Bodies affedled ly Priciirji. j S 7 



will be as ^ X ^^C, b x i?C, c x cQ^ &c. alfo the ettccl of the iiiciti.i 

 of the correfpoadlng parts of the body will be as A x ^;C', 

 B X ^C", C X ^C% &c. Now when the whole furface of the 

 bafe and mafs of the body are concentrated in P, the effect of 

 the friction will be as ii + ^ + ^ + &c. x CP, and of the inertia as 



A + B -}- C 4- &c. X CP" ; confequently a y. aO. -^ h a bO, ^ c x cQ 

 + &c. : T+T+TT" &c, X CP :: Ax^C+B x hC^Q a cQ' 

 -j- &c. : A + B + C + &c. X CP' ; and hence 



pp — -■- .^==: — = ( it S = the lu;il 



^ aX<jC+^x^C + <:x^C + &c. xA + B + C-i-&c. ^ 



of the produ61:s of each particle into the fquare of its diilanco 



from the axis of motion, T = the fum of the products of each 



part of the bafe into its dilliance from the center, j == the are;i 



of the bafe, / = the folid content of the bodv") '777—. 



? it O P O S I T I O N IV. 



Given tht velocity with which a body begins to revolve about the 

 center of its bafe^ to determine the number of revolutions which the 

 body will make before all its motion be dejiroyed. 



Let the fridion, cxpreiTed by the velocity whicli it is able to 



deftroy in the body if it were projecled in a right line horizon ' 



tally in one fecond, be determined by experiment, and called F; 



.and fuppofe the initial velocity of the center of friclion P about 



C to be a. Then conceivinsf the whole furface of tl^e bafe and 



tnafsof the body to be colleOed into the point P, and (as has 



.-■■'•. (P" ■ 



been proved In Prop. II.) —.will be the fpace which the body 



fo concentrated' will defcribe before all its motion be deflroyed j 



B b 2 hci\ce 



