The relation between an increase in length of fine and the expenses of Items 24, and 46 to 50 are quite indefinite. In some respects they would be unaffected by slight changes of distance, and yet it is difficult to prove that the expenses should not be considered proportionate for the distance. For example, the added train-mileage will increase repairs of rolling-stock, and will therefore hasten the deterioration and increase the cost of "repairs and renewals of shop machinery and tools" (Item 46). Fortunately, all these items are so small, even in the aggregate, that little error will be involved, whatever decision is made. It will therefore be assumed that these items are affected 100% for large additions in distance and 50% for small additions.

Items 40 to 42 are evidently unaffected by any change of distance. Electrical equipment, items 28-30 and 37-39, which are used on so few steam railroads, is ignored in this discussion.

There only remain the four groups of items, the repairs, renewals and depreciation of steam locomotives and of passenger and. freight-cars and of work equipment. The deterioration of rolling stock, which requires its repair and finally its ultimate abandonment and therefore renewal, is caused by a combination of a large number of causes, of which the mere distance they travel on the road is but one cause. They deteriorate first with age; second, on account of the strains due to stopping and starting; third, on account of the strains and wear of wheels due to curved track; fourth, on account of the additional stresses due to grade and change of grade, and fifth, on account of the work of pulling on a straight level track. In addition to this, locomotives suffer considerable deterioration due to expansion and contraction, especially of the fire-box when the fires are drawn and the fire-box and boiler become cold, and again when the fire is started up. A large part of the expenses of maintaining passenger-cars is the expense of painting, which is a matter of mere time. Considering that the changes of distance, whose economic value the engineer tries to compute, will never make a difference in the number of round trips the engine or car would make in a day or month, the added distance which may be traveled does not add to the exposure of the car to the weather. Therefore, whatever deterioration of the car paint is due to weather, it will be incurred regardless of whether the length of the division of the road is 100 miles or 99 or 101. That element of the cost of car maintenance is absolutely independent of the precise length of that division of the road. On the other hand, the wear of car- and engine-wheels, although largely affected by curvature, is certainly affected to some extent by wear on a straight tangent. To determine the proportion of total wear due to these various causes is a matter of estimation and judgment. An approach to accuracy may be made by a compilation of the shop records of rolling-stock, repairs, showing the amount which is spent in various kinds of repairs, and estimating as closely as possible what is the cause of each form of deterioration. A check on any such estimate is the consideration that the total deterioration is simply the summation of the deterioration due to all causes combined. It is therefore a question of dividing 100% into as many portions as there are contributing causes, and to assign to each cause its relative importance in per cent, so that the sum total shall reach 100. A. M. Wellington, in his "Economic Theory of Railway Location," distributed the cost of engine repairs to its various contributing causes, as shown in the following tabular form. He did not claim that such an estimate was accurate and applicable to all cases, but he did claim that the error was probably not sufficient to be of importance. A comparison of these percentages, with the data given by shop records on any particular road, would not probably show a very material difference, and the writer will not attempt to claim that any figures he might obtain will be any more accurate in general, although they might be more accurate as applied to some particular conditions.

Table XXIII. Distribution Of The Cost Of Engine Repairs To Its Various Contributing Causes. (Copied From Wellington.)

Total cost of item.

Distribution.

Item.

Effect of time, age. and exposure, per cent.

Stopping and starting at way stations, per cent.

Terminal: getting up steam, making up trains, per cent.

Curvature and grades, percent. (Approximate average).

Distance on tangent between stations, per cent.

Bouler .......

20.0

2.

7.

4.

7.

Running gear...........

20.0

4.

2.

7.

7.

Machinery .................

30.0

1.

7.

3.

5.

14.

Mountings ...............

Lagging and painting.. ..

12.0

4.

2.

6.

Smoke-box etc ..................

5.0

1.

1.

3.

Tender:

Running gear .................

10.0

2.

1.

3.

4.

Body and tank ...................

3.0

1.

1.

1.

Total .....................

100.0

7.

15.

17.

19.

42.

It may be noted from the above table that 42% of engine repairs has been assigned to distance on a tangent between stations. If the added distance does not imply an extra stoppage of the train, there is but little, if any, reason to differentiate between the effect on repairs of a large or small addition to distance. We will therefore consider Items 25-27 to be affected in this ratio of 42%.

Wellington similarly distributed the cost of freight-car repairs to its various causes, and by a very similar method estimated that 36% of such repairs was due to distance on a tangent between stations. The considerable transformation in the construction of freight-cars, since the time that Wellington compiled this table, has certainly utterly changed the absolute cost of car repairs, even if it has not changed the relative percentage of the cost of the various items. In the lack of any better figures this same figure will be used for Items 34-36. Although there are evidently enormous differences between Items 34-36 and 43-45, Items 43-45 are so small that it is hardly worth the calculation of any more precise figures, and therefore the same ratio, 36%, will be used for Items 43-45. Wellington made no definite calculations for the itemized cost of passenger-car repairs, but contented himself with using the same figure as for freight-cars, 36%. Such a percentage is probably very much too high, since it is estimated that about one-half the cost of passenger-car repairs is due to the work of painting, inside and out, and of maintaining the seats and upholstery in proper condition. Such repairs are chiefly a function of time, and are but little, if any, dependent on mere distance between stations. It is therefore considered that Items 31-33 will not be affected more than 20% by any addition of distance. Traffic expenses will be unaffected.

140. Effect On Conducting Transportation

Items 61-78, superintendence and dispatching, all station and yard expenses, and the joint expenses of yards and terminals, may be considered as unaffected. Item 79, motormen's wages, is ignored.

141. Item 80. Road Enginemen

In a previous chapter, §32, the wages of road enginemen were discussed. The discussion showed that the enginemen are rarely, although sometimes, paid on a strict mileage basis. They are usually paid on a trip basis, in accordance with which a slight change in the distance will not affect the classification of the trip, and therefore would make no difference in the wages. We will therfore say that for small changes of distance, especially such as would be measured in feet, this item will be unaffected; but that for larger changes, such as would be measured in miles, this item will be affected by the full amount of the enginemen's wages.

Although there might be some justification for saying that the engine-house expenses for road engines (Item 81) might be somewhat increased by additions to distance, the addition may be considered as already covered by the increase in maintenance charges (Items 25-27), and no further allowance will be made.