Rigidity produced by Centrifugal Force. 101 



a path of slower to a path of quicker curvature, and after th9 

 rotation has been imparted to the links they tend to keep up 

 their rate of rotation, and thus continue the curve much fur- 

 ther round than if the chain were not in motion. If the chain 

 were infinitely thin, this would not be the case. The part of 

 the links in the line of tension has no such tendency ; it is 

 the parts of the links on the inside and outside of this line 

 which produce the result. 



The outside of the curve of the chain, when passing from a 

 straight path to a curved one, is moving too slow, and the inside 

 too quick, to pass round the curve ; the chain therefore resists 

 bending ; and after the outside of the curve has acquired in- 

 creased velocity and the inside lost it, the chain cannot move 

 in a straight path till the inside and outside parts have again 

 acquired the same velocity. The different velocities of the 

 outside and the inside of the loop in passing round a curve 

 therefore cause the chain to continue to curve further round 

 than it would do if not in motion. This tendency to cause the 

 chain to continue curving farther round would cause the chain 

 to deviate further from its original shape if it were not resisted 

 by the tension produced by gravitation. This varying rota- 

 tion also explains why the quickest part of the curve is not at 

 the lowest part of the path of the chain, but at a short distance 

 up the ascending side of the chain. The links at the lowest 

 point are still acquiring an increased rate of rotation ; and it 

 is not till past this point that they acquire their maximum 

 rate. 



IX. These points may be illustrated by a chain in which 

 the links are short and the chain thick, so that the moment 

 of inertia of the links round an axis perpendicular to the plane 

 of motion of the links is as great as possible, and the moment 

 of the tension round this same axis as small as possible. A 

 simple method of constructing such an experimental chain is to 

 fix by means of glue a series of pieces of wood about 1 inch 

 long and of the section shown in fig. 2, PI. VII., on each side 

 of a strong piece of tape about 1 inch broad. When this 

 chain is hung over the pulley D (fig. 2, PL IV.) and put in 

 motion, the reverse curve is very marked (fig. 3, PI. VII.). So 

 great is the effect of the varying rate of rotation of the links 

 in this chain, that they never take up a steady motion of trans- 

 lation ; the links are constantly rotating too quickly the one 

 way or the other, which gives rise to the well-marked series of 

 waves all the way up one side of the loop and down the 

 other. 



At A and B (fig. 4, PL VII.) I have shown what I suppose 

 to be the manner in which the varying rate of rotation of the 



