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.

In every class of lever, the distances from the fulcrum, to the 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

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.

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

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

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?

quires no description, and the latter will be explained further on. From these machines, as elements, are formed by combination, the pulley, the wheel and axle, the screw, and the wedge. These seven make up what are commonly called the Mechanical Powers, and from them may be constructed every machine, however complicated. For a more detailed account of the general principles of Mechanism and Machines, the reader is referred to Chapter XI.

III. PRINCIPLES DEPENDENT ON THE ATTRACTION OF GRAVITATION.

Universal Gravitation,

34. THE earth exerts a force of attraction upon all bodies near it, tending to draw them towards its centre. This force, called the Force of Gravity, when unresisted imparts motion, and the body is said to fall; when resisted it gives rise to pressure, which is called Weight.

NEWTON showed that the force of gravity, as exhibited at the earth's surface, is only a particular case of a general attraction extending throughout the Universe, and continually tending to draw bodies together. This general attraction he called Universal Gravitation. It is mutually exerted between any two bodies whatever, and it is by virtue of it that the heavenly bodies are retained in their orbits.

The law of universal gravitation may be easily explained. If we take the mutual attraction of two units of mass, at a unit's distance from each other, as 1, then will their mutual attraction at any other distance be equal to 1 divided by the square of that distance; thus, if the distance is 2, their attraction will be of what it was at the

What machines are formed by combinations of simple machines? Name the seven mechanical powers. (34.) What is the Force of Gravity? What is its effect when unresisted? When resisted? What is Universal Gravitation? Explain the law of Universal Gravitation.