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



form cross section with its axis placed parallel to X were arti- 

 ficially prevented from any deformation in planes parallel to 

 its terminal surfaces and one of these surfaces were strained 

 by a suitable stress into a position in which its central point no 

 longer coincided with the axis, the same differential equation 

 would express the distribution of energy. This result follows 

 quite independently of any analogy, but the steps necessary to 

 show it are a mere repetition of those given in detail for a 

 compressive strain. Now imagine such an elastic rod thus 

 strained to be suddenly intersected by any number of planes 

 parallel to its ends. If these surfaces presented no frictional 

 resistance the centers of inertia of the intervening sheets of 

 elastic material will have no tendency to move and they will 

 remain on the simple or composite logarithmic locus. Or sup- 

 pose them to present a frictional resistance independent of the 

 velocity. At the instant when the partings are formed the sys- 

 tem is in equilibrium and the center of inertia of each sheet 

 may be regarded as held in check by the forces exerted upon 

 it by its two neighbors. Two suppositions may then be made : 

 the frictional resistance may be conceived either as that pre- 

 sented by inelastic substances or as that presented by partially 

 elastic substances. (If the interlocking particles were wholly 

 elastic no motion would take place). In the former case no 

 energy could be transmitted from one sheet to the next and 

 the whole energy potentialized between the planes of the cen- 

 ters of inertia of two adjoining sheets would be expended 

 upon the contact between them and the curve of the centers 

 would coincide with that found when the surfaces are friction- 

 less. If the resistance is partially elastic, e remaining constant, 

 a certain proportion of the energy potentialized would be ex- 

 pended at each contact and the locus of the centers of inertia 

 would vary from the preceding only in the value of the con- 

 stants. 



Coefficient of friction — If, as in the experiments to be de- 

 scribed presently, a rigid mass W moves over a system of 

 sheets with a fixed quantity of energy, it will move precisely 

 as far as if the upper sheet of the system were fixed and no 

 energy were communicated to the remainder of the system. If 

 A is the distance which W moves and/ is the frictional resist- 

 ance per linear unit, the energy expended in friction is Af. 

 If the mass of W is M and its initial velocitv v and were the 



My 2 

 system of sheets totally inelastic, Af would equal -. Were 



the sheets wholly elastic (or more exactly wholly restitutional), 

 no energy would be expended in friction and there would be 

 no permanent deformation. (The whole energy would be first 

 converted into " molar" vibrations, and in any actual case 



