180 Mr . Vince on the Motion of 
they will be tq each other as : za or as *n x CB: a x CA;. 
hence, when the body rolls without Jliding, as \ar \\tnx 
CB : a x CA. 
/ac 
Cor. 4. The time of defcent down CA is = — ; but by 
the laft Cor. when the body rolls withou tJUding, a = *■ 
now 
hence the time of defcent in that cafe =;AC J 
the time of defcent, if there were no fridion, would be sr 
AC • ■ ■ , hence the time of defcent, when the body rolls with- 
A«xBC . 
out fi ding : time of free defcent :: v/ *s a :• v / r a* 
Cor. 5. By the laft Cor. it appears, that when the body juft rolls 
without Jliding , or when the fridion is juft equal to the accelera- 
tive force, the time of defcent =AC ; now it is mar 
nifeft, that the time of defcent will continue the fame, if the 
fridion be increafed, for the body will ftill freely roll, as no 
increafe of the fridion ading at a can affed the motion of the 
point s. 
If the body be projeded from C with a velocity, and at the 
fame time have a rotatory motion, the time of defcent and 
the number of revolutions may be determined from the com- 
mon principles of uniformly accelerated motions, as we have 
already inveftigated the accelerative force of the body dowji 
the plane and of its rotation about its axis ; it feems therefore, 
unneceflary to lengthen out this paper with the jayeftigations*. 
? & o- 
