iBodies affedled hy FriSlloHk 187 



^Vlll be as ^ X rtC, h x 1>C, c x cC, &c. alfo the efFc6t of the Inertia 

 of the correfponding parts of the body will be as A x aC\ 

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

 bafe and mafs of the body are concentrated in P, the effecl: of 

 the fri(5lion will be as ^ + ^ 4- ^ + &c. x CP, and of the inertia as 

 A + B + C + &c. X CP'" ; confequently a x aC -{■ b x 5C -^r c x cC 

 + &c. : T+T+TT &c. X CP :: Ax^C'" +B x bC+CxcC^- 

 + &C. : A + B 4- C + &c. x CP' ; and hence 



CP = --^ ■- - - - — — - — ^ ^^— ■— (itS=:tneluni 



a XaC -\-b X l^C + c X cC i- &:c. X A + ii i- C -\-&.c. 



of the produces of each particle into the fquare of its diftance 

 from the axis of motion, T:=::the fiim of the products of each 



part of the bafe into its diftance from the center, s = the area 



s J ' 

 of the bafe, / = the folid content of the body) 7^7—^. 



PROPOSITION ly. 



Given the velocity with which a body begins to revolve ahotit the- 

 •center of its bafe, to determine the number of revolutions which the 

 body will make before all its motion be dejlroyed^ 



-- [U hi 



■'Let the fridion, expreffed by the velbcityl.whieh' it Is kbie to' 

 deftroy in th6' body if it were proiefted in a right line hoi-i'zbn^ 

 tally in one fecolid,- be detefmirieid 'by' experiment, dnd cail^^F;' 

 and fappofe th'e initikl velocity *of' the- center of -fri^V-ion- P t about* 

 ^ to be a[ "Then 'conceiving the whole fu-rfice of the bafe- ati^i 

 m^fsT)f "the body to 'be- coUsfHed^ntS the'^l5?iit P,^ aft-d §^s -hks-^ 



B b 7. 



