242 Equilibrium between Living and Dead Forces. 



in driving piles shows that a certain pressure may put a certain 



»# 



percussion in equilibrio. 



" One of the circumstances which creates the greatest diffi- 

 culty in the theory of the wedge, is the very heterogeneous na- 



ture of the resistance, and the force or power by which it is 



overcome. The resistance is generally tlflt modification of force 

 called pressure. The power which is opposed to the resistance 

 is commonly that species of action called percussion. These 

 are modifications of force so totally different as not even to ad- 

 mit of comparison. It has been generally thought that there is 

 no blow or impact, however slight, which will not overcome a 

 pressure or resistance however great. From which it would 

 seem to follow, that an infinitely small impact is equivalent to 

 an infinitely great pressure. Be this as it may, however, the 

 great difference between these modifications of force is suffi- 

 ciently evident to demonstrate the total impossibility of estab- 

 lishing the condition of equilibrium of a machine in which the 



power 



force of the other species."f 



With the view of presenting this subject in as familiar a man- 

 ner as possible, let us consider the case of the pile, regarding i 

 for the present without weight or vis inertias, and as resisting per- 

 cussion by friction alone, considered as a constant retarding torce. 

 We may, without error, suppose this friction to exert a retarding 

 force in all respects similar to an imaginary force equal to t e 

 friction, and acting as gravity, only in an opposite direction a 

 with greater energy. Let this imaginary force be called W , a rl 

 the distance through which it acts upon the ram be called x. 

 Now it is evident that if the force W be permitted to react upon 

 the ram through the same distance x, through which it was ac 

 ed upon by the ram in its descent, it will, like gravity, genera e 

 the same velocity in the ram which it had at the instant of pe 

 cussion. It is also evident, that if this force be opposed by a 

 dead weight equal to its effort to move the ram, it would be 

 in equilibrio by such dead weight,* and no motion could ensue 

 after such a state of rest had been established. 



* Sganzin's Civil Engineering, p. 123,— a work of high reputation, an < . 

 in the Royal Polytechnic School in Paris, and the United States Military 

 my at West Point. 4 ■ *fc 



t Natural Philosophy, No. 1, Library of Useful Knowledge, p. 43, Baldwin 

 Cradock, 1629. 



