HYDROSTATICS.
110. =What Hydrostatics Teaches.=--Hydrostatics is that branch of
Natural Philosophy which treats of the pressure and equilibrium
of liquids. The phenomena which it brings to view all results
_from the influence of the attraction of the earth upon liquids_.
It is for this reason that this subject calls naturally for our
consideration after examining the general subject of attraction,
as we have done in the previous chapters. In order to understand
fully the phenomena of Hydrostatics, you must continually bear in
mind the two grand characteristics of liquids. One is, that the
particles move freely among each other (§ 9). The other is, that a
liquid is almost entirely incompressible (§ 36).
111. =Level Surface of Liquids.=--It is the influence of
gravitation upon liquids that gives them a level surface whenever
they are not agitated by any cause. Observe how this is. A still
body of water you may consider as being made up of layers of
particles. Each layer will have all its particles equally attracted
by the earth, and must therefore be level. If any of the particles
were less attracted than their neighbors they would rise, as is
the case when heat is applied, as you will see hereafter. Whenever
the upper layers of the particles are disturbed by wind or any
other cause, as soon as the disturbance ceases the particles will
again take their places in level layers under the influence of
gravitation.
112. =A Comparison.=--The particles of water may be compared to
shot. If you have shot in a vessel, and they are heaped up in
any portion of the surface, on shaking the vessel those that are
highest will roll down, and the result will be a level surface.
They would do this without agitation if they were as smooth as
the particles of water are. If we could have a microscope strong
enough to distinguish the shape of the particles of water, the
surface would probably appear like the level surface of shot in
a vessel. But the particles of water are so exceedingly minute
that the surface of water, when entirely free from agitation, is
so smooth as to constitute a perfect mirror, often feasting our
eyes with another world of beauty as we look down into its quiet
depths. Water was man's first mirror, and one of the most beautiful
passages in the "Paradise Lost" is the description of Eve's first
waking after her creation at the side of a lake, and seeing her
form reflected in its smooth waters.
[Illustration: Fig. 66.]
113. =Surface of Liquids not Truly Level.=--Strictly speaking,
the surface of a liquid is not level, but rounding. But it is so
little so that it can not be perceived unless we take into view a
very large surface, as the ocean. Here it is very manifest, for
whenever a ship comes into port the first thing seen from the shore
is the topmost sail, the rest of the ship being concealed by the
water rounded up between it and the observer. This is illustrated
in Fig. 66. At _a_ the ship is just in sight, while at _b_ it is
so near shore that the eye sees the whole of it. If the earth had
no elevations of land, or if there was water enough to cover them,
the water would make a perfectly globular covering for the earth,
being held to it by the force of attraction. The reason for this
is precisely the same as was given in § 58 for the disposition of
a drop of liquid to take the globular form. As in that case, so in
this, it can be demonstrated that each particle is attracted toward
a common centre, and that this will produce in the freely-moving
particles a uniformly rounded surface. What could thus be shown to
be true if the earth were wholly covered with water, is true of the
portions of water which now fill up the depressions in the earth's
crust; and it can be perceived, as shown in the first part of this
paragraph, in the case of any extended portion of it.
[Illustration: Fig 67.]
114. =Spirit-Level.=--What we call a perfectly level surface is,
then, one all parts of which are equally distant from the centre
of the earth, and is therefore really a spherical surface. But
the sphere is so large that any very small portion of it may be
considered for all practical purposes a perfect plane. A hoop
surrounding the earth would bend eight inches in every mile. In
cutting a canal, therefore, there is a variation in this proportion
from a straight level line. As the variation is but an inch in
an eighth of a mile, it is of no account in taking the level for
buildings. Levels are ascertained by what is called a spirit-level.
This consists of a closed glass tube, Fig 67, nearly filled with
alcohol. The space not occupied by alcohol is occupied by air. The
tube is placed in a wooden box for convenience and security, there
being an opening in the box at _a_. Now when the box with its glass
tube is perfectly level, the bubble of air will be seen in the
middle at _a_; but if one end be higher than the other, the bubble
will be at or toward that end.
115. =Rivers.=--If a trough be exactly level, the water will be of
the same depth at one end as at the other, for the surface of the
water at both ends will be at the same distance from the centre of
the earth. But raise up one end, and it is now deepest at the other
end. If it were not so, the surface at the two ends would not be at
the same distance from the centre of the earth. Now if, with the
trough thus placed, water run in at the upper end and out at the
lower, you have exemplified what is taking place in all rivers--the
water is in constant motion from the influence of gravitation,
causing it to seek to be on a level. A very slight slope will give
the running motion to water, for the particles are so movable among
each other that in obedience to gravity they flow down the inclined
plane to seek a level. Three inches declivity in every mile in a
smooth straight channel will make a river run at the rate of about
three miles an hour. The Ganges, which receives its waters from
the Himalaya Mountains, in running 1800 miles falls 800 feet. The
Magdalena, in South America, falls only 500 feet in running 1000
miles between two ridges of the Andes.
116. =How some Rivers have been Made.=--Changes are constantly
produced in the earth by the disposition of water to seek a level.
In doing this the water carries solid substances of various kinds
from elevated places into depressed ones, tending to fill up the
latter. New channels are also sometimes made by the water. The
boy who makes a little pond with his mud-dam, and lets the water
overflow from it into another pond on a lower level, as he sees a
channel worked by the water between the two ponds becoming larger
and larger, witnesses a fair representation on a small scale of
some extensive changes which have in ages past taken place in some
parts of the earth. It is supposed, and with good reason, that many
rivers had their origin in the way above indicated. For example,
where the Danube runs its long course there was once a chain of
lakes. These becoming connected together by their overflow, the
channels cut between them by the water continually became larger,
until at length there was one long, deep, and broad channel, the
river, while the lakes became dry, and constituted the fertile
valley through which that noble river runs to empty into the Black
Sea. It is said that a similar process is manifestly going on in
the Lake of Geneva, the outlet of it becoming continually broader,
while the washing from the neighboring hills and mountains is
filling up the lake. Towns that a century ago lay directly upon the
borders of the lake have gardens and fields now between them and
the shore; and Dr. Arnot says, "If the town of Geneva last long
enough, its inhabitants will have to speak of the river in the
neighboring valley, instead of the picturesque lake which now fills
it."
[Illustration: Fig. 68.]
[Illustration: Fig. 69.]
117. =Canals.=--The management of the locks of a canal is in
conformity with the disposition of water to seek a level. A ground
view of a lock and a part of two adjacent locks is given in Fig.
68. The lock, C, has two pair of flood-gates, D D and E E. The
water in A is higher than in C, but the level is the same in C and
B, because the gates, E E, are open. Suppose now that there is a
boat in the lock B that you wish to get into the lock A. It must
be floated into the lock C, and the gates E E must be closed. The
water may now be made to flow from the higher level, A, into C,
till the level is the same in both A and C. But this can not be
done by opening the gates D D, for the pressure of such a height of
water in the lock A would make it difficult, perhaps impossible, to
do this; and besides, if it could be done, the rapid rush of water
into C would flood the boat lying there. The discharge is therefore
effected by openings in the lower part of the gates D D. These
openings are covered by sliding shutters, which are raised by racks
and pinions, as represented in Fig. 69. When the water has become
of the same level in A and C, the gates DD can be easily opened,
and the boat may be floated from C into A. If a boat is to pass
downward in the locks, the process described must be reversed.
Canals are also extensively used for supplying water by side
openings to turn water-wheels for the working of machinery. The
water turns the wheel by the force which gravitation gives it as it
descends from the level of the canal to the level of the river.
[Illustration: Fig. 70.]
[Illustration: Fig. 71.]
118. =Other Illustrations.=--We see the tendency of fluids to be
on the same level in other ways. In a coffee-pot the liquid has
the same level in the spout as in the vessel itself, whatever may
be its position, as seen in Fig. 70 (p. 86). If it be turned up so
far that the level of the fluid in the vessel is higher than the
outlet of the spout, the fluid runs out. If two reservoirs of water
be connected together the water will stand at the same height in
both, whatever the distance between them may be. So, also, in the
aqueduct pipes that extend from a reservoir, the water will rise
as high as the surface of the water in the reservoir itself. If
the outlets of the pipes be lower than this level the water will
run from them, as in the case of the coffee. The cause of these and
similar facts is the same as that of the level surface in vessels
and reservoirs--the action of gravitation. This may be made plain
by Fig. 71. Let the figure represent a vessel with divisions of
different degrees of thickness, these divisions, however, not
extending to the bottom of the vessel. Water in this would stand
at the same level in the different apartments, just as it would if
the vessel had no such divisions, as represented. This is simply
because the attraction of the earth acts upon the water in the
same way with the divisions as without them. And you can see that
it will make no difference whether these divisions be thick or
thin, or whether the apartments be near, as you see here, or far
apart, as they are when branch pipes extend from a reservoir. A
branch pipe may be considered as having the same relation to the
reservoir, as one of the narrow apartments in the figure has to the
rest of the vessel. The result is not at all affected by either
the size or form of the tubes that may be connected with a common
reservoir--a fluid will stand at the same height in all. Thus we
have, in Fig. 72, tubes of various size and shape, _a b c d e_,
connected with a reservoir, _r_, and if water be poured into one
of them it will rise to the same height in all, just as in the
different apartments of the vessel represented in Fig. 71. A man
once thought that he had gained the great desideratum, perpetual
motion, by a vessel constructed as in Fig. 73. He reasoned in this
way: If the vessel contain a pound of water, and the tube only an
ounce, as an ounce can not balance a pound, the water in the vessel
must be constantly forcing that in the tube upward. It therefore
must constantly run out of the outlet of the tube, and as it flows
into the vessel the circulation must go on, and the only hindrance
to its being a perpetual circulation would be the evaporation of
the water. He was confounded when he found, on pouring water into
the vessel, that it stood at precisely the same level in the vessel
and the tube.
[Illustration: Fig. 72.]
[Illustration: Fig. 73.]
119. =Aqueducts.=--The ancients built aqueducts of stone at immense
expense, in some cases spanning valleys at great heights, to
supply their cities with water. At the present day the same object
is effected at comparatively small expense with iron pipes laid
under ground. No matter how much lower than the reservoir a valley
crossed by the pipes may be, the water flowing through them will
rise any where in their branches to the same height as it stands in
the reservoir. It is supposed by some that the ancients were not
aware of this fact; but by others that they were aware of it, and
built their immense aqueducts because they had no material for
constructing large pipes.
[Illustration: Fig. 74.]
120. =Springs and Artesian Wells.=--The principles which I have
developed in the previous paragraphs will explain the phenomena of
springs, common wells, and Artesian wells. The crust of the earth
is largely made up of layers of different materials, as clay, sand,
gravel, chalk, etc. When these were formed they were undoubtedly
horizontal, but they have been thrown up by convulsions of nature
in such a way that they present every variety of arrangement. As
some of these layers are much more pervious to water than others,
the rain which falls and sinks into the ground often makes its way
through one layer lying between two others which are impervious
to water, and so may make its appearance at a great distance from
the place of its entrance, and at a very different height. How
this explains the phenomena of springs, common wells, and Artesian
wells may be made clear by Fig. 74. A A and B B B are designed to
represent porous layers of earth lying between other layers which
are impervious to water. The water in A A will flow out at C,
making what is commonly called a spring. If we dig a well at F,
going down to the porous layer, B B B, the water will rise to G,
because this is on a level with the surface of the ground, H, where
the supply of water enters. From this point it may be raised by
a pump. If the well be dug at D, the water will rise not only to
the surface but to E, because this is on a level with H. Water is
sometimes obtained under such circumstances from very great depths.
In this case the porous stratum containing the water is reached
by boring, and then we have what is termed an Artesian well. The
name comes from Artois, in France, where this operation was first
executed. There is a celebrated well of this sort in Paris over
1800 feet deep, and the water rises 112 feet above the surface.
More than 600 gallons are discharged every minute. "London," says
Dr. Arnot, "stands in a hollow, of which the first or innermost
layer is a basin of clay, placed over chalk, and on boring through
the clay (sometimes of 300 feet in thickness) the water issues, and
in many places rises considerably above the surface of the ground,
showing that there is a higher source or level somewhere--probably
among the Surry hills or those north of London."
121. =Pressure of Liquids in Proportion to Depth.=--The pressure of
a fluid is in exact proportion to its depth. For, as the particles
are all under the influence of gravity, the upper layer of them
must be supported by the second, and these two layers together by
the third, and every layer must bear the weight of all the layers
above it. The increase of pressure at great depths produces the
most striking effects. Thus if an empty corked bottle be let down
very deep at sea, either the cork will be driven in or the bottle
will be crushed in. A gentleman tried the following experiment: He
made a pine-wood cork, so shaped that it projected over the mouth
all around. He then covered this with pitch, and fastened over the
whole several pieces of tarpaulin. The bottle, thus prepared, he
let down to a great depth by attaching to it a weight. On raising
it up he found that it contained about half a pint of water
strongly impregnated with pitch, showing that the pressure of the
water forced water through the several pieces of tarpaulin, the
pitch, and the pores of the wooden cork. When a ship founders near
land, the pieces of the wreck, as it breaks up, float to the shore;
but when the accident happens in deep water, the great pressure
forces water into the pores of the wood, and thus makes it so
heavy that no part of the vessel will ever rise again. When a man
dives very deep he suffers much from the pressure on his chest. If
we watch a bubble of air rising in water it is small at first, but
it grows larger as it approaches the surface, because it sustains
less pressure than when it was deep in the water. The force with
which a fluid is discharged from an opening in a vessel depends on
the height of the fluid above the opening. The difference in this
respect between a full barrel and one nearly empty is very obvious.
Most fishes, probably, can not bear the pressure of great depths,
and so are commonly found on the coast, or on banks, as they are
called, in the midst of the ocean.
[Illustration: Fig. 75.]
122. =Sluice-Gates, Dams, etc.=--The application of the above
principles in the construction of sluice-gates, dams, etc., is
a matter of great practical importance. Let us look at this. As
pressure in a fluid is always in proportion to the height of the
fluid above the point of pressure, the pressure upon any portion
of the side of a vessel containing a fluid must be in proportion
to its distance from the surface; or, in other words, it is the
weight of a column of water extending from this portion to the
surface. Let A B C D (Fig. 75) represent a _section_ of a cubical
vessel, that is, one in which each side is of the same size with
the bottom. The pressure on the point _a_, in the line A B, is
that of a column of particles, A _a_. But A _a_ is equal to _c
b_, and _c b_ is equal to _b a_. Therefore _b a_ may represent
the pressure on _a_. In the same way it can be shown that _e d_
represents the pressure on _d_, _n m_ the pressure on _m_, C B that
on B. Therefore the pressure on all the points in A B will be
represented by lines filling up all the triangular space A B C, and
this is half of A B C D, which represents the pressure on the line
C B. It is clear, then, that as the pressure on a vertical line
in the side is half that on a line at right angles to it in the
bottom, the pressure on the whole side is half that on the whole
bottom.
[Illustration: Fig. 76.]
We see from the above demonstration why it is that a dam is built
in the form represented in Fig. 76. We see, also, why in the
monstrous vats in some of the English breweries (some of them
holding many thousand barrels) the hoops and other securities at
the lower part of them require to be made of very great strength.
It is manifest, also, that if a sluice-gate is to be kept shut by a
single support, this must be applied at one third of the distance
from the bottom, there being as much pressure, as seen by Fig. 75,
on the lower third as on the upper two thirds of the gate.
123. =Lateral Pressure in Fluids.=--The pressure of a liquid on
the side of a vessel, of which I have spoken above, is a _lateral_
pressure, and it is caused by the downward pressure of gravitation
in the liquid. But how? The particles of a fluid are freely movable
among each other, and therefore are ready to escape from pressure
in any direction. The particles at _a_, Fig. 75, pressed upon by
the column of particles extending above them to the surface, are
ready to escape laterally, and would do so if there were an opening
made in the vessel at that point. But if the vessel contained
a block of ice, fitting it as accurately as the body of water,
there would be no escape at the opening, because the particles of
the solid are so held together that the downward pressure of the
earth's attraction occasions no lateral pressure.
[Illustration: Fig. 77.]
[Illustration: Fig. 78.]
The manner in which the downward pressure of the earth's attraction
causes lateral pressure may be made clear by Figs. 77 and 78. We
will suppose that the particles of solids and liquids are alike
round, and that a solid differs from a liquid only in having its
particles firmly united by attraction. Let _a_, _b_, and _c_,
in Fig. 77, represent three particles of a solid. As they are
united firmly they will have a united pressure from the centre of
gravity directly toward the centre of the earth, as represented
by the arrow. Let now _d_, _e_, and _f_, Fig. 78, represent three
particles of water. These being but very slightly coherent, will
make each an independent pressure toward the earth's centre, as
indicated by the arrows. It is plain that _d_ tends to separate _e_
and _f_, and will do so if they are left free to move in a lateral
direction. For example, if _e_ be at the side of a vessel, and an
opening be made there, the downward pressure of _d_ will give _e_ a
lateral movement, forcing it out of the opening.
124. =Another View.=--To return to Fig. 75, observe that the
lateral pressure at any point in the side of a vessel, as _a_,
is occasioned _wholly_ by the downward pressure of a vertical
column of particles extending from that point to the surface. The
neighboring columns of particles have nothing to do with it. The
same thing is true in regard to any other point either in the
line A B or another line drawn on the side of the vessel. It is
therefore true of the whole side, that the pressure upon it is
occasioned alone by the columns of particles that are in close
proximity to the side, and not at all by the other columns of
particles in the vessel. The number of these columns, therefore, in
the vessel, or, in other words, the breadth of the body of water
in it, makes no difference with the pressure on its side. For this
reason two flood-gates so little apart that a few hogsheads or
even pails of water fill up the space between them, are as much
pressed upon as they would be if a lake or an ocean of water lay
between them. It has been objected to the project of digging a ship
canal between the Red Sea and the Mediterranean, that as the water
in the former is twenty feet higher than in the latter, it would
burst through the flood-gates with such force as to produce most
disastrous results. But according to the principle which I have
illustrated, there would be no more danger of this than there would
be if two ponds were united by a canal, in one of which the water
is twenty feet higher than in the other.
[Illustration: Fig. 79.]
125. =Pressure in Liquids Equal in all Directions.=--We are
now prepared to go a step farther. The pressure occasioned by
gravitation in fluids operates equally in all directions when the
fluid is at rest. That is, any particle of a liquid is pressed
equally in all directions. If it were not so it would not remain
at rest, but would be moved in the direction in which the superior
pressure operates. Suppose that _a_, Fig. 79, is a stratum of
particles in a vessel containing water at rest. The upward pressure
on it being equal to the downward pressure, the stratum neither
rises nor falls. If a body of liquid be disturbed by wind or any
other cause, those particles which are raised above the common
level in waves are pressed downward more than upward or laterally
in obedience to the action of gravitation. They therefore move
downward, pushing laterally and upward the neighboring particles,
till the liquid regains its level surface and its state of rest.
So, also, if any particles become heated they are lighter than
their neighboring particles, and the latter being more strongly
attracted than the former, push them upward in order to take their
places. When all the liquid comes to have the same temperature it
is at rest, each particle having an equal pressure upon it in all
directions.
[Illustration: Fig. 80.]
126. =Illustrations.=--If a bladder filled with water be
compressed by the hand, the water is pressed no more immediately
under the hand than in any other part of the bladder, and wherever
an opening be made the water will rush out with equal readiness.
A hose-pipe as readily bursts upward as in any other direction. A
large cork, if sunk in very deep water, will be uniformly reduced
in its dimensions, showing that it has been pressed equally on all
sides. In the experiments with the closed bottles (§ 121), the
result is the same if the bottle be so sunk as to have its mouth
downward. If two tubes, shaped as in Fig. 80, be thrust down into
water, the water will rise with equal facility in both, although in
the straight one the pressure which carries up the water is wholly
upward, while in the bent one it is at the first downward.
[Illustration: Fig. 81.]
127. =Upward Pressure as the Depth.=--It has been shown that the
downward and the lateral pressures are as the depth. The same
is true of the upward pressure, for it is produced by the same
cause--the attraction of the earth. Let us look at this. Why is any
particle of a fluid pressed upward at all? It is from the struggle
on the part of the neighboring particles to get below it. And why
this struggle? It is from the attraction of gravitation, and so
the greater this attraction the greater is the upward as well as
the downward pressure. The upward pressure therefore differs at
different depths as the downward pressure does. Thus, in Fig. 81,
the upward pressure against the layer or stratum of particles, _b_,
is greater than that against _a_, for the same reason that the
downward pressure on _b_ is greater than that on _a_. But the two
pressures at _b_ are equal, and so are they at _a_, and therefore
each stratum remains at rest.
[Illustration: Fig. 82]
128. =Experiments.=--Some very neat experiments can be tried,
showing that the upward pressure varies with the depth. Take a
large glass tube, A B C D, Fig. 82, and let there be fitted to one
end a circular plate of brass, which may be held there by a string,
F. Thus arranged, plunge it quite deep into water, and you will
find that you will not need to hold on to the string, for the brass
disk will be held tight to the tube by the upward pressure of the
water. Now draw up the tube slowly, and at length the disk will
fall from the end of the tube. Why? Because the end of the tube has
come to a point where the upward pressure of the water is less than
the downward pressure of the disk. To have this experiment succeed,
the end of the tube where the disk is applied must be very even and
smooth. Another experiment may be tried in this way. Tie to one end
of a glass tube a piece of thin India-rubber or bladder, and fill
the tube partly with water. The India-rubber will of course bulge
out or be convex from the weight of the water. Press the closed
end down a little way in a vessel of water, so that the level in
the tube shall be above the level in the vessel. The India-rubber
is still somewhat convex, because, as the upward pressure upon it
is in proportion to its distance from the surface of the water
outside of the tube, it is not as great as the pressure downward
of the higher water in the tube. Push the tube now so far down
that the level in the tube is the same with that in the vessel.
The India-rubber is now flat, because the downward and upward
pressures upon it are equal, just as would be the case with a
stratum of water in place of it. But press the tube lower down, and
the India-rubber bulges upward into the tube, because the upward
pressure is now greater than the downward.
129. =Great Effects from Small Quantities of a Fluid.=--You are
now prepared to understand the explanation of some very striking
phenomena in the pressure of liquids. If you take a perfectly
tight cask, and, filling it with water, screw into its top a long
tube, by pouring water into the tube you can burst the cask. To
understand this you must bear in mind two facts--that the fluid
in the cask is not compressible, and that its particles move
freely among each other. Any pressure, therefore, exerted upon it
is felt through the whole of it equally. "If the tube," says Dr.
Arnot, "have an area of a fortieth of an inch, and contain when
filled half a pound of water, this produces a pressure of half a
pound upon every fortieth of an inch all over the interior of the
cask; which is more than a common cask can bear." Suppose a small
reservoir of water exists in the side of a mountain wholly closed
up, and that water from a height above finds its way to it by a
crevice, it may by its pressure even burst open the side of the
mountain. And it matters not how large or small the crevice may be,
for pressure in a liquid is only as the height. If the reservoir be
ten yards square and an inch deep, and the fissure leading to it
be but an inch in diameter and two hundred feet in height, it is
calculated that the pressure of the water in the fissure would be
equal in force to the weight of 5000 tons.
[Illustration: Fig. 83.]
130. =Explanation.=--The manner in which these effects are produced
may be made clear by Fig. 83. Let A be a close vessel filled with
water, and let a tube, _b_, be made fast in it, with a movable
plug or piston at _c_. If the surface of the water be pressed
upon by this piston with the force of a pound, as the water is
incompressible and its particles are freely movable among each
other, the pressure will be extended equally through all the
water, and every portion of the vessel of equal extent with the
tube's opening at _c_ will be pressed upon with the force of a
pound. If another tube, _d_, of the same size were inserted with a
piston, _i_, the force of a pound applied to the piston _c_ would
push upward the piston _i_ with the same force. And if there were
several pistons of the same size, by pushing upon one with the
force of a pound they would all be pressed upward with exactly this
force. Farther, if _e_ be a tube five times as large as _b_, its
piston, _n_, will be forced upward with a pressure of five pounds
by the downward pressure of a pound upon _c_. Suppose now that
a pound of water were substituted for the piston _c_, the other
pistons would be pressed upward as before. And if all the pistons
be removed, the pound of water in _b_ will press the water up the
tube _d_ with the force of a pound, and up the tube _e_ with the
force of five pounds.
[Illustration: Fig. 84.]
To make this still more clear I will present it in a little
different form. Let B, Fig. 84, be a close vessel with two tubes,
one of which is five times as large as the other. If sufficient
water be poured into the vessel to occupy a part of the tubes, it
will stand at the same height in both tubes, as indicated. If there
be a pound of water, then, in the tube _c_, there will be five
pounds in _a_. Now if the five pounds of water in _a_ made any more
pressure on the whole body of water in B than the pound of water in
_c_ does, it would press up the water in _c_ to a greater height.
But this is impossible, as has been shown in § 118. Observe that
the five pounds of pressure in _a_ is spread over five times the
area or extent of surface that the pound's pressure in _c_ is. If
the tube _c_ have an area of an inch square, the water in it will
exert a pressure of a pound on every square inch in the vessel.
The water in _a_ exerts a pressure of five pounds; but it must be
remembered that it does not press with this force on every square
inch, but on every space of five square inches, and that therefore
its pressure on every inch is the same as that in the tube _c_.
131. =Hydrostatic Paradox.=--You see in the phenomena and
explanations given above that a small quantity of a fluid can,
under certain circumstances, exert an enormous pressure. This fact
has been called the Hydrostatic Paradox. It does seem, at first
view, incredible or paradoxical, when one asserts that a few ounces
of water can be made to raise weights of hundreds or even thousands
of pounds. But the explanations which I have given show you that
there is no unexplainable mystery in the fact. The cause of it is
the same as that which gives a level surface to liquids; viz., the
force of gravitation acting upon a substance whose particles are
freely movable among each other.
[Illustration: Fig. 85.]
132. =Hydrostatic Bellows.=--The instrument called the Hydrostatic
Bellows is represented in Fig. 85. It consists of two circular
boards, A and B, united together by strong leather, and having a
tube, C, through which water can be poured into it. The amount of
weight which can be sustained on the bellows without forcing the
water out of the tube depends on the size of the bellows. If the
area of the tube is only one thousandth of that of the top of the
bellows, a pound of water in the tube will balance a thousand
pounds' weight on the bellows. It is for the same reason that in
Fig. 84 one pound of water in the tube _c_ balances five pounds in
_a_. As the weight presses upon the top as a whole, it is the same
as if there was a vessel of the same size with the bellows resting
upon it and containing a thousand pounds of water. The water, in
that case, would stand at the same height in the vessel and the
tube. This shows that the Hydrostatic Paradox is only one of the
exemplifications of the great fact that a fluid, from the influence
of gravitation, seeks to be on a level. It is the water in the
bellows seeking to be on a level with that in the tube that causes
the upward pressure sustaining the weight.
When the weight on the bellows is less than is required to balance
the water in the tube, the weight can be raised continually by
pouring water into the tube. But observe that although the lifting
force be so strong, it is very slow in its operation. If the
comparative areas of the tube and the bellows be as above supposed,
the water must fall in the tube ten inches in raising the weight
the one hundredth part of an inch.
[Illustration: Fig. 86.]
133. =Bramah's Hydrostatic Press.=--The principles which I have
elucidated have been applied by Mr. Bramah in his Hydrostatic
Press. This consists of a small metallic forcing-pump, Fig. 86, in
which the water, _a_, is pumped up by the piston, _s_, worked by
the lever, _c b d_, and forced into a strong and large cylinder,
A. In this cylinder is a stout piston, S, having a flat head, P,
above. Between this plate and another, R, is placed the body, W,
which is to be compressed. It is obvious that the pressure exerted
will be in proportion to the difference between the size of the
pump, _a_, and the cylinder, A, just as in the case of the bellows,
it depended on the difference between the areas of the tube and
of the top of the bellows. In the press the force of a pump is
substituted for the pressure of a very high column of water, simply
because it is more convenient. This press is of great service
in the mechanic arts. It is used in pressing paper, cloth, hay,
cotton, etc. It has also been recently used in raising enormous
weights. The tubes of the celebrated bridge over the Straits of
Menai were raised by a machine constructed on this principle.