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

The best adaptation of locomotive power to any system of grades, would be that which should render the mileage a minimum; and this will be done, as nearly as possible, by applying engines, the strength of which shall be proportional to the resistance to be overcome. The best mode of comparing different adaptations of power is by reducing the grades to a level; or by equating for grades by means of the capacity of motive power.

This is done as follows:—

The length of an incline being	L,
The resistance on a level being	R,
The ratio of the resistance due to the grade to the resistance on a level by	r,
The equivalent horizontal length by	L′,

and we shall have,

(R + r)L = L′.

Example.—Let the length of a grade be seventy-five miles; the value of

r = R
3;

and we have

(3
3R+R
3)L = (4R
3)75 = 100 miles.

Let us now compare the mileage of some of the large roads of America, as given by a good, and also by a bad adaptation of power.