Of all these, the best is the straight or uniformly inclined, or level road, although at the same time it is the most expensive. If the importance of the traffic passing between the places is not suffi cient to warrant so great an outlay, it will become a matter of consider ation whether the course of the road should be kept straight, its surface being made to undulate with the natural face of the country; or whether; a level or equally inclined line being adopted, the course of the road should be made to deviate from the direct line, and follow the winding course which such a condition is supposed to necessitate.
In the second case, that of two places situated on opposite sides of the same valley, there is, in like manner, the choice of a perfectly straight line to connect them, which would probably require a big embankment if the road was kept level, or steep inclines if it followed the surface of the country; or by winding the road, it may be carried across the valley at a higher point, where, if the level road be taken, the embankment would not be so high, or, if kept on the surface, the inclination would be reduced.
' In the third case, there is, in like manner, the alternative of carrying the road across the intervening ridge in a perfectly straight line, or of deviating it to the right and left, and crossing the ridge at a point where the elevation is less.
The proper determination of the question which of these courses is the best under certain circumstances involves a consideration of the comparative advantages and disadvantages of inclines and curves. What additional increase in the length of a road would be equivalent to a given inclined plane upon it; or conversely, what inclination might be given to a road as an equivalent to a given de crease in its length? To satisfy this question, the comparative force required to draw different vehicles with given loads must be known, both upon level and variously inclined roads.
The route which will give the most general satisfaction consists in following the valleys as much as possible and rising afterward by gentle grades. This course traverses the cultivated lands, regions studded with farmhouses and factories. The value of such a line is much more considerable than that of a route by the ridges. The water courses which flow down to the main valley are, it is true, crossed where they are the largest and require works of large dimen sions, but also they are fewer in number.
Intermediate Towns. Suppose that it is desired to form a road between two distant towns, A and B, Fig. 6, and let us for the present neglect altogether the consideration of the physical features of the intervening country, assuming that it is equally favorable whichever line we select. Now at first sight, it would appear that under such circumstances a perfectly straight line drawn from one town to the other would be the best that could be chos en. On more careful exam ination however, of the lo cality, we may find that there is a third town, C, situated somewhat on one side of the straight line which we have drawn from A to B; and although our primary object is to connect only the two latter, that it would nevertheless be of considerable service if the whole of the three towns were put into mutual connection with each other.
'Phis may be effected in three different ways, any one of which might, under the circumstances, be the best. In the first place, we might, as originally suggested, form a straight road from A to B, and in a similar manner two other straight roads from A to C, and from B to C, and this would be the most perfect way of effecting the object in view the distance between any of the two towns being reduced to the least possible. It would, however, be attended with considerable expense, and it would be requisite to construct a much greater length of road than according to the second plan, which would be to form, as before, a straight road from A to B, and from C to con struct a road which should join the former at a point D, so as to be per pendicular to it. The traffic between A or B and C would proceed to the point D and then turn off to C. With this arrangement, while the length of the roads would be very materially decreased, only a slight increase would be occasioned in the distance between C and the other two towns. The third method would be to form only the two roads A C and C B, in which case the distance between A and B would be somewhat increased, while that between A C or B and C would be diminished, and the total length of road to be constructed would also he lessened.