G. F Becker — Impact Friction and Faulting. 121 



or in general, 



W=A(e- x / c -€- 2a /°£ x / c ). 



Here $— 2a / c is independent of A, and the latter retains the same 

 value even when a = cc, or when the passive mass is infinite. 

 In this case of course the entire energy of the system is poten- 

 tialized (or expended if the material is inelastic). If m is the 

 mass which the unit volume would possess were it compressed 

 to the density which the impact produces at the face of the 

 infinite rod and if c is so chosen that cm = M. 



uu 



/ 



niv c 

 wdx=Ac=~7T~ i 



o 



_ mv 

 or 



10= €~ x / c . 



2 



It will be convenient to retain for c the signification which it 

 assumes when the passive mass is infinite because of the simple 

 relations which it then bears to the energy of the impinging 

 body. The unit chosen in any case is of course entirely 

 arbitrary, but the results are much simplified by establishing 

 some rational relation between the units adopted for different 

 cases. Let the product of the entire energy potentialized in 

 any case into the corresponding unit be a constant; then if V 

 is the energy potentialized in an infinite rod, and V, the energy 

 potentialized in a finite rod, Vc~V 1 c v or 



n + 1 



so that the equation for a finite rod may be written 



Now for n = go, c t = c, and therefore the value of A already 

 found is valid for the new equation. From 



w== n ^l( £ -x/c l _ £ -la/ci e x/c 1 ). 

 it follows that 



/^-^(l-^O^— — • 



J(j wax— 2 \i / — 2 n + 1 



Eeintroducing the value of c in terms of c„ it will readily be 

 seen that 



e a / c ^=n + l, 

 a value which can also be otherwise obtained. This also gives 



It r. Ct,/Cl\ 



C,(l — £ ' )=1C. 



The equation of the distribution of energy in a finite rod, 

 Am. Jour. Sci.— Third Series, Vol. XXX, No. 176.— August, 1885. 



