G. F. Becker — Impact Friction and Faulting. 197 



friction is independent of velocity not being rigidly correct 

 however, if two partially elastic sheets are in contact one of 

 them may as a matter of fact receive an impulse so slight that 

 the elastic resistance of the interlocking projections will not be 

 overcome. An elastic strain but no motion on the contact 

 plane will be the consequence. 



Independent kinetic theory of system of sheets. — While there 

 thus seems every reason to suppose that friction is the resist- 

 ance due to the impact of the minute projections which dis- 

 tinguish material surfaces from mathematical planes, the kinetic 

 theory of a system of sheets is not dependent upon it, but 

 merely upon the existence of some resistance which allows of 

 relative motion yet converts "molar" energy into molecular 

 energy. Whatever may be the nature of this resistance it can- 

 not conflict with the principle of the stability of the center of 

 inertia of a system upon which no external forces act and it is 

 a necessary conclusion that, if no obstacle exists to intercept 

 the transmission of energy, the motion of the first of an in- 

 finite series of sheets necessitates the motion of all. If these 

 sheets are infinitely thin as well as infinite in number, the 

 diminution of the energy between two successive surfaces, or 

 dw can be neither more or less than wdx, and the distribution 

 of energy is simply logarithmic. The argument may be ex- 

 tended to the case of a finite system of sheets exactly as the 

 behavior of a finite rod under compression was inferred from 

 that of an infinite rod. In short 



tfdfw 



=. 10. 



dx* 



But if the results derived from the consideration of friction as 

 mere resistance of unknown character coincide mathematically 

 with those deduced from considering friction as a form of im- 

 pact, this conclusion is certainly strongly confirmatory of the 

 physical hypothesis. 



Elastic mass under shearing strain. — Exactly as a series of 

 inelastic cylinders in contact (or an inelastic rod) and a similar 

 series of elastic cylinders accurately coincide in behavior dur- 

 ing the period which elapses between the first contact of an 

 impinging mass and the moment of maximum compression, so 

 also does the behavior of a series of sheets in contact repre- 

 sent the behavior of a solid completely elastic mass. In other 

 words precisely as the energy actually expended in the deforma- 

 tion of inelastic substances during an impact ma}' be conceived 

 as potentialized, so also may the energy expended in friction 

 be treated as potentialized. This statement which is almost 

 self-evident has ample authority.* If an elastic rod of uni- 

 * Thomson & Tait, Nat. Phil., 1st ed., § 452. 



