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The most important consideration in the construction of railways, is the arrangement of the gradients. To effect this arrangement, two distinct and opposite systems present themselves, each having its advocates ready with arguments in support of their particular theory.
In the one system, the rises and falls are distributed over the whole length of the line, in planes of gradual inclination; while the other proceeds on the principle of concentrating the acclivities in a few points, and thus gaining the summits at once, by short and steep inclined planes, at the same time obtaining levels throughout the rest of the line.
To decide which of these systems is the most judicious, an investigation of the principles connected with the laws of retardation becomes necessary.
In Mr. Gibbs's ‘Report upon the several proposed Lines for the Brighton Railway’, this subject has been examined and illustrated with great simplicity and ability: to this Report we therefore with pleasure refer our readers, contenting ourselves with giving the results of his investigations; which are these:-
First, That on a series of railway inclinations, the power required to transport a weight from one given point to another, is precisely the same whatever inclinations are adopted, provided none of these inclinations exceed 21 feet in a mile, which is the limiting slope of a plane, on which the force of gravity becomes equal to, and consequently capable of balancing; or by any increase, of overcoming the retarding force of friction.
Second, On any series of inclinations, the power required to transport a weight both ways, is exactly equal to the power required to convey the goods on a level plane. This must be clear if we consider that a certain amount of power most be expended in order to overcome the gravity in ascending, in addition to the power employed to overcome the resistance of friction; and also in descending it is evident that a less quantity. of power is necessary than that required to overcome the friction.
Now the increased power in the one case is exactly equal to the decreased power in the other case; the gears amount, taking the two together, being equal to that required to overcome friction; this, of course, is equal to the power required on a level; and hence the conclusion, that whatever be the inclinations of a railway, provided none of these inclinations exceed 21 feet in a mile, the same power will work the railway both ways, as would be required to work the same distance on a level railway.