234 REPORT — 1875. • 



Further, if the two ends of the pipe are in the same straight line, pointing away 

 from one another (sse Plate IX. tig. 4), since the tensions on the ends of the pipe 

 are equal and opposite, the flow of the fluid through it does not tend to push it 

 bodily endways*. 



This is the point which it was my object to prove; but in the course of this 

 proof there has incidentally appeared the further proposition, that a flexible, tor- 

 tuous pipe, if fastened at the ends, will not tend to be disturbed in any way by the 

 flow of fluid through it. This proposition may to some persons seem at first sight to 

 be so paradoxical as to cast some doubt on the validity of the reasoning which has 

 been used ; but the proposition is nevertheless true, as can be proved by a closely 

 analogous experiment, as follows : — 



Imagine the ends of the flexible tortuous pipe to be joined so as to form a closed 

 figure (see fig. 5), there will then be no need for the imaginary fastenings at the 

 ends, since each end will supply the fastening to the other. Then substitute for 

 the fluid flowing round the circuit of the pipe, a flexible chain, running in the same 

 path. In this case the centrifugal forces of the chain running in its curved path are 

 similar to those of the fluid flowing in the pipe ; and the longitudinal tension of the 

 chain represents in every relevant particular the longitudinal tension on tbe pipe. 



As a simple form of this experiment, if a chain be set rotating at a very high 

 velocity over a pulley in tlie manner shown in fig. 6, it will be seen that the cen- 

 trifugal forces do not tend to disturb the path of the ruiming cliain ; and indeed, 

 the velocity being extremely' great, the forces, in fact, tend to preserve the path of 

 the chain in opposition to any disturbing cause. On the other hand, if by sufli- 

 cient force we disturb it from its path, it tends to retain the new figure which has 

 been thus imposed upon it (see fig. 7). 



The apparatus with which I am about to verify this proposition has been lent to 

 me by Sir W. Thomson. It is one which he has used on many occasions for the 

 same purpose ; and I must add that the proposition in his hands has fori7icd the 

 basis of conclusions incomparably deeper and more important than those to which 

 I am now directing your attention. 



You observe, the cham when at rest hangs, in the ordinary catenary form, from 

 a large pulley with a very wide-moutlied groove and mounted in a frame which is 

 secured to the ceiling. By a simple arrangement of multiplying bauds the pidley 

 is driven at a high speed, carrying the chain round by the frictional adhesion of 

 its upper semi-circumference. "\A'hen at its highest speed the chain travels about 

 40 per second. 



The idea that the chain when thus put in motion will be disturbed by its centri- 

 fugal force from the shape it holds while at rest, must point to one of two con- 

 clusions ; either (1) the chain will tend to open out into a complete circle, or (2) 

 it wiU on the contrary tend to stretch itself at its lower bend to a curvature of 

 infinite sharpness. 



But you oDserve that no tendency to eitlier change of form appears. On the 

 contrarj', the chain, instead of taking spontaneously any new form in virtue of its 

 centrifugal force, has plainly assumed a condition imder which it is with difficulty 

 disturbed, alike from its existing form, or from any other v/hich I communicate to 

 it by violently striking it. Such blows locally indent it almost as they would bend 

 a bar of lead. 



In spite, however, of this quasi-rigidity which its velocity has imparted to it, it 

 does, if left to itself, slowly assume, as you perceive, a curious little contortion, 

 both as it approaches and as it recedes from the lower bend of the catenary ; and it 

 is both interesting and instructive to trace the cause of the deformalion. 



I have ah'cady explained that the speed of the chain subjects it throughout to 

 longitudinal tension. Speaking quantitatively, the tension is equal to the weight 



of a length of the chain twice the height due to the velocity. This is — ; and this, 



as the speed is about 40 feet per second, =-77^- = 50 feet, or with this chain about 

 14 lbs. 



* See Appendix, Note A, 



