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hardly necessary to discuss here how or why the different units were made what they are, nor to mention more than the three or four most commonly used. As is generally known, the units have been given the names of the physicists who have done most for electrical science. Thus the unit of electro-motive force or electrical pressure, corresponding to "pounds per square inch" in hydraulics, is called the "volt," and the electro-motive force is often spoken of as the "voltage." The unit of current, corresponding to "gallons per minute" in hydraulics, is called the "ampere." There is no unit of resistance in hydraulics: it is recognized by its effect upon the pressure and is spoken of as being equivalent to so much loss of "head" or "pounds per square inch" pressure. In electrics the resistance may also be recognized by its effect upon the pressure, but it is readily measured as a resistance simply, and is expressed in terms of a unit called the "ohm."

These quantities come to have a definite meaning as they become familiar through use. One mentally forms a rough idea of the number of units of electro-motive force, current, and resistance in an electric circuit, from the actions that take place, from the visible manifestations of the electrical energy. By continued experience one gradually gets an idea of the relative resistance of conductors of different sizes and materials; an idea is formed of the amount of current that is necessary to heat them or to cause the different magnetic effects, and of the amount of electro-motive force necessary to force different currents through a certain length of conductor.

There is nothing in an object to tell of its hardness or of its softness except its similarity in various ways to other objects that we have felt; there is nothing to show the temperature of a body except the effects that are seen when the heat energy is changed to other forms; but continued experience teaches us to appreciate all these slight changes and small actions. Electrical forces and quantities become familiar and seem real by the same process, and with experience one intuitively forms rough judgments just as one does of weight or temperature.

It will, perhaps, help to form an idea of a few of the electrical quantities, if their magnitudes in some common instances are mentioned:

The electro-motive force of a voltaic cell, such as is used in batteries for telegraph and telephone work or for ringing electric bells, is from 1 to 2 volts.

The pressure at the terminals of an incandescent lamp is usually either 50 or 110 volts.

The pressure used in electric-railway work is nearly always 500 volts.

The current through an incandescent lamp when made for a pressure of 50 volts is about 1 ampere; when made for a pressure of 110 volts the current is about £ ampere.

The current through an arc lamp when it is of 2000 nominal candle-power, is about 10 amperes.

The resistance of a copper wire .01 inch in diameter and 10 feet long is almost exactly 1 ohm.

The resistance of a German silver wire .01 inch in diameter and 1000 feet long is about 1500 ohms.

A copper wire .5 inch in diameter and a mile long has a resistance of about .2 ohm. The same wire 10 miles long would have a resistance of 2 ohms, the resistance being proportional to the length. If the same wire were one-half the diameter it would have four times the resistance, the resistance being inversely proportional to the sectional area and consequently inversely proportional to the square of the diameter.

CHAPTER II.

THE PROPORTIONING OP WIRES. —THE HEATING EFFECT OF THE CURRENT.—LOSS OF FORCE.— OHM'S LAW.—WIRE CALCULATION.

A Matter of great importance in electrical work, with regard to both safety and satisfactory service, is the correct proportioning of wires to the currents they have to carry. Conductors always offer a resistance to the passage of the current, and this not only causes heating of the wire and waste of energy, but it diminishes the pressure at the lamp, motor, or other device operated.

A current of electricity, however small, will heat in some degree a wire of any size, and if the current be large and the wire small this heat may become of great intensity. The effect is not different from that in any case where resistance is overcome by force. When a nail is driven into lead it is very plain that the energy is transformed into heat. Meteors falling through the atmosphere are heated to incandescence, and even when water is forced through a pipe, a part

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of the energy is transformed into heat because of the resistance of friction. We may not know exactly how a current of electricity sets the molecules of a conductor in motion and thus produces heat, but we do know that it requires a certain force to make a current flow in a wire, and that if we make the wire smaller it takes more force to send the same current through it. We know, too, that if the heat generated is measured it is found to be equal to the energy expended. By making the wire smaller, the resistance is increased and more force must be applied so that this resistance may be overcome.

If a pump is to deliver 100 gallons of water per minute through a pipe, it will take a certain amount of force even though the pipe be a foot in diameter, but if it be reduced to one-tenth the size, it will take enormously more force and the additional amount will all be used simply in overcoming friction—in heating the pipe and water. In this case the heat is carried away so fast by the water itself that it is of course only the waste of power that is serious. In forcing electric currents through wires, however, not only is energy wasted, but the heat is left in the wire to dissipate as best it can. The wire goes on heating until the generation of heat is balanced by the dissipation, and if the current be much too large the wire, in the meantime, may become of such a temperature that it

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