STRUCTURAL RESULTS OF FATTLTING. ] 59 



given instances from which it appears certain that friction, like other forces, 

 may cause or accelerate motion as well as retard it. He does not, liowever, 

 explain how positive forces I'esiilt from friction. 



Transmission of energy by friction. — Material surfaccs are distinguished from 

 mathematical planes by the presence of minute projections and depressions. 

 If a material sheet W is forced to move over a sheet Pj, the ])rojections 

 interlock, and if the sheets are prevented from moving in the direction of 

 the normal to their contact plane, the projections must either be ground ofl' 

 or be bent and compressed. If W begins its motion with a fixed quantity 

 of energy, and if P^ is fixed, the entire energy will ultimately be expended 

 in heat, sound, etc., on the contact. But if Pj is movable a portion of the 

 energy of W will be communicated to P„ because the projections on the 

 under surface of W exert a pressure on those presented by the upper sur- 

 face of Pi, which is either in the direction of the motion of W or which may 

 be resolved into two pressures, one of which is in the direction of the 

 movement and the other normal to the contact plane. 



Distribution of energy through a system of sheets. If Pj is iu COUtaCt with a tllird plate 



or sheet P, the energy received by Pj will be expended wholly or in part 

 in overcoming tke resistance on the contact Pj Pj. If these sheets are the 



earlier members of a series of sheets W, P„ P2, P3, , of indefinite 



number, then each sheet which moves will communicate a certain amount 

 of energy to the next, and since the resistance of friction is proportional to 

 the distance through which it acts, each sheet which receives energy from 

 its predecessor must move. 



Thevelocitiesof moving sheets maybe treated as uniform. SuppOSC a SyStem of CqUal 



sheets of indefinite extent vertically arranged and terminated at the top 

 by the horizontal plane A B. Let the system be under a compressive hori- 

 zontal pressure. If, through the action of some external force, W rises 

 through a distance h, it will communicate a certain energy to Pj, which will 

 in turn impart energy to P2, and so on. Since the sheets are in all respects 

 alike and the pressure at each contact is the same, the frictional resistance 

 or negative force at each contact will also be the same, while, as more oi- 

 less vibration must always accompany faulting, the friction of quiescence 

 does not need to be taken into consideration ; but as energy is dissipated at 



