G. F. Becker — Impact Friction and Faulting. 117 



those interested from a scientific point of view in structural 

 geology, and of those who desire to take advantage of such assist- 

 ance as theory affords for economical purposes. 



Plan of discussion. — While the extremely simple argument 

 as to the distribution of energy in a system of material sheets 

 in contact with one another and of the resulting geometrical 

 effects, which was offered in the paper on faulting referred to, 

 seems to me rigidly correct, the fact that friction plays a lead- 

 ing part in the problem lends it a somewhat unfamiliar char- 

 acter. It appears desirable, therefore, to subject friction itself 

 to a closer examination and to show that a study of the char- 

 acter of this force leads to results embracing those formerly 

 reached. Much of the material which will be presented in the 

 following pages was prepared for my former discussion, but 

 was omitted as not sufficiently germane to the subject of the 

 report in which it was included. I shall first make an attempt 

 to elucidate the distribution of energy in a rod, or any other 

 system in which the centers of inertia of the members are 

 arranged in the line of force, when subjected to an impact ; next, 

 to show that the results are immediately applicable to frictional 

 problems, and then that the same results may be reached inde- 

 pendently of any hypothesis as to the nature of a frictional sur- 

 face. Finally, these results will be applied to a characterization 

 of friction and their application to problems of structural geol- 

 ogy will be indicated. 



System of inelastic balls. — Suppose a series of inelastic bodies 

 of equal mass, arranged in a straight line, at rest and uncon- 

 strained. If the first of these masses is started at a velocity v 

 in the direction of its next neighbor, it will strike it, a loss of 

 energy will ensue, the two will move off together and impinge 

 upon the third, and so on. The loss of energy at each impact 

 can be extremely easily calculated from the principle of the 

 stability of the center of inertia of a system upon which no 

 external forces act. If M is the mass of the moving body, the 

 loss of energy when the first x bodies having coalesced and 

 moving as one mass strike the (x+1) body is say* 



2 x(x+iy 



the equation of a locus belonging to the class of hyperbolic 



* The momentum of the moving- mass is constant. If therefore v x is the 

 velocity with which x masses move after they have coalesced 



Mxv x =Mv, 

 and therefore 



v=xv x = (x + n)v x+n . 

 The kinetic energy of the moving mass before the x bodies strike the next is 



%— , and after they strike it 9 , .. , and the difference of these quantities is TV, 

 the energy expended. 



