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calculations are predicated on data which are exceedingly difficult, ifnot impossible, to procure, in anticipation of the experimental result.It is certainly true that such inquiries are not free from some difficultyand uncertainty; and it is also true that the engineer must overcomethis difficulty or proceed to his work entirely at random. The valuesof grades and distances turn upon these facts, and they must either beregulated without regard to any principle, or by these, or some similarequations. The application of the equations will, of course, be some-what inconvenient, since they compel 11s to know something aboutthe thing we are doing; they compel us, when we propose to cut downa hill or fill up a hollow, to know what it is to be done for, and tojudge how much we shall cut, and when we shall stop. I 3 ut, how-ever inconvenient it may bo to answer such inquiries, it is not the lessimportant to study the subject, and learn how to answer them bysome better mode than mere conjecture.

It is unnecessary to make additional application of the formulae.They are remarkably simple and obvious, and by supplying a readyand convenient mode of comparing different lines, or different loca-tions of the same line, they remove many of the difficulties with whichevery engineer must have felt himself embarrassed in the explorationor establishment of important improvements. They indicate the pro-per and only convenient general mode of estimating the aggregatecost of transportation under different assumed quantities of tonnage;and teach us, in the location of a line, the correct value of distance—in the calculation of which the cost of freight is the essential element—and at the same time enable us so to regulate the grades that thetransportation may not be improperly embarrassed, and that the com-pany may not be induced to pay more for the reduction of the cost offreight than the reduction is worth. These are all matters of greatinterest, and questions which can never be overlooked by an engineerwho faithfully performs his duty. Indeed, they must all be met, andmaturely considered, at every step of his progress, or the work whichis placed under his professional charge will bo found to be a failure,and in all probability soon pass into the hands of assignees, or comeunder the hammer of the Sheriff. They are always objects of immenseconsequence in the decision of the great questions of general location,which arise in determining the proper routes for railroads of great ex-tent, passing through districts where different lines, having variouspretentions, are presented, and where the comparisons of distances,grades, and elevations are of constant occurrence. They are also im-portant where no such general choice is presented, in determining onthe details of the location of every line. A road is scarcely ever sur-veyed on which there is not found some one gradient which controlsthe average load of the engino, and which it is desirable to reduce.