7

ble labour, and at the least possible cost, the number of miles actuallytraveled ought to approach very nearly the number corresponding withthe assumption of full trains; and consequently, except in extremecases, the estimate should not be much in excess. But if the situationand circumstances of the line be such as will preclude the probabilityof loading all the tonnage trains to the proper limit, some allowancemay be made, in the application of the formula, for that portion of thetrade which it does not embrace.

Now, if the limiting gradient of the road be changed, the number ofmiles traveled by the locomotive engines will also be changed. If theload be reduced one half by the introduction of any plane, the numberof trips, and, consequently, the cost of locomotive power, will be verynearly doubled by the admission of that plane.

But the number of miles traveled by the engines in the course ofa year, supposing them to convey full loads, and the transportation,accordingly, to be effected with the greatest possible economy of power,will be expressed by

Where n is put for the average gross load in tons, up the limitinggrade, and T' for the gross weight in tons carried in full trains onemile in the direction to which that gradient is opposed.

We know, from satisfactory experiments, that an inclination oftwenty feet per mile, on a road in good adjustment, requires for itsascent a power nearly double; and one forty feet per mile a powertreble, and one of sixty feet a power quadruple (or, for grades undereighty feet, very nearly in this proportion) that which is required todraw the same weight on a level. In other words, if W be the grossload an engine is capable of drawing with safety and certainty on alevel road, and x the inclination, in feet per mile, of the gradient whichlimits the load, then

20

20 + a;

W=n

will be the load, near enough for our object, with which it can mountthe plane ascending x feet in a mile.

If we now designate by C the cost of running the engine, with itstender only, one mile; by c the additional cost of motive power permile, due. to each ton gross added to the load—then C + cn will be thewhole cost of motive power per mile run. This sum may be written

C + c

20 W20 +x'

by substituting for n its value expressed in terms of the grade and thepower of the engine.