G. F. Becker — Impact Friction and Faulting. 125 



and this gives an expression for e a ' c which makes 



£ 2a / c =(^+l)^((«+l)^-l). 



If the origin is removed to the base of the ordinate of the hori- 

 zontal point of the curve the equation may be written 



mv* s- x /° + e x / c mv* e~ x / c + s x / c 



10 = 



2 s a/c 2 f/lc^a/c^ 



^ X/C , gJC/C 



- (n + l)-»T((n + l)— -l) T 



the equation of a " projected catenary." If the strain is pro- 

 portional to the stress, this corresponds to the form assumed by 

 a cold rivet, and it is under this law that the head of a drill 

 spreads in use. For n=l the equation assumes the simple 

 form 



w = mv 2 s ~ x / c + £ X//c . 

 ~2~ 2^3 



Application to incompressible masses. — The problem of the dis- 

 tribution of energy in a finite or infinite cylinder, compressible 

 in the direction of its axis only and subjected to an impact or a 

 constant force, thus appears capable of entirely satisfactory 

 solution on the supposition that the transmission of energy is 

 instantaneous. The conditions as to compressibility answer to 

 those of a gas confined in a rigid cylinder and are not those of 

 solids. But since solid masses act as though concentrated at 

 their centers of inertia, the formulas deduced are applicable to 

 the positions of the centers of inertia of incompressible elastic 

 or inelastic bodies. They therefore also represent completely 

 the distribution of energy in incompressible rods capable of 

 lateral deformation for infinitely small strains produced by 

 impact, and approximately for small but finite strains. For 

 constant forces acting in parallel lines or from a center at an 

 infinite distance, in short when the equipotential surfaces are 

 planes, the equations appear to represent the distribution of 

 energy even for finite strains. 



The character of the divergence when the equipotentials are 

 not planes, or for central forces, is best seen by taking the 

 extreme case of an impact acting at a point in the center of a 

 thin sheet of elastic or inelastic material. Here the energy 

 w'll be distributed at right angles to the direction of the impact, 

 and the mass of matter over which it is distributed instead of 

 increasing with x will increase with td* 2 . If this area is denoted 

 by 2, and if the sheet is supposed infinitely thin or of finite 



