i '-S Mr, ViNCE on the Motion of 



PROPOSITION !► 



Let c^ f, g, (tig. i.) reprefent either a cylinder^ or that circular 

 Jecfion of a body on which it rolls down the inclined plane CA im 

 coufeqiience of its fridfion^ to find the time of defcetit and tht 

 number of revolutions. 



As it has been proved in Art. 5. that the fri£lion of a body^ 

 does not iiicreafe in proportion to its weight or prefllire, we 

 cannot therefore, by knowing the friction on any other plane,, 

 determine the friction on CA ; the friction therefore on CA can 

 only be determined by experiments made upon that plane, that 

 is, by letting the body defcend from red:, and obferving the 

 fpace dclcribed in the firft fecond of time ; call that fpace a^. 

 and then, as by Art» 3. friction is a uniformly retarding force, 

 the body muft be uniformly accelerated, and confecjuently the; 



/AC 



whole time of defcent in feconds will be = \/— . Now to deter-- 



mine the number of revolutions^ let j be the center of ofcillatioii^^ 

 to the point of fufpenfion a * j then, becaufe no force acting at a 

 can affe£t the motion of the point j, that point, notwithftanding; 

 the action of the fri£tion at a, will always have a motion pa- 

 rallel to CA uniformly accelerated by a force equal to that 

 with which the body would be accelerated if it had no friction ;. 

 hence, if 2;;^/ = 3.2-3- feet, the velocity acquired by the point s 



iii'tKe'firil: fecond will be = "^^^. - ; now the excefs of the ve- 



* a and s are not fixed points in the body, but the former always repreffenti 

 that point of the body in contaft with the plane, and the latter the correfponding 

 ■ center of ofciIlation» 



2 loeity 



