ed. This idea would have place, at least to a certain extent, if the whole momentum was allowed to accumulate during the descent; but even supposing there would be no danger from acquiring so great a speed, a mechanical difficulty was brought to light at once, namely, that the resistance of the atmosphere to the motion of the train increased nearly, if not quite, as the square of the speed; so that after the train on the descent acquired a certain speed, a regular motion was obtained by the balance of momentum and resistance, —whence a fall great enough to produce this regular speed would be advantageous, but no more. On the other hand, the extra power required to draw the train up the grades much overbalances the gain by gravity in going down.
Here, then, we have the two extremes: first, spending more money than the expected traffic will warrant, to cut down hills and fill up valleys; and second, introducing grades so steep that the amount of traffic does not authorize the use of engines heavy enough to work them.
The direction of the traffic, to a certain extent, determines the rate and direction of the inclines. Thus, the Reading Railroad, from Philadelphia up the Schuylkill to Reading, and thence to Pottsville, is employed entirely in the transport of coal from the Lehigh coal-fields to tide-water in Philadelphia; and it is a very economically operated road, considering the large amount of ascent encountered, because the load goes down hill, and the weight of the train is limited only by the number of empty cars that the engine can take back.
This adoption of steep inclines may be considered as an American idea entirely, and to it many of our large roads owe their success. The Western Railroad of Massachusetts ascends from Springfield to Pittsfield, for a part of the way, at 83 feet per mile. The New York and Erie Railroad has grades of 60 feet per mile. The Baltimore and Ohio climbs the Alleghanies on inclines of 116 feet per mile. The Virginia Central Road crosses the Blue Ridge by grades of 250 and 295 feet per mile; and the ridge through which the Kingwood Tunnel is bored, upon the Baltimore and Ohio Railroad, was surmounted temporarily by grades of 500 feet per mile, up which each single car was drawn by a powerful locomotive.
Another element, of which American engineers have freely availed themselves, is curvature. More power is required to draw a train of cars around a curved track than upon a straight line. In England the radius of curvature is limited to half a mile, or thereabouts. The English railway-carriage is placed on three axles, all of which are fixed to the body of the vehicle; the passage of curves, of even a large diameter, is thus attended by considerable wear and strain; but in America, the cars, which are much longer than those upon English roads, are placed upon a pintle or pin at each end, which pin is borne upon the centre of a four-wheeled truck,—by which arrangement the wheels may conform to the line of the rails, while the body of the car is unaffected. This simple contrivance permits the use of curves which would otherwise be entirely impracticable. Thus we find curves of one thousand feet radius upon our roads, over which the trains are run at very considerable speed; while in one remarkable instance (on the Virginia Central Railroad, before named) we find the extreme minimum of 234 feet. Such a track does not admit of high speeds, and its very use implies the existence of natural obstacles which prevent the acquirement of great velocities.
In fine, the use which the engineer makes of grades and curves, when the physical nature of the country and the nature and amount of the traffic expected are known, may be taken as a pretty sure index of his real professional standing, and sometimes as an index of the moral man; as when, for example, he steepens his grades to suit the contractor's ideas of mechanics,—in other words, to save work.
Not less in the construction of bridges
