From the foregoing table we see :

1. That the force necessary to move a vehicle at a certain velocity on a level road must be decreased on a descending grade to precisely the same extent that it must be increased in ascending the same grade, in order to maintain the same velocity.

2. It must not, however, be inferred from this that the animal force expended in passing and repassing on the same road, will gain as much in descending the several grades as it will lose in ascending them. The animal force must be

adequate, either in number or in power, for achieving the steepest ascending grades on any route, and no reduction in the number of animals will be practicable in the general case, in descending that or the lower grades, or upon the level portions of the line.

CHAPTER II.

EARTHWORK, DRAINAGE AND TRANSVERSE FORM OF

COUNTRY ROADS.

Excavations and Embankments.

DUE regard to economy in the cost of constructing a road generally requires that its location shall be such that the cuttings shall balance the fillings, or in other words that the excavations, at points where the ground is higher than the road, shall furnish the contiguous embankments at points where the road is higher than the natural surface. Such, however, is not always the case, it being cheaper, under some circumstances, to deposit the excavations in spoilbanks, and procure the earth for embankment from side-cuttings near by.

The first location of the road upon the map will seldom be more than an approximation to the best line, which must finally be ascertained after successive approximations, for each of which a series of new sections must be drawn, and new calculations made. The contour lines referred to, of which an example is given in Fig. 3, or the parallel crosssections as shown in Fig. 4, will be of great assistance in making these computations, and will materially abridge the labor of locating the line.

The "Lead."

Prof. Mahan says, "In the calculations of the solid contents required in balancing the excavations and embankments the most accurate method consists in subdividing the

different solids into others of the most simple geometrical forms as prisms, prismoids, wedges and pyramids, whose solidities are readily determined by the ordinary rules for the mensuration of solids." Other methods "consist in taking a number of equidistant profiles, and calculating the solid contents between each pair, either by multiplying the half sum of their areas by the distance between them, or by taking the profile at the middle point between each pair, and multiplying its area by the same length as before." In order to save labor and insure accuracy, tables for these calculations have been prepared and published.

Care must be taken in determining the lead, or the average distance to which the cuttings must be transported in making the fillings, a distance usually assumed, in each case, to be the length of the right line joining the centre of gravity of the solid of excavation and that of embankment. The least possible lead is essential from considerations of economy, and this is usually secured when such conditions are interposed that the paths over which the different portions of the solid of excavation are conveyed away to the solid of embankment, shall not cross each other either horizontally or vertically.

These conditions require that the sum of the products, obtained by multiplying all the elementary volumes by the distances over which they are respectively transported, shall be a minimum. As the computations involve the employment of the higher mathematics, they are not inserted here.

Growth of Excavated Earth.

It must be remembered that the different kinds of earth do not fill the same volume in artificial embankments that