I" 



SoJies affecled by Fri^iGn. V^^ 



^locity of tlie point s above that of r (r being the center) is ma- 

 nifeftly the velocity with v^hich j is carried about r ; hence the 



velocity of s about the center =' q^ ~^^ — c"-^: > 



r ^1 . ^^ . 2mXCB-2rtxCA 2OTXrtfxCB — 2<7X''«xCA 



confequentlv rs : r^ :: prr : — ttx-^- — 



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

 ried about the center, and which therefore expreffes the force 

 \vhich accelerates the rotation; now as 2a expreffes the accele'- 

 rative force of the body down the plane, and the fpaces dc- 

 fcribed In the fame time are in proportion to thofe forces, wo 



have 2a : CA :: —prr — ' — ^- — ^- 



th® 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 x ra (where 



* = 6.282 fee.') will ffive^^ '^ '• for the whole numbcf 



'of revolutions required. . , 



Cor, I. If ^ X QA^m ^ BC/ the number of revolutions = o,. 

 and therefore the body will then only flide ; confequently the 

 fridion Vanifhes, 



Cor, 2, Let ^^rV (ng. 2.) be the next pofition of ars, and 

 draw / r'^ parallel to sa, then will s' i reprefetit the retardatioii 

 of the center r arifingfrom friction, and a^ ly v/ill reprefent the 

 acceleration of a point of the circumference about its center; 

 hence the retardation of the center : aceeleration of the cir- 

 cumference about the center :: s^f : a' b v. (by lim. A'f) 

 ir' : hr' :: rs : ra. 



Cor. 3. If y coincides with /t, the body doQS not Jliik but 

 t>nly roi/; now in this cafe s s' : r/ :: as : ar; but as s s^ and 

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



A a 2 they 



