126 G. F Becker — Impact Friction and Faulting. 



thickness and infinitely little strained, the distribution of energy 

 will be represented by 



w_ £-*/*-- s^A* 



The resulting depression will be a figure of revolution, and if 

 the strain and stress are simply proportional, the curve gener- 

 ating this figure will be of the form 



£ — b/2c, _ € x/2d 



c, — n + l 



This result can be at least qualitatively tested by experiment. 

 For this purpose I clamped a thin sheet of elastic rubber to a 

 block of wood by a metal ring, and inserted a pointed instru- 

 ment from beneath the block through a vertical hole at the 

 center of the ring. The rubber was of course strained to 

 conoidal shape, which was more or less sharply pointed accord- 

 ing to the pressure. It was found that the generating curves 

 for various pressures sensibly coincided with curves plotted 

 from the above equation for various values of n. A form of 

 the same character must be produced when a pointed instru- 

 ment is being driven through a metallic sheet, just before pen- 

 etration. 



It is now easy to see the general character of the deformatiou 

 which takes place when two spheres strike one another. If 

 the sphere is supposed divided into segments of equal mass by 

 planes at right angles to the direction of the impact, and each 

 mass is considered as concentrated at its center of inertia the 

 energy potentialized will be distributed among these centers as 

 in a compressible finite cylinder. The plane section however, 

 will not remain plane but will be indented in the direction of 

 the force. At the point opposite that at which impact takes 

 place, the surface will remain spherical while the contact of the 

 two spheres will be a plane. An exact analysis of this case 

 would probably be somewhat complex. 



Effect of imperfect restitution. — Certain comparisons may 

 easily be made between the behavior of totally inelastic or 

 totally elastic bodies as hitherto treated and actual matter 

 which is neither absolutely elastic nor perfectly plastic. 

 Except under conditions which cannot be realized in practice, 

 a portion of the energy received by any one of a series of 

 bodies from an impact is always expended in internal work. 

 Newton found that when the impact is not violent enough to 

 produce sensible permanent deformation, the relative velocity 

 of impinging bodies, after impact bears a proportion to their 

 relative velocity before impact which is constant for the same 

 two bodies. It is well known that at least a part of the 



