Curve. Radius in Feet. 1° 5729.65 2° 2864.93 3° 1910.08 4° 1432.69 5° 1146.28 6° 955.36 7° 819.02 8° 716.78 9° 637.27 10° 573.69 12° 478.74 15° 383.06 20° 287.91 =258. Resistance of Curves and Compensation in Grades.=—Inasmuch as the resistance offered to hauling the train around a curve increases quite rapidly as the radius of curvature decreases, it is obvious that in constructing a railroad the degree of each curve should be kept as low as practicable, and that there should be no more curves than necessary. While no definite rule can be given as to such matters, curves as sharp as 10° (573.69 feet radius) should be avoided wherever practicable. It is not advisable to run trains at the highest attainable speeds around such curves, nor is it done. Inasmuch as curve resistance has considerable magnitude, as well as the resistance of grades, it is natural that wherever curves occur grades should be less than would be permissible on straight lines or, as they are called, tangents. If a maximum gradient is prescribed in the construction of a railroad, that gradient will determine the maximum weight of train which can be hauled on the straight portions or tangents of the road. If one of these grades should occur on a curve, a less weight of train could be handled by the same engine than on a tangent. Hence it is customary to reduce grades by a small amount for each degree of curvature of a curve. This operation of modifying the grades on curves so as to enable a locomotive to haul the same train around them as up the maximum grade on a tangent is called compensating the curves for grade. There is no regular rule prescribed for this purpose, because the combination may necessarily vary between rather wide limits in view of speed, condition of track, and other influencing elements. The compensation, however, has perhaps frequently been taken as lying between .03 and .05 per cent of grade for each degree of curvature. In other words, for a 5° curve the grade would be .15 to .25 per cent less than on a tangent. This compensation for grades is carefully considered in each case by civil engineers in view of experience and such data as special investigations and general railroad operation have shown to be expedient. [Illustration: FIG. 1. GRAVEL BALLAST] [Illustration: FIG. 2. STONE BALLAST NEW YORK CENTRAL & HUDSON RIVER RY.] [Illustration: FIG. 3. PENNSYLVANIA RY.]