358 A. S. Kimball— Laws of Friction. 



I have been able to verify experimentally the law stated 

 early in this paper in the following cases : wood sliding on 

 wood, wood on iron, leather on in mi. zinc on iron, and copper 

 on iron ; and to obtain results verifying the first half of the 

 law in the case of leather on wood. 



The experiments above detailed make it easy to ex 

 various results obtained by the three authorities quoted at the 

 beginning of this paper. Morin experimented under conditions 

 which gave him a coefficient very near the maximum, and thus 

 his results are approximately constant. Bochet experimented 

 with railway trains, his conditions were high speeds, hard 

 rubbing surfaces, and great intensity of pressure. All these 

 circumstances are favorable to the result he obtained, namely, 

 a coefficient decreasing as the velocity increases. Hirn, on the 

 other hand, employed very light pressures, less than two pounds 

 on a square inch, and kept his rubbing surfaces so t ion>u-hh 

 is between oil and oil instead of 

 two metal surfaces; his speeds were not very great. These 

 conditions. are precisely the ones I have found' favorable to the 

 results he reached, — a coefficient, increasing as the velocity 

 increases. It would be very easy to form a theory which 

 would account for the- variation of friction with the velocity, 

 under the rule I have given. 



It is well known, that if a given deflection in a bar is pro- 

 duced by a weight acting for five seconds, for exam] 

 the same deflection may be produced, by a less weight, acting 

 for a longer time. Now, as the force required to overcome 

 friction is. partially at least, expended in bending down the 

 minute irregularities on the surface of the rubbing bodies, it 

 becomes evident how, other things being equal, a rapid motion 

 would call for the exertion of a greater force than would he 

 required if the motion were slow. 



On the other .hand, the longer two surfaces under pressure 

 are in contact the greater must be the interlocking of the irregu- 

 larities upon the rubbing surfaces. On this account a rapid 

 motion would not require the expenditure of so great a force to 

 overcome the friction. Thus, we have two effects, varying 

 with the velocity, but having opposite signs. Now it is not 

 probable, from the nature of the case, that these effects are 

 'qua!, or even proportional, and thus we can, at 

 are favorable to the existence 

 of a maximum resultant effect. Having, however, ascertained 

 the fact by experiment, the explanation becomes a matter of 

 minor importance. 



It may be said that these facts have no practical importance 



at the velocities ordinarily employed. I would call attention 



a the veloc- 



t the velocities ordinarily employed. I 

 > Table V, where it will be seen that by 



