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some way seems to gain clearness when this much is understood. It is, however, largely a question of familiarity, and it is doubtful that our knowledge of the ultimate meaning of pounds and feet is much clearer than our knowledge of volts and ampères.

Analogies are sometimes confusing because they are taken too literally, and the attempt to reconcile the analogous ideas in all particulars will sometimes cause more confusion than if a more abstract conception were attempted at the start. Thus, although it is often helpful, it is not necessary to compare electrical forces and quantities with those that seem to have a more material existence. Instead of comparing them with pressure of steam, currents of water, or resistance of friction, we may compare them, for instance, with the "pressure of public opinion," "currents of feeling," "resistance to changes." These expressions have a definite meaning to us even though the ideas themselves do not appeal to the five material senses. If there were a way to measure "the pressure of public opinion," we should probably do so, fix upon a unit and give a name to it; but when we cannot do this and yet can measure "electrical pressure," it would seem as if the latter should be not less clearly recog nized.

We have these abstract ideas of pressure, resistance, and current, and if they are kept in mind while the

names are looked upon as figures of speech rather than as literal definitions, the ideas are of great usefulness.

There is what is termed "electrical pressure" or electro-motive force. It is a definite force and can be measured, although it does not show its effect in quite the same way that water-pressure or steam-pressure does. We do not see it push masses of substance before it, but the abstract idea of pressure can be applied to it just as we apply the idea to "pressure of public opinion." It causes certain actions in an electric circuit. When the force is great the action is great, when it is small the action is accordingly small. It agrees with our idea of pressure, and by thinking of it as such, a clear conception of its nature is helped. Resistance, current, and other electrical quantities may be looked at in the same way. It is not necessary to assume that there is an actual flow of something material. It is not known that anything material actually passes through a wire, but it is known that there is a progressive effect along it as if there were a "current of something, and that this effect is produced by the electro-motive force which acts "like a pressure."

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When once it became known that definite electrical forces and quantities exist and give rise to certain effects, and when these had been named, it remained of course to decide upon units, so that these forces and quantities might be measured and compared. It is

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 "ampère." 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 ampère;

when made for a pressure of 110 volts the current is about ampère.

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

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.

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