the element of time must be introduced in order to compute the amount of transmitted energy. If the system could be kept at work during twenty-four hours a day at full capacity, the delivered energy would be represented by the product of the numbers which stand for the capacity and for the total number of hours yearly.

Unfortunately, however, the demands for electric light and power vary through a wide range in the course of each twenty-four hours, and the period of maximum demand extends over only a small part of each day. The problem is, therefore, to find what relation the average load that may be had during the twenty-four hours bears to the capacity required to carry this maximum load. As the answer to this question depends on the power requirements of various classes of consumers, it can be obtained only by experience. It has been found that some electric stations, working twenty-four hours daily on mixed loads of lamps and stationary motors, can deliver energy to an amount represented by the necessary maximum capacity during about 3,000 hours per year. Applying this rule to the present case, the transformers at the sub-station, if loaded to their maximum capacity of 10,000 horse-power by the heaviest demands of consumers, may be expected to deliver energy to the amount of 3,000 × 10,000 = 30,000,000 horse-power hours yearly.

The total cost of operation for this transmission system was found above to be $66,750 per annum, exclusive of the cost of energy at the generating plant. This sum, divided by 30,000,000, shows the cost of energy transmission to be 0.222 cent per horse-power hour, exclusive of the first cost of the energy. To obtain the total cost of transmission, the figures just given must be increased by the value of the energy lost in transformers and in the line conductors. In order to find this value, the cost of energy at the generating plant must be known.

The cost of electrical energy at the switchboard in a water-power station is subject to wide variations, owing to the different investments necessary in the hydraulic work per unit of power developed. With large powers, such as are here considered, a horse-power hour of electrical energy may be developed for materially less than 0.5 cent in some plants. As the average efficiency of the present transmission has been found to be 85.7 per cent of the energy delivered by the generators, it is evident that 1.17 horse-power hours must be drawn from the generators for every horse-power hour supplied by the transformers at the sub-station for distribution. In other words, 0.17 horse-power hour is wasted for each horse-power hour delivered.

The cost of 0.17 of a horse-power hour, or say not more than 0.5 × 0.17 = 0.085 cent, must thus be added to the figures for transmission cost already found, that is, 0.222 cent per horse-power hour, to obtain the total cost of transmission. The sum of these two items of cost amounts to 0.307 cent per horse-power hour, as the entire transmission expense.

It may now be asked how the cost of transmission just found will increase if the distance be extended. As an illustration, assume the length of the transmission to be 150 instead of 100 miles. Let the amount of energy delivered by the sub-station, the loss in line conductors, and the energy drawn from the generating plant remain the same as before. Evidently the cost of the pole line will be increased 50 per cent, that is, from $70,000 to $105,000. Transformers, having the same capacity, will not be changed from the previous estimate of $150,000. If the voltage of the transmission remain constant, as well as the line loss at maximum load, the weight and cost of copper conductors must increase with the square of the distances of transmission. For 150 miles the weight of copper will thus be 2.25 times the weight required for the 100-mile transmission.

Instead of an increase in the weight of conductors a higher voltage may be adopted. The transformers for the two great transmission systems that extend over a distance of about 150 miles, from the Sierra Nevada Mountains to San Francisco Bay, in California, are designed to deliver energy to the line at either 40,000 or 60,000 volts, as desired. Though the regular operation at first was at the lower pressure, the voltage has been raised to 60,000.

The lower valleys of the Sacramento and the San Joaquin rivers, which are crossed by these California systems, as well as the shores of San Francisco Bay, have as much annual precipitation and as moist an atmosphere as most parts of the United States and Canada. Therefore there seems to be no good reason to prevent the use of 60,000 volts elsewhere.

The distance over which energy may be transmitted at a given rate, with a fixed percentage of loss and a constant weight of copper, goes up directly with the voltage employed. This rule follows because, while the weight of conductors to transmit energy at a given rate, with a certain percentage of loss and constant voltage, increases as the square of the distance, the weight of conductors decreases as the square of the voltage when all the other factors are constant.

Applying these principles to the 150-mile transmission, it is evident that an increase of the voltage to 60,000 will allow the weight of conductors to remain exactly where it was for the transmission of 100 miles, the rate of working and the line loss being equal for the two cases.

The only additional item of expense in the 150-mile transmission, on the basis of 60,000 volts, is the $35,000 for pole line. Allowing 15 per cent on the $35,000 to cover interest, depreciation, and maintenance, as before, makes a total yearly increase in the costs of transmission of $5,250 over that found for the transmission of 100 miles. This last sum amounts to 0.0175 cent per horse-power hour of the delivered energy.

The cost of transmission is thus raised to 0.307 + 0.0175 = 0.324 cent per horse-power hour of delivered energy on the 150-mile system with 60,000 volts.

Existing transmission lines not only illustrate the relations of the factors named above to the cost and weight of conductors, but also show marked variations of practice, corresponding to the opinions of different engineers. In order to bring out the facts on these points, the data of a number of transmission lines are here presented. On these lines the distance of transmission varies between 5 and 142 miles, the voltage from 5,000 to 50,000, and the maximum rate of work from a few hundred to some thousands of horse-power. For each transmission the single length and total weight of conductors, the voltage, and the capacity of the generating equipment that supplies the line is recorded. From these data the volts per mile of line, weight and cost of conductors per kilowatt capacity of generating equipment, and the weight of conductors per mile for each kilowatt of capacity in the generating equipment are calculated. In each case the length of line given is the distance from the generating to the receiving station. The capacity given for generating equipment in each case is that of the main dynamos, where their entire output goes to the transmission line in question, but where the dynamos supply energy for other purposes also, the rating of the transformers that feed only the particular transmission line is given as the capacity of generating equipment.