We may write this in the form of an equation: Annual cost of energy wasted = on capital outlay for conductor.
The cost of one electrical horsepower hour at the terminals of the generator, including interest and depreciation on the budding, motive power, and electric generator, multiplied by the number of horse-power hours per year wasted in the conductor, must be considered "cost of energy." The interest on capital outlay for conductor plus allowance for repairs and depreciation, taken for the year, gives the other side of the equation. Both sides of the equation added together, :give the annual cost of transmitting the electrical energy.
Gishert Kapp (Electric Transmission of Power) remarks very pertinently in this connec tion: " It should be remembered that this law, in the form here given, only applies to eases where the capital outlay is strictly proportional to the weight of metal contained in the con ductor. In practice this is, however, seldom correct. If we have an underground cable, the cost of digging the trench and filling in again will be the same, whether the cross-sectional area of the cable be one-tenth of a square inch or one square inch; and other items, such as insulating material, are, if not quite independent of the area, at least dependent in a lesser degree than assumed in the formula. In an overhead line we may vary the thickness of the wire within fairly wide limits without having to alter the number of supports, and thus there is here also a certain portion of the capital outlay which does not depend on the area of the conductor. Hence we should state more correctly that the most cconomicrel area of conductor is that .for which the annual cost of energy wasted is equal to the annual interest on that por tion of the capital outlay which can be considered to be proportional to the weight of metal used.
" Prof. George Forbes, in his Cantor lectures on "The Distribution of Electricity,' delivered at the Society of Arts, in 1885, called that portion of the capital outlay which is proportional to the weight of metal used, The Cost of Laying One Additional Ton of Copper,' and he showed that for a given rate of interest inclusive of depreciation, and a given cost of copper, the most economical section of the conductor is independent of the electro motive force and of the distance, and is proportional to the current. Having in a given
system of electric transmission settled what current is to be used, we can, by the aid of Sir William Thomson's law, proceed to determine the most economical size of conductor. To do this we must know the annual cost of an electrical horse-power inclusive of interest and depreciation on the building, prime mover, and dynamo ; we must know what is the cost of laying one additional ton of copper, and we must settle in our mind what interest and depre ciation shall be charged to the line. These points will serve to determine the constants of our formula', and then the calculation can easily be made." In order to facilitate these computations. Professor Forbes published some tables. Tables II. and Ili., calculated by Prof. II. S. Carhart on the basis of dollars instead of pounds sterling, are here given. These tables have been calculated iu such a way that when the investigator has decided upon the proper allowance to be made for cost of laying one addi tional ton of copper under the conditions of his particular plant, the percentage of allowance for interest, he can then determine at once the proper size of conductors to employ. Thus, in Table 11. he follows the columns headed with the assigned cost of conductors until he reaches the line corresponding to percentage allowed for interest, etc.. and there finds a number. With this number he turns to Table HI., and starting at the left, on the line marked with the number expressing the cost of one electrical horse-power per annum, he follows along to the right till he comes to the number nearest the one taken from Table II. The number standing at the head of the column in which he finds this exact or nearest approximate number is the sectional area of the conductor, in square inches or circular mils required to carry 100 amperes with maximum economy under the conditions assumed.