266 Remarks on the Central Forces of Bodies 



a second. It is done by turning the hand in a small circle AB, 

 about a moving axis of rotation. The velocity in the large circle 

 = 12.57x2 = 25. 14 feet per second; and, as shown above, if S rep- 

 resent the weight of the stone, v its velocity, r the radius of the 



■y 3 V^ S 



circle and x the centrifugal velocity, then r : ^: ;S : oo", = x=- 



25. 14^ 



3 2 x2 ~^'^^ pounds. The velocity in the circle being 25.14 



its force in that direction is equal to 1.58 lbs..;* and if we add 1.42 

 lb. for the weight of the stone and atmospheric resistance, which 

 is more than sufficient, we have three pounds as the force with 

 which it is impelled in the circle ST, To enable him to move 

 the stone in the circle the operator has to resist a force nearly 

 equal to ten pounds, which urges his hand from the centre at eve- 

 ry ijistant of time. He must therefore exert his strength at A in 

 the direction of the resultant of the two forces with an effort 

 which is equal in amount to their mechanical equivalent. If we 

 make Ae and Ac in length proportionate to the forces 3 and 10 

 respectively, then the diagonal A/ of the parallelogram Aefc, 

 will show the direction in which he draws at the string, and 

 v^lO^ +32 =10.44 lbs. will be the amount of force necessary to 

 give the required velocity ; of which, as shown above, two-thirds 

 are expended in retaining the stone in the circle. Now it would 

 be about as easy to show that a man can draw at a flexible cord 

 secured to a stationary object with a force equal to 10 pounds, 

 and at the same time press against that object, by m,eans of the 

 cord, with a force equal to six pounds, as to prove that the centri- 

 fugal force in this case is the immediate effect of the moving 

 power. The man moves his hand in a small circle and pulls at 

 a stone, nearly in the direction of the string to which it is attach- 

 ed, with a force equal to six times the weight of the stone, and 

 yet, according to the popular belief, he not only imparts directly to 

 it all the force with which it is projected, but dashes it off at right 

 angles to the thong, as if it were moved at the end of a lever. 



The thong of the sling, from what is said above, may be con- 

 sidered as in the place of an inflexible rod, the hand resisting the 

 pressure that would act as a strain upon an axle at c ; and if 

 such a rod had a handle at A, the same effect might be produced. 

 But it would cause great friction and strain upon the axle, and 



* Cavallo's Philosophy, p. 66. 



