Rigidity produced by Centrifugal Force. 85 



in the bend in A B C is twice as great as in D E F, there will 

 be twice the number of links in ABC that there are in D E F, 

 but the centrifugal force will only be one half what it is in 

 DEF; so that in the bend in A B we shall have 20 links each 

 acting with a force of 10 units ; the result of which is, the total 

 force is the same in both cases, namely 200. 



The next point to be considered is, What is the effect of the 

 amount of bend or deflection on the tension of the chain? 

 Suppose the chain to be bent to the angle A C B, fig. 2, PL III., 

 what tension will it put on the chain ? 



Let C D = force required to destroy the whole momentum 

 of the chain in the line A D. 



Draw B E perpendicular to A D. Join D B. 

 Then E D = force required to destroy momentum at the bend 



in the line AD ; 

 and E B = force required to establish momentum in the 

 direction P Q ; 

 D B = total deviating force at C required to produce 



the bend ACB; 

 B D = the centrifugal force at C in direction and 

 magnitude. 



On A C, C B construct the parallelogram A C B F. Join C F. 



F C is equal and parallel to B D ; 

 .*. F C = the centrifugal force at the bend ACB. 



It is evident from the construction that F C is always equal 

 to B D (that is, always equal to the centrifugal force), what- 

 ever the angle ACB may be. 



The centrifugal force F C acting at the angle ACB will 

 produce a tension in the chain equal to C A or C B, because 

 F C is equal and opposite to the resultant of C A and C B ; and, 

 further, it is evident from the construction, that, while the angle 

 or bend ACB may vary and the centrifugal force F C vary 

 along with it, the tension C A or C B does not vary. 



From these considerations we see that, though the centri- 

 fugal force in a chain moving in such a path as that shown at 

 fig. 7, PI. VII., varies at the different points, being greater the 

 quicker and the greater the curvature, yet the tension produced 

 by the centrifugal force at the different points is the same, 

 and is independent of the rate or the amount of curvature, and 

 that therefore the chain while in motion has no tendency to 

 alter its shape. 



These observations only refer to the tension in the chain 

 produced by centrifugal force. It is, however, necessary for 

 us, in order to understand some of the results we shall presently 

 see, to remember that there are other tensions in the chain 

 besides this one. There is, for instance, the tension produced by 



