BoJics aJfeShd by Friciion. i § I 



PROPOSITION II. 



Let the My be pro'iecied on an horizontal plane LM (fig. j.) 

 with a given velocity to determine the fp.ice through which the 

 jbody ivill move bejore it JtopSy or bcjore its motion becomes latijorni. 



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

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

 per lecond measured hi feet, and let the retarding force of the 

 fri£lion of the body, meal u red by the velocity of the body 

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

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

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

 when projeded with the velocity a, and retarded by a force F ; 

 then, from the principles of uniformly retarded motion, a=i 



2, 



— , and if /^rtime of defcribing that fpace, we have / — 

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



= . Now it is manifeil, 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 x\\q farmer motion as much 

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

 eonta(ft of the body with the plane will then have no motion 

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

 that inftant ceafe, and the body will continue to roll on uni- 

 formly without Jliding with the velocity which it has at that 

 point. Put therefore s^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: 



