Equilibrium between Livitig and Dead Forces. 24.5 



By similar process we prove that when a pile heavier ^'S- ^• 



than the ram is driven to the depth x by the ram iv, ^J a. 



falling through the height AC=a, if we subtract from 

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

 bound by perfect elasticity, we shall have for the dead 

 weight which will hold the pile in equilibrio, 



(a—h)w 



__JD 



When the ram and pile are of the same weight, the 



expression B becomes 

 aw 

 W=— (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 undergoes between the 

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

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



From the result at (C) we infer the following approximate 

 method of deriving by experiment the force lost in consequence 

 of such disturbing elements as the momentary yielding of the 

 substance penetrated by its elasticity, the alteration in form, 

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

 produced during their impingement, &c. ; viz. 



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

 until that height of fall is found at which the pile will just begin 

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

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

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

 to a nearly. 



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

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

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

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



W=:— -i-2z; . (E) 



For the wedge of unappreciable weight, considered without 

 friction on its sides, putting I for its length, and b for its thickness 

 at the heel, and considering the resistance as constant and acting 



Vol. xLvii, No. 2.— July-Sept. 1844. 32 



