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effect of the current.

There is a great resistance
Even the small current pass-

per foot in the filament.
ing through generates heat so fast that it can be
dissipated at an equal rate only when the whole is
incandescent. The construction of the lamp gives a
conductor of considerable resistance in small space, and
it is designed to give the filament "long life," but any
conductor will be heated to incandescence provided
sufficient current be passed through it.

A lamp is made to be used at a certain electrical pressure, and it is only at this pressure that the proper amount of current will go through it and thus cause the proper amount of light. It is for this reason that it is so important to calculate the sizes of the wires and thus give every lamp as nearly as possible the same pressure. Every branch of a line requires a separate calculation, for there are different volumes of current in each branch, and the lamps are at different distances. It is at this point that rule-of-thumb methods fail, and some degree of engineering ability becomes necessary to prevent excessive loss in the wires and on the other hand to prevent unnecessary expenditure for copper in the conductors. In buildings improperly wired, it will frequently be noticed that lamps in one part will be much brighter than those in other parts, or it will be found that when all lamps are turned on the light is poor, and that it improves when some of

the lamps are switched off. In these cases it will almost invariably be found that some of the wires, usually the longer ones, are too small.

There is no excuse for this sort of work except the saving it effects in the cost of material. It is not a matter of judgment nor of experience, but simply of calculation. It is known how much current each lamp requires, and exactly how much the pressure will be lessened when the necessary current is forced over a given length of wire of a certain size. With no other force that we use can results be so easily and so exactly predicted.

Of course, with wires of reasonable size there must always be some difference in the lighting effects of any two lamps, but it is not a difficult matter to make it so small that the eye cannot detect it. It is now ordinarily specified that the electrical pressure at any two lamps in a building shall not differ by more than two per cent under any conditions of use. This difference is within reasonable limits, and is sufficiently small to prevent noticeable change in lights when others are turned on or off. Not infrequently it is required that the pressure at no two lamps shall differ by more than one per cent.

The prediction of results in electric circuits and the laying out of systems of distribution are greatly facilitated by the simplicity of the law that controls the

To

relation between current, pressure, and resistance. quote an expression of this law: it "is a special statement of the results of ordinary observation and it may be generalized thus: a result is equal to the effort put forth, divided by the opposing resistance or opposition." Thus the result is twice as great if there be half the opposition or only half as great if there be onehalf the effort. This general law is easily applied to electric circuits because of the independence of the factors. The law applies to water flowing in pipes, but upon attempting calculations, one at once sees the complicated nature of the resistance. This depends not only upon the size of pipe, but upon the number and sharpness of the bends, and even upon the velocity of the water itself, so that what promised to be a simple determination, becomes an intricate web of dependent factors. With electricity, however, except under special conditions, we have to deal with only the three factors, effort, resistance, and result, in their simplest form.

This one law, called in electriès "Ohm's law," is so widely applicable in engineering work that its expression in the form of an equation is looked upon as almost symbolic of electrical engineering. The electromotive force is the effort and is usually represented by E. The resistance is the opposition to this effort and is represented by R. The current is the result and is

represented by C. Thus the general law, "a result is equal to the effort put forth, divided by the opposing resistance or opposition," when applied to electric circuits takes the simple form (C It is of course

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E

= R

necessary to know only two of these quantities to determine the third.

Suppose there is to be a current of ten ampères in a circuit that is known to have a resistance of two ohms. The substitution in the formula shows at once that the electro-motive force or pressure necessary to

give this result is twenty volts (10 =

(10) Or, there

may be an electro-motive force of ten volts, and the circuit may be composed of a coil of copper wire .162 inch in diameter and 2000 feet long. Copper wire of this size and length is known to have a resistance of .8 ohm so that with ten volts pressure and with the .8 ohm resistance there will be a current of 12

ampères (α = 10). C

With the aid of this law, circuits

and parts of circuits may be examined, and losses or results determined with exactness. In the illustrations given, the complete circuits were taken, but the formula is applicable also to any part of a circuit, if the resistance of this part and only the portion of the electro-motive force used in overcoming this resistance, be substituted in the formula.

The "drop" in pressure may be shown graphically, as in Figure 1, which illustrates the loss of pressure between wires leading to incandescent lamps.

Suppose the dynamo or other source of electricity is at A, and that the pressure at that point is 110 volts.

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FIG. 1.-Illustration of the Loss of Pressure in Electric Circuits.

Suppose that at C, 500 feet away, there is a cluster of 20 lamps, each requiring one-half ampère to make it burn at the proper candle-power. Then there should. be a total of 10 ampères flowing in the circuit. If the lamps were at A, attached directly to the leads from

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