then will r s reprefent the accelerating force of the point O, 

 perpendicular to the plane of the ring; butrj-; nh:: Qr : Rad. 



(r), therefore rs — — , • 



ConseouentLy, if R = the matter of the ring, a rnotive 

 irce a fling upon the point Q, = — X ^ R v. 

 the whole efficacious motive force on the ring. 



force afling upon the point Q, = — X i R v/ill be equivalent to 



The momentary axis PT^ is in a plane perpendicular to the 

 plane of the ring, and which pafles through Qjj. • Make P T = tlie 

 radius of the ring, and draw Pr perpendicular to Q^y, and we have 



Vr:Tr::d: c, or Pr = ^ , and T r ^ =-=-. Let PT 



(in fig. 4.) reprefent the momentary axis, and Q.RN a quadrant 

 of the ring. From any point E of the ring draw E v perpen- 

 dicular to P T, and v w perpendicular to 0,T. The centri- 

 fugal force of E : centrifugal force of N : : En; NT, or the 



Ij<y c' + d^ 

 centrifuaial force of E = centrifugal force of N X ^-p^ = x 



•p . 



particle E X =;t^, becanfe the velocity of N = </€'■ + d'. But the 



efficacious part of this force in a diredion perpendicular "to the 



plane of the ring = whole X ■r= — ; and a fcirce ading at O equi-' 

 o Ek 



valent 



