voltage, the percentage of line loss, and the length of the line mainly determine the relative importance of the transformers, pole line, and conductors in the total cost of delivered energy.

First cost of transformers varies directly with the maximum rate of transmission, and is nearly independent of the voltage, the length of the transmission, and the percentage of line loss. A pole line changes in first cost with the length of the transmission, but is nearly independent of the other factors. Line conductors, for a fixed maximum percentage of loss, vary in first cost directly with the square of the length of the transmission and with the rate of the transmission; but their first cost decreases as the percentage of line loss increases and as the square of the voltage of transmission increases.

If a given amount of power is to be transmitted, at a certain percentage of loss in the line and at a fixed voltage, over distances of 50, 100, and 200 miles, respectively, the foregoing principles lead to the following conclusions: The capacity of transformers, being fixed by the rate of transmission, will be the same for either distance, and their cost is therefore constant. Transformer losses, interest, depreciation, and repairs are also constant. The cost of pole line, depending on its length, will be twice as great at 100 and four times as great at 200 as at 50 miles. Interest, depreciation, and repairs will also go up directly with the length of the pole lines.

Line conductors will cost four times as much for the 100- as for the 50-mile transmission, because their weight will be four times as great, and the annual interest and depreciation will go up at the same rate. For the transmission of 200 miles the cost of line conductors and their weight will be sixteen times as great as the cost at 50 miles. It follows that interest, depreciation, and maintenance will be increased sixteen times with the 200-mile transmission over what they were at 50 miles, if voltage and line loss are constant.

A concrete example of the cost of electric power transmission over a given distance will illustrate the practical application of these principles. Let the problem be to deliver electrical energy in a city distant 100 miles from the generating plant. Transformers with approximately twice the capacity corresponding to the maximum rate of transmission must be provided, because one set is required at the generating and another at the delivery station. The cost of these transformers will be approximately $7.50 per horse-power for any large capacity.

Reliability is of the utmost importance in a great power transmission, and this requires a pole line of the most substantial construction. Such a line in a locality where wooden poles can be had at a moderate price will cost, with conductors in position, about $700 per mile, exclusive of the cost of the conductors themselves or of the right of way but including the cost of erecting the conductors. The 100 miles of pole line in the present case should, therefore, be set down at a cost of $70,000.

A large delivery of power must be made to warrant the construction of so long and expensive a line, and 10,000 horse-power may be taken as the maximum rate of delivery. On the basis of two horse-power of transformer capacity for each horse-power of the maximum delivery rate, transformers with a capacity of 20,000 horse-power are necessary for the present transmission. At $7.50 per horse-power capacity, the first cost of these transformers is $150,000.

Before the weight and cost of line conductors can be determined, the voltage at which the transmission shall be carried out and the percentage of the energy to be lost in the conductors at periods of maximum load must be decided on. The voltage to be used is a matter of engineering judgment, based in large part on experience, and cannot be determined by calculation. In a transmission of 100 miles the cost of conductors is certain to be a very heavy item, and, as this cost decreases as the square of the voltage goes up, it is desirable to push the voltage as high as the requirements for reliable service permit.

A transmission line 142 miles long, from the mountains to Oakland, Cal., has been in constant and successful use for several years with 40,000 volts pressure. This line passes through wet as well as dry climate. It seems safer to conclude, therefore, that 40,000 volts may be used in most places with good results.

Having decided on the amount of power and the voltage and length of the transmission, the required weight of conductors will vary inversely as the percentage of energy lost as heat in the line. The best percentage of loss depends on the number of factors, some of which, such as the cost of energy at the generating plant, are peculiar to each case.

As a provisional figure, based in part on the practice elsewhere, the loss on the line here considered may be taken at 10 per cent. when transmitting the full load of 10,000 horse-power. If the line is constructed on this basis the percentage of loss will be proportionately less for any smaller load. Thus, when the line is transmitting only 5,000 horse-power, the loss will amount to 5 per cent. During the greater portion of each day the demand for power is certain to be less than the maximum figure, so that a maximum loss of 10 per cent will correspond to an average loss on all the power delivered to the line of probably less than 7 per cent.

In order to deliver 10,000 horse-power by the transformers at a receiving station from a generating plant 100 miles distant where the pressure is 40,000 volts, the copper conductors must have a weight of about 1,500,000 pounds, if the loss of energy in them is 10 per cent of the energy delivered to the line. Taking these conductors at a medium price of 15 cents per pound, their cost amounts to $225,000.

The combined cost of the transformers, pole line, and line conductors, as now estimated, amounts to $445,000. No account is taken of the right-of-way for the pole line, because in many cases this would cost nothing, the public roads being used for the purpose; in other cases the cost might vary greatly with local conditions.

The efficiency of the transmission is measured by the ratio of the energy delivered by the transformers at the receiving station for local distribution to the energy delivered by the generating plant to the transformers that supply energy to the line for transmission. If worked at full capacity the large transformers here considered would have an efficiency of nearly 98 per cent; but as they must work, to some extent, on partial loads, the actual efficiency will hardly exceed 96 per cent.

The efficiency of the line conductors rises on partial loads, and may be safely taken at 93 per cent for all of the energy transmitted, though it is only 90 per cent on the maximum load. The combined efficiencies of the two sets of transformers and the line give the efficiency of the transmission, which equals the product of 0.96 × 0.93 × 0.96, or almost exactly 85.7 per cent. In other words, the transformers at the water-power station absorb 1.17 times as much energy as the transformers at the receiving station deliver to distribution lines in the place of use.

Interest, maintenance, and depreciation of this complete transmission system are sufficiently provided for by an allowance of 15 per cent yearly on its entire first cost. As the total first cost of the transmission system was found to be $445,000, the annual expense of interest, depreciation, and repairs at 15 per cent of this sum amounts to $66,750.

In order to find the bearings of this annual charge on the cost of power transmission the total amount of energy transmitted annually must be determined. The 10,000 horse-power delivered by the system at the sub-station is simply the maximum rate at which energy may be supplied, and