel; so that if water is constantly
supplied to the higher vessel, the flow will be continuous.
It is claimed that this rising of the water comes from nature’s honor of the vacuum which would
be made in the siphon if the water in the two legs fell from each into the corresponding vessels, as
it actually does fall when an opening is made in the top of the siphon through which the air call get
in.
There are several other like e↵ects I omit because they are all similar to those of which I have
spoken and because in all mere appears only this, that all the contiguous bodies resist the e↵ort
made to separate them when air cannot get in between them, whether this e↵ort comes from their
own weight, as in the examples in which water rises and remains suspended in spite of its weight,
or whether it comes from forces we use to separate them, as in the first examples.
These are the e↵ects commonly attributed to the horror of the vacuum; I am going to show that
they come from the weight of the air.
t
Second Section That the weight of the mass of the air produces all the e↵ects that
have been attributed to the horror of the vacuum.
Dr
af
If we have dearly understood in the Treatise on the equilibrium of liquids how liquids act with
their weight against all bodies in them, we shall have no difficulty in understanding how the weight
of the mass of air, acting upon all bodies, produces all the e↵ects that had been attributed to the
horror of the vacuum, for they are exactly alike, as we shall show in each instance.
1. That the weight of the mass of the air causes the difficulty in opening a bellows with all its
apertures stopped.
That it may be understood how the weight of the mass of the air causes the difficulty we
experience in opening a bellows when the air cannot get in, I shall point out a like resistance caused
by the weight of water. All that is needed is to recall what I said in the Equilibrium of liquids
[Fig. 14.1, XIV], that a bellows with a cube of twenty feet or more, placed in a tank of water in such
a way that the end of the tube emerges from the water, is hard to open, and so much the harder
as the water is deeper; which comes obviously from me weight of the water above, for when there
is no water, the bellows opens very easily; and in proportion as water is poured in, the resistance
increases and is always equal to the weight of the water carried by the bellows, because since the
water cannot get in because the tube is outside, we could not open the bellows without lifting and
holding up the whole mass of the water; for the water displaced by opening the bellows, not being
able to enter it, is forced to go elsewhere and thus to raise the level of the water, which cannot
be done without e↵ort; whereas if the bellows were broken and the water could get in, we could
open and dose it without resistance because the water would go in through the breaks as fast as
the bellows was opened, and so we could open it without having to lift up the water.
I do not think anyone will be tempted to say that this resistance comes from the horror of the
vacuum, and it is absolutely certain that it comes from the weight of the water alone.
But what I say of water should be understood of any other fluid; for if we put the bellows in a
tank filled with wine, we shall feel a like resistance to opening it, and likewise if we put it in milk,
in oil, in quicksilver, and in short in any fluid whatsoever. It is then a general rule and a necessary
e↵ect of the weight of fluids: that if a bellows is put in any fluid whatsoever in such a way that
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it cannot get into the body of the bellows, the weight of the fluid above prevents our opening the
bellows without feeling resistance, because we could not do it without holding up the fluid; and
consequently, applying this general rule to the particular case of the air, it will be true that when
the air is kept from entering a bellows, the weight of the mass of the air above prevents our opening
the bellows without feeling resistance, because we could not open it without lifting the whole mass
of the air; but as soon as we make an opening in it, we open and close it without resistance because
the air can get in and out, and so when we open the bellows, we do not have to lift the mass of the
air; which is entirely conformable to the example of the bellows in water.
Whence we see that the difficulty in opening a sealed bellows is only a particular case of the
general rule concerning the difficulty of opening a bellows in any fluid whatsoever when the fluid
has no access to it.
What I have said of this e↵ect I shall say of each of the others, but more succinctly.
2. That the weight of the mass of the air is the cause of the difficulty we experience in separating
two polished bodies when placed together.
That it may be understood how the weight of the mass of the air causes the resistance we
feel when we want to separate two polished bodies that have been placed together, I shall give an
example of an altogether similar resistance caused by the weight of the water, which will leave no
room for doubt that the air causes this e↵ect.
We must here again recall what was set forth in the Equilibrium of liquids [Fig. 14.1, XI].
That if we put a copper cylinder, turned on a lathe, in the opening of a funnel, also turned on
a lathe, so that they fit so perfectly that the cylinder easily enters and slides back and forth in the
funnel but without letting any water escape between, and if we put this machine in a tank of water
in such a way that the stem of the funnel emerges from the water (which stem may have a length
of twenty feet if necessary); if with the cylinder at a depth of fifteen feet in the water, holding the
funnel with the hand, we let loose the cylinder and abandon it to its fate, we shall see that not only
will it not fall although it seems there is nothing to hold it up, but even that it will be difficult to
pull it out of the funnel although it is in no way stuck to it; whereas it would fall by its own weight
with violence if it were at a depth of only four feet in the water, and still more violently if it were
entirely outside the water. I have also shown the reason for this, which is that the water, in contact
with the cylinder from below and not from above (for it does not touch its upper surface because
the funnel keeps it from getting there), pushes it from the side it touches toward the side it does
not touch, and thus pushes it up and presses it against the funnel.
The same thing should be understood of every other fluid; and consequently if two bodies are
polished and placed together and if we hold the upper one with the hand and let the other go,
the lower one remains suspended because the air is in contact with it from beneath and not from
above, for it cannot get in between the two bodies and consequently it cannot reach the surfaces in
contact; whence it follows by a necessary e↵ect of the weight of all fluids in general that the weight
of the air must push this body up and press it against the other so that if we try to separate them,
we meet with great resistance; which is entirely conformable to the e↵ect of the weight of water.
Whence we see that the difficulty in separating two polished bodies is only a particular case
of the general rule concerning the pressure of all fluids in general when they are in contact with a
body on one of its surfaces and not on the opposite surface.
3. That the weight of the mass of the air is the cause of the rise of water in syringes and pumps.
To explain how the weight of the mass of the air makes water rise in pumps as the plunger
is lifted, I shall show an entirely similar e↵ect of the weight of water, which will make the reason
perfectly clear as follows:
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Dr
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If we fit a syringe with a long piston, ten feet say, hollow throughout its length, with a valve at
the lower end so arranged that it opens downward but not upward, so that the syringe is incapable
of lifting water or any liquid above the level of the liquid because the air can enter it perfectly freely
through the hollow piston; if now we put the opening of the syringe in a vessel filled with quicksilver
and the whole in a tank of water in such a way that the top of the piston emerges from the water,
when we lift the piston, the quicksilver will rise and follow it as if it adhered to it; whereas it would
not rise at all if there were no water in the tank, because the air is entirely free to enter the body
of the syringe through the hollow piston.
So the fear of the vacuum is not the cause; for if the quicksilver did not rise to fill the place left
by the piston, there would be no vacuum since the air may freely enter; but it is only because the
mass of the water weighing upon the quicksilver in the vessel and pressing it in all its parts except
where the opening of the syringe is (for the water cannot reach there since it is kept away by the
body of the syringe and by the piston), the quicksilver, pressed in every place but one, is pushed
by the weight of the water toward that one as soon as the piston by being lifted leaves it a free
place to enter, and balances in the syringe the weight of the water which weighs on the quicksilver
outside.
But if holes are made in the syringe so the water can get in, the quicksilver will no longer
rise because the water enters and is as much in contact with the quicksilver at the mouth of the
syringe as elsewhere, and thus since all of it is equally pressed, none of it rises. All this was dearly
demonstrated in the Equilibrium of liquids.
We see in this example how the weight of the water makes the quicksilver rise; and we could
produce a similar e↵ect with the weight of sand by removing the water from the tank; if instead of
water we pour in sand, the weight of the sand will make the quicksilver rise in the syringe because
it presses, just as the water did, everywhere except at the mouth of the syringe, and thus it pushes
the quicksilver and forces it to rise in the syringe.
And if we put our hands on the sand and press it, we shall make the quicksilver rise higher
inside the syringe and keep on rising to a height at which it can counterpoise the pressure outside.
The explanation of these e↵ects makes it very easy to understand why the weight of the air
causes water to rise in ordinary syringes as the piston is drawn up; for since the air is in contact
with the water in the vessel everywhere except at the opening of the syringe (from which it is kept
away by the syringe and the piston), it is obvious that the weight of the air, pressing the water
in every place but that one, must push it thither and make it rise, as the piston by being lifted
leaves room for it to come in and counterbalance within the syringe the weight of the air. which
weighs outside, for the same reason and by the same necessity as the quicksilver rose, pressed by
the weight of the water and by the weight of the sand, in the example we have just given.
It is then obvious that the rising of water in syringes is only a particular case of the general rule
that when a fluid is pressed in every place but one by the weight of some other fluid, this weight
pushes it toward the place where it is not being pressed.
4. That the weight of the mass of the air causes water to be suspended in tubes stopped at the
upper end.
To make it understood how the weight of the air holds water suspended in tubes stopped at the
upper end, I shall point out an entirely similar example of a like suspension caused by the weight
of water, which will make the reason perfectly dear.
And first it may be said at once that this e↵ect is entirely comprehended in the preceding; for
Just as I have shown that the weight of the air makes water rise in syringes and holds it suspended
there, so the same weight of the air holds water suspended in a tube. That this e↵ect may not
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lack, any more than the rest, another entirely like it to which it may be compared, I shall say
that nothing is needed to this end but to remember what was said in the Equilibrium of liquids
[Fig. 14.1, IX], namely, that a tube ten feet long or more, recurved at the bottom and filled with
mercury, having been put in a tank of water so that the upper end emerges from the water, part of
the mercury remains suspended inside the tube, that is, at the height where it can counterbalance
the water which weighs outside; and that a the suspension takes place even in a tube not recurved,
simply open at both ends, with the upper end emerging from the water.
Now it is obvious that this suspension does not come from the horror of a vacuum, but only
from this, that the water, weighing outside and not inside the tube and in contact with the mercury
on one side and not on the other, holds it suspended by its weight at a certain height; therefore if
the tube is pierced so that the water can get in, straightway all the mercury falls, because since the
water is in contact with it everywhere and acting within as well as without, the mercury no longer
has a counterpoise. All this was said in the Equilibrium of liquids.
Since this is a necessary e↵ect of the equilibrium of fluids, it is not strange that when a tube
is filled with water, stopped at the top and recurved at the bottom the water remains suspended
in it; for the air, weighing on the part of the water at the recurved end and not on the part in
the tube (since it is prevented by the stopper), must of necessity hold the water suspended inside
to counterbalance its own weight outside, exactly as the weight of the water held the mercury in
equilibrium in the example we just gave.
And similarly when the tube is not recurved; for because the air is in contact with the water from
below and not from above (since the stopper prevents contact there), it is absolutely necessary that
the weight of the air hold up the water, exactly as the water held up the mercury in the example
just given, and as the water pushes up and holds suspended a copper cylinder it is in contact with
from below and not from above; but if the stopper is removed, the water falls, for the air is in
contact with the water below and above and weighs inside and outside the tube.
Whence we see that the action of the air in holding liquids suspended with which it is in contact
on one side and not on the other is a case of the general rule that fluids contained in any kind of
tube whatsoever, immersed in another fluid which presses them from one side and not from the
other, are suspended by the equilibrium of the fluids.
5. That the weight of the mass of the air makes water rise in siphons.
To explain how the weight of the air makes water rise in siphons I am going to show that the
weight of water makes quicksilver rise in a siphon open at the top so that it is freely accessible to
the air; whence we shall see how the weight of the air produces this e↵ect. This I shall do as follows.
If one leg of a siphon is about one foot high and the other about one foot, one inch, and if we
make an opening in the top of the siphon in which we insert a tube twenty feet long and carefully
soldered to the opening, and if, having filled the siphon with quicksilver, we put each of its legs in
a vessel also filled with quicksilver and the whole in a tank of water, fifteen or sixteen feet deep in
the water, with the end of the tube therefore out of the water, then if there is any di↵erence at
all in level between the two vessels, say an inch, all the quicksilver in the higher vessel will rise in
the siphon to the top and will pass through the other leg into the lower vessel in a continuous flow;
and if we keep the higher vessel supplied with quicksilver, the flow will never cease; but if we make
an opening in the siphon through which the water can get in, immediately the quicksilver will fall
from each leg into the vessels and water will take its place.
This rising of quicksilver does not come from the horror of the vacuum, for the air has perfectly
free access to the siphon; accordingly if we emptied the tank of water, the quicksilver would fall
from each leg into the corresponding vessel, and the air would take its place, coming in through the
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open tube.
It is then obvious that the weight of the water causes the quicksilver to rise, because the water
weighs upon the quicksilver in the vessels and not upon that in the siphon; and for this reason the
water by its weight forces the quicksilver to rise and to flow as it does; but as soon as the siphon
has been pierced and the water can enter, it no longer makes the quicksilver rise, because it weighs
inside as well as outside the siphon.
But for the same reason and by the same necessity as the water thus makes the quicksilver rise
in a siphon when it weighs on the vessels and has no access to the interior of the siphon, so also the
weight of the air makes water rise in ordinary siphons, because it weighs on the vessels in which the
legs of the siphon dip and has no access to the body of the siphon, which is entirely closed; and as
soon as an opening is made in the siphon, the water no longer rises, but on the contrary falls into
each vessel, and air takes its place because then the air weighs inside as well as outside the siphon.
It is obvious that this last e↵ect is only a case of the general rule, and that if we really understand
why the weight of the water makes the quicksilver rise in the example we gave, we shall see at the
same time why the weight of the air makes water rise in ordinary siphons; this is the reason it must
be made perfectly clear why the weight of the water produces this e↵ect, and why it is the higher
vessel which empties into the lower vessel rather than the other way around.
To this end it must be observed that, the water weighing on the quicksilver in each of the vessels
and not at all on that in the legs of the siphon dipping in the vessels, the quicksilver in the vessels
is urged by the weight of the water to rise in each leg of the siphon all the way up and still higher,
if that were possible, because the water is sixteen feet deep and the siphon is only one foot high,
and one foot of quicksilver is equal in weight to only fourteen feet of water; whence it is seen that
the weight of the water pushes the quicksilver in each leg all the way up and still has some force
left; whence the quicksilver in each leg being pushed up by the weight of the water, they contend
at the top of the siphon, pushing each other, so that the one having the greater force must prevail.
Now that will be easy to calculate; for it is clear that since the water has greater depth above
the vessel which is an inch lower, it pushes up the quicksilver in the longer leg more forcibly than
that in the other leg by the force which an inch of depth gives it; whence it seems at first the
result should be that the quicksilver should be pushed from the longer leg into the shorter; but we
must consider that the weight of the quicksilver in each leg resists the e↵ort made by the water
to push it up, but they do not resist equally, for since the quicksilver of the long leg has an inch
more of height, it resists more forcibly by the force given it by the height of one inch; therefore the
mercury in the longer leg is more pushed up by the weight of the water by the force of an inch of
water, but it is more pushed down by its own weight by the force of an inch of quicksilver; but an
inch of quicksilver weighs more than an inch of water; therefore the quicksilver in the shorter leg is
pushed up with more force, and consequently it must rise and continue to rise as long as there is
any quicksilver in the vessel in which it dips.
Whence it is apparent that the reason why the higher vessel empties into the lower is that
quicksilver is a heavier liquid than water. The opposite would happen if the siphon were filled with
oil and the whole were in the same tank of water, for then the oil in the lower vessel would rise and
flow through the top of the siphon into the higher vessel for the same reasons just given; for the
water still pushing the oil in the lower vessel with more force because it has an inch more of depth
and the oil in the long leg resisting and weighing more by its extra inch of height, since an inch of
oil weighs less than an inch of water, the oil in the long leg would be pushed up with more force
than the oil in the other leg, and consequently it would flow and would pass from the lower vessel
to the higher vessel.
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And finally if the siphon were filled with a liquid which had the same weight as the water in the
tank, then neither would the water in the higher vessel pass into the other vessel nor that in the
lower pass into the higher, but everything would remain at rest, for by calculating all the forces we
shall see that they are all equal.
That is what had to be firmly grasped if we were to have a thorough understanding of why
liquids rise in siphons; after which it is too easy to see why the weight of the air makes water rise
in ordinary siphons and pass from the higher vessel into the lower for us to give more time to it,
since it is only a case of the general rule we have just given.
6. That the weight of the mass of the air causes the swelling of the flesh when a cupping glass
is applied.
To explain how the weight of the mass of the air makes the flesh swell where a cupping glass
is applied, I shall cite an entirely similar e↵ect caused by the weight of water, which will leave no
doubt in the mind.
It is the e↵ect recorded in the Equilibrium of liquids [Fig. 14.1, XVII], where I showed that
a man applying to his thigh the end of a glass tube twenty feet long and seating himself in this
condition at the bottom of a tank of water in such a way that the upper end of the tube emerges
from the water, his flesh swells at the opening of the tube as if there were suction in that place.
Now it is evident that this swelling does not come from the horror of the vacuum, for the tube is
completely open and the swelling would not occur if there were only a little water in the tank; and
it is altogether certain that it comes from the weight of the water only, because the water, pressing
the flesh everywhere except at the entrance of the tube (for it finds no access there), drives the
blood and the flesh there to make the swelling.
And what I say of the weight of the water is to be understood of the weight of any other liquid;
for if our man seats himself in a tank of oil, the same thing will happen as long as that liquid is in
contact with every part of his body but one. But if the tube is removed, the swelling goes down
because the water now exerting its action upon that part as well as on the others, there will be no
more e↵ect there than elsewhere.
This being understood, we shall see that when we put a candle on the flesh and a cupping glass
over it, as soon as the flame is extinguished, the flesh necessarily swells; for the air in the cupping
glass, which was highly rarefied by the flame, having become condensed by the cold following upon
the extinction of the flame, the weight of the air is in contact with the body everywhere except
beneath the cupping glass (for there is no access there); and consequently the flesh must swell there,
and the weight of the air must drive the adjacent blood and flesh, which it presses, into that part
which it does not press, for the same reason and by the same necessity that the weight of the water
did in the example I gave, when it was in contact with the body in every place but one; whence
it is apparent that the behavior of the cupping glass is only a particular case of the general rule
concerning the action of all fluids upon a body with all pans of which they are in contact save one.
7. That the weight of the mass of the air is the cause of the attraction that takes place in suction.
Only a word is now required to explain why when we apply our mouth to water and suck, the
water comes in; for we know that the weight of the air presses the water everywhere except where
the mouth is, for it is in contact with it everywhere except there; and thence it is that when the
respiratory muscles, lifting the chest, enlarge the capacity of the interior of the body, the air inside,
having more space to fill than before, has less force to prevent the water from entering the mouth
than the air outside, which weighs on the water everywhere except in this one place, has force to
make it enter.
That is the cause of this attraction, which di↵ers in no respect from the attraction of syringes.
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8. That the weight of the mass of the air is the cause of the drawing of milk by infants from
their nurses’ breasts.
Similarly a baby with its lips about the nipple of its nurse’s breast, when it sucks, draws in milk,
because the breast is pressed on all sides by the weight of the surrounding air except in the part
which is in the child’s mouth; and that is why as soon as the respiratory muscles make more room
in the child’s body, as has just been said, and nothing is in contact with the nipple of the breast
but the air inside, the air outside, which has more force and compresses the breast, pushes the milk
through this opening where there is less resistance; which is as necessary and as natural as for the
milk to come out when the nipple is pressed between the hands.
9. That the weight of the mass of the air is the cause of the drawing in of air in breathing.
And for the same reason when we breathe, air enters the lungs, because when the lungs open
and the nose and all the passages are free and open, the air which is in contact with these passages,
pushed by the weight of all its mass, enters and falls by the natural and necessary action of its
weight; which is so understandable, so easy, and so simple that it is strange recourse should have
been had to the horror of the vacuum, to occult qualities, and to causes so remote and so chimerical,
to find a reason, since it is as natural for air to enter and to fall in this way into the lungs when
they open as for wine to fall into a bottle when it is poured in.
This is the way in which the weight of the air produces all the e↵ects hitherto attributed to the
horror of the vacuum. I have explained the chief of them; if any remain, it is so easy to understand
them after these that I should think I was being both superfluous and tedious if I sought out others
to treat in detail; and it may even be said they had all been seen already, as in their source, in the
preceding treatise, since all these e↵ects are only particular cases of the general rule concerning the
equilibrium of fluids.
Study questions
Ques. 16.1. Does air have weight? How do you know?
a.) As air is added to a balloon, does it grow lighter or heavier? How does Pascal address the
concern that only pure air exhibits levity, or lightness, and that all other air exhibits gravity,
or weight.
b.) Does Pascal claim that the mass of air has infinite, or finite, weight? Does it act on every point
of the earth’s surface equally?
c.) In which direction does the weight of liquid press upon immersed bodies? And why do we not
feel the enormous weight of the air?
d.) Is the density of the air surrounding the earth uniform? Describe Pascal’s balloon experiment,
and its implications.
Ques. 16.2. Does Pascal’s treatise on the weight of air proceed empirically or deductively?
a.) What consequences does Pascal deduce from the axiom that air has weight? Does Pascal believe
that these consequences must be confirmed by experiment? And more generally, what role (if
any) does experimental observation play in his treatise?
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b.) What would Pascal conclude if experimental observations failed to confirm these consequences?
Did his balloon experiment, in fact, confirm his predictions?
Ques. 16.3. For each of the following phenomena, attributed to nature’s abhorrence of a vacuum,
identify the corresponding diagram in Fig. 16.1 and evaluate Pascal’s explanation of their occurrence
using his general rule concerning the Equilibrium of Fluids. (a.) Why does a sealed bellows resists
opening? (b.) Why do two polished surface seem glued together? (c.) Why is water is drawn up by
the piston of a syringe dipped into water? (d.) Why, in the act of breathing, is air drawn through
the mouth and into the lungs? (e.) Why, when air in an inverted glass in a pool of water cools, does
it draw the pool of water upwards into the glass? (f.) Why does the water in an inverted bottle
does not fall out? (g.) Why is a wine cask not drained when the spigot is opened? (h.) Why does
a siphon filled with water draw water from a higher bucket into a lower bucket, and not the other
way around? (i.) Why is an infant is able to draw milk from a nurse’s breast?
Exercises
t
Ex. 16.1 (Suction cup). What is the maximum weight solid copper block which can be lifted
after pressing a four centimeter diameter suction cup to its top surface? What if this procedure
were performed ten meters underwater?
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Ex. 16.2 (Rising bubble). Suppose that a scuba diver ten meters beneath the surface of the
water exhales a tenth of a liter of carbon dioxide, forming a spherical bubble which ascends toward
the surface.
a.) What is the ambient pressure at the diver’s depth? And how many moles of carbon dioxide
does he exhale? (Hint: Use the ideal gas law, which relates the pressure, volume, temperature
and number of moles of a gas. What do you think is the gas temperature?)
b.) Does the radius of the bubble change as it ascends? If so, what is its initial radius, and what
is its radius when it reaches the surface? For simplicity, assume that the bubble temperature
does not change appreciably during its ascent.(Answer: ri /rs = 2.9/3.6)
c.) As a challenge, can you write down an equation (perhaps involving derivatives) which involves
the speed, v(t), of the bubble as it rises? Can this equation be solved for v(t)?
Ex. 16.3 (Inverted siphon). Consider a deep pool filled with water. Two buckets, A and B are
filled with olive oil and placed underwater (the buckets must be inverted so that the oil does not
float up to the water’s surface). A siphon, consisting of a U-tube made of glass, is also filled with
olive oil and placed underwater with one leg in each bucket.
a.) What happens if the buckets are held at the same depth beneath the water?
b.) What happens if bucket A is raised one inch higher than bucket B? Would the oil flow? If so,
in which direction?
c.) What would happen if a small hole were drilled in the peak of the inverted U-tube? Would the
siphon work? Explain.
d.) What would happen if the buckets were filled with water instead of oil? Explain.
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Ex. 16.4 (Valved siphon). Fig. 16.2 depicts two thin vertical glass tubes connected by a short
horizontal section of tube which can be opened or closed using a valve. The bottom ends of the
vertical tubes are dipped into separate vessels filled with an unknown fluid whose specific gravity
is four. The valve is initially closed, and the left vessel is situated somewhat higher than the right
one. The entire apparatus is placed gently into an aquarium which is then filled with water. Before
Air
A
Water
Valve
G
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E
B
F
C
Figure 16.2: Submerged siphon apparatus.
the valve is opened: (i) the vertical distance from the surface of the water, A, to the surface of
the fluid in the left vessel, B, is 80 cm; (ii) the vertical distance between B and the left end of the
horizontal tube, D, is 10 cm; (iii) the vertical distance between the right end of the horizontal tube,
G, and the surface of the fluid in the right vessel, F , is 20 cm.
a.) What is the pressure at points A, B, C and D? What is the height, E, of the fluid in the left
tube?
b.) What is the pressure at points F and G? What is the height, H, of the fluid in the right tube?
c.) Is the pressure at points D and G the same? What happens when the valve is opened? Is the
system in equilibrium?
d.) Will the heights E and H ever be equal? If so, under what condition(s)?
Ex. 16.5 (Newton’s beads). An experimenter claims that he has created a siphon which operates
in a vacuum. In other words, the siphon moves liquid from a higher to a lower vessel even when the
open-top vessels and the siphon are placed in an evacuated chamber. Do you believe him? Why?
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Would such a vacuum siphon work for a string of beads rather than a column of liquid? If so, why?
What is the essential di↵erence between a solid and a liquid?4
Ex. 16.6 (Bell-jar laboratory). On pages /123-127/ of the First Day of his Dialogues, Galileo
suggests that the specific gravity of air can be determined by weighing a jar before, and then after,
air is forced into it. Alternatively, if one has access to a vacuum pump, he or she can measure
the specific gravity of air by weighing a jar of air before and after it is evacuated. Using a small
bell-jar, one-way valve, a large syringe, and a sensitive balance, find the weight of the air enclosed
in a small bell-jar before and after evacuation.5 Can you also determine the specific gravity of air?
In analyzing your results, you might consider: can the bell-jar be completely evacuated using a
syringe and a one-way valve? If not, how much air has been removed, and how much is still in
it when it is “evacuated”? Consider measuring this by holding an evacuated bell-jar underwater,
then opening a valve to allow water to rush in. With what precision can your determination of the
specific gravity of air be accomplished? For fun, you might also observe the behavior of modestly
inflated small balloons, marshmallows or small vials of very hot tap water placed in the bell-jar, as
the air is removed. Can you get the water to boil?
pressure
immerse
invalidate
fathom
discourse
abhorrence
aperture
adhesion
bellows
rarefied
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
condense
siphon
vessel
adhere
counterpoise
equilibrium
prevail
recourse
occult
chimerical
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2.
3.
4.
5.
6.
7.
8.
9.
10.
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Vocabulary
4 In most cases dissolved gasses prevent the internal cohesion of liquids; siphoning is thus limited by atmospheric
pressure, as described by Pascal. Very pure liquids, however, can exhibit significant internal cohesion. See, for
instance, the measurements described in Reynolds, O., On the Internal Cohesion of Liquids and the Suspension of a
Column of Mercury to a Height more than Double that of the Barometer, in Memoirs of the Manchester Literary
and Philosophcical Society, Third, pp. 1–18, London, 1882 and Briggs, L. J., Limiting Negative Pressure of Water,
Journal of Applied Physics, 21, 721–722, 1950.
5 The Microscale Vacuum Apparatus (Model VAC-10) from Educational Innovations, Inc. in Norwalk, CT works
quite well.