ON MODES OF CHANGING THE FOllMS OF BODIES.

greater as the edge is thinner. The resistance opposed by a solid, or evenh y a soft substance, to the motion of a body tending to penetrate it, appearsto resemble in some measure the force of friction, which is nearly uniform,w hether the motion be slow or rapid, destroying a certain quantity ofMomentum in a certain time, whatever the whole velocity may be, or what-ever may be the space described. Hence arises the advantage of giving aSreat velocity to a body which is to penetrate another, the distance to whicha b °dy penetrates being as the square of its velocity, or as its energy ; and aCc 'tain degree of energy being required in order to make it even penetrate atIt is true that when we exchange a slow motion for a more rapid one, bytbe immediate action of any mechanical power, we can only obtain the sameeilei 'gy from the same power, for we must diminish the mass in the same pro-P°ftion as the square of the velocity is increased ; but a very small part of thelCe > which is consumed in the operation of a machine of any kind, is em-Idoyed

in generating momentum; hy much the greatest part is spent in over-timing resistances which vary but little with the velocity; a small portionof the resistance increasing in proportion to the square of the velocity;that by applying a triple force, we may obtain more than a double velocity,m ore than a quadruple effect: and besides it has already been observedj at "'hen the velocity begins to exceed a certain limit, the effect is increasedd much greater proportion than that of its square. The same work is alsoVe] °!‘ med w *th less pressure, and less strain on the machinery, where a greatin Cl ^ * S em P lo yed. It is on account of the efficacy of velocity, in facilitat-P & Penetration, that soft substances, moving very swiftly, will readily per-rnucb harder ones; and for the same reason a gunshot wound, and^ the loss of a limb, takes place with so little disturbance of the neigh-^ ln g parts, that it is sometimes scarcely felt. The advantage of an impulse,J^Vever inconsiderable, above a pressure, however great, may be easily undcr-t 0(1 from the ease with which a moderate blow of a hammer causes a nailv P Cr >etrate a substance, into which the whole force of the arm could nothaVe thrust it.

Cn gine for driving the piles, or upright beams, used for the founda-a c °! bui hlings in water, or in soft ground, the weight is raised slowly toe Her Sl< e,ab ^ e height, in order that, in falling, it may acquire sufficientP°\ve f ° P r °P e * the pile with efficacy. The same force, if applied hy very11 machinery immediately to the pile, would perhaps produce an equal

u l., j

eg