Bodies ajfecled by Friciion. \ % r 



PROPOSITION II. 



l^et the body be projedled on an horizontal plane LM (fig. 3.) 

 with a given velocity^ to deter^nine the fpctce through -which the 

 body zvill move before itjlops, or before its motion becomes uniform. 



Case I. i. Suppofe the body to have no rotatory motion 

 when it begins to move; and let ^ = the velocity of proje6iion 

 per fecond meafured in feet, and let the retarding force of the 

 fridion of the body, meafured by the velocity of the body 

 which it can deftroy in one fecond of time, be determined by 

 experiment and called F, and let x be the fpace through which 

 the body would move by the time its motion was all deftroyed 

 when projedled with the velocity <?, and retarded by a force F ; 

 then, from the principles of uniformly retarded motion, x = 



— , and if /=:time of defcribing that fpace, we have t~ 



2. 



- , and hence the fpace defcribed m the firft fecond of time 



2a— ¥ 



F 



Now it is manifefb, that when the rotatory motion 



of the body about its axis is equal to its progreflive motion, the 

 point a will be carried backwards by the former motion as much 

 as it is carried forwards by the latter ; confequently the point of 

 contaft of the body with the plane will then have no motion 

 in the direction of the plane, and hence the friction will at 

 that inftant ceafe, and the body will continue to ro/I on uni- 

 formly without Jliding with the velocity which it has at that 

 point. Put therefore z = the fpace defcribed from the com- 

 mencement of the motion till it becomes uniform, then the 

 body being uniformly retarded, the fpaces from the end of 

 7 the 



