Rigidity produced by Centrifugal Force. 91 



in a direction away from the driving-pulley , then the chain 

 passes through a series of shapes such as those shown in fig. 

 5, PI. III., after which the chain again falls through a series 

 of forms similar to those shown in fig. 4, PI. III., before it ar- 

 rives at its position of equilibrium fig. 3, PL III., because the 

 upper part of the chain in fig. 5, PI. III., is now approaching 

 the driving or suspending pulley. 



The reason for these different series of forms in the two 

 cases is very simple. Take the case represented in fig. 4, 

 PI. III. Here the links, where they leave the underside of the 

 pulley, begin to be acted on by gravitation ; but as they are 

 moving rapidly, gravitation only acts a short time on them ; 

 their downward motion is therefore very slow. As the links 

 move further and further from this point, gravitation has had a 

 longer and longer time to act on them, so that their downward 

 motion becomes quicker and quicker ; and therefore the links as 

 they approach the driving-pulley are falling quicker than those 

 leaving it — the result of which is, the chain in falling passes 

 through a series of forms such as those represented in fig. 4, 

 PI. III. Similar reasoning applies to the case represented in 

 fig. 5, PL III. 



IV. We have shown by means of the diagrams figs. 1 and 2, 

 PL III., that the tension just balances the centrifugal force at 

 all points, and that therefore the chain has no tendency to 

 change the shape in which it is moving. The next experi- 

 ments (figs. 1 to 5, PL Y.) show how this equilibrium may 

 be destroyed, and also the effect of destroying it. A short 

 endless chain forming a loop about 20 inches long is hung 

 over the driving-pulley A, fig. 1, PL IV.; and the lower end of 

 the chain, instead of hanging free, is allowed to rest on the 

 platform R, fig. 1, PL V. When the chain is now put in 

 motion there is no tension at the lower part of the loop, due to 

 centrifugal force, because the downward motion of the links 

 is now destroyed by striking the platform R; and there is but 

 little tension on the descending side of the loop, and the 

 tension on the ascending side is due to putting the links in 

 motion in an upward direction. As the velocity of the chain 

 increases, the centrifugal force of the part of the chain resting 

 on the driving-pulley being unbalanced by the centrifugal 

 force at the lower end, the chain tends to rise off the pulley — 

 the result of which is, the weight of the chain is gradually 

 taken off the pulley ; and as this diminishes the friction be- 

 tween the chain and the pulley, a limit in the velocity of the 

 chain is soon reached, beyond which it is impossible to drive 

 the chain, however quickly the pulley is driven. The chain acts 

 in the opposite way, but with a similar result, to a self-acting 



