iSTi Mr* Vince on the Motion bf 
the motion vary as the fquares of the velocities, hence 
a 
(:: i • 2 
a 
2F 
z : : ■ a 2 ■- aFz = fquare of the prog ref- 
aF ' 
live velocity when the ‘hiotibii becomes uniform j therefore the 
velocity deftroyed. by friction —a - s/a — 2 F&; hence, as the 
velocity -generated or -deftroyed in the fame time is ill 
proportion to ' the force, 'we . have by Cor. 2. Prop. 1. 
r s : r a ; ; :: ar— / a — 2 b'z : x a — / a - 2 Fz the velocity "of 
r s 
the circumference efg. generated about the center, confequently 
%/a — 2F2 — — x a C a* — 2b" z, and hence z — 
r s 
r 2 -f ars x ra X a z 
as 2 x 2F 
the; fp ace; which the body deferibes before the motion becomes 
uniform. 
2 - If we fubflitute : this value of z into the expreffioti for the 
V Cl ' 
velocity, we ihall hdve a * -- for the velocity of the body wheft‘ 
its motion becomes uniform ; hence therefore it appears, that 
the velocity of the body, wheil the 'fridtion ceafes, will be th© 
fame whatever be the quantity of the frkdion. If the body be 
the circumference of a circle, it will always lofe half the ve- 
locity before its motioii becomes uniform. 
Case Ho i.yLet the body, befides having a progreffive 
velocity in the diredtion LM (fig. have alfo a rotatory mo- 
tion about its ‘center in the direction gf,e 9 and let v reprefen t 
tire initial velocity df any point of the circumference about thp 
center, and fuppofe. it firft to be lefs than a ; then friqtidn being 
a uniformly retarding force, no alteration of,. tile velocity p£ 
the point of con tact: of the body upon the .plane •camaffedt.jb.p. 
’quantity of fridtion ; hence th,e‘ prqgreffiveyelocit-y of the body 
Hvillie the, fame as before, and confe^nently..t^e, lytafdfy j Velio- • 
city 
