In the first edition, the author followed the general argument of the late A. M. Wellington, who insisted that the expenses of track maintenance were more dependent on number of trains than on the gross tonnage passing over the track, and that the net effect on maintenance of way and structures of running (n+1) light trains rather than n heavier trains was to add to the maintenance of way cost a part of the usual average cost of maintenance of way per train-mile. While reviewing the line of argument and endeavoring to make it more logical and positive, the author considered the following numerical case. Assume a gross tonnage of 2400 tons of freight, including the cars. Assume that a 125-ton engine can haul 600 tons over the grades of the road; four trains would be required. Assume that a 100-ton engine can haul 480 tons over the road; five trains would be required. Assume D = damage done to road-bed and track by one ton of ordinary freight; assume that the greater concentration of the locomotive does a damage of 4D per ton. Then the damage for one heavy train = (125X4D) + 600D = 1100D and for four trains, 4400D. Note that the total damage done by the locomotive is nearly one-half of the total, which agrees with the generally accepted opinion. The damage for one lighter train = (100XW) + 480D = 880D, and for five trains, 4400D, which is precisely the same as before. If the relative locomotive damage per ton is assumed at 3D or 5D, the relative results for the two systems of trains are still identical. If the relative locomotive damage per ton is assumed to be still higher for the heavier locomotive, then the damage done by the four heavier trains would be somewhat greater and the system of lighter trains would be cheaper, so far as maintenance of way goes. A larger number of light loads always produces less wear and strain under any form of mechanical stress than a few concentrated loads, the gross tonnage remaining constant. On this account the author cannot now see the justification of charging anything for maintenance of way and structures, on account of the operation of a greater number of lighter trains. There appears to be argument for a balance either way. The difference cannot be large in either direction.

All electric traction items are considered unaffected.

## 87. Maintenance Of Equipment

Under the items of maintenance of equipment, the repairs of locomotives (Items 25-27) are the first important items to consider. The real question regarding this item is, Will the cost of engine repairs on four light engines be greater than on the three heavier engines which will do the same work? If we apply the rule that the cost of engine repairs equals 1 c. per ton of average tractive force per mile, plus 1 c. per engine-mile, we will find, since the sum of the tons of tractive force required to haul the total tonnage of cars must be considered the same, that part of the item will balance. The other part of the item of repairs will vary according to the number of engine-miles; but the total item consists partly of the cost of renewals, and, since we may assume that the cost of the four light engines is nearly the same as that of three heavier engines, we may consider that the part of the item which has to do with renewals balances. Evidently no one figure will be a correct answer for every case, but the method may be indicated as follows: Assume that we are comparing two types of engines, one of them having a tractive force of 15 tons and the other a tractive force of 20 tons. Then four of the lighter engines will be required to haul the same load which can be hauled by three of the heavier engines. Assume that an average of 50% of the maximum tractive force is utilized for the entire trip. Then according to the rule the cost of repairs for the three heavy engines would be (.50X20)3+3 and for the light engines (.50x15)4+4, or 33 c. and 34 c. per mile respectively. It should be noted that, under the assumptions made, the largest part of the above items are identical for the two cases, and that the difference is very small. In fact, the difference is probably smaller than the probable error of the method of computation, and therefore we can probably say that, so far as Items 25-27 are concerned, the additional cost for engine repairs of using one additional locomotive to do the work, or the saving accomplished by using the heavier locomotive, will be practically zero. When we consider the repairs to the rolling-stock, we have an actual advantage in using light engines, since the average draw-bar pulls with the lighter train and the impact due to sudden stoppage is less, and, although some of the items of repairs will evidently be unaffected, none of them will be increased. The amount which they can be decreased is almost non-computable, since it depends on circumstances which in general cannot be foreseen. If the particular question involved concerns only the use of freight-locomotives, then we must ignore Items 31-33, the repairs of passenger-cars. If we analyze the cost of repairs of freight-cars, and consider that a very large proportion of them are due to causes which have nothing to do with this question, we can see the justification of the estimate which has been made, that the cost of repairs of freight-cars may be reduced 10% by the adoption of a greater number of trains to handle a given traffic. Even though this estimate may be considered as guesswork, it is quite evident that its error cannot be a very large percentage of itself, and it is quite certain that the error is only a very small percentage of the total quantity which we are trying to compute. The remaining items up to 52 are unaffected. Traffic items are unaffected.