The steam engine familiarly explained and illustrated; with an historical sketch of its invention and progressive improvement; its applications to navigation and railways; with plain maxims for railway speculators. By the Rev. Dionysius Lardner ... With additions and notes by James Renwick ...

314 THE STEAM ENGINE.
XIV.
A railroad which has gradients above thirty feet in a mile
will require such gradients to be worked by assistant locomotive engines, which will be attended with a waste of
power, and an increase of expenditure, more or less, according to the number and length of such gradients.
XV.
A very long inclined plane cannot be worked by an assistant locomotive without a wasteful expense. Gradients
exceeding seventeen feet per mile must, therefore, be short.
XVI.
Gradients exceeding fifty feet in a mile cannot be profitably worked except by stationary engines and ropes, an
expedient attended with so many objections as to be scarcely
compatible with a large intercourse of passengers.
XVII.
Steep gradients, provided they descend from the extremities of a line, are admissible provided they be short.
It is evident that in this case the inclined planes will help
at starting to put the trains in motion, at the time when, in
general, there would be the greatest strain upon the moving
power; and, in approaching the terminus, the momentum
would be sufficient to carry the train to the top of the plane,
if its length were not great, since it must, at all events, come
to a stop at the extremity.
XVIII.
The effect of gradients in increasing the resistance during
the ascent may be estimated by considering that a gradient