on a new Friction Sledge for stopping Railway Trains. 231 



From the remarkable agreement of all these results, I think we are entitled to 

 assume, that equation (4), or its equivalent <& = 0, is fully £stablished. 



In order to determine the lowest velocities for which equation (4) might 

 be considered proved, I added to the third and fourth series of experiments a 

 set of experiments, the object of which was to ascertain the point from which 

 the waggon should be allowed to descend, so as just to move the Friction Sledge. 

 The result of these trials -was as follows: ° 



Substituting these expressions in equation (4), and replacing A by -1681 

 and -1491 on the third and fourth days respectively, we obtain 



K = -031 1, K = -0310. 

 The agreement of these results with (5) is sufficient to prove, that the equation 

 Irom which they are deduced is true for velocities as low as 3 feet per second 



The experimental truth of equation (4) being thus established, the results 

 obtamed from the foregoing series of experiments may be briefly summed up as 

 follows : ^ 



1st The momentum possessed by the waggon at the moment of impact on 

 the bledge is destroyed by two causes, which may be considered separately first 

 the loss of momentum occasioned by the shock itself, and the adhesion of the 

 Sledge to the rails; this I have called the Friction of Rest: secondly, the lo«s 

 of momentum which takes place after the Sledge is set m motion, caused by 

 friction against the rails ; this is the Friction of Motion. 



2nd The friction of rest is directly proportional to the pressure against the 

 rails, and to the velocity of impact, jointly. 



3rd. The friction of motion is directly proportional to the pressure against 

 the rails, and is independent of the velocity. 



