SPECIFIC GRAVITY.
134. =Nature of the Subject.=--We now come to a very interesting
subject, which is at least intimately connected with Hydrostatics,
if it may not be considered a part of it. The principles which
have been developed in the chapter on Hydrostatics in relation to
liquids are to be applied here to various kinds of substances. And
as we proceed you will see that all the phenomena brought to view
in this chapter are to be referred to the same cause with those of
the previous chapter; viz., the attraction of gravitation.
135. =Specific Gravity Defined.=--Before proceeding with the
investigation I will give you the definition of specific gravity.
The specific gravity of any substance is its weight as compared
with the same bulk or volume of other substances. Water is taken as
a standard, and its specific gravity is for convenience called 1.
Mercury, then, is said to have a specific gravity of 13.5, for it
is thirteen and a half times as heavy as the same volume of water.
It is easy to see how the specific gravities of different fluids
may be ascertained. One mode, and the most obvious one, is to weigh
in a vessel equal quantities of them. In what way the specific
gravities of solids are ascertained will be explained in another
part of this chapter.
136. =Action of Gravity on Solids in a Liquid.=--The reason that
a very heavy substance, as a stone, sinks in water is simply that
the earth attracts it more strongly than it does the water, and so
drags the stone down through it. If the stone lay upon a bladder
filled with water, it would press upon it with the force with which
it is attracted by the earth. But where water is not thus confined,
the stone thrusts its particles to the one side and the other till
it gets to the bottom.
It is the attraction of gravity, also, that makes light substances,
as wood and cork, rise in water. In this case the water is
attracted by the earth more strongly than the wood or cork, and
so gets below it, and in so doing pushes the lighter substance up
above itself.
[Illustration: Fig. 87.]
But you will observe that the wood, on rising in the water, does
not come completely out of it and lie upon the surface, but a
part of it remains immersed in the water. The explanation of this
will furnish you with the key to the understanding of many very
interesting facts. Suppose that half of a block of wood, A, Fig.
87, weighing a pound, is above the surface of water. As it is
attracted to the earth with the force of a pound, it has pushed to
the one side and the other just a pound of water, and taken its
place. It is drawn down toward the earth with the same force with
the pound of water on either side of it, _b_ or _c_. If it were
attracted any more than with the force of a pound, that is, if
it weighed more than a pound, it would displace more than a pound
of water. If it were of just the same weight with the same volume
of water, it would displace a volume of water equal to itself; it
would be wholly immersed, and would stay any where in the water,
wherever you placed it, because it is attracted by the earth with
the same force that the same bulk of water is.
[Illustration: Fig. 88.]
137. =Farther Explanation.=--Suppose water in a vessel divided
into equal portions of a pound each, as represented in Fig. 88.
Now suppose that the portion _a_ should at once change into solid
ice without at all altering its bulk or weight. It would not move
from its position, because it is attracted by the earth precisely
as much as when it was water, and as much as is each of the equal
portions of water around it. But as water on becoming ice does
really increase in bulk, and therefore become lighter, this block
of ice would rise so that a part of it would be above the surface.
[Illustration: Fig. 89.]
The lighter a substance is that is immersed in water, the more
there will be of it above the surface. Take two blocks of wood of
different weights though of the same size. Suppose the heaviest
one, A, Fig. 89, is one third lighter than the same bulk of water.
One third of it will be above the surface. If the other, B, is
half the weight of water, half of it will be above the surface.
We should say, then, that the specific gravity of the wood in
the first block is two thirds of that of water, and the specific
gravity of the wood in the second is one half that of water.
138. =Illustrations.=--There are many interesting facts that
illustrate the principles which I have developed. A stone is lifted
much more easily in water than in air, because of the support
afforded by the upward pressure of the water. A boy will often
wonder why he can lift a very heavy stone to the surface, but
can get it no farther. When a bucket of water is drawn up a well
much less exertion is required to raise it through the water than
through the air after it emerges from the water. While it is in the
water you raise only the bucket itself, the water in it having no
weight, being sustained by the water around it. But when it comes
to the air you have the weight of the water added to that of the
bucket. When a person lies in a bath for some time, on raising his
arm from the water it seems to be very heavy. The reason is, that
it has had for so long a time the support of the water that when
it is lifted into the air the want of this support is sensibly
felt, just as we perceive the difference between raising a bucket
of water through water and raising it through air. It is said that
Archimedes took in the full idea of the principles of specific
gravity as his limbs felt the liquid support of a bath, and so
overjoyed was he with the discovery, that he ran home crying out
all the way, "Εὕρηκα! εὕρηκα!"--I have found it! I have found it!
It was a rational joy, for he had found a principle of immense
value to science and to the world.
139. =Boats and Life-Boats.=--A boat of iron will float with as
much of it out of water as one of wood of the same size, provided
that the iron be made so thin that the boat is not heavier than the
wooden one. For what is it that floats? Not the iron or wood, but a
wooden or iron boat filled with air. If it were filled with water
instead of air it would sink, the specific gravity of the materials
of which it is built being on the whole of greater specific gravity
than water. Life-boats have in their structure either a large
quantity of cork or air-tight vessels of tin or copper, and in this
way they are made so light that they will float even when filled
with water.
As the weight of a body can be estimated from the quantity of water
which it displaces, we can very readily estimate the weight of
the load of a canal-boat, as its form is so simple and regular. In
order to do this we must first know how far the boat sinks in the
water when empty, or, in other words, how much water it displaces.
140. =Specific Gravity of Animals.=--Birds have a much less
specific gravity than animals that walk, in order that they may
mount up easily in the air. Their light feathers increase greatly
their bulk, as you may see whenever a bird is stripped of them.
Besides this, the bones are hollow and communicate with the lungs.
Birds that swim, as ducks, swans, etc., have so small a specific
gravity--that is, are so large in proportion to their weight--that
but a small part of the body is under water, and the motion of
their feet is not required at all to sustain them, but only,
like the action of oars, to propel them along. Insects are of
small specific gravity, those that fly the most swiftly being the
lightest. Fishes are very nearly of the same specific gravity with
water, and hence require but little muscular effort to move about
in their element. They are assisted much in rising and falling
by a contrivance by which they can instantaneously alter their
specific gravity. They have an air-bladder, which they can dilate
or contract at pleasure. When dilated, the bulk of the fish is
increased and his specific gravity lessened, and he rises easily
and at once. By compressing it he as readily sinks.
141. =Specific Gravity of the Human Body.=--The human body, when
the chest is filled with air, is so much lighter than water that it
will float with about half the head above the surface. A knowledge
of this fact, with proper presence of mind, might ordinarily
save persons from drowning; for if the body be put in the proper
position, the feet downward and the head thrown backward, the nose
and mouth will be out of the water. So little is required in the
way of support to keep the whole head out of water, that persons
who can not swim are often saved from drowning by catching hold of
very small pieces of wood. An oar would support half a dozen men,
if they would be satisfied with keeping only the head out of water;
but if each one struggle to get his whole body upon the oar, they
may all be lost.[1] A life-preserver is a great aid in preservation
from drowning, for it diminishes the specific gravity of the body.
It is commonly an air-tight bag fastened round the upper part of
the body, which can be filled by blowing into it through a pipe
which has a valve in it. "On the great rivers of China," says Dr.
Arnot, "where thousands of people find it more convenient to live
in covered boats upon the water than in houses on the shore, the
younger male children have a hollow ball of some light material
attached constantly to their necks, so that in their frequent falls
overboard they are not in danger."
When a person is drowned the body sinks because in the struggle
much of the air in the lungs is lost, just as the fish sinks when
his air-bladder is contracted. It is, however, so little heavier
than water after this is done, that it very readily rises when
any gas is produced in it by putrefaction. It is a common popular
notion that firing cannon over the water will raise the drowned.
But it can produce no effect, unless perhaps the agitation caused
by the concussion may hasten a very little the rising of a body
which from commencing putrefaction is about to rise.
In wading a river the feet press upon the bottom with only a force
equal to the weight of half the person's head, this being the
difference between the weight of the body and the weight of the
same bulk of water. Now this pressure is not sufficient to give a
sure footing against even a moderate current. Many persons have
been drowned from ignorance of this fact. A man carrying a load
may often ford a river safely where without a load to press him
down, and thus give him a sure footing, he would be carried down
the stream. So a man may walk in deep water upon broken glass with
impunity.
[Illustration: Fig. 90.]
142. =How to Ascertain the Specific Gravity of Solids.=--It results
from the upward pressure of water that a body weighs less in water
than in air. Take a piece of gold or any other substance, _a_,
Fig. 90 (p. 107), and weigh it suspended as you see from one of
the scales. Introduce the gold now into a cup of water, and you
will find that a part of the weight must be taken from the opposite
scale to preserve the balance. The weight which you take from the
scale will be the weight of a quantity of water equal in bulk
to the piece of gold; for the immersed body is supported with a
force equal to the weight of the water it displaces (§ 137). By
comparing, therefore, its weight in water with its weight in air
we determine its specific gravity. Thus if a lump of gold weigh
nineteen ounces, and on being weighed in water weighs eighteen, it
will prove that gold is nineteen times as heavy as water. And if
a lump of copper weigh nine ounces in air and eight in water, it
is nine times as heavy as water. Calling water, therefore, 1, the
specific gravity of gold is 19, and of copper 9. It is obvious that
a body of the same specific gravity with water would weigh nothing
when immersed in water, for it would be supported with an upward
pressure precisely equal to its own weight, just as the same bulk
of water is. A pound of water, therefore, will weigh nothing in
water. The experiment can easily be tried. Weigh a glass bottle,
suspended on one arm of the scale-beam, and then put a pound of
water in it. On immersing it in water it will be balanced if you
take out the pound weight in the opposite scale.
143. =Archimedes and the Crown.=--Hiero, King of Syracuse,
stipulated for a crown of pure gold. But suspecting the maker of it
of adulterating the gold, he called upon Archimedes to detect the
imposture. He did it in this way: He procured two lumps of gold and
silver of the same weight with the crown, and observed the quantity
of water which each displaced. He then tried the crown, and found
that it displaced less than the silver and more than the gold, and
therefore concluded that it was an alloy of the two metals. All
this was suggested to him by his experience in the bath, referred
to in § 138.
[Illustration: Fig. 91]
144. =How to Ascertain the Specific Gravity of Liquids.=--There are
several modes of ascertaining the specific gravities of different
liquids. The instrument called a Hydrometer furnishes the most
common mode. This is used chiefly in determining the quality of
spirit. The more alcohol and the less water spirit contains the
less is its specific gravity. The Hydrometer consists of two bulbs
of glass, A B, Fig. 91, with a slender stem, C, which is graduated.
In the lower bulb are a few shot or a little mercury, to give the
instrument its proper weight, and to make its centre of gravity
to be in the lower part. The lighter the fluid to be tested is
the lower will the instrument sink in it. This is a very accurate
instrument, detecting the slightest adulteration in spirits. Dr.
Arnot tells an amusing story of the detection of a Chinese trader
in liquors. He had sold a quantity of liquor to the purser of a
ship, averring it to be of the same quality with a sample which
he had given him. The purser tried it with his Hydrometer, and
found it to be of greater specific gravity than the sample. The
Chinese promptly denied the fraud; but on being told the exact
quantity of water which he had added, he was so much confounded
that he immediately confessed his guilt, and made ample amends.
When the Hydrometer was shown to him he offered a large price for
what appeared to him to be a magical instrument, foreseeing that it
would be of great advantage to him in his business.
In Switzerland and in the north of Italy, where the peasants bring
their milk to a common dairy, and are allowed a quantity of cheese
at the end of the season in proportion to the amount of milk which
they have brought, a Hydrometer is used to test the quality of
the milk. There is a propriety in this, not only as a safe-guard
against adulteration, but because there is a difference of quality
in the milk of different cows, some giving a much more watery milk
than others.
145. =Centre of Gravity in Floating Bodies.=--The same principles
which apply to the centre of gravity in bodies standing on a firm
basis apply also to floating bodies. That the centre of gravity
may be low in a loaded vessel the heavy part of the cargo is put
underneath, and generally ballast of stone or iron is necessary
for the same purpose. In large flat-boats, the base of support
being extensive, there is not the same need of taking care that
the centre of gravity be low. If a ship be laden in part with an
article which will dissolve in water, there is much danger, if the
ship should leak, that this portion of the cargo shall be dissolved
and be pumped out with the bilge-water, thus altering the trim of
the vessel, or removing the centre of gravity from over the middle
line, and bringing it too far forward, or carrying it too far back,
making the ship wholly unmanageable. Four large English ships, in
part loaded with saltpetre, were supposed to be lost from this
cause in 1809 off the Isle of France. The immense ice-islands,
or icebergs, which float about in summer in the polar regions,
by melting irregularly often change the place of their centre
of gravity, and in turning over present one of the most sublime
spectacles in nature. A mountain of ice, extending high in the air
and deep in the sea, suddenly turns over, and produces a rolling of
the ocean which is often felt at the distance of many leagues.