G. F. Becker — Impact Friction and Faulting. 199 



would pass over by friction against the atmosphere, internal 

 friction, etc., into molecular energy). If the system is partially 

 restitutional it is clear that 



/.A = ^-(l-e 2 ), 



where e is the coefficient of restitution for velocity and (1 — e 2 ) 

 the coefficient of expended energy. If Tc is the coefficient of 

 friction and the normal pressure is Kg (where g is the accelera- 

 tion of gravitation if the pressure in the system is due to the 

 weight of the mass "W, or a corresponding velocity if the pres- 

 sure is otherwise induced), 



f=kMg, 



1 e 2 



andifA=l Jc = v* , 



2g ' 



so that the coefficient of friction may be reduced to two deter- 

 minable velocities and the coefficient of restitution. Here how- 

 ever the extent to which the inequalities of the frictional surfaces 

 overlap is supposed constant, or the elasticity of the rubbing 

 masses considered as represented by their centers of inertia, is 

 not taken into account, nor shall I attempt to discuss it. 



The equation of the distribution of energy in an infinite sys- 

 tem of sheets will then be 



My 2 1-e 2 _ x/c 

 2 c ' 



c being the subtangent. If the coefficient of friction is uni- 

 form throughout the system, the differences of the movements 

 of successive sheets will be in precisely the same ratio as the 

 absolute movement of the sheets, so that if y is the distance 

 moved by any sheet and ju the ratio of the movement of adjoin- 

 ing sheets, 



y = As ~ x / c = A/x ~" x . 



For this case therefore 



f__ w _ Mv^_ 1 — e 2 

 c y 2 Ac 



The frictional resistance being uniform its actual value will 

 affect the zero value of w, while p. and c are entirely indepen- 

 dent of f, or, if the subscript indices 1 and 2 are used to indi- 

 cate successive sheets^in any portion of the system, 



and /appearing both in the numerator and denominator does 

 not affect p. so long as / is constant. On the other hand if 



