In the preceding chapters it has been tacitly implied that the extent of the traffic in the two directions is equal, and that it is just as desirable to obtain a low grade in one direction as in the other. But it frequently happens that the freight traffic in one direction is far greater than the freight traffic in the opposite direction. Even on the main trunk lines running east and west, the east-bound ton-mileage has at times amounted to four or five times the west-bound ton-mileage. Between the years 1851 and 1885 the east-bound ton-mileage on the Pennsylvania Railroad averaged 3.7 times the west-bound ton-mileage. As an actual consequence, the west-bound freight-trains consisted very largely of "empties." As another corollary, a locomotive which could haul a certain number of loaded cars up a grade of 0.6%, which was against the east-bound traffic, could just as easily haul such cars as were loaded, together with the empties, which must be returned, up a considerably steeper grade, say 1.0%. Under such conditions there is little or no object (from the ruling-grade standpoint) of making the grade against the west-bound traffic any less than 1% when the east-bound traffic is as steep as 0.6%. The two grades, 0.6 and 1.0, have been selected offhand as two grades which might balance each other under certain conditions of relative traffic in the two directions. They illustrate the principle involved that the ruling grades in opposite directions should not necessarily be equal, but should probably be made unequal. It now remains to determine what should be the relation between the ruling grades in the two directions on any given road.

210. Illustrations In The Balancing Of Grades

This subject is one that chiefly concerns the great trunk lines of the country, which are constructed almost regardless of cost and at grades which are reduced to a low figure by a great expenditure of money. A very large number of railroads, especially branch lines which run from a main road up into the mountains, have one terminus much higher than the other, are laid out largely as "surface lines," and are therefore laid on such grades as can be obtained with a minimum of constructive work. On such a road the heavy grades may be almost entirely in one direction, which may or may not be against the heavy traffic. Unless a road is of such importance that it can be largely rebuilt after its original construction, in order to correct the errors and deficiencies of the original work, we must consider the original location as a finality. It is frequently impossible to predict, with any great accuracy, what the traffic of the road will be, and especially that the traffic in one direction will be materially greater by any definite percentage than that in the other. The engineer is therefore seldom justified in attempting to make precise calculations of this sort previous to the construction of a new road.

211. Principles On Which The Theoretical Balance Must Be Computed

A little thought will show the truth of the following statements. First, the number of locomotive? and passenger-cars running in each direction is necessarily equal. Second, the number of passengers carried in opposite directions is practically equal. Even if we allow that there is a considerable immigrant traffic which increases slightly the load of passengers carried, it is useless to base any calculations on this, since the ratio of live load to dead load in passenger-cars is so very small that such a slight difference in the number of passengers carried in opposite directions as may exist can have absolutely no effect on the proper rate of grade. Third, empty cars have a greater resistance per ton than loaded cars; therefore, in computing the hauling capacity of a locomotive hauling so many tons of "empties," a larger figure must be used for the ordinary tractive resistances. This fact, so far as it goes, tends to equalize the differences in the two grades which might otherwise be computed. Fourth, owing to greater or less imperfections of management, a small percentage of cars will run empty or partly full in the direction of the greatest traffic. Fifth, freight having great bulk and weight (such as grain, lumber, coal, etc.) runs from the rural districts to the cities and manufacturing districts. Sixth, freight from manufacturing districts, although it pays comparatively high freight-rates and is actually more profitable to handle, weighs far less, and occupies less bulk. Seventh, changes in traffic conditions which are more or less permanent will alter the direction of the hauling of bulk freight. For instance, a farming district which is largely a dairying country frequently will not raise as much feed (hay and grain) as is needed to feed the cattle, and we have the apparent paradox of importing grain and feed into a farming country. Eighth, a change in the character of the country may permanently alter the ratio of the freight tonnage in the two directions. Such changes are already discernible in the traffic of the east and west lines and also in the north and south lines. The discovery of extensive coal-fields in the western part of the United States has largely changed the direction of the movement of this class of bulk freight. The exhaustion of supplies of timber in one section and the development of that industry in another has also had material influence in changing the relative flow of traffic. The development of the coal and iron industries in the South has largely changed the relative traffic flow in north and south lines.