Bodies affected by Friction. i &i 
/ l 
PROPOSITION II. 
Let the body be projected on an horizontal plane LM (fig. 3.} 
with a given velocity , to determine the fpace through which the 
body will move before it fops?, or before its motion becomes uniform*. 
Ca se L 1. Suppofc the body to have no rotatory motion 
when it begins to move ; and let a — the velocity of projection 
per fecond meafured in feet, and let the retarding force of the 
friCtion of the body, meafured by the velocity of the body 
which it can deltroy 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 projeded with the velocity a? 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~ 
- , and hence the fpace defcribed in the fxrft fecond of time 
2a — F 
= — - — Now it is manifest,. that when the rotatory motion 
of the body about its axis is equal! to its progreffive 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 
contact of the body with the plane will then have no motion 
in the direction of the plane, and hence the friCHon will at 
that inflant ceafe, and the body will continue to roll on uni- 
formly without fiding with the velocity which ft 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 off 
2 the 
