268 Remarks on the Central Forces of Bodies 



site direction with the same velocity."* The force applied to 

 the winch, in the case above, was wholly expended in giving ve- 

 locity to the rim, with the shght exceptions mentioned. Conse- 

 quently, whatever other forces may have operated on the rim whilst 

 revolving must have originated in some other way. And yet those 

 extraneous forces would amount to 1480 lbs., as shown by the above 

 formula, the rim weighing 150 lbs. and being revolved at the rate 

 of two entire revolutions in a second. No part of this force could be 

 communicated to the arm of a man who would stop such a wheel 

 by seizing one of the spokes, because each particle of the rim is act- 

 ed upon by the central forces, which are always opposite and equal, 

 in the direction of the radius of the circle at that point ; and it 

 has just been shown that the moment of rotation of each particle 

 is equal to the moment of rotation of the power that impels it, 

 but "as the direction of the central forces is in that of the ra- 

 dius, their moment of rotation is equal to nothing."! Conse- 

 quently the centrifugal force cannot act upon the hand that stops 

 the wheel. If, indeed, the centrifugal force were increased to 

 sixteen times the above amount, the result would be the same. 

 By giving the wheel eight revolutions in a second we would have 

 the central force = 1480 X 16=23680 lbs. and the force in the cir- 



12.57x8x150 .^ , 



cle would be = ^^ = 925 lbs. Here the centrifugal 



force is twenty times greater than the force in the circle, and yet 

 as the central force would act in the direction of the radii, its 

 moment of rotation would be = 0. Or, what is more strictly the 

 fact, the central force acts by pressure, and a resultant from that 

 pressure and the force in the circle is the consequence, but so 

 long as resistance from cohesion continues, neither motion nor 

 pressure can be imparted to another body by the central force. 

 These are the obvious reasons why no greater force could be 

 communicated by the rim than the 925 lbs., which it only pos- 

 sesses as a mass of matter moving in a circle. 



The following experiment may be considered as a practical 

 illustration of the theoretical views given above. A whirling 

 table may be made of any convenient size, we will say, for the 

 present occasion, rather more than four feet in diameter, to revolve 

 horizontally on friction rollers placed near the center ; the axle 

 being a hollow cylinder, through which four cords pass to the 



* Kater and Lardner on Mechanics, p. 24. 



i Renwick's Mathematics, Art. Composition of Forces. 



