interesting of which is the electrical eel of South America.

This fish was studied by HUMBOLDT and BONPLAND, who have given a complete description of it.

The shocks given by electrical fishes are due to electricity generated in the body of the fish. MATTEUCI showed that sparks could be obtained from the fish, and also that the galvanometer is affected when one of its wires is brought into connection with the back of the fish, and the other with its belly.

In all cases the shock is voluntary, and serves as a means of defense against enemies.

To what are their shocks due? What observations were made by MATTEUCI?

CHAPTER XI.

APPLICATION OF PHYSICAL PRINCIPLES TO MACHINES.

I. GENERAL

PRINCIPLES.

Definition of a Machine.

414. A MACHINE is a contrivance by means of which a force applied at one point, is made to produce an effect at some other point.

The force applied is called the power, and the force to be overcome is called the resistance.

Motors.

445. The working of a machine requires a continued application of power. The source of this power is called the MOTOR.

Some of the most important motors are muscular effort, as exerted by man or beast, in various kinds of work; the weight and impulse of water, as in water-mills; the impulse of air, as in wind-mills; the elastic force of springs, as in watches; the expansive force of vapors and gases, as in steam and hot-air engines. The last is, perhaps,

the most useful of the motors mentioned.

Object and Utility of Machines.

446. The object of a machine is to transmit the power furnished by the motor, and to modify its action in such a manner as to cause it to produce a useful effect.

(444.) What is a machine? The power?

The resistance? (445.) What is a motor? Mention some of the most important. (446.) What is the object of a machine?

In no case does a machine add anything to the power applied to it; on the contrary, it absorbs more or less of this power, according to the nature of the work to be done and the connection existing between the parts.

Some of the circumstances which cause an absorption of power are the rubbing of one part upon another, the stiffness of bands and belts, the resistance of the air, the adhesion of one part to another, and the want of hardness and elasticity in the materials of which the machine is constructed. The resistances arising from these causes are called hurtful resistances. They not only absorb much of the power applied, but they also contribute to wear out the machine. The existence of these resistances in every machine requires a continued supply of power to overcome them, in addition to that necessary to perform the useful work. Hence the absurdity of attempting to obtain perpetual motion.

Quantity of Work of a Force.

447. The idea of WORK, in mechanics, implies that a force is continually exerted, and that the point at which it is applied moves through a certain space. Thus, in raising a weight, the work performed depends first upon the weight raised, and secondly upon the height through which it is raised. The quantity of work of a force in any given time, is measured by the intensity of the force, expressed in pounds, multiplied by the distance through which it is exerted, expressed in feet. This distance is called the path described.

Equilibrium of a Machine.

448. A machine is in EQUILIBRIUM when the power and resistance exactly balance each other.

In determining the circumstances of equilibrium, it is customary to neglect the hurtful resistances in the first approximation, and then to

Their effect!

Can a machine create power? What are hurtful resistances? (447.) What is meant by work? Illustrate. What is the measure of the quantity of work? (448.) When is a machine in equilibrium? What is the condition of equilibrium when the hurtful resistances are neglected?

take account of them as corrections.

If the hurtful resistances be

neglected, it will be found that any machine, working uniformly, is in equilibrium, when in any given time the quantity of work of the power is equal to that of the resistance.

449. The elementary machines are seven in number, viz., the cord, the lever; the inclined plane; the pulley; the wheel and axle; the screw; and the wedge. These seven are called mechanical powers. The first three are simple elements; the remaining ones are combinations of these three.

The principles of the lever and inclined plane, so far as necessary to an understanding of the principles of Physics, have already been explained in Chapter I. In the following articles those principles are repeated, in connection with a description of the other mechanical powers. In the cuts which follow, the power and resistance are represented by arrow-heads, the former being denoted by the letter P, and the latter by R.

The Cord.

450. CORDS, and BANDS or BELTS, are used for transmitting motion from one point to another, as in the pulley. Chains are often employed for the same purpose, as in the

watch.

Cords, belts, and chains, should be as flexible as is consistent with sufficient strength.

The Lever.

451. A LEVER is an inflexible bar, free to turn about an axis. This axis is called the FULCRUM. (See Arts. 30, 31, and 32.) Levers may be either straight or curved.

The dis

(449.) How many mechanical powers are there? Name them. (450.) What

the use of a cord or band in machinery? (451.) What is a lever?

tances from the fulcrum to the lines of direction of the power and resistance are called lever

A

M

Fig. 309.

B

arms.

In the lever, MN, F is the fulcrum, MP and NR are the lines of direction of the power and resistance, FA is the lever arm of the power, and FB is the lever arm of the resistance.

Levers are divided into three classes:

In the first class (Fig. 310), the fulcrum is between the power and the resistance. The steelyard is a lever of this class.

In the second class (Fig. 311), the resistance is between the power and fulcrum. The rudder of a ship is a lever of this class.

In the third class (Fig. 312), the power is between the resistance and the fulcrum. The treadle of a lathe is a lever of this class.

In all cases the paths described by the points of application of the power and resistance will be proportional to their lever arms, and when in equilibrium, the power will be to the resistance as the lever arm of the resistance is to the lever arm of the power.

Compound Levers.

452. A COMPOUND LEVER is a combination of simple levers, sc arranged that the resistance in one, acts as a power in the next, throughout the combination.

Compound levers are used for magnifying small motions, as in showing the expansion of bodies; or to enable a small weight to balance a large one, as in the hay-scale and in other weighing machines. The principle of the compound lever applies in trains of wheelwork.

Fulcrum? Lever arms? Illustrate. How many classes of levers are there! De scribe each class, and illustrate. (452.) What is a compound lever? Its uses?