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



finite compressible rod. In the latter case I have shown that 

 the energy of an impact is to be regarded as divided into two 

 portions acting from opposite directions upon the passive mass 

 and that the energy curve is a projected catenary, while if the 

 strain is proportionate to the stress, the geometrical result is of 

 the same character. In the same way, if a finite system of sheets 

 rests on a rigid mass and the topmost sheet is moved against 

 friction by an impulsive application of force, this force is to be 

 regarded as decomposed into two shearing stresses acting on the 

 upper and under surfaces respectively in opposite directions. 

 The energy curve is the same as for a rivet, but the geometri- 

 cal result differs because, as the rivet may be conceived as at 

 first forming part of an infinite rod and then as receiving the 

 energy which would be distributed over the whole mass beyond 

 the point x=a from the opposite direction, so a finite system of 

 sheets is to be regarded as at first of infinite thickness and ar- 

 ranging itself on the simple logarithmic curve and then as re- 

 ceiving the energy potentialized beyond x=a in a direction 

 parallel to that of the original impulse, but differing from it by 

 an angle of 180°. If the strain is proportionate to the stress, 

 the geometrical result will clearly be a curve of the form 



y = A (e~ x / c — £ x / c ) } 



the origin being taken at the point of inflection which will be 

 on the same ordinate as the horizontal point of the energy curve. 



There is a corresponding difference between the results 

 of the impact of two compressible masses and the mutual 

 action of two systems of sheets, if the two systems move rela- 

 tivety on the only plane common to both. In each case the 

 energy curves of the two systems will meet in a salient point 

 on a line corresponding to the contact plane. For the imping- 

 ing compressible masses the geometrical result will be of the 

 same character as the distribution of energy. The two systems 

 of sheets on the other hand will arrange themselves on two 

 (simple or composite) logarithmic curves with opposite curva- 

 ture, so that if the material of the two systems is the same the 

 junction will be a point of inflection instead of a salient point.* 



A similar reversal takes place in certain cases of what may 

 be called negative impact. If an iron rod is brought in con- 

 tact with the surface of a mass of melted glass and withdrawn, 

 the thread obtained will be logarithmic (for evidently dw will 

 equal minus wdx). If instead of an iron rod a glass rod is 

 substituted, and this is allowed to remain in proximity to the 

 heated mass long enough to become somewhat softened, the 

 hot end of the glass rod will be drawn down by the resistance 



* The subject is treated at length and illustrated in Geology of the Comstock 

 Lode, p. 173, et seq. 



