J -5 ^Ir. ViNCE on I he Motion of 



PROPOSITION!. 



Let e, f, g, (fig. !•) reprefent either a cylinder^ or that circular*- 

 feB'ion of a body on which it rolls down the inclined plane CA in^ 

 eonj'equencc cf its fricfion, to find the time of defcent and the* 

 number of revolutions. 



As it has been proved in Art. 5. that the fridion of a ho^f^- 

 does not increase in proportion to its weight or preflure, we 

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

 determine the fridion on CA ; the fri£lion therefore on CA can 

 only be determined by experiments made upon that plane, that 

 is, by letting the body defcend from reft, and obferving the 

 fpace defcribed 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 confequently the 



/AC 



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

 mine the number of revolutions, let j be the center of ofcillation 

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

 can afFed the motion of the point j, that point, notwithftanding 

 the a£lion of the fridion at ^, 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 friftion ; 

 hence, if zm^'^i^ feet, the velocity acquired by the point j 



ill the firfl fecond will be ~ ^ - ; now the excefs of the ve- 



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

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

 •;| center of ofcillation, 



2 locity 



