Equilibrium between Living and Dead Forces. 



245 



By similar process we prove that when a pile heavier F 'g- 3. 

 than the ram is driven to the depth x by the ram w, 



a, if we subtract from 



falling through the height AC 

 AC the height DC=h, to which the ram would re- 

 bound by perfect elasticity, we shall have for the dead 

 weight which will hold the pile in equilibrio, 



W 



h)w 



x 



When the ra 



expression B becomes 



(C) 



, C 



W 



aw 



x 



(D) 



In this and the two preceding cases, the height a is 

 to be measured before the stroke is made, because the draw does 

 not act upon the pile by its own weight through the distance x. 

 Therefore, all the difference which W unde w 

 results of equations (A) and (D) can never exceed the weight of 

 the ram w, regarding the ram and pile as elastic bodies. 



Frc>m the result at (C) we infer the following approximate 

 method of deriving by experiment the force lost in consequence 

 °* such disturbing elements as the momentary yielding of the 



the alteration in form, 



penetrated 



Aether permanent or not, of the body driving and body driven, 

 produced during their impingement, &c. ; viz. 



^et the ram, for instance, be let fall from several small heights, 

 un «il that height of fall is found at which the pile will just begin 

 10 penetrate farther. Call this small height k, the whole work- 



o height being a, we shall then obtain a useful effect which 



be to that obtained by the appropriate formula as(a-k) is 

 to « nearly. 



lf a bar of unappreciable weight, perfectly elastic till broken, 

 s objected to pressure or is broken by a dead weight W, pro- 

 Ucin g a deflection x, and the same effect is produced by a weight 

 > falling the height a, measured before the stroke, we have 



W 



2aw 



+ 



(E) 



. 0r the wedge of unappreciable weight, considered without 

 c ion on its sides, putting / for its length, and b for its thickness 



the 



Vol. 



s me resistance as cuusuiui and 



o 



Sl *ii, No. 2.— July-Sept. 1844. 



32 



