ON MODES OF CHANGING THE FORM% OF BODIES. 225 



greater as the edge is thinner. The resistance opposed by a solid, or even 

 by a soft substance, to the motion of a body tending to penetrate it, appears 

 to resemble in some measure the force of friction, Avhich is nearly uniform, 

 whether the motion be slow or rapid, destroying a certain quantity of 

 momentum in a certain time, whatever the whole velocity may be, or what- 

 ever may be the space described. Hence arises the advantage of giving a 

 great velocity to a body which is to penetrate another, the distance to which 

 a body penetrates being as the square of its velocity, or as its energy ; and a 

 certain degree of energ-y being required in order to make it even penetrate at 

 all. It is true that when we exchange a slow motion for a more rapid one, by 

 the immediate action of any mechanical power, we can only obtain the same 

 energy from the same power, for we must diminish the mass in the same pro- 

 portion as the square of the velocity is increased ; but a very small part of the 

 force, which is consumed in the operation of a machine of any kind, is em- 

 ployed in generating momentum ; by much the greatest part is spent in over- 

 coming resistances which vary but little with the velocity ; a small portion 

 only of the resistance increasing in proportion to the square of the velocity; 

 so that by applying a triple force, we may obtain more than a double velocity, 

 and more than a quadruple effect: and besides it has already been observed 

 that when the velocity begins to exceed a certain limit, the effect is increased 

 in a much greater proportion than that of its square. The same work is also 

 performed with less pressure, and less strain on the machinery, where a great 

 velocity is employed. It is on account of the efficacy of velocity, in facilitat- 

 ing penetration, that soft substances, moving very swiftly, will readily per- 

 forate much harder ones ; and for the same reason a gunshot wound, and 

 even the loss of a limb, takes place with so little disturbance of the neigh- 

 bouring parts, that it is sometimes scarcely felt. The advantage of an impulse, 

 however inconsiderable, above a pressure, however great, may be easily under- 

 stood from the ease with which a moderate blow of a hammer causes a nail 

 to penetrate a substance, into which the whole force of the arm could not 

 have thrust it. 



In the engine for driving the piles, or upright beams, used for the founda- 

 tions of buildings in water, or in soft ground, the weight is raised slowly to 

 a considerable height, in order that, in falling, it may acquire suthcient 

 energy to propel the pile with efficacy. The same force, if applied by very 

 powerful machinery immediately to the pile, would perhaps produce an equal 



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