bodies affeBed by PriBim, 
locity of the point s above that of r (r being the ceil ter) is ma» 
iiifeftly the. velocity with which s is carried about r; hence the 
velocity of s about the center = ■ ■ — -2 a = • — ? 
■ , r . . X CB — in x C A a my rax CB — 2 a'XraxC \ 
confidently rs : ra :: 
— the velocity with which a point of the circumference is car- 
ried about the tenter, and which therefore expreffts the force 
which accelerates the rotation ; now as 2 a expreffes the accele- 
rative force of the body down the plane, and the fpaces de- 
fcribed in the fame time are in proportion to thofe forces, we 
, - i-s * im X X CB — 2a X ra X C A m.x r a x CTy~~ a x ra xQh 
nave 2 a i LA •:? — ■ 
n xCA 
a >< rs 
the fpace which any point of the circumference defcribes about 
the center in the whole time of the body’s defcent down CA ; 
which being divided by the circumference p k ra (where 
p = 6 . 283 Bee.) Will give ^^^7“ for the whole number 
of revolutions required-. 
Cor . i. If a k CA =: m x BC, the number of revolutions =: o, 
and therefore the body will then only hide % confeqiiehtly the 
friction vanities. 
Cori 2 . Let </rY (fig. "2.) he the next pofidoh of cbr% 
draw ir'h parallel to sa, theii wiil s' t reprefent ’ the retardation 
of the center r arifing from fridtion, and a' b will reprefent the 
acceleration of a point of the circumferehce about its center; 
lienee the retardation of the center 1 acceleration of the cir-' 
Tumferencq about the 'center ' s't : B b :: (by lira. Ab) 
* ■ 1 y ' ■*/ •' ■ • ■ <. ' i / 
tr : or t: rs 1 ra. 
Cor . 3. If ^ coincides with the body does not Jlide but 
only roll; now in this cafe s s' : rr' :* as : ar; but as s s' and 
7/ jeprefent the ratio of the velocities of the points s and r, 
A a 2 they 
