In theory through rates are divided between the roads run over in proportion to the mileage. Frequently there is an arbitrary deduction made from the gross amount received to pay for "terminal charges" before the division is made. It sometimes happens that a road has sufficient financial strength in its dealings with other roads to demand and obtain the concession of a "constructive mileage," which is in excess of the actual mileage. For instance, the railroad may have been running for many years with a certain mileage between termini. Then a cut-off is made by means of a tunnel or some other very expensive construction, and there may be an actual saving of several miles in the length of the road. If the road is financially strong, it may succeed in obtaining the concession of dividing the freight receipts according to the old system rather than to submit to the reduction on account of the improvement. Nevertheless the fact remains that receipts are supposed to be divided according to the relative mileage. The words "through rate" in the following discussion refer to the amount actually divided after preliminary deductions have been made. Our discussion must therefore be based on that method, and any variations from it must be considered as exceptions. On account of this method of division and on account of the fact that non-competitive rates are almost invariably fixed according to the mileage, there results the unusual feature that, unlike curvature and grade, there is a compensating advantage in increased distance, which applies to all of the above classes of traffic except one (c - competitive local), and that the compensation is sometimes sufficient to make the added distance an actual source of profit. It has just been proved that the cost of hauling a train an additional mile is only from 33 to 50% of the average cost. Therefore in all non-competitive business (local and through) where the rate is according to the distance, there is an actual profit in all such added distance. In competitive local business, in which the rate is fixed by competition and has practically no relation to distance, any additional distance is but dead loss without any compensation. In competitive through business the condition of profit or loss will depend on the ratio of the length of the home haul to that of the foreign haul. The effect of this ratio and the law under which it works may best be illustrated by numerical examples.

153. Effect Of A Change In The Length Of The Home Road On Its Receipts From Through-Competitive Traffic

Suppose that the home road is 100 miles long and the foreign road is 150 miles long. Then the home road will receive 100/(100+150) = 40% of the through rate. Suppose that the home road is lengthened five miles. Under this condition it will receive 105/(105+150) = 41.176% of the through rate.

The traffic being competitive, the rate will be a fixed quantity regardless of this change of distance. To simplify the numerical work we will consider how much the home road will receive on a total freight charge, which, on account of the competition, is fixed at $1. By the first plan the home road will receive 40 c. and therefore handles that consignment of freight at the rate of .4 c. per mile. When the distance is increased to 105 miles it receives for the handling of that consignment of freight 41.176 c. Instead of computing the average rate per mile, we will consider it as though it received the same rate for the original hundred miles, and that it received 1.176 c. for the additional five miles, or at the rate of .235 c. per mile; but this is at the rate of 59% of the original rate per mile. We have determined above that the cost per train for an additional mile averages about 50% of the average cost of a mile, and therefore it may be seen that the net effect of adding that five miles is to leave to the original 100 miles the full rate of profit, and also that the amount received for the additional five miles will more than pay the cost of it, even though the additional profit is small. On the other hand, if the line is shortened five miles it may be similarly shown that not only are the receipts lessened in gross amount, but that the saving in operating expenses by the shorter distance is less than the reduction in receipts.

This line of argument was used by the manager of a railroad in opposing the plan of the directors to shorten a road by means of an expensive tunnel. He argued that under their traffic agreements the receipts of the road would not only be less, but also that the resultant saving in operating expenses would not equal the reduction in receipts.