1 8o Mr. ViNCE on the Motion of 



thev will be to each other as '-^^ : 2? or as m x CB: a x CA; 



hence, when the body ro//s Without Jli ding ^ a s : a r y, m x 

 CB : ^ X CA. 



Cor, 4. The tune of dcfcent down CA is=^ sJ' — » but by 



the lad Cor. when the body rolls without Jli J/ nq;. ^/ = ' — r- • 



hence the tune of defcent in that cafe —AC 4/ ^^^7^, ; now 



\ OT X r^ X BC 



the tune of defcent, if there were no friclion, would be = 



AC 

 -7 , hence the time of defcent, wlien the body rol/s with- 



^w X BC ^ 



out ^fliding : time of free defcent :: K^sa : \/r a. 



Cor, 5. By the laft Cor. it appears, that when the body juft rolls 

 without Jli ding, or when the fridion is juft equal to the accelera- 



tiv€ force, the time of defcent =AC\J .,,, ; now it is ma- 



' \m xra X BCl 



nifeft, that the time of defcent will continue the fame, if the 

 friction be increafed, for the body will ftill freely roll, as no 

 increafe of the fridion ading at a can affect the motion of the 

 point J. 



If the body be projetfled from C with a velocity, and at the 

 fame time have a rotatory motion, the time of defcent and 

 the number of revolutions may he determined from the com- 

 mon principles of uniformly accelerated motions, as we have 

 already inveftigated the accelerative force of the body down 

 the plane and of its rotation about its axis ; it feems therefore, 

 xjnneceilary to lengthen out this paper with the iuvefligations* 



p s a- 



