246 Equilibrium between Living and Dead Forces. 



at right angles to its direction, measuring a before the stroke, we 

 have 



bx 

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

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



w=|^ (F) 



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 

 driving the battens from | to IJ inches at a blow, the motions 

 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. For 

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

 metallic hammer will penetrate when a wooden wedge, driven 

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

 penetration remains the same, and neither wedge undergoes per- 

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

 will result from the diff"erence in intensity of the impingements, 

 which intensity will be inversely proportioned to the amount of 

 compression which takes place in the wedge and hammer dur- 

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

 the investigation. 



If the foregoing remarks should stimulate inquiry on the part 

 of others better qualified than the .writer, to a degree at all pro- 

 portioned to the importance of the subject, his highest aim will 

 be gratified. 



