The gross receipts obtained for transporting a given amount of freight is a definite sum which is independent of the number of train-loads required to handle it. On the other hand, the cost of a train-mile is nearly constant. If it were actually so, we could say at once that the cost of handling the traffic would be proportional to the number of trains, and that the saving of even one train-load, or of handling in four trains what would otherwise require five train-loads, would reduce the operating expenses proportionally. The problem is a very similar one to that already worked out in Chapter VII (Motive Power. Economics Of The Locomotive. 74. Total Cost Of Power By The Use Of Locomotives), but with a very important difference in some of the conditions. In both cases the object to be gained is the reduction in the number of trains to handle a given gross tonnage of freight traffic In the case worked out in Chapter VII, this is accomplished by merely increasing the power of the locomotives, so that a given amount of traffic can be handled in three trains instead of four, or in six trains instead of seven, the grades of the road being the same in each case. By the method discussed in this chapter, the grade is so reduced that an engine of given type may haul a larger number of cars, and therefore a certain gross amount of freight tonnage can be handled in three trains instead of four, or in six trains instead of seven, using engines of the same type and weight. In the first case, the power of the engine is increased; in the second case, the demand on its capacity is reduced by a reduction in the grade.

We will estimate as before the difference in the cost of operating, say, four light trains on heavy grades, or three heavier trains on the lighter grades. In either case the gross tonnage of cars, with their contents, is supposed to be the same. The difference consists in the cost of operating the extra engine and also the extra cost for train service, etc., which is a function of the number of trains on the road rather than of their tonnage. The additional cost of maintenance of way is confined to the effect of the extra engine, and this will evidently effect only Items 2 to 6 and 9. On the basis that an engine produces one-half of the track deterioration, we may allow 50% of these items as the total effect on maintenance of way.