Handbook of Railroad Construction; For the use of American engineers. / Containing the necessary rules, tables, and formulæ for the location, construction, equipment, and management of railroads, as built in the United States.

by George L. Vose

and if the length of the inclined line is ten miles, the equivalent level length is

L = 41.2 × 52800
20 = 108768 feet, or 20.6 miles.

Also 10 miles × 41.2 lbs. = 412,

and 20.6 miles × 20 lbs. = 412.

54. The above may be somewhat abridged as follows: Let R be the resistance on a level. The resistance due to any grade is expressed by

W × 1
a,

where 1
a is the fraction showing the grade, and W the weight of the load.

The vertical height in feet, to overcome which we must expend an amount of power sufficient to move the train one mile on a level, must be such that

W × 1
a = R,

or