^Bodies affeSied by Fndlion. ig-^ 



city generated by fridioii will alfobe the fame, to which if wc 

 add the velocity about the center at the beginning of the mo- 

 tion, we (hall have the whole rotatory motion ; hence there- 



fore, v-^-- X a~ s/a - 2F3 = s/c.i' — zFs, confequently % =z 



a y.ai —V xrsA-ii'>^-ri 



aF xas^ 



the fpace defcribed before the motion be- 



comes uniform. 



2. If this value of z be fubftituted into the expreflion for the 



velocity, we ftiall have — ^ for the velocity when the 



friction ceafes. 



^. If T'=/7, then z—o, and hence the body will continue to 

 move uniformly with the firfl velocity. 



4. If 'i; be greater than a, then the rotatory motion of the 

 point a on the plane being greater than its progreffive motion 

 and in a contrary diredion, the abfolute motion of the point 

 a upon the plane will be in the direction ML, and confequently 

 fridion will now ad in the diredion LM in which the body 

 moves, and therefore will accelerate t\\Q progrejjtve and retard 

 the ro/^/orj; motion ; hence it appears, that the pro grejjive mo- 

 tion of a body may be accelerated by ff-'iclion. Now to deter- 

 mine the fpace defcribed before the motion becomes uniform, we 

 may obferve, that as the progreffive motion of the body is now 

 accelerated, the velocity after it has defcribed any fpace % will- 



be = v^^' -f 2F.S, hence the velocity acquired^: v^^' + 2Fz -^j, 

 and confequently the rotatory velocity deflroyed — x 



^fl^+2Fz — ^, hence v — ~ x v/ir + 2Fz -^ = x/^' 4- 2F 



z^ 



rsxvArray.a —a X as 



thererore %=;- -^ . the Ipace required. 



n. ir 



