G. F. Becker — Impact Friction and Faulting. 205 



system, sufficient friction can be induced by fastening round 

 it paper of the same kind used for the sheets. The resulting 

 curve is the same as that produced by applying the edge at 

 right angles to the direction of motion. 



In experiments with slips of paper it is easy and desirable 

 to apply the pressure and draught mechanically, although an 

 excellent coincidence with the logarithmic curve can be ob- 

 tained with a ruler merely held in the hand. If in mechanic- 

 ally conducted experiments the velocity is about that which 

 one would naturally employ in a trial by hand, say six or eight 

 inches per second, the coincidence with the logarithmic curve 

 is almost perfect.* If, however, by a very light pressure and 

 slow mechanical movement with an edge or soft blunt point 

 the uppermost sheet is given an extremely slow motion so that 

 the rate of movement of say the tenth sheet is scarcely percep- 

 tible, the curve produced has a subtangent which increases 

 rapidly from the first sheet onward. So also must therefore 

 the quantity I have called v and with it the coefficient of kin- 

 etic friction for these extremely low velocities, or as the value 

 of the statical coefficient is approached. Judging from this 

 indication it would appear that a good empirical approximation 

 to the relation of k to v might be obtained by adopting the 

 tractory (or "anti-friction" curve h — c e~ s ' c ) rather than the 

 hyperbola to represent experimental results, but the value of 

 Jc in terms of v might then be too complex for practical use. 

 The value of the coefficient of restitution indicated by experi- 

 ments on paper is as it should be, very high. In my former 

 paper I noted a case in which fi was 1*4. This answers to 

 €=•81. With other qualities of paper I have obtained values 

 of fi. indicating a restitution of considerably above 90 per 

 cent. 



Conclusions reached. — In the foregoing pages the attempt has 

 been made to approach the subject of friction as a problem in 

 elasticity. I began by discussing the distribution of energy in 

 an elastic compressible rod and showed that this is represented 

 in general by the simple equation w = cW. Applications 

 of this equation to some special cases were made and some of 

 the modifications necessary for incompressible substances were 

 pointed out. By regarding friction as the impact of the minute 

 inequalities of material surfaces, a passage was effected from 

 impact to friction and from a compressive to a shearing strain. 

 The significance of Morin's laws under this supposition was 

 enlarged upon. It was then shown that the same conclusions 

 followed independently of the physical hypothesis adopted, a 

 fact regarded as confirmatory of this hypothesis. It was at last 



* See Geol. Comstock Lode, p. 167, fig. 4.. 



