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



curves. It is clear that W does not become zero until x = oo, 

 and consequent^ the energy is distributed over an infinite 

 series of masses. The equation accounts for the entire energ}^ 

 and no more for 



00 1 



2 — =1 



1 x(x-\-l) 



This equation does not accurately represent the distribution of 

 energy in the system ; for when x bodies strike the next in the 

 series, although most of the energy will be expended at the 

 contact, a portion will be propagated backward, and work will 

 be done at previous contacts as well. On the other hand, it 

 demonstrates that the distribution of energy in such a s}' , stem 

 may be discussed entirely apart from the effects which the 

 energy exerted at any point produces upon the material of the 

 system. If the masses of the members of the system remain 

 constant, their density may vary regularly or irregularly with- 

 out affecting the above equation. If two or more of the equal 

 members of the system were joined together before impact, 

 this would not in any way affect the distribution of energy, so 

 that the equation holds good for bodies of which the mass 

 varies regularly or irregularly, provided that x varies as the 

 mass. 



Distribution of energy in finite masses. — The transmission of 

 energy in solids or liquids is not instantaneous. It follows that 

 if two elastic bodies of the same material, but of unequal 

 length, meet one another, a portion of the energy is converted 

 into vibration. This is not the case with inelastic bodies, 

 which remain permanently in the condition of maximum 

 deformation. The transmission of energy however is extremely 

 rapid, and Messrs. Thomson and Tait estimate that the entire 

 impact of two balls a yard in diameter of copper, glass or 

 steel, occupies a period within the thousandth part of a second. 

 I shall consider the transmission instantaneous. On this sup- 

 position the centers of inertia of equal masses of a form varying 

 from that of a cylinder will behave like the centers of inertia 

 of such cylinders, and the distribution of energy among the 

 centers of inertia in a rectilinear series of balls (for example) 

 become reducible to that in a cylinder of invariable cross sec- 

 tion but compressible in the direction of its axis. The distri- 

 bution of energy in a perfectly elastic mass of constant temper- 

 ature at the moment of maximum compression is also that 

 which would be produced by the action of a constant force of 

 appropriate intensity on the same body. It represents too the 

 permanent effect of an impact upon a perfectly inelastic mass, 

 so that the solution of one of these cases is the solution of all 

 three. 



