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use a combination of two pulleys, as in Fig. 206, B. Here two lengths of rope support the weight, while we pull down on the third length. Do you see that we must pull downward twice as far as we can raise the weight? Is there any gain in this? The gain is that a force of one pound used as power will support two pounds of weight.

A

FIG. 206. One simple and two compound pulleys. In A a one-pound pull on the one cord will lift 1 pound on the other cord. In B and C a onepound pull will lift 2 and 3 pounds respectively.

If we use three pulleys to support the weight, as in Fig. 206, C, one pound can support three pounds, and so on. However, we must pull down three feet of rope for every foot we lift the weight. So in the pulley, as in the lever

FIG. 207. - This pile-driver has a simple pulley, but there is a second wheel near the ground, so that the horse can pull in a horizontal direction.

and inclined plane, the power, multiplied by the distance the power moves, is equal to the weight, multiplied by the distance the weight

moves.

278. Why Do We Use a Wheel and Axle? Have you ever seen workmen raising large timbers, or steel

girders, or loads of bricks or stone, to the top of a tall building? Do they carry these materials to the top? No; they use a machine. This is usually a winch, or windlass, together with a system of pulleys. The whole apparatus is called a derrick, or crane (Fig. 208).

FIG. 208.

(Courtesy of the American Hoist & Derrick Co.)

- A powerful modern crane operated by motors; it is able to pick up 3 tons of sugarcane at a "grab."

Examine a winch (Fig. 209). You will see that it consists of a crank, or handle, attached to an axle. When the crank is turned, a rope or cable may be wound up on the axle. But as the handle of the crank must be turned through a large circle to wind a little of the rope on the axle, a small force applied to the crank will lift a great weight attached to the axle.

The winch is a form of the simple machine called the wheel and axle. Examine the works of an old clock. Do you find any cases of the wheel and axle principle there? Why is it used? Do you see that the law of machines is true in the case of the wheel and axle, as well as in the case of the lever, inclined plane, and pulley?

FIG. 209.- Another way of raising water from a well (see Fig. 199).

279. Of What Use is a Wedge? Have you ever seen a woodman split a great log into boards or rails? He uses a block of hardwood, or of iron, that is thick on one side, and tapers down to a thin edge (Fig. 210). This simple machine is called a wedge; it is really a double inclined plane.

FIG. 210. How a log may be split in two.

The thin edge of the wedge must be driven into the log by means of a hammer, or maul. The deeper it is driven in, the farther the two halves of the log are forced apart. It is easy for the woodman to overcome the cohesion of the wood (see § 107), if he need force the wood apart only a little way at a time.

Can

you see that the more slender the wedge is, the farther he must drive it in, but the greater is the force with which the wedge pushes the wood apart?

280. Of What Use is the Screw? Have you ever climbed to the top of a tower or a lighthouse? You

FIG. 211. - By turning the handle of the screw driver you make the screw ad

could have climbed a ladder straight up to the top, but this would be very tiring, and would take a great deal of effort. In most towers you will

vance only a short distance, but with find a spiral stairway which winds around and

great force.

around the tower. In using the stairway you will have to walk many times the distance to the top, but you will not find yourself nearly so tired when you reach the top, because the ascent is so gradual.

Examine a metal screw, or a screw bolt, such as is used to hold boards, or pieces of metal, together; is not the thread of the screw, also, a spiral inclined plane? When you use the screw driver (Fig. 211), your hand must go through a large circle to make the screw move forward the short distance between the threads. But as a result of this great difference, a small force applied on the handle of the screw driver exerts a very great force on the threads, and forces the screw into the wood.

FIG. 212. How a jackscrew may be used to lift a house.

You are familiar with the jackscrew used to raise a house (Fig. 212), or a wagon in repairing its wheel, or an automobile in changing tires.

Compare the force you must exert in using the jackscrew with the weight you can lift with it.

The screw is used also to produce the great pressure needed in book and letter presses (Fig. 213). How about the baling press in which many schools collect and compress their waste paper, and in which farmers bale hay and straw? Have you ever used a screw-press nut-cracker?

281. Why Do We Oil a Machine? Do you know of a surface that is perfectly smooth? No; not even the finest workmen can get a surface free from all roughness, and every engineer knows that although the bearings of his engine are made as smooth as possible, yet each of the two surfaces which rub together wears the other down, instead of sliding perfectly over it. We have already learned (see § 103) that this rubbing together is called friction.

The

FIG. 213. book press has a screw to give great pressure.

From Fig. 195, § 272, we learned how we can lift hay into a hayloft by means of a pulley and a rope. Could we not lift the hay by passing the rope over a horizontal pole instead of the wheel, and then pulling down on the rope? Of course we could, but we would have to pull much harder, because there should be so much more friction between the pole and the rope than between the pulley wheel and its axle. What are some other illustrations of the fact that rolling friction is less than sliding friction? How about the wheelbarrow? Why are there casters on furniture? Wheels on wagons and cars?