The locomotive engine may be so proportioned as to run at any speed from ten to sixty miles per hour, over grades from ten to two hundred feet per mile, and to carry loads from two hundred to two thousand tons.

The rules by which the necessary dimensions to perform any required duty are fixed, depend upon the very simplest mechanical laws.

Note.—The formulæ expressing the most proper relations to exist between the several steam-producing and steam-consuming parts are more reliable than the assertions of any machinist in America, and though taken from books, are the result of the experience of the most able and practical men for twenty years. Operatives are too apt to despise book knowledge, forgetting that the very knowledge so despised is the result of more practice than a lifetime can afford them. Railroad managers are too apt to receive as indisputable, the opinions of men who are practical, simply because they understand nothing of principle.

Since the work of D. K. Clark (England) has appeared, any dimension from the beginning to the end of a locomotive may be fixed, to the eighth of an inch, with absolute correctness, and there is no excuse for departing from the proper proportions. It does not follow that because a locomotive does actually start off and draw the train, that it is properly made. A race-horse can draw a plough, and a yoke of oxen a “trotting buggy,” but this is by no means the correct adaptation of power.

310. The elements which govern the requirements of power are

The maximum grades.

The weight of the train.

The required speed.

And the elements which govern our ability to produce the power needed,

The grate area.