But since he needed a lever that would have been as long as from here to the farthest star whose distance has ever been measured, and since he would have had to push his end of the lever something like a quintillion (1,000,000,000,000,000,000) miles to lift the earth one inch, his proposition was hardly a practical one.

But levers are practical. Without them there would be none of our modern machines. No locomotives could speed across the continents; no derricks could lift great weights; no automobiles or bicycles would quicken our travel; our very bodies would be completely paralyzed. Yet the law back of all these things is really simple.

You have often noticed on the see-saw that a small child at one end can be balanced by a larger child at the other end, provided that the larger child sits nearer the middle. Why should it matter where the larger child sits? He is always heavier--why doesn"t he overbalance the small child? It is because when the small child moves up and down he goes a longer distance than the large child does. In Figure 26 the large boy moves up and down only half as far as the little girl does.

She weighs only half as much as he, yet she balances him.

[Ill.u.s.tration: FIG. 26. The little girl raises the big boy, but in doing it she moves twice as far as he does.]

You will begin to get a general understanding of levers and how they work by doing the following experiment:

EXPERIMENT 18. For this experiment there will be needed a small pail filled with something heavy (sand or stones will do), a yardstick with a hole through the middle and another hole near one end and with notches cut here and there along the edge, and a post or table corner with a heavy nail driven into it to within an inch of the head. The holes in the yardstick must be large enough to let the head of this nail through.

Put the middle hole of the yardstick over the nail, as is shown in Figure 27. The nail is the _fulcrum_ of your lever.

Now hang the pail on one of the notches about halfway between the fulcrum and the end of the stick and put your hand on the opposite side of the yardstick at about the same distance as the pail is from the fulcrum. Raise and lower the pail several times by moving the opposite end of the lever up and down. See how much force it takes to move the pail.

Now slide your hand toward the fulcrum and lower and raise the pail from that position. Is it harder or easier to lift the pail from here than from the first position? Which moves farther up and down, your hand or the pail?

Next, slide your hand all the way out to the end of the yardstick and raise and lower the pail from there. Is the pail harder or easier to lift? Does the pail move a longer or a shorter distance up and down than your hand?

If you wanted to move the pail a long way without moving your hand as far, would you put your hand nearer to the fulcrum or farther from it than the pail is?

[Ill.u.s.tration: FIG. 27. The yardstick is a lever by which he lifts the pail.]

[Ill.u.s.tration: FIG. 28. A lever with the weight between the fulcrum and the force.]

Suppose you wanted to lift the pail with the least possible effort, where would you put your hand?

Notice another fact: when your hand is at the end of the yardstick, it takes the same length of time to move a long way as the pail takes to move a short way. Then which is moving faster, your hand or the pail?

EXPERIMENT 19. Put the end hole of the yardstick on the nail, as shown in Figure 28. The nail is still the fulcrum of your lever. Put the pail about halfway between the fulcrum and the other end of the stick, and hold the end of the stick in your hands.

Raise and lower your hand to see how hard or how easy it is to lift the pail from this position. Which is moving farther, your hand or the pail? Which is moving faster?

Now put your hand about halfway between the fulcrum and the pail and raise and lower it. Is it harder or easier to raise than before? Which moves farther this time, your hand or the pail? Which moves faster?

If you wanted to make the pail move farther and faster than your hand, would you put your hand nearer to the fulcrum than the pail is, or farther from the fulcrum than the pail? If you wanted to move the pail with the least effort, where would you put your hand?

EXPERIMENT 20. Use a pair of long-bladed shears and fold a piece of cardboard once to lie astride your own or some one else"s finger. Put the finger, protected by the cardboard, between the two points of the shears. Then squeeze the handles of the shears together. See if you can bring the handles together hard enough to hurt the finger between the points.

Now watch the shears as you open and close the blades. Which move farther, the points of the shears or the handles? Which move faster?

Next, put the finger, still protected by the cardboard, between the _handles_ of the shears and press the points together. Can you pinch the finger this way harder or less hard than in the way you first tried?

Do the points or handles move farther as you close the shears?

Which part closes with the greater force?

[Ill.u.s.tration: FIG. 29. You cannot pinch hard enough this way to hurt.]

[Ill.u.s.tration: FIG. 30. But this is quite different.]

EXPERIMENT 21. Use a Dover egg beater. Fasten a small piece of string to one of the blades, so that you can tell how many times it goes around. Turn the handle of the beater around once slowly and count how many times the blade goes around.

Which moves faster, the handle or the blade? Where would you expect to find more force, in the cogs or in the blades? Test your conclusion this way: Put your finger between the blades and try to pinch it by turning the handle; then place your finger so that the skin is caught between the cogs and try to pinch the finger by turning the blades. Where is there more force? Where is there more motion?

EXPERIMENT 22. Put a spool over the nail which was your fulcrum in the first two experiments. (Take the stick off the nail first, of course.) Use this spool as a pulley. Put a string over it and fasten one end of your string to the pail (Fig. 32). Lift the pail by pulling down on the other end of the string. Notice that it is not harder or easier to move the pail when it is near the nail than when it is near the floor.

When your hand moves down from the nail to the floor, how far up does the pail move? Does the pail move a greater or less distance than your hand, or does it move the same distance?

Next fasten one end of the string to the nail. Set the pail on the floor. Pa.s.s the string through the handle of the pail and up over the spool (Fig. 33). Pull down on the loose end of the string. Is the pail easier to lift in this way or in the way you first tried? As you pull down with your hand, notice whether your hand moves farther than the pail, not so far as the pail, or the same distance. Is the greater amount of motion in your hand or in the pail? Then where would you expect the greater amount of force?

[Ill.u.s.tration: FIG. 31. When the handle is turned the blades of the egg beater move much more rapidly than the hand. Will they pinch hard enough to hurt?]

The whole idea of the lever can be summed up like this: one end of the contrivance _moves_ more than the other. But energy cannot be lost; so to make up for this extra _motion_ at one end more _force_ is always exerted at the other.

This rule is true for all kinds of levers, blocks and tackles or pulley systems, automobile and bicycle gears, belt systems, cog systems, derricks, crowbars, and every kind of machine. In most machines you either put in more force than you get out and gain motion, or you put in more motion than you get out and gain force. In the following examples of the lever see if you can tell whether you are applying more force and obtaining more motion, or whether you are putting in more motion and obtaining more force:

Cracking nuts with a nut cracker.

Beating eggs with a Dover egg beater.

Going up a hill in an automobile on low gear.

Speeding on high gear.

Cutting cloth with the points of shears.

Cutting near the angle of the shears.

Turning a door k.n.o.b.

Picking up sugar with sugar tongs.

Pinching your finger in the crack of a door on the hinge side.

[Ill.u.s.tration: FIG. 32. His hand goes down as far as the pail goes up.]

_APPLICATION 16._ Suppose you wanted to lift a heavy frying pan off the stove. You have a cloth to keep it from burning your hand. Would it be easier to lift it by the end of the handle or by the part of the handle nearest the pan?

_APPLICATION 17._ A boy was going to wheel his little sister in a wheelbarrow. She wanted to sit in the middle of the wheelbarrow; her brother thought she should sit as near the handles as possible so that she would be nearer his hands.

Another boy thought she should sit as near the wheel as possible. Who was right?

_APPLICATION 18._ James McDougal lived in a hilly place. He was going to buy a bicycle. "I want one that will take the hills easily," he said. The dealer showed him two bicycles.

On one the back wheel went around three times while the pedals went around once; on the other the back wheel went around four and a half times while the pedals went around once. Which bicycle should James have chosen? If he had wanted the bicycle for racing, which should he have chosen?

_APPLICATION 19._ A wagon stuck in the mud. The driver got out and tried to help the horse by grasping the spokes and turning the wheel. Should he have grasped the spokes near the hub, near the rim, or in the middle?

[Ill.u.s.tration: FIG. 33. With this arrangement the pail travels more slowly than the hand. Will it seem heavier or lighter than with the arrangement shown in Figure 32?]

INFERENCE EXERCISE