According to this definition every tool used in the arts is a machine; in common language, however, the term is only applied to more complex combinations. In this sense, a machine consists of a collection of moving pieces called elements, kept in position by a frame. The piece to which the motive power is applied is called the recipient, the piece that performs the work is called the tool, and these, with their connecting pieces, make up a train of mechanism. The elements of a train are called Elementary Machines, or mechanical powers, and are seven in number (Art. 449).

Of these the lever is most important to the student of Physics. The others are fully discussed in Chapter XI.

The Lever.

30. A LEVER is an inflexible bar free to turn about a fixed point, called the Fulcrum, and acted upon by two forces which tend to turn it in opposite directions. The force which acts as a motor, is called the Power, the other one is called the Resistance.

Levers are of three classes, according to the position of the fulcrum with respect to the power and resistance.

Lever of the first class. In this class the fulcrum is between the power and the resistance. Such a lever is represented in Fig. 15. The hand is the power, the weight P is the resistance, and the fixed point C is the fulcrum.

What is a train of mechanism? What is the recipient? Tool? (30.) What is a lever? How many classes are there? Examples of each.

Lever of the second class.-In this class the fulcrum is beyond both the power and resistance, and nearest the resistance. Such a lever is shown in Fig. 16. The power is applied at B, the resistance at A, and the fulcrum is at C.

Lever of the third class.-In this class the fulcrum is beyond both the power and the resistance, and nearest the power, as shown in Fig. 17.

the

In every class of lever, the distances from the fulcrum, to power and resistance, are called Lever Arms. In each of the figures in this article, CB is the lever arm of the power, and CA the lever arm of the resistance.

Conditions of Equilibrium of the Lever.

31. It is demonstrated in Mechanics (Art. 78), that the effect of a force produced by the aid of a lever increases as its lever arm increases, so that, if the lever arm be doubled or tripled, the effect of the force is always doubled or tripled.

What are the Lever Arms? (31.) What is the relation between the power and resistance?

Hence it was that ARCHIMEDES was able to say, that he could lift the world if he had a place on which to rest his lever.

B

P

Fig. 17.

Since the effect of a force increases with its arm of lever it is necessary, in order that the power and resistance may be in equilibrium, that they should be to each other inversely as their lever arms. That is, if the power is three times the resistance, the lever arm of the former should only be one third as long as that of the latter, and so on. If the power is equal to the resistance, they will be in equilibrium when their lever arms are equal.

From what has been said, it follows, that the power is always greater than the resistance in the third class of levers, and less than it, in the second class. In the first class the power may be either greater or less than the resistance. We say in common language

Between the power and velocity?

that there is a loss of power in using a lever of the third class, and a gain of power in using one of the second class.

In performing any work with a lever, the paths passed over by the points of application of the power and resistance are proportional to their lever arms; that is, the longer the lever arm the greater the path passed over, and the greater its velocity. This is expressed by saying, that what is gained in power is lost in velocity. It is for this reason that we say there is no real gain of power in the employment of a lever.

Examples of Levers.

32. Levers are of continual use in the arts, forming component parts of nearly every machine.

C

Fig. 18.

A pair of scissors affords an example of the first class of levers. The fulcrum is at C, Fig. 18, the hand furnishes the power, and the substance to be cut the resistance.

The common balance, yet to be described, is a lever of this class as is also the handle of a pump.

The ordinary nut-cracker is an example of levers of the

C

Fig. 19.

second class. The fulcrum is at C, Fig. 19; the power is the hand, and the resistance is the nut to be cracked.

Is there any gain of power in using a lever? (32) Applications. Explain the scissors. The nut-cracker.

The oars of a boat are levers of the second class. The end of the oar in the water is the fulcrum, the hand is the power, and the boat, or rather the resistance of the water which it has to overcome, is the The shears employed for cutting metals belong to this

resistance.

class of levers.

The treadle of a flax-spinner, or of a lathe, is an example of a lever of the third kind. The fulcrum is at C, Fig. 20, the foot is the power, and the work to be done is the resistance.

'The bones of the animal frame are many of them levers of this class. Thus, in the bone of the forearm in man, the elbow joint is the fulcrum, the muscle attached just below the joint is the power, and a weight to be raised is the resistance.

33.

Other Machines.

Besides the lever there are two other simple machines, the cord and the inclined plane. The former re

Oars of a boat. Treadle of a spinner. Bone of the forearm. (33.) What are the other simple machines?