present practice, the average transformation into electricity does not account for more than 4 per cent of the energy in the fuel which is burned in the furnace; although under best conditions 15 per cent has been realized, it would not be safe to assume that in commercial enterprises more than 5 per cent could be transformed into electrical energy. In transmitting this to a point where it could be applied losses will take place amounting to from 10 to 20 per cent, so that the amount of electrical energy which can be usefully applied for heating would probably not average over 4 per cent of that in the fuel. In heating with steam or hot water or hot air the average amount utilized will probably be about 60 per cent, so that the expense of electrical heating is approximately as much greater than that of heating with coal as 60 is greater than 4, or about 15 times. If the electrical current can be furnished by water-power which otherwise would not be usefully applied, these figures can be very much reduced. The above figures are made on the basis of fuel cost of the electrical current, and do not provide for operating, profit, interest, etc., which aggregate many times that of the fuel. With coal at $3.30 per ton this cost on above basis is about .97 cent per thousand watt-hours. The lowest commercial price quoted, known to the writer, for the electric current was 3 cents; per thousand watt-hours the ordinary price for lighting current varies from 10 to 20 cents. It may be said that for lighting purposes 10 cents per thousand watt-hours is considered approximately the equivalent of gas at $1.25 per thousand cubic feet.

It may be a matter of some interest to consider the method of computation employed for some of these quantities. The ordinary steam-engine requires about 4 pounds of coal for each horse-power developed; on account of friction and other losses about 1.5 horse-power are required per kilowatt, or in other

for one hour, in which case one horse power could be produced by the combustion of 0.175 lb. of carbon. The best authenticated actual performance is one horse-power for 1.2 lb., corresponding to 14.6 per cent efficiency. The usual consumption is not less than 4 to 6 pounds per indicated horse-power, or from 3 to 5 times the above. A kilowatt is very nearly 1 horse-power, but because of friction and other losses requires an engine of 1.5 indicated horse-power.

words 6 pounds of coal are required for each thousand watts of electrical energy. In the very best plants where the output is large and steady this amount is frequently reduced 20 to 30 per cent from the above figures in cost. The cost of 6 pounds

of coal at $3.33 per ton is one cent. To this we must add transmission loss about 10 per cent, attendance and interest 20 per cent, making the actual cost per kilowatt 1.3 cents per hour. As one pound of coal represents from 13,000 to 15,000 heat-units, depending upon its quality, and one kilowatt-hour is equivalent to 3415 heat-units, if there were no loss whatever in connection with transformation of heat into electricity, one pound of coal should produce 4 to 5 kilowatts per hour of electrical energy. This discussion is sufficient to show that at cost prices electrical heating obtained from coal will amount under ordinary conditions to 15 to 20 times that of heating with steam or hot water, and at commercial prices which are likely to be charged for current its cost will be from 2 to 10 times this amount.

The following table gives the cost of a given amount of heat,

10.000

20.000

30,000

40,000

50,000

60, осо

70,000 80,000 90,coo 100,000

2.93 5.86 8.78 11.71 14.64 17.57 20.50 23.42 26.35 29.28 5.85 11.68 17.57 23.42 29.28 35.13 40.99 46.84 52.70 58.56 8.78 17.57 26.35 35.14 43.92 52.70 61.49 70.28 79.06 87.84 11.7122.4235.14 46.84 58.56 70.28 81.98 93.68 105.40 117.12 14.64 29.28 43.92 58.56 73.20 87.84 102.48 117.12 131.86 146.40 17.57 35.14 52.70 70.28 87.84 105.40 122.98 140.56 158.12 175.68 20.50 40.99 61.49 81.98 102.48 122.98 143.47 163.96 184.46 204.96 23.42 46.81 70.28 93.68 117.12 140.56 163.97 187.36 210.80 234.24 26.35 52.70 79.06 105.42 131.76 158.10 184.46 210.84 237.17 263 52 29.28 58.56 87.84 117.12 146.40 175.68 204.96 234.24 263.52 292.80

NOTE. 10,000 heat-units is equal to two thirds the heat contained in one pound of the best coal, and is very near the average amount that can be realized per pound in steam or hot-water heating, hence the table can also be considered as showing the relative price of electricity and coal for the same amount of heating. For instance, if 5 cents per kilowatt hour is charged for electric current, the expense would be the same as that of good coal at 14.64 cents per pound, which is at rate of $392.80 per ton.

if obtained from the electric current, furnished at different prices. Thus 30,000 heat-units if obtained from electric current furnished at 8 cents per kilowatt hour would cost 70.28 cents per hour. The amount of heat needed for various buildings can be determined by methods stated in Chap. III.

There are some conditions where the cost is not of moment and where other advantages are such as to make its use desirable. In such cases electricity will be extensively used for heating.

For the purposes of cooking it will be found in many cases that electrical heat, despite its great first cost, is more economical than that obtained directly from coal. This is due to the fact that of the total amount of heat, which is given off from the fuel burned in a cook stove very little, perhaps less than one per cent, is applied usefully in cooking: the principal part is radiated into the room and diffused, being of no use whatever for cooking, while the heat from the electric current can be utilized with scarcely any loss.

161. Formulæ and General Considerations.-The following formulæ express the fundamental conditions relating to the transformation of the electric current into heat:

In which the symbols represent the following quantities: E, electromotive force in volts; C. intensity of current in amperes; R, resistance of conductor in ohms; 7, the length in metres; w, the area of cross-section in square centimetres; k, coefficient of specific resistance; W, kilowatts; H, the heat in minor calories, and h, in B. T. U. per second, ha the heat in B. T. U. per hour.

The amount of heat given off per hour is given in equation (6), and is seen to be dependent upon both the resistance and the current, and apparently would be increased by increase in either of these quantities. The effect, however, of increasing the resistance as seen by equation (1) will be to reduce the amount of current flowing, so that the total heat supplied

=

would be reduced by this change. On the other hand, if there were no resistance no heat would be given off, for to make Ro in equation (6) would result in making , o. From these considerations it is seen that in order to obtain the maximum amount of heat, the resistance must have a certain mean value dependent upon the character of material used for the conductor in the heater, its length and diameter.

For purposes of heating, a constant electromotive force or voltage is maintained in the main wire leading to the heater. A very much less voltage is maintained on the return wire, and the current in passing through the heater from the main to the return drops in voltage or pressure. This drop provides the energy which is transformed into heat.

The principle of electric heating is much the same as that involved in the non-gravity return system of steam-heating. In that system the pressure on the main steam-pipes is essentially that at the boiler, that on the return is much less, the reduction of pressure occurring in the passage of the steam through the radiators; the water of condensation is received into a tank and returned to the boiler by a steam-pump. In a system of electric heating the main wires must be sufficiently large, to prevent a sensible reduction in voltage or pressure between the dynamo and the heater, so that the pressure in them shall be substantially that in the dynamo. The pressure or voltage in the main return wire is also constant but very low, and the dynamo has an office similar to that of the steampump in the system described, viz., that of raising the pressure of the return current up to that in the main. The power which drives the dynamo can be considered synonymous with the boiler in the other case. All the current which passes from the main to the return current must flow through the heater, and in so doing its pressure or voltage falls from that of the main to that of the return.

Thus in Fig. 215 a dynamo is located at D, from which main and return wires are run, much as in the two-pipe system of heating, and these are so proportioned as to carry the required current without sensible drop or loss of pressure. Between these wires are placed the various heaters; these are arranged so that when electric connection is made, they

draw current from the main and discharge into the return wire. Connections which are made and broken by switches take the

FIG. 215.-DIAGRAM OF ELECTRIC HEATING.

place of valves in steam-heating, no current flowing when the switches are open.

The heating effect is proportional to the current flowing,

and this in turn is affected by the length, cross-section, and relative resistance of the material in the heater. The resistance is generally proportioned such as to maintain a constant temperature with the electromotive force available, and the amount of heat is regulated by increasing the number of conductors in the heater.

162. Construction of Electrical Heaters. -Various forms of heaters have been employed. Some of the simplest consist

FIG. 216.-ELECTRIC HEATER AT THE merely of coils or loops of iron wire arranged in parallel rows

so that the current can be passed through as many wires as are needed to provide the heat required. In other forms of