In § 204 we found that a through grade corresponding to a 1.9% pusher grade was 0.99%, or, in other words, that two engines of equal capacity could handle on a 1.9% grade a train which could be hauled by one engine on a 0.99% grade. Suppose that we have a road or division 100 miles long, which has a traffic of ten trains per day each way which must be assisted by pusher-engines. Two of the grades, 5 and 6.5 miles respectively, are against the traffic in one direction, and the other grade, with a length of 7.5 miles, is against the traffic in the other direction. There will therefore be a total of 19 miles of pusher-engine grade, on which ten trains per day must be assisted. Suppose that these maximum grades have been limited by suitable development to 1.9%. Suppose that the other grades are less than 1% or are so little above it that, with a comparatively small expenditure, they may be reduced to 1% or to 0.99%. How much money could justifiably be spent to accomplish the reduction of the other grades to keep them within the limit of 0.99%? There will be no object in cutting down these intermediate grades, unless by so doing we can double the train-load, even though doubling the train-load adds the expense of operating the pusher service. If the traffic of the road is sufficient for ten trains, such as could be hauled with one engine over the 0.99% grades, it will require twenty such trains to haul that traffic with one engine over 1.9% grades. Therefore, utilizing the pusher-engine service will save the operation of ten trains per day each way. If this particular division of the road is 100 miles long, the annual saving by cutting down the number of trains from twenty to ten, computed as in the previous chapter, will be 10 x $0.625 x 100 x 365 = $228,125.

But this saving is accomplished only by the pusher service, which will cost 10 x 19 x 2 x 67.57 c. x 365 = $93,720 per year.

Capitalizing the net saving, $134,405 at 5%, we have $2,688,010, which represents the amount which might justifiably be spent in reducing all grades except the three pusher grades down to the limit of 0.99%. The above estimate may need to be modified somewhat as to the cost of the pusher service. If these three pusher grades were so widely separated that each must be operated independently, then the pusher-engine mileage per day for the three grades would be 100, 130, and 150 miles respectively. Unless the schedules were favorably arranged for the pusher-engine service, it is quite possible that one engine might not be able to do the entire work on each of the grades'. Freight-trains which require pusher-engine help usually move at a very low speed, probably less than 15 miles per hour, and at times not more than 10 miles per hour. One hundred and fifty miles per day for a pusher-engine implies a very well-arranged schedule, and therefore two pusher-engines might be needed instead of one. This would add considerably to the cost of the pusher-engine service. The cost of reducing these grades is a quantity which can be readily computed with all desired accuracy, therefore we can usually determine by an investigation like the above whether the plan of using a pusher-engine service is desirable, since the cost of reducing the grades might be very much less than the computed capitalization. In that case it would show that it would probably be justifiable to adopt such a policy and that any allowable inaccuracy in the method of estimating the difference in operating expenses would not alter the final result. On the other hand, if the cost of reducing the grades is materially greater than the capitalized value, the proper method is again clearly indicated. When the two values are substantially equal, it shows that there is but little choice, and that the choice must probably be determined by the facility with which the money for the improvement can be obtained. In applying the above methods to any particular case, the values given above should be closely studied and revised to agree as nearly as possible with the local conditions. The value of the cost of a pusher-engine mile given above is to be considered as merely illustrative of what the cost will be under some conditions. Under other conditions the variation will be considerable, and a value which will correspond with the local conditions should be determined.