TRACT 3S.

MISCELLANEOUS PROBLEMS.

317

PROBLEM II.

To determine the Effects of Pile-Engines.

The form of the pile-engine, as used by the ancients, is notknown. Many have been invented and described by themoderns. Among all these, that appears to be the best whichwas invented by M. Vauloue, as described by Dr. Desaguliers,and was used at piling the foundations at building Westmin-ster Bridge. Its chief properties are, that the ram or weightbe raised with the least expence of force, or with the fewestmen ; that it fall freely from its greatest height; and that,having fallen, it is presently laid hold of by the forceps, andso raised up to its height again. By which means, in theshortest time, and with the fewest men, or the least force,the most piles can be driven to the greatest depth.

Belidor has given some theory as to the effect of the pile-engine; but it appears to be founded on an erroneous prin-ciple : he deduces it from the laws of the collision of bodies.But who does not perceive that the rules of collision supposea free motion and a non-resisting medium ? It cannot there-fore be applied in the present case, where a very great re-sistance is opposed to the pile by the ground. We shalltherefore here endeavour to explain another theoiy of thismachine.

Since the percussion of the weight acts on the pile duringthe whole time the pile is penetrating and sinking in theearth, by each blow of the ram, during which time its wholeforce is spent; it is manifest that the effect of the blow is ofthat nature, which requires its force to be estimated by thesquare of the velocity. But the square of the velocity ac-quired by the fall of the ram, is as the height it falls from ;therefore the force of any blow will be as the height fallenthrough. But it is also more or less in proportion to theweight of the ram ; consequently the effect or force of eachblow must be directly in the compound ratio of both, viz, asaw, where w denotes the weight, and a the altitude it falls