G. F. Becker — Impact Friction and Faulting. 127 



energy not returned must be employed in producing elastic 

 vibrations of the body struck. Messrs. Thomson and Tait 

 therefore call the coefficient representing the relation of the 

 velocities the coefficient of restitution instead of the coefficient 

 of elasticity as it has commonly been designated. If this 

 coefficient is e, the coefficient of energy potentialized is express- 

 ed by 1 - e 2 . If an infinite series of bodies, say spheres, not 

 wholly inelastic, receive an impact they will be compressed as 

 if totally without elasticity, a portion of the energy received 

 by each will be expended in permanent deformation and in 

 vibration and each will recoil with less force than that with 

 which it was compressed. Now if e is constant for the system, 

 the same proportion of the energy received by each member 

 of the sj^stem (viz : 1— e") will be expended in it; and as the 

 quantities of energy received stand as has been shown in a 

 geometrical ratio, so also will the quantities of energy ex- 

 pended. The coefficient e is not constant for partially elastic 

 bodies and so far as I know it has been but little studied. 

 There is reason to suppose, however, that it varies slowly with 

 the velocity and that it is therefore approximately the same for 

 similar bodies within considerable ranges of velocity. 



Passage tofrictional sheets. — Having discussed the distribution 

 of energy in a finite or infinite system when the centers of 

 inertia are rectilinearly arranged in the direction of the active 

 force and endeavored to check the results by reference to ex- 

 perience, I now pass to the application of these results to 

 friction. Impinging bodies may be given any desired .form 

 under proper restrictions. Suppose for example a series of 

 inelastic plates like the following : 



let them be restricted to motion in horizontal planes and pass 

 over one another without friction. If the first of this series is 

 started in the direction of its neighbor and the system is left to 

 itself, the momentum will remain constant, the energy intro- 

 duced into the system will be distributed over the whole infi- 

 nite series and, in short, the distribution of energy in a direc- 

 tion vertical to the line of motion will be exactly the same as 

 it has been found to be for a rod in the line of force. Instead 

 of a single lug at the extremity of a sheet an indefinite number 

 of small teeth may be supposed to be distributed over the sur- 

 faces of the sheets, and if these teeth are very minute in size 

 and very numerous, a frictional surface as I understand it is 

 the result. It might for an instant seem an objection to this 

 supposition that as such sheets pass over one another the teeth 

 will be ground off and the frictional resistance will diminish. 

 This fact however affords an argument in favor of the truth 



