5

to the reduction of the formula. In its present state it gives a measurebelow the actual performance on any road in the United States .

I am also aware that, in not presenting the average cost of freight inany particular number of cents per ton per mile; or in any particularsum per mile traveled by the locomotive engines, I have deviated fromthe popular and most approved methods of treating the subject. But Iregard the aggregate cost per mile run as no guide whatever to theeconomy which characterizes the management of a railroad; and deemit an unauthorized assumption that because this sum is, in any instance,unusually low, the work is conducted with more than ordinary suc-cess. The fact, where it exists, can only be used to prove, if othercircumstances remain the same, that the engines have taken smallerloads, and made a greater number of trips, and run more miles, thanwas absolutely necessary. In fact, if we admit, what cannot well bedenied—that under similar circumstances, and with engines of thesame class, the cost of locomotive power is proportional to the distancerun—or that the cost of running one mile is not diminished by in-creasing the load, it follows as a consequence that, cseteris paribus,the more economical the administration of a road, the greater willbe the aggregate cost per mile run by the locomotive engines.

Neither is the circumstance that the aggregate expenses of a linefor one year divided by the number of tons conveyed, exhibits a lowaverage per ton per mile, any test of good management. The fact, byitself, is more likely to prove that the tonnage was great than that theadministration was judicious.

I shall now proceed to deduce from this general expression of thecost of freight, certain consequences of the utmost importance in thelocation and establishment of railroad lines, which I believe havehitherto been little, if at all, regarded.

What is the Value of Gradients? I mean by this question, howmuch more is a railroad having gradients of thirty feet per mile worththan the same road with grades of forty feet per mile? Or, how muchmoney would good economy authorize an engineer to expend, in theconstruction of his road, in order to reduce the limiting gradient anygiven amount?

I have seen various intricate and laborious solutions of questionswhich involve the loss of time and the consumption of steam in theascent of gradients; but I have never yet met with any examinationof this interesting and all important problem. The loss of time, inthis country, is usually a matter of little consequence in the transpor-tation of merchandize; and experience teaches that the cost ofmotive power is very nearly proportional to the distance traveled bythe engine, and very little affected, within the limits which ordinarily