'i^'t 'Mr. ViNCE on the Motion of 



the motion vary as the fquares of the velocities, hencfe 



2 2 



~ : ^' (:: i^ 2F) :: — -z : a" ~ 2F% = fquare of the progref- 



live velocity when the motion becomes uniform ; therefore the 

 velocity deflroyed by fri£tion =:^ — s/ a" — 2Fz ; hence, as the 

 velocitv generated or deftroyed in the fame time is iu' 

 proportion to the force, we have by Cor. 2= Prop. i. 



r s : r a :'. a — \/a— zYz : - x a~\/a — 2 Fa the velocity o£ 

 the circfimferenee ^/"^ generated about the center, confequently 



s/ci — 2r zzz — x a - s/^ — 2rz, and hence 2 = ^ — =r- — 



^ rs ' , «r X 2F - 



the fpace which the body defcribes before the motion becomes^ 



uniform. il 



2. If we fubftitute this value of % into the exprcffion for ther 



velocity, we fliall have a x ~ for the velocity of the body when' 



its motion becomes uniform ; hence therefore it appears, that- 

 the velocity of the body, when the fridion ceafes, will be the^^ 

 iame whatever be the quantity of the fri6lion. If the body be^ 

 the circumference of a circle, it will always iofe half the ve-^ 

 locity before its motion becomes uniform. 



Case II. i. Let the body, befides having a progreflive, 

 velocity in the direflion LM (fig. 3.) have alfo a rotatory mo-^ 

 tion about its center in the diredlion gfe, and let 1; reprefeut^ 

 the initial velocity of any point of the circumference about the 

 center, and fuppofe it firft to belefs than a ; then friction being, 

 a uniformly retarding force, no alteration of the velocity of-i 

 the point of contad of the body upon the plane can afFecl the . 

 '^quantity of friction ; hence the progrefTive velocity of the body 

 Hvill be the fame as before, and confequently the rotatory velo- ; 



city 



> 



