i8o Mr. ViNCE on the Motion of 



they will be to each other as "^^^ ■ : 2^ or asm x CB: a x CA; 



hence, wheu the body rolls without JliJlngy a s : a r ;: m x 



CB :ax CA. 



/ac 

 Cor, 4. The time of defcent down CA ls= \l — ; but by 



the laft Cor. when the body rolls without Jli Jin q- a = - — ^" ^,. • » 



hence the time of defcent in that cafe = AC v/ ^^ 1; now 



y mxraX BC 



the time of defcent, if there were no fri6:ion, would be =1 

 , hence the time of defcent, when the body rolls with- 



'^m X BC 



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



Cor, 5. By the laft Cor. it appears, that when the bodyjuft rc//f 

 without Jli cling, or w^hen the friftion is jufl equal to the accelera- 



tive force, the time of defcent zzACd- 



„„ , now It IS ma- 



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 fridlion afling at a can afFecl the motion of the 

 point s. 



If the body be projected 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 invefligated the accelerative force of the body down 

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

 •unneceliary to lengthen out this paper with the iiiveftigations-. 



PRO- 



