246 Equilibrium between Living and Dead Forces. 



at ri^ht angles to its direction, measuring a before the stroke, we 



have 



(a-\-x)wl 



W — - — ! — - — • 

 W_ bx 



If the friction on the sides of the wedge be just sufficient to 

 prevent its recoil, measuring a after the stroke, we have 



awl /-ni\ 



*~W (F \ u 



The results of equations A, B, C and D, the writer has roughly 

 tested by experiments made with small battens of yellow poplar 

 weighing one pound and under, clamped between boards and 

 driven by small weights of the same material varying from a 

 quarter to two pounds, falling heights from one to four feet, and 



£> 



H 



being in the direction of the fibres. All these experiments gave 

 results less than the equations, but some of the most successful 

 came within six per cent, of the calculated results. Equation 

 (E) also was roughly tested by experiment, and came still nearer 

 the calculated result. Equation F has not been tested. 



The reader will observe that several elements connected with 

 these propositions have not been considered in detail, the present 

 article being intended merely as an introduction to the subject. 

 Among the most important of these elements are those arising 

 from the elastic properties of all the materials concerned, 

 instance, it is quite evident that a metallic wedge driven by a 

 metallic hammer will penetrate when a wooden wedge, driv 

 by the same blow, would not, although the actual resistance to 



remains the same, and neither wedge undergoesper- 

 manent alteration in form, and each is considered as elastic, 

 will result from the difference in intensity of the impingemen * 

 which intensity will be inversely proportioned to the anioun 

 compression which takes place in the wedge and hammer 

 ing the impingement. Equation (E) will assist in this par 

 the investigation. t 



If the foregoing remarks should stimulate inquiry on the p^ 

 of others better qualified than the writer, to a degree at al P^ 

 portioned to the importance of the subject, his highest aim 

 be gratified. 



penetration 



Tins 



