Rigidity produced by Centrifugal Force. 83 



elastic band on the pulley diminishes, and if the velocity is 

 sufficient it ceases to press on the pulley; and at length the ten- 

 sion produced by the centrifugal force opens out the band to 

 such a size that it becomes larger than the pulley, its form and 

 motion becoming irregular, and at last it flies off the pulley. 



If all the bodies in the system are moving at the same ve- 

 locity and in paths of the same curvature (that is, in a circle), 

 then the tension and the centrifugal force will evidently be in 

 equilibrium at all points, and the chain will keep its circular 

 shape, because, as the rate of deviation is the same for all 

 the bodies, the resistance of each of the bodies to this devia- 

 tion (or what we call the centrifugal force) will be the same at 

 all points, and the tension due to this resistance will also be 

 the same. The question may now be asked, Is this chain in a 

 condition of stable or of unstable equilibrium ? If the circular 

 form were to be slightly destroyed, would the chain tend to re- 

 turn to the circular shape, or would it tend to depart further 

 and further from it ? Is the equilibrium of the chain the 

 stable equilibrium of an egg resting on its side, or the unstable 

 equilibrium of an egg balanced on its end ? The answer we 

 shall get to this question will be that the equilibrium of the 

 moving chain corresponds to neither of these forms, but might 

 be compared to the equilibrium of a perfectly spherical and 

 homogeneous body resting on a perfectly horizontal plane, or 

 floating in a fluid of the same specific gravity as itself, all 

 positions being positions of equilibrium. 



First, let us see what answer experiment gives to this ques- 

 tion. If we hang an endless chain over a pulley, and the 

 pulley is caused to rotate at a great velocity, it has long been 

 well known that the motion so communicated to the chain 

 has but little tendency to alter the form of the curve in which 

 the chain hangs, and that the principal effect of the motion is 

 to confer on the chain a quasi-rigidity which enables it to re- 

 sist any force tending to alter its curvature. This statement 

 must not, however, be taken as representing the facts of the 

 case very accurately ; for while it may possibly be true of some 

 ideal form of chain, yet I shall presently show that in all 

 chains we can experiment on there are forces in action in the 

 moving chain which cause it to depart from the form it had 

 while at rest ; and if these forces were not balanced by 

 gravitation, the form of the chain would soon become very 

 different from what it was. 



What some of these disturbing forces are I shall point out 

 later on. For the present we shall neglect them, as in most 

 chains they are small, and shall simply consider the balance 

 between the centrifugal force and the tension. When the 



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