Rigidity produced by Centrifugal Force. 99 



it to the form shown at B, fig. 1, PL VII., we get quite a dif- 

 ferent set of results : 1st, the bent part does not rotate with 

 the disk, but keeps its original position, if the motion of the 

 disk is kept uniform; if the speed is either increasing or 

 decreasing, the bend will go very slowly either forwards or 

 backwards ; 2nd, there is no centrifugal force tending to 

 unbend the disk ; and, 3rd, the elasticity of the disk only very 

 slowly restores it to its original form, as it is resisted by the 

 rigidity produced by the motion. 



Although a disk of paper illustrates these points, yet the 

 experiment is much improved by loading the circumference of 

 the disk, as this increases its rigidity without increasing its 

 statical stiffness. The disks used in the experiments were 

 about 18 inches in diameter, made of cartridge drawing-paper. 

 The circumference was loaded with flattened pellets of shot 

 placed about -| inch apart, and fixed to the disk by means of a 

 strong solution of india-rubber. If the weight added to the 

 disk is such that it just balances the elasticity of the paper, 

 then the bend remains in the same place, and the disk keeps 

 the same shape for a very long time, while the disk is rotating 

 rapidly. The disk may be bent till the circumference touches 

 the centre (B, fig. 1, PI. VII.) ; and while the bend keeps its 

 position the chain of shot passes through many different 

 planes; and as the tension just balances the centrifugal force 

 at all points, the disk has no tendency to alter its shape. 



The change in the form of the rotating disk will produce an 

 alteration in the internal strains in the disk. When the disk 

 or any other body, such as an ordinary fly-wheel, is rotating, 

 the centrifugal force is resisted in two ways — partly by radial 

 tension, and partly by tangential tension ; and the amount 

 borne in each of these directions will depend on the relative 

 elasticity of the material in the rim and in the spokes, and on 

 the manner in which the wheel is constructed. The principal 

 part of the strain may be borne by either the spokes or the 

 rim of the wheel, as may be desired. In the paper disk, when 

 its motion is all in one plane the strain will be borne in both 

 ways, but when it is bent the strain will be almost entirely 

 tangential. 



Before proceeding further it will be necessary for me to 

 refer to some of the disturbing forces which I have already 

 stated to be in action in the moving chain, tending to cause 

 it to alter its shape. When looking at a chain hung over a 

 pulley and in rapid motion, fig. 3, PL III., the most marked 

 effect of the motion which we notice is a flattening of the curve 

 of the chain, just before it begins to turn at the lowest point; 

 and after the chain has turned and begun to ascend, there is a 



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