ON MODES OF CHANGING THE FORMS OF BODIES. 173 



sure, however great, may be easily understood 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 sufficient 

 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 effect in driving it, but it would be absolutely impossible in practice 

 to construct machinery strong enough for the purpose, and if it were pos- 

 sible, there would be an immense loss of force from the friction. For ex- 

 ample, supposing a weight of 500 pounds, falling from a height of 50 feet, 

 to drive the pile 2 inches at each stroke ; then, if the resistance be con- 

 sidered as nearly uniform, its magnitude must be about 150 thousand 

 pounds, and the same moving power, with a mechanical advantage of 300 

 to 1, would perform the work in the same time. But for this purpose some 

 parts of the machinery must be able to support a strain equivalent to the 

 draught of 600 horses. In the pile driving engine, the forceps, or tongs, 

 sometimes called the monkey, or follower, is opened as soon as the weight 

 arrives at its greatest height ; and at the same time a lever detaches the 

 drum, employed for raising the weight, from the axis or windlass, at which 

 the horses are drawing ; the follower then descends after the weight, un- 

 coiling the rope from the drum, and the force of the horses is employed in 

 turning a fly-wheel, until the connexion with the weight is again restored. 

 (Plate XVIII. Fig. 284.) 



When we throw a stone, or a missile weapon of any kind, with the hand, 

 the stone can acquire no greater velocity than the hand itself, accompanied 

 by the neighbouring part of the arm ; so that the whole velocity must be 

 produced in a mass of matter comparatively very large. A sling enables 

 us to throw a stone or a ball much further ; for here the stone may be 

 moved with a velocity far greater than the hand that impels it, although 

 the action of the force on the stone is indirect, and the resistance of the air 

 considerable. An elastic bow, furnished with a strong and light string, 

 enables us to apply to an arrow or to a ball the whole force of our arms, 

 unencumbered with any considerable portion of matter, that requires to be 

 moved with the arrow ; hence a very great velocity may be obtained in 

 this manner. An air gun possesses the same advantage in a still greater 

 degree, and the force of fired gunpowder excels perhaps all others from its 

 concentrating an immense force in the form of an inconceivably light elastic 

 fluid ; of course a ball impelled by this force, becomes a most effectual 

 instrument in penetrating the most refractory substances. We may easily 

 calculate the velocity of an arrow, by comparing its motion with that of a 

 pendulum, if we know the proportion of its weight to the force that bends 

 the bow ; including in the weight a small addition for the inertia of the 

 bow and bowstring ; the height to which the arrow will rise, being about as 

 much greater than the space through which the bowstring acts on it, as the 

 greatest force applied in drawing the bow is greater than twice the weight 

 to be moved. 



