Rigidity produced by Centrifugal Force. 97 



motion in the shape shown in fig. 4, PL VI., by means of the 

 movable pulleys E and F. If, while the pulley E is kept 

 steady, a downward motion is given to the pulley F, the chain, 

 instead of pressing harder on the pulley E, rises quite off it, 

 as shown in the dotted lines in the figure ; and if the down- 

 ward motion of F be continued, the circular part which 

 formerly rested on E rises till it strikes the driving-pulley H, 

 The downward motion of F requires to be quick at first ; but 

 after the chain begins to rise a very slow motion is all that is 

 necessary. The reason for the chain rising from the pulley E 

 is, that the downward motion of the pulley F increases the 

 velocity of the chain at q r ; therefore the centrifugal force of 

 the part of the chain resting on E is increased, while the 

 centrifugal force at s is not increased. The chain therefore 

 yields at s and rises at r. 



This change in the shape of the chain is perhaps easiest 

 studied in a chain not in motion, but simply fixed at one end, 

 the other end hanging free. If we hang the lower end of the 

 chain over the pulley E,as in fig. 4, PI. VI., and pull the free 

 end of the chain at F, we get a similar result to what we get 

 when the chain is in rapid motion. But in this case the down- 

 ward motion of the end of the chain must be much quicker ; 

 and the upward motion of the curved part s q r is correspond- 

 ingly quick — so quick that the eye can scarcely follow it. 

 When we pull the free end of the chain at F we thereby give 

 the chain at sqr an upward motion. Suppose that we stop 

 pulling at F after the chain has acquired a motion sufficiently 

 quick to enable it to rise off the pulley E. The curved part 

 will form a regular wave motion, the links at q being in rapid 

 upward motion, while those at r are gradually losing their 

 motion, the energy of their motion being transmitted by the 

 chain at q to put the links in motion at s. It is very evident 

 that all the energy lost at the last part of the wave at r is not 

 spent in putting the links in motion at the beginning of the 

 wave at s, but has to do work against the force of gravitation — 

 because if the energy were simply transferred from r to s, as 

 in many wave-forms, then the wave s g r might travel up 

 any length of chain, and in so doing lift the whole chain the 

 height 5 r, when the energy put into the part s q r was only 

 sufficient to raise the part s q r to r. To enable the wave to 

 travel up the chain we must communicate energy to it while 

 in motion, by keeping up a tension at the lower end of the 

 chain at F. The end of the chain must therefore yield to the 

 tension, and the part s q r become less and less as it travels 

 up the chain. 



The wave-forms represented in figs. 1, 3 and 4, PI. VI., 

 Phil. Mag. S. 5. Vol. 5. No. 29. Feb. 1878. H 



