3IS

AlISCElX ANEC5U S

TRACT 38j

from ; or it will be simply as the altitude a, when the weightw is constant.

Again, the force of the blow is opposed by the mass of thepile, and by the consistence of the earth penetrated by thepoint of the pile, and also by the friction of the earth againstthe sides of the pile that have penetrated below the surface.Consequently the effect of the blow, or the depth penetratedby the pile, will be inversely in the compound ratio of thesethree, viz, inversely as mif, where m denotes the mass of thepile, t the tenacity or cohesion of the earth, and / the fric-tion of the surface penetrated in the earth. But, in thesame soil and with the same pile, m and t arc both constant,in which case the depth of penetration will be inversely onlyas /the friction. On all accounts then the penetration willbe as or simply as ~ only, for the same weight and pileand soil.

To determine the depth sunk by the Pile , at each stroke of the

ram.

After a few strobes, so as to give the pile a little hold inthe ground, to make it stand firmly, the blows of the rammay be considered as commencing, and causing the pile tosink a little at every stroke, by which small successive sink-ings of the pile, the space the ram falls through will be suc-cessively increased by these small accessions, and the force ofthe successive blows proportionally increased. But these,on the other hand, are resisted and opposed by the frictionof the part of the pile which has been sunk before, and whichalso sinks at each stroke ; and as the quantities of these rub-bing surfaces increase in a greater ratio to each other, thanthe heights fallen through, that is, the resisting forces in-creasing faster than the impelling forces, it is manifest thatthe depths successively sunk by the blows must graduallydecrease by little and little every time ; which is also foundto be quite conformable to experience. Thus then the suc-cessive sinkings will proceed gradually diminishing, till theybecome so small as to be almost imperceptible.