(a) In all non-competitive business (local and through) the added distance is actually profitable. On some small roads practically all of the business is non-competitive. A considerable proportion of it is always non-competitive.
(b) When the competitive local business is very large and the competitive through business has a large average home haul compared with the foreign haul, the added distance is a source of loss. Such conditions apply almost exclusively to trunk lines and to competitive lines between large cities.
(c) The above conclusions may be still further condensed to the general conclusion that there is always some compensation for the added cost of operating an added length of line, and that it may sometimes be a source of profit.
(d) There is a danger in the application of the above argument which should not be forgotten. The argument might be carried to the logical conclusion that if added distance is profitable the engineer would be justified in purposely lengthening the line. But added distance means adding operating expenses. The increased tariff to meet these is a tax on the community, a tax which more or less discourages traffic. It is not only contrary to public policy but contrary to the ultimate best interests of the road to burden an enterprise with avoidable expenses. The locating engineer frequently has to choose between two locations, one of which saves distance by very expensive construction, such as deep cutting, high embankments, a tunnel or a bridge, while a longer line may be constructed at considerably less total expense, because it is almost a surface line. In such a situation the engineer should consider that if the bulk of the business of his road will be "non-competitive local," he would hardly be justified in increasing the cost and thereby actually reducing the mileage and the gross receipts of his road. On the other hand, if the road is a very important line, on which the bulk of the business is apt to be "competitive through" business, the added distance would probably be operated at a considerable loss, and therefore should be avoided even at a considerable added expenditure.
(e) Finally, although there is a considerable and uncompensated loss resulting from curvature and grade which will justify a considerable expenditure to avoid them, there is by no means as much justification to incur additional expenditure to avoid distance. Of course, needless lengthening should be avoided as a matter of broad policy. A moderate expenditure to shorten the line may be justifiable, and its justification will increase with the increase in probabilities of a heavy through competitive traffic. A short branch line, whose business will consist chiefly of non-competitive local business or of through business, in which the proportion of foreign haul to home haul will be large, will receive a very considerable compensation if not actual profit on added haul, and therefore will not be justified in paying any great amount of money to reduce distance.
A little study of this question will show that the cases are rare where a minor change in distance will accomplish any material saving in the time required to make a trip. It will also be clear that such a saving of time will have no effect on freight business which is worth considering. The competition for passenger business between two cities like New York and Philadelphia, or even New York and Chicago, render the time element of considerable financial importance, but it may readily be demonstrated that the saving of even ten minutes on such a trip by means of a change of alinement, the average speed of the trains remaining the same, could only be accomplished by enormous expenditure. The cases are very rare where the element of time as affected by reduction of distance can be given financial weight.
All of the above calculations have assumed for simplicity that the business done by the road is a definite quantity which is unaffected by any proposed changes. A common defect in the location of a cross-country line, whose business will virtually be that of a branch to some great trunk line with which it may connect, even though the small road is an independent road, is that too much importance will be given to the effort to obtain "a short, straight line" rather than a line which will reach sources of traffic. Of course there is a danger in either extreme. A line which zigzags across country in an effort to reach every possible source of traffic may be so long that the whole traffic is burdened with an excess haul which will literally discourage traffic. The number of elements entering into the problem is so large that it is difficult to state a general rule, but the following will usually be safe. Adopt a route of such a length that the annual traffic per mile of line is a maximum. We may make the rule somewhat more complicated and allow for the element of cost of construction by saying - Adopt a route of such length that the annual traffic per mile of line divided by the average cost per mile is a maximum. Even the above rules take no account of the effect of curvature and grade, which will, of course, have a considerable effect on the operating expenses; but a road whose receipts per mile of line is maximum is evidently obtaining the maximum profit from the community, especially if the cost of construction has been kept so low that the profits per mile of line divided by the average cost is also a maximum.
No attempt has been made to estimate the effect of a saving of time on the passenger business of the very few trunk lines on which the competition in the matter of speed is so great that millions are freely spent in the attempt to reduce it, not only by a reduction of distance but by the elimination of curvature and steep grades. A gain in traffic which is secured wholly by competition only holds good as long as the advantage can be maintained and until a competitor will offer still greater advantages. Under these conditions any exact analysis of the question is practically impossible, and considering the fact that such a question does not apply to any appreciable extent to nine-tenths of the mileage of the country, it will not be here further considered.