bodies aj^ediei hy TriBlon. i ^j ^j 



Joclty df the point s above that of r (r being the center) is ma- 

 n.ifeftly the velocity with which s is carried about r; hence the 



velocity of s about the center ——-t\ tazn — - — y— _ ^ ^.^ , 



•^ UA CA ' 



r ^\ ^ 2WXCI3-2^XCA 2?«Xr^xCB— 2«X''^XCA 



confequentiv rs \ ra w — r : — ^ — iJiJ: 



^ J CA ;.fXCA 



p the velocity with which a point of the circumference is car- 

 ried about the center, and which therefore express the force 

 which accelerates the rotation ; now as za exprefles the accele- 

 rative force of the body down tiie plane, and the fpaces de- 

 fcribed in the fame time are in proportion to thofe forces, we 



have 2 a : CA :: ■ ttt— '• — - 



the fpace which any point df the circumference defcribes about 

 the center in the whole time of the body's defcent down CA ; 

 which being divided by the circumference p x ra (where 



^ = 6.282 Sec.) will p-ive^- ^ for the whole number 



of revolutions required. 



Cor. I. If a X CA = ;« x BC, the number of revolutions — o, 

 and therefore the body will then only Aide ; confequentlj/ the 

 friction vanifhes. 



Cor. 2. Let a^r's^ (fig. 2.) be the next polltion of ars, and 

 draw / r^^ parallel to sa, then will j'/ reprefent the retardation 

 of the center r arifing from friction, and a^ b will reprefent the 

 acceleration of a point of. the circumference about its center; 

 hence the retardation of the center : accetef^tion of the cir- 

 cumference about the center :: s't : a' b :: (by fim. a's) 

 ir' : hr' :: rs \ ra. 



Cor. 3. If ^^ coincides with /?, the body does not y7/^<? but 

 only roll; now in this cafe s s' : rr' \\ a s\ ar\ but as ^ s' and 

 r r' reprefent the ratio of the velocities of the points s and r, 



A a '2 they 



