264 Remarks on the Central Forces of Bodies 



in the circle can have no influence upon the deflecting force. 

 But a body moving in a curve or circle is always found to be act- 

 ed upon by a third force, which is opposite and equal to the de- 

 flecting or centripetal force ; and as there cannot be an efl"ect 

 without a cause, this third force must either be derived from one 

 of those mentioned above, or their resultant — or from some other 

 source. Supposing the circle BD, in which the bar moves, to be 

 one foot in diameter and the velocity of the bar to be 25.14 feet 

 per second, or at the rate of eight entire revolutions in a second, 



v^ 25.14^ 

 its centrifugal velocity would be=2~= — i — =632 feet per se- 

 cond, and its centrifugal force =39 lbs. its weight being one pound, 

 V representing the velocity in the circle, and r its radius ; for if a 

 be the weight of the bar, g equal to 32 y^^ feet, and x the force re- 



V2 v^a 25. 14^ 



quired, then r : — : :a : — =3;-=— jg — =39 lbs.* But the force 



25.14 

 in the circle=-jj^— =1.55 lbs. only, consequently the centrifu- 

 gal force could not have been caused by the projectile force. And 

 it is evident that it cannot be a part of the magnetic force, for it 

 acts in a directly opposite direction ; and it is equally evident that 

 it cannot be the resultant of the other two forces, for then its di- 

 rection would be to some point within the circle. The pressure 

 from the centre of thirty-nine pounds must therefore have origin- 

 ated in some other way. 



Such are the facts when the deflection from a straight line is 

 caused by a centripetal force directed to a fixed centre of rota- 

 tion, and the projectile or moving force is applied before the body 

 is constrained to move in a circle. We will now stop the revolv- 

 ing rod r, leaving the bar A attached to m, by the magnetic force. 

 If by means of a winch the same number of revolutions in a 

 second be given to the bar that it had in the first experiment, the 

 centripetal or magnetic force will perform the part of cohesion, 

 and the circumstances in every other respect will be the same 

 that would attend such a rotation if the bar were welded to m. 

 Does the moving power, applied in this manner, directly produce 

 the central force or immediately impart it to the moving body? 

 or, in other words, is centrifugal force a part of the force employ- 

 ed to revolve the body ? Without attempting to prove the nega- 



* Hutton's Mathematical Dictionary, and Gregory's Mechanics. 



