CHAPTER ONE GRAVITATION

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Section 1. A real place where things weigh nothing and where there is no up or down.

Why is it that the oceans do not flow off the earth?

What is gravity?

What is "down," and what is "up"?

There is a place where nothing has weight; where there is no "up" or "down"; where nothing ever falls; and where, if people were there, they would float about with their heads pointing in all directions. This is not a fairy tale; every word of it is scientifically true. If we had some way of flying straight toward the sun about 160,000 miles, we should really reach this strange place.

Let us pretend that we can do it. Suppose we have built a machine that can fly far out from the earth through space (of course no one has really ever invented such a machine). And since the place is far beyond the air that surrounds the earth, let us imagine that we have fitted out the air-tight cabin of our machine with plenty of air to breathe, and with food and everything we need for living. We shall picture it something like the cabin of an ocean steamer. And let us pretend that we have just arrived at the place where things weigh nothing:

When you try to walk, you glide toward the ceiling of the cabin and do not stop before your head bumps against it. If you push on the ceiling, you float back toward the floor. But you cannot tell whether the floor is above or below, because you have no idea as to which way is up and which way is down.

As a matter of fact there is no up or down. You discover this quickly enough when you try to pour a glass of water. You do not know where to hold the glass or where to hold the pitcher. No matter how you hold them, the water will not pour—point the top of the pitcher toward the ceiling, or the floor, or the wall, it makes no difference. Finally you have to put your hand into the pitcher and pull the water out. It comes. Not a drop runs between your fingers—which way can it run, since there is no down? The big lump of water stays right on your hand. This surprises you so much that you let go of the pitcher. Never mind; the pitcher stays poised in mid-air. But how are you going to get a drink? It does not seem reasonable to try to drink a large lump of water. Yet when you hold the lump to your lips and suck it you can draw the water into your mouth, and it is as wet as ever; then you can force it on down to (or rather toward) your throat with your tongue. Still you have left in your hand a big piece of water that will not flow off. You throw it away, and it sails through the air of the cabin in a straight line until it splashes against the wall. It wets the wall as much as water on the earth would, but it does not run off. It sticks there, like a splash-shaped piece of clear, colorless gelatin.

Suppose that for the sake of experimenting you have brought an elephant along on this trip. You can move under him (or over him—anyway between him and the floor), brace your feet on the floor, and give him a push. (If he happens to step on your toes while you are doing this, you do not mind in the least, because he does not weigh anything, you know.) If you push hard enough to get the elephant started, he rises slowly toward the ceiling. When he objects on the way, and struggles and kicks and tries to get back to the floor, it does not help him at all. His bulky, kicking body floats steadily on till it crashes into the ceiling.

No chairs or beds are needed in this place. You can lie or sit in mid-air, or cling to a fixture on a wall, resting as gently there as a feather might. There is no need to set the table for meals—just lay the dishes with the food on them in space and they stay there. If the top of your cup of chocolate is toward the ceiling, and your plate of food is turned the other way, no harm is done. Your feet may happen to point toward the ceiling, while some one else's point toward the floor, as you sit in mid-air, eating. There is some difficulty in getting the food on the dishes, so probably you do not wish to bother with dishes, after all. Do you want some mashed potatoes? All right, here it is—and the cook jerks the spoon away from the potatoes, leaving them floating before you, ready to eat.

It is literally a topsy-turvy place.

Do you want to know why all this would happen? Here is the reason: There is a great force known as gravitation. It is the pull that everything in the universe has on everything else. The more massive a thing is, the more gravitational pull it has on other objects; but the farther apart things are, the less pull they have on each other.

The earth is very massive, and we live right on its surface; so it pulls us strongly toward it. Therefore we say that we weigh something. And since every time we roll off a bed, for instance, or jump off a chair, the earth pulls us swiftly toward it, we say that the earth is down. "Down" simply means toward the thing that is pulling us. If we were on the surface of the moon, the moon would pull us. "Down" would then be under our feet or toward the center of the moon, and the earth would be seen floating up in the sky. For "up" means away from the thing which is pulling us.

Why water does not flow off the earth. It was because people did not know about gravitation that they laughed at Columbus when he said the earth was round. "Why, if the earth were round," they argued, "the water would all flow off on the other side." They did not know that water flows downhill because the earth is pulling it toward its center by gravitation, and that it does not make the slightest difference on which side of the earth water is, since it is still pulled toward the center.

Why the world does not fall down. And people used to wonder "what held the earth up." The answer, as you can see, is easy. There simply is no up or down in space. The earth cannot fall down, because there is no down to fall to. "Down" merely means toward the earth, and the earth cannot very well fall toward itself, can it? The sun is pulling on it, though; so the earth could fall into the sun, and it would do so, if it were not swinging around the sun so fast. You will see how this keeps it from falling into the sun when you come to the section on centrifugal force.

Why there is a place where things weigh nothing. Now about the place where gravitation has no effect. Since an object near the sun is pulled more by the sun than it is by the earth, and since down here near the earth an object is pulled harder by the earth than by the sun, it is clear that there must be a place between the sun and the earth where their pulls just balance; and where the sun pulls just as hard one way as the earth pulls the other way, things will not fall either way, but will float. The place where the pulls of the sun and the earth are equal is not halfway between the earth and the sun, because the sun is so much larger and pulls so much more powerfully than the earth, that the place where their pulls balance is much nearer the earth than it is to the sun. As a matter of fact, it can be easily calculated that this spot is somewhere near 160,000 miles from the earth.

There are other spots like it between every two stars, and in the center of the earth, and in the center of every other body. You see, in the center of the earth there is just as much of the earth pulling one way as there is pulling the other, so again there is no up or down.

Application 1. Explain why the people on the other side of the earth do not fall off; why you have weight; why rivers run downhill; why the world does not fall down.

Section 2. "Water seeks its own level."

Why does a spring bubble up from the ground?

What makes the water come up through the pipe into your house?

Why is a fire engine needed to pump water up high?

You remember that up where the pull of the earth and the sun balance each other, water could not flow or flatten out. Let us try to imagine that water, here on the earth, has lost its habit of flattening out whenever possible—that, like clay, it keeps whatever shape it is given.

First you notice that the water fails to run out of the faucets. (For in most places in the world as it really is, the water that comes through faucets is simply flowing down from some high reservoir.) People all begin to search for water to drink. They rush to the rivers and begin to dig the water out of them. It looks queer to see a hole left in the water wherever a person has scooped up a pailful. If some one slips into the river while getting water, he does not drown, because the water cannot close in over his head; there is just a deep hole where he has fallen through, and he breathes the air that comes down to him at the bottom of the hole. If you try to row on the water, each stroke of the oars piles up the water, and the boat makes a deep furrow wherever it goes so that the whole river begins to look like a rough, plowed field.

When the rivers are used up, people search in vain for springs. (No springs could flow in our everyday world if water did not seek its own level; for the waters of the springs come from hills or mountains, and the higher water, in trying to flatten out, forces the lower water up through the ground on the hillsides or in the valleys.) So people have to get their water from underground or go to lakes for it. And these lakes are strange sights. Storms toss up huge waves, which remain as ridges and furrows until another storm tears them down and throws up new ones.

But with no rivers flowing into them, the lakes also are used up in time. The only fresh water to be had is what is caught from the rain. Even wells soon become useless; because as soon as you pump up the water surrounding the pump, no more water flows in around it; and if you use a bucket to raise the water, the well goes dry as soon as the supply of water standing in it has been drawn.

You will understand more about water seeking its own level if you do this experiment:

Experiment 1. Put one end of a rubber tube over the narrow neck of a funnel (a glass funnel is best), and put the other end of the tube over a piece of glass tubing not less than 5 or 6 inches long. Hold up the glass tube and the funnel, letting the rubber tube sag down between them as in Figure 1. Now fill the funnel three fourths full of water. Raise the glass tube higher if the water starts to flow out of it. If no water shows in the glass tube, lower it until it does. Gradually raise and lower the tube, and notice how high the water goes in it whenever it is held still.

This same thing would happen with any shape of tube or funnel. You have another example of it when you fill a teakettle: the water rises in the spout just as high as it does in the kettle.

Why water flows up into your house. It is because water seeks its own level that it comes up through the pipes in your house. Usually the water for a city is pumped into a reservoir that is as high as the highest house in the city. When it flows down from the reservoir, it tends to rise in any pipe through which it flows, to the height at which the water in the reservoir stands. If a house is higher than the surface of the water in the reservoir, of course that house will get no running water.

Why fire engines are needed to force water high. In putting out a fire, the firemen often want to throw the water with a good deal of force. The tendency of the water to seek its own level does not always give a high enough or powerful enough stream from the fire hose; so a fire engine is used to pump the water through the hose, and the stream flows with much more force than if it were not pumped.

Application 2. A. C. Wheeler of Chicago bought a little farm in Indiana, and had a windmill put up to supply the place with water. But at first he was not sure where he should put the tank into which the windmill was to pump the water and from which the water should flow into the kitchen, bathroom, and barn. The barn was on a knoll, so that its floor was almost as high as the roof of the house. Which would have been the best place for the tank: high up on the windmill (which stood on the knoll by the barn), or the basement of the house, or the attic of the house?

Fig. 2.

Fig. 2. Where is the best location for the tank?

Fig. 3.

Fig. 3. When the tank is full, will the oil overflow the top of the tube?

Application 3. A man was about to open a garage in San Francisco. He had a large oil tank and wanted a simple way of telling at a glance how full it was. One of his workmen suggested that he attach a long piece of glass tubing to the side of the tank, connecting it with an extra faucet near the bottom of the tank. A second workman said, "No, that won't do. Your tank holds ever so much more than the tube would hold, so the oil in the tank would force the oil up over the top of the tube, even when the tank was not full." Who was right?

Section 3. The sea of compressed air in which we live: Air pressure.

Does a balloon explode if it goes high in the air?

What is suction?

Why does soda water run up a straw when you draw on the straw?

Why will evaporated milk not flow freely out of a can in which there is only one hole?

Why does water gurgle when you pour it out of a bottle?

We are living in a sea of compressed air. Every square inch of our bodies has about 15 pounds of pressure against it. The only reason we are not crushed is that there is as strong pressure inside of our bodies pushing out as there is outside pushing in. There is compressed air in the blood and all through the body. If you were to lie down on the ground and have all the air pumped out from under you, the air above would crush you as flat as a pancake. You might as well let a dozen big farm horses trample on you, or let a huge elephant roll over you, as let the air press down on you if there were no air underneath and inside your body to resist the pressure from above. It is hard to believe that the air and liquids in our bodies are pressing out with a force great enough to resist this crushing weight of air. But if you were suddenly to go up above the earth's atmosphere, or if you were to stay down here and go into a room from which the air were to be pumped all at once, your body would explode like a torpedo.

When you suck the air out of a bottle, the surrounding air pressure forces the bottle against your tongue; if the bottle is a small one, it will stick there. And the pressure of the air and blood in your tongue will force your tongue down into the neck of the bottle from which part of the air has been taken.

In the same way, when you force the air out of a rubber suction cap, such as is used to fasten reading lamps to the head of a bed, the air pressure outside holds the suction cap tightly to the object against which you first pressed it, making it stick there.

We can easily experiment with air pressure because we can get almost entirely rid of it in places and can then watch what happens. A place from which the air is practically all pumped out is called a vacuum. Here are some interesting experiments that will show what air pressure does:

Fig. 4.

Fig. 4. When the point is knocked off the electric lamp, the water is forced into the vacuum.

Experiment 2. Hold a burned-out electric lamp in a basin of water, break its point off, and see what happens.

All the common electric lamps (less than 70 watts) are made with vacuums inside. The reason for this is that the fine wire would burn up if there were any air in the lamps. When you knock the point off the globe, it leaves a space into which the water can be pushed. Since the air is pressing hard on the surface of the water except in the one place where the vacuum in the lamp globe is, the water is forced violently into this empty space.

It really is a good deal like the way mud comes up between your toes when you are barefoot. Your foot is pressing on the mud all around except in the spaces between your toes, and so the mud is forced up into these spaces. The air pressure on the water is like your foot on the mud, and the space in the lamp globe is like the space between your toes. Since wherever there is air it is pressing hard, the only space into which it can force water or anything else is into a place from which all the air has been removed, like the inside of the lamp globe.

The reason that the water does not run out of the globe is this: the hole is too small to let the air squeeze up past the water, and therefore no air can take the place of the water that might otherwise run out. In order to flow out, then, the water would have to leave an empty space or vacuum behind it, and the air pressure would not allow this.

Why water gurgles when it pours out of a bottle. You have often noticed that when you pour water out of a bottle it gurgles and gulps instead of flowing out evenly. The reason for this is that when a little water gets out and leaves an empty space behind, the air pushing against the water starts to force it back up; but since the mouth of the bottle is fairly wide, the air itself squeezes past the water and bubbles up to the top.

Experiment 3. Put a straw or a piece of glass tube down into a glass of water. Hold your finger tightly over the upper end, and lift the tube out of the water. Notice how the water stays in the tube. Now remove your finger from the upper end.

The air holds the water up in the tube because there is no room for it to bubble up into the tube to take the place of the water; and the water, to flow out of the tube, would have to leave a vacuum, which the air outside does not allow. But when you take your finger off the top of the straw or tube, the air from above takes the place of the water as rapidly as it flows out; so there is no tendency to form a vacuum, and the water leaves the tube. Now do you see why you make two holes in the top of a can of evaporated milk when you wish to pour the milk out evenly?

Fig. 5.

Fig. 5. The water is held in the tube by air pressure.

Experiment 4. Push a rubber suction cap firmly against the inside of the bell jar of an air pump. Try to pull the suction cap off. If it comes off, press it on again; place the bell jar on the plate of the air pump, and pump the air out of the jar. What must have been holding the suction cap against the inside of the jar? Does air press up and sidewise as well as down? Test this further in the following experiment:

Fig. 6.

Fig. 6. An air pump.

Experiment 5. Put a cork into an empty bottle. Do not use a new cork, but one that has been fitted into the bottle many times and has become shaped to the neck. Press the cork in rather firmly, so that it is air-tight, but do not jam it in. Set the bottle on the plate of the air pump, put the bell jar over it, and pump the air out of the jar. What makes the cork fly out of the bottle? What was really in the "empty" bottle? Why could it not push the cork out until you had pumped the air out of the jar?

Experiment 6. Wax the rims of the two Magdeburg hemispheres (see Fig. 7). Screw the lower section into the hole in the plate of the air pump. Be sure that the stop valve in the neck of the hemisphere is open. (The little handle should be vertical.) Fit the other section on to the first, and pump out as much air as you can. Close the stop valve. Unscrew the hemispheres from the air pump. Try to pull them apart—pull straight out, taking care not to slide the parts. If you wish, let some one else take one handle, and see if the two of you can pull it apart.

Fig. 7.

Fig. 7. The experiment with the Magdeburg hemispheres.

Before you pumped the air out of the hemisphere, the compressed air inside of them (you remember all the air down here is compressed) was pushing them apart just as hard as the air outside of them was pushing them together. When you pumped the air out, however, there was hardly any air left inside of them to push outward. So the strong pressure of the outside air against the hemispheres had nothing to oppose it. It therefore pressed them very tightly together and held them that way.

This experiment was first tried by a man living in Magdeburg, Germany. The first set of hemispheres he used proved too weak, and when the air in them was partly pumped out, the pressure of the outside air crushed them like an egg shell. The second set was over a foot in diameter and much stronger. After he had pumped the air out, it took sixteen horses, eight pulling one way and eight the opposite way, to pull the hemispheres apart.

Experiment 7. Fill a bottle (or flask) half full of water. Through a one-hole stopper that will fit the bottle, put a bent piece of glass tubing that will reach down to the bottom of the bottle. Set the bottle, thus stoppered, on the plate of the air pump, with a beaker or tumbler under the outer end of the glass tube. Put the bell jar over the bottle and glass, and pump the air out of the jar. What is it that forces the water up and out of the bottle? Why could it do this when the air was pumped out of the bell jar and not before?

How a seltzer siphon works. A seltzer siphon works on the same principle. But instead of the ordinary compressed air that is all around us, there is in the seltzer siphon a gas (carbon dioxid) which has been much more compressed than ordinary air. This strongly compressed gas forces the seltzer water out into the less compressed air, exactly as the compressed air in the upper part of the bottle forced the water out into the comparative vacuum of the bell jar in Experiment 7.

Experiment 8. Fill a toy balloon partly full of air by blowing into it, and close the neck with a rubber band so that no air can escape. Lay a saucer over the hole in the plate of the air pump, so that the rubber of the balloon cannot be sucked down the hole. Lay the balloon on top of this saucer, put the bell jar over it, and pump the air out of the jar. What makes the balloon expand? What is in it? Why could it not expand before you pumped the air out from around it?

A toy balloon expands for the same reason when it goes high in the air. Up there the air pressure is not so strong outside the balloon, and so the gas inside makes the balloon expand until it bursts.

Fig. 8.

Fig. 8. A siphon. The air pushes the water over the side of the pan.

Experiment 9. Lay a rubber tube flat in the bottom of a pan of water, so that the tube will be filled with water. Let one end stay under water, but pinch the other end tightly shut with your thumb and finger and lift it out of the pan. Lower this closed end into a sink or empty pan that is lower than the pan of water. Now stop pinching the tube shut. This device is called a siphon (Fig. 8).

Experiment 10. Put the mouth of a small syringe, or better, of a glass model lift pump, under water. Draw the handle up. Does the water follow the plunger up, stand still, or go down in the pump?

When you pull up the plunger, you leave an empty space; you shove the air out of the pump or syringe ahead of the plunger. The air outside, pressing on the water, forces it up into this empty space from which the air has been pushed. But air pressure cannot force water up even into a perfect vacuum farther than about 33 feet. If your glass pump were, say, 40 feet long, the water would follow the plunger up for a little over 30 feet, but nothing could suck it higher; for by the time it reaches that height it is pushing down with its own weight as hard as the air is pressing on the water below. No suction pump, or siphon, however perfect, will ever lift water more than about 33 feet, and it will do well if it draws water up 28 or 30 feet. This is because a perfect vacuum cannot be made. There is always some water vapor formed by the water evaporating a little, and there is always a small amount of air that has been dissolved in water, both of which partly fill the space above the water and press down a little on the water within the pump.

Fig. 9.

Fig. 9. A glass model suction pump.

If you had a straw over 33 feet long, and if some one held a glass of lemonade for you down near the sidewalk while you leaned over from the roof of a three-story building with your long straw, you could not possibly drink the lemonade. The air pressure would not be great enough to lift it so high, no matter how hard you sucked,—that is, no matter how perfect a vacuum you made in the upper part of the straw. The lemonade would rise part way, and then your straw would be flattened by the pressure outside.

Some days the air can force water up farther in a tube than it can on other days. If it can force the water up 33 feet today, it will perhaps be able to force it up only 30 feet immediately before a storm. And if it forces water up 33 feet at sea level, it may force it up only 15 or 20 feet on a high mountain, for on a mountain there is much less air above to make pressure. The pressure of the air is different in different places; where the air is heavy and pressing hard, we say the pressure is high; where the air is light and not pressing so hard, we call the pressure low. A place where the air is heavy is called an area of high pressure; where it is light, an area of low pressure. (See Section 44.)

What makes winds? It is because the air does not press equally all the time and everywhere that we have winds. Naturally, if the air is pressing harder in one place than in another, the lower air will be pushed sidewise in the areas of high pressure and will rush to the areas where there is less pressure. And air rushing from one place to another is called wind.

Fig. 10.

Fig. 10.

Application 4. A man had two water reservoirs, which stood at the same level, one on each side of a hill. The hill between them was about 50 feet high. One reservoir was full, and the other was empty. He wanted to get some of the water from the full reservoir into the empty one. He did not have a pump to force the water from one to the other, but he did have a long hose, and could have bought more. His hose was long enough to reach over the top of the hill, but not long enough to go around it. Could he have siphoned the water from one reservoir to the other? Would he have had to buy more hose?

Application 5. Two boys were out hiking and were very thirsty. They came to a deserted farm and found a deep well; it was about 40 feet down to the water. They had no pump, but there was a piece of hose about 50 feet long. One boy suggested that they drop one end of the hose down to the water and suck the water up, but the other said that that would not work—the only way would be to lower the hose into the water, close the upper end, pull the hose out and let the water pour out of the lower end of the hose into their mouths. A stranger came past while the boys were arguing, and said that neither way would work; that although the hose was long enough, the water was too far down to be raised in either way. He advised the boys to find a bucket and to use the hose as a rope for lowering it. Who was right?

Inference Exercise

Explanatory Note. In the inference exercises in this book, there is a group of facts for you to explain. They can always be explained by one or more of the principles studied, like gravitation, water seeking its own level, or air pressure. If asked to explain why sucking through a straw makes soda water come up into your mouth, for instance, you should not merely say "air pressure," but should tell why you think it is air pressure that causes the liquid to rise through the straw. The answer should be something like this: "The soda water comes up into your mouth because the sucking takes the air pressure away from the top of the soda water that is in the straw. This leaves the air pressing down only on the surface of the soda water in the glass. Therefore, the air pressure pushes the soda water up into the straw and into your mouth where the pressure has been removed by sucking." Sometimes, when you have shown that you understand the principles very well, the teacher may let you take a short cut and just name the principle, but this will be done only after you have proved by a number of full answers that you thoroughly understand each principle named.

Some of the following facts are accounted for by air pressure; some by water seeking its own level; others by gravitation. See if you can tell which of the three principles explains each fact:

1. Rain falls from the clouds.

2. After rain has soaked into the sides of mountains it runs underground and rises, at lower levels, in springs.

3. When there are no springs near, people raise the water from underground with suction pumps.

4. As fast as the water is pumped away from around the bottom of a pump, more water flows in to replace it.

5. After you pump water up, it flows down into your pail from the spout of the pump.

6. You can drink lemonade through a straw.

7. If a lemon seed sticks to the bottom of your straw, the straw flattens out when you suck.

8. When you pull your straw out to remove the seed, there is no hole left in the lemonade; it closes right in after the straw.

9. If you drop the seed, it falls to the floor.

10. If you tip the glass to drink the lemonade, the surface of the lemonade does not tip with the glass, but remains horizontal.

Section 4. Sinking and floating: Displacement.

What keeps a balloon up?

What makes an iceberg float?

Why does cork float on the water and why do heavier substances sink?

If iron sinks, why do iron ships not sink?

Again let us imagine ourselves up in the place where gravitation has no effect. Suppose we lay a nail on the surface of a bowl of water. It stays there and does not sink. This does not seem at all surprising, of course, since the nail no longer has weight. But when we put a cork in the midst of the water, it stays there instead of floating to the surface. This seems peculiar, because the less a thing weighs the more easily it floats. So when the cork weighs nothing at all, it seems that it should float better than ever. Of course there is some difficulty in deciding whether it ought to float toward the part of the water nearest the floor or toward the part nearest the ceiling, since there is no up or down; but one would think that it ought somehow to get to the outside of the water and not stay exactly in the middle. If put on the outside, however, it stays there as well.

A toy balloon, in the same way, will not go toward either the ceiling or the floor, but just stays where it is put, no matter how light a gas it is filled with.

The explanation is as follows: For an object to float on the water or in the air, the water or air must be heavier than the object. It is the water or air being pulled under the object by gravity, that pushes it up. Therefore, if the air and water themselves weighed nothing, of course they would be no heavier than the balloon or the cork; the air or water would then not be pulled in under the balloon or cork by gravity, and so would not push them up, or aside.

Fig. 11.

Fig. 11. The battleship is made of steel, yet it does not sink.

Why iron ships float. When people first talked about building iron ships, others laughed at them. "Iron sinks," they said, "and your boats will go to the bottom of the sea." If the boats were solid iron this would be true, for iron is certainly much heavier than water. But if the iron is bent up at the edges,—as it is in a dish pan,—it has to push much more water aside before it goes under than it would if it were flattened out. The water displaced, or pushed aside, would have to take up as much room as was taken up by the pan and all the empty space inside of it, before the edge would go under. Naturally this amount of water would weigh a great deal more than the empty pan.

But suppose you should fill the dish pan with water, or suppose it leaked full. Then you would have the weight of all the water in it added to the weight of the pan, and that would be heavy enough to push aside the water in which it was floating and let the pan sink. This is why a ship sometimes sinks when it springs a leak.

You may be able to see more clearly why an iron ship floats by this example: Suppose your iron ship weighs 6000 tons and that the cargo and crew weigh another 1000 tons. The whole thing, then, weighs 7000 tons. Now that ship is a big, bulky affair and takes up more space than 7000 tons of water does. As it settles into the water it pushes a great deal of water out of the way, and after it sinks a certain distance it has pushed 7000 tons of water out of the way. Since the ship weighs only 7000 tons, it evidently cannot push aside more than that weight of water; so part of the ship stays above the water, and all there is left for it to do is to float. If the ship should freeze solid in the water where it floated and then could be lifted out of the ice by a huge derrick, you would find that you could pour exactly 7000 tons of water into the hole where the ship had been.

But if you built your ship with so little air space in it that it took less room than 7000 tons of water takes, it could go clear under the water without pushing 7000 tons of water aside. Therefore a ship of this kind would sink.

The earth's gravity is pulling on the ship and on the water. If the ship has displaced (pushed aside) its own weight of water, gravity is pulling down on the water as hard as it is on the ship; so the ship cannot push any more water aside, and if there is enough air space in it, the ship floats.

Perhaps the easiest way to say it is like this: Anything that is lighter than the same volume of water will float; since a cubic foot of wood weighs less than a cubic foot of water, the wood will float; since a quart of oil is lighter than a quart of water, the oil will float; since a pint of cream is lighter than a pint of milk, the cream will rise. In the same way, anything that is lighter than the same volume of air will be pushed up by the air. When a balloon with its passengers weighs less than the amount of air that it takes the place of at any one time, it will go up. Since a quart of warm air weighs less than a quart of cold air, the warm air will rise.

You can see how a heavy substance like water pushes a lighter one, like oil, up out of its way, in the following experiment:

Experiment 11. Fill one test tube to the brim with kerosene slightly colored with a little iodine. Fill another test tube to the brim with water, colored with a little blueing. Put a small square of cardboard over the test tube of water, hold it in place, and turn the test tube upside down. You can let go of the cardboard now, as the air pressure will hold it up. Put the mouth of the test tube of water exactly over the mouth of the test tube of kerosene. Pull the cardboard out from between the two tubes, or have some one else do this while you hold the two tubes mouth to mouth. If you are careful, you will not spill a drop. If nothing happens when the cardboard is pulled away, gently rock the two tubes, holding their mouths tightly together.

Fig. 12.

Fig. 12. The upper tube is filled with water and the lower with oil. What will happen when she pulls the cardboard out?

Oil is lighter than water, as you know, because you have seen a film of oil floating on water. When you have the two test tubes in such a position that the oil and water can change, the water is pulled down under the kerosene because gravity is pulling harder on the water than it is pulling on the kerosene. The water, therefore, goes to the bottom and this forces the kerosene up.

Application 6. Three men were making a raft. For floats they meant to use some air-tight galvanized iron cylinders. One of them wanted to fill the cylinders with cork, "because," he said, "cork is what you put in life preservers and it floats better than anything I know of." "They'd be better with nothing in them at all," said a second. "Pump all the air out and leave vacuums. They're air-tight and they are strong enough to resist the air pressure." But the third man said, "Why, you've got to have some air in them to buoy them up. Cork would be all right, but it isn't as light as air; so air would be the best thing to fill them with."

Which way would the floats have worked best?

Application 7. A little girl was telling her class about icebergs. "They are very dangerous," she said, "and ships are often wrecked by running into them. You see, the sun melts the top off them so that all there is left is under water. The sailors can't see the ice under water, and so their ships run into it and are sunk." Another girl objected to this; she said, "That couldn't be; the ice would bob up as fast as the top melted." "No, it wouldn't," said a boy. "If that lower part wasn't heavier than water, it never would have stayed under at all. And if it was heavier at the beginning, it would still be heavier after the top melted off."

Who was right?

Inference Exercise

Explain the following:

11. When you wash dishes, a cup often floats on top of the water, while a plate made of the same sort of china sinks to the bottom of the pan.

12. If you put the cup in sidewise, it sinks.

13. The water in the cup, when lying on its side, is exactly as high as the water in the dish pan.

14. If you put a glass into the water, mouth first, the water cannot get up into the glass; if you tip it a little, there are bubbles in the water and some water enters the glass.

15. If you let a dish slip while you are wiping it, it crashes to the floor.

16. It is much harder to hold a large platter while you are wiping it than it is to hold a small butter plate.

17. If you set a hot glass upside down on the oilcloth table cover, the oilcloth bulges up into it when the hot air and steam shrink and leave a partial vacuum within the glass.

18. If you spill any of the dishwater on the floor, it flattens out.

19. You may use a kind of soap that is full of invisible little air bubbles; if you do, the soap will float on top of the water.

20. When you drop a dry dishcloth into water, it floats until all the pores are filled with water; then it sinks.

Section 5. How things are kept from toppling over: Stability.

Why is it harder to keep your balance on stilts than on your feet?

Why does a rowboat tip over more easily if you stand up in it?

Fig. 13.

Fig. 13. The Leaning Tower of Pisa.

In Pisa, Italy, there is a beautiful marble bell tower which leans over as if it were just about to fall to the ground. Yet it has stood in this position for hundreds of years and has never given a sign of toppling. The foundations on which it rested sank down into the ground on one side while the tower was being built (it took over 200 years to build it), and this made it tip. But the men who were building it evidently felt sure that it would not fall over in spite of its tipping. They knew the law of stability.

All architects and engineers and builders have to take this law into consideration or the structures they put up would topple over. And your body learned the law when you were a little over a year old, or you never could have walked. It is worth while for your brain to know it, too, because it is a very practical law that you can use in your everyday life.

If you wish to understand why the Leaning Tower of Pisa does not fall over, why it is hard to walk on stilts, why a boat tips when a person stands up in it, why blocks fall when you build too high with them, and how to keep things from tipping over, do the following experiment and read the explanation that follows it:

Fig. 14.

Fig. 14.

Experiment 12.2 Unscrew the bell from a doorbell or a telephone. You will not harm it at all, and you can put it back after the experiment. Cut a sheet of heavy wrapping paper or light-weight cardboard about 5 × 9 inches. Roll this so as to make a cylinder about 5 inches high and as big around as the bell. Hold it in shape by pasting it or putting a couple of rubber bands around it. Cut two strips of paper about an inch wide and 8 inches long; lay these crosswise; lay the bell, round side down, on the center of the cross. Push a paper fastener through the hole in the bell (the kind shown in Figure 14) and through the crossed pieces of paper, spreading the fastener out so as to fasten the paper cross to the rounded side of the bell. Bend the arms of the cross up around the bell and paste them to the sides of the paper cylinder so that the bell makes a curved bottom to the cylinder, as shown in Figure 15.

Footnote 2: To the Teacher. If you have a laboratory, it is well to have this cylinder already made for the use of all classes.

Fig. 15.

Fig. 15. In this cylinder the center of weight is so high that it is not over the bottom if the cylinder is tipped to any extent. So the cylinder falls over easily and lies quietly on its side.

Fig. 16.

Fig. 16. But in this one the center of weight is so low that it is over the base, no matter what position the cylinder is in.

Fig. 17.

Fig. 17. So even if the cylinder is laid on its side it immediately comes to an upright position again.

Try to tip the cylinder over. Now stuff some crumpled paper loosely into the cylinder, filling it to the top. Tip the cylinder again. Will it stay on its side now? Force all the crumpled paper to the bottom of the cylinder. Now will it stay on its side? Take out the crumpled paper and lay a flat stone in the bottom of the bell, holding it in place by stuffing some crumpled paper in on top of it. Will the cylinder tip over now? Take the stone out, put the crumpled paper in the bottom of the cylinder, put the stone on top of the paper, and again try to tip the cylinder over. Will it fall?


The center of the cylinder was always in one place, of course. But the center of the weight in that cylinder was usually near the bottom, because the bell weighed so much more than the paper. When you raised the center of weight by putting the stone up high or filling the cylinder with crumpled paper, just a little tipping moved the center of weight so that it was not directly over the bell on which the cylinder was resting. Whenever the center of weight is not over the base of support (the bottom on which the thing is standing), an object will topple over. Moving the center of weight up (Figs. 15 and 16) makes an object less stable.

The two main points to remember about stability are these: the wider the base of an object, the harder it is to tip over; and the lower the center of the weight is, the harder it is to tip over.

If you were out in a rowboat in a storm, would it be better to sit up straight in the seat or to lie in the bottom of the boat?

Why is a flat-bottomed boat safer than a canoe?

Fig. 18.

Fig. 18. Which vase would be the hardest to upset?

Where do you suppose the center of weight of the Leaning Tower of Pisa is,—near the bottom or near the top?

Application 8. If you had a large flower to put into a vase and you did not want it to tip over easily, which of the three vases shown in Figure 18 would you choose?

Application 9. Some boys made themselves a little sail-boat and went sailing in it. A storm came up. The boat rocked badly and was in danger of tipping over. "Throw out all the heavy things, quick!" shouted one. "No, no, don't for the life of you do it!" called another. "Chop down the mast—here, give me the hatchet!" another one said. "Crouch way down—lie on the bottom." "No, keep moving over to the side that is tipped up!" "Hold the things in the bottom of the boat still, so they'll not keep rolling from side to side." "Jump out and swim!" Every one was shouting at once. Which parts of the advice should you have followed if you had been on board?

Inference Exercise

Explain the following:

21. A ship when it goes to sea always carries ballast (weight) in its bottom.

22. If the ship springs a leak below the water line, the water rushes in.

23. The ship's pumps suck the water up out of the bottom of the ship.

24. The water pours back into the sea from the mouths of the pumps.

25. As the sailors move back and forth on the ship during a storm, they walk with their legs spread far apart.

26. Although the ship tips far from side to side, it rights itself.

27. However far the ship tips, the surface of the water in the bottom stays almost horizontal.

28. While the ship is in danger, the people put on life preservers, which are filled with cork.

29. When the ship rocks violently, people who are standing up are thrown to the floor, but those who are sitting down do not fall over.

30. If the ship fills with water faster than the engines can pump it out, the ship sinks.

                                                                                                                                                                                                                                                                                                           

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