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the dynamo, they would of course have the benefit of the full pressure, and the whole resistance of the outside circuit would then be only the resistance of the lamps. But if they are 500 feet away from the dynamo, long wires will have to be used; these will have a certain amount of resistance, and a certain amount of electro-motive force will have to be used up in overcoming this. Let it be assumed that No. 10 copper wire is used to connect the lamps to the dynamo. Five hundred feet of this wire will have a resistance of almost exactly one-half ohm. The wire runs to the lamps and back again, however, so the resistance of the wire part of the circuit will be one ohm. Thus it will be necessary to force 10 ampères through this one ohm resistance and also through the lamps. The amount of electro-motive force that it will take to force 10 ampères through one ohm resistance can be seen at once by substituting in the formula;

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Ten volts will be used up in the wires, and since there is a pressure at the dynamo of but 110 volts there will remain only 100 volts for forcing the current through the lamps to produce light. By letting A-C in the figure represent the distance between the lamps and the dynamo, and the perpendicular lines the amount of

pressure at different points, it can be seen how the pressure falls along the line; at 100 feet, for instance, the pressure has fallen two volts, which is the amount. required to force the ten ampères through the first 100 feet of the wires.

If the lamps are made to burn properly at about 110 volts, the wire must be about 10 times as large in sectional area or else the dynamo must be made to give 120 volts, so that there will still be 110 volts left at the lamps after the resistance of the line has caused a loss of 10. But the effect of raising the pressure at the dynamo can be realized by imagining all but one of the lamps turned off. There will now be only onehalf ampère flowing and only one-half volt will be used up in forcing this against the resistance of the wire. This will leave 119.5 volts at the lamp, which is such an excess over the voltage for which it was made, that it would soon be destroyed. If, on the other hand, the wire is made ten times the sectional area, it will have only one-tenth the resistance, or .1 ohm. When all the lamps are on, the pressure lost in the wire

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will be one volt (10 (10 = 27). and if the pressure at the

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dynamo is 110 volts, there will be 109 volts left for useful effect at the lamps. When one lamp is on, the

pressure lost in the wire will be .05 volt

E

=

and

there will be 109.95 volts at the lamp. Thus, if the resistance of the wires leading to the lamps be kept as low as .1 ohm, either one lamp or twenty may be turned on and there will not be a difference in the pressure of more than .95 volt, an amount so small that no change in the strength of the light could be detected by the eye. Even at the dynamo or at any intermediate point, a lamp would have practically the same pressure.

It can be seen from the examination of this case how necessary it is for satisfactory service, that there be equality of pressure at all lamps at all times. The calculations are often complicated by the number of branches and the positions of the lamps, and experience assists one to see quickly what will probably be the best arrangement; but the loss may always be found by an application of Ohm's law, and even with experience one must in the end rely upon this to ascertain the exact sizes of wire.

The first cost of a plant and the cost of maintenance may in several ways be affected by the proportions of the wires and the method of laying out the system. The wires may be so small that a large part of the energy delivered by the dynamo is wasted in worse than useless heat, as has been shown; but the conductors may be of sufficient size to prevent excessive loss and to keep the pressure constant at the lamps, and yet be arranged so that a much larger amount of copper is used

than is necessary. Since the length of the wire, as well as the sectional area, makes a difference in the resistance, there is need of judgment in placing the main wires, in choosing "centres of distribution," and in dividing the circuit into the different branches. In a large building there is opportunity for a good grade of engineering skill and to have this work done by any one except those who have studied this branch of engineering and who are familiar with the requirements, is sure to result in loss.

There should always be equality of pressure at the lamps for another reason that is not commonly considered. All lamps are not made of the same "efficiency." That is, for a light of sixteen candle-power, some will require more energy than others more coal will be burned under the boilers. The most efficient lamps require a practically constant pressure, of the amount for which they are designed. If the pressure rises more than a very little above this, the lamps have a "short life," and it is only in plants where the regulation at the dynamo is of the best, and where the wiring is calculated for a very small loss, that they can be used. If the wires are so small that turning off a number of the lamps causes the pressure at those remaining to increase by several volts, the more efficient lamps cannot be used on account of the expense of renewals, and it is necessary to use those that will not be too much affected

by the variation. Such lamps can be had and are widely used, because there has been much poor engineering and the breakage must be kept small. Their use is, however, made necessary only by the variation of the pressure, and they are a constant expense because of the greater cost to operate them.

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