52 



NATURE 



\Nov. 1 8, 1875 



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 flow- 



FiG. s. 



ing in the pipe ; and the longitudinal tension of the chain repre- 

 sents in every particular the longitudinal tension on the pipe. 



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

 at a very high velocity over a pulley in the manner shown in 

 Fig 6, it will be seen that the centrifugal forces do not tend to 

 disturb the path of the running chain ; 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 



I 



I 



Fig. 6. 



Fig. 7. 



other hand, if by sufficient 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 proposi- 

 tion 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 formed the basis 

 of conclusions incomparably deeper and more important than 

 those to which I am now directing your attention. 



You observe the chain when at rest hangs in the ordinary 

 catenary form, from a large pulley with a very wide-mouthed 

 groove and mounted in a frame which is secured to the ceiling. 

 By a simple arrangement of multiplying bands the pulley is 

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

 adhesion of its upper semi-circumference. When at its highest 

 speed the chain travels about 40 per second. 



The idea that the chain when thus put in motion will be dis- 

 turbed by its centrifugal force from the shape it holds while at 

 rest must point to one of two conclusions ; either (i) the chain 

 will tend to open out into a complete circle, or (2) it will on the 

 contrary tend to stretch itself at its lower bend to a curvature 

 of infinite sharpness. 



But you observe that no tendency to either change of form 

 appears. On the contrary, the chain, instead of taking spon- 

 taneously any new form in virtue of its centrifugal force, has 

 plainly assumed a condition under which it is with difficulty dis- 

 turbed, alike from its existing form, or from any other which 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 deformation. 



I have already 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 Jo the velocity. This is —, and thus, as the 



speed is 40" feet per second, = 50 feet, or with this chain 



32 

 about 14 lbs. 



Now in travelling through the lower bend of the catenary, 

 the chain passes from being nearly straight, to being sharply 

 curved and immediately straightened again, and this change of 

 form involves a continued pivoting of link within link, the fric- 

 tion being called into action by the tension which presses the 

 surfaces together. Each link thus in succession resists t 

 pivoting with a definite force, and the resistance, in effect, c< 

 verts what appears to be a perfectly flexible combination iii:,u 

 one possessing a tangible degree of stiffness, and the oblique 

 attitude assumed by the chain as it approaches the bend, and 

 the shght back turn which it assumes as it emerges from the 

 bend, are alike consequences of this factitious stiffness. 



For in virtue of gravity, the runnmg chain, like the chain at rest, 

 tends always to maintain the original catenary ; and in virtue of 

 its speed of rotation, it seeks to maintain (not preferentially the 

 catenary, but) whatever fo'^m it for the moment possesses. 

 Hence its departure from the true catenary was, as you saw, 

 gradual. But when the figure of equilibrium is once attained, 

 the persistency of form imparted by velocity serves to maintain 

 this figure as indifferently as any other. Hence the figure is 

 that in which equilibrium subsists between the force of gravity 

 seeking to restore the catenary, and the factitious stiffness resist- 

 ing the necessity of bending and unbending. 



The slowness with which the form is assumed, and its steady 

 persistency when once assumed, alike bear witness to the truth 

 of the proposition which it is the object of the experiment to 

 verify. 



The stream of fluid in the tortuous flexible pipe would be- 

 have in a strictly analogous manner. 



{To be continued.) 



NOTES 



It is with great regret that we hear of the death of Dr. von 

 Willemoes-Suhm, the distinguished naturalist assisting Prof. 

 Wyville Thomson in the Challenger. Information of the sa 

 occurrence has just been received at the Admiralty. 



At the opening meeting of the Royal Geographical Society on 

 Monday, 'the president. Sir H. Rawlinson, reviewed the progress 

 of the Society and of geographical discovery during the past year. 

 He announced that the Prince of Wales, the Vice-patron of the 

 Society, had just sent the Society, as the first geographical 

 result of ; his tour in the East, a very interesting collection 

 of route-maps of Upper Egypt and its recently acquired 

 dependencies, which had been executed in the Topographical 

 Department of the Egyptian War Office by General Stone, 

 Chief of the Etat Major, from materials furnished in one 

 direction by Col. Gordon and the officers serving under his 

 orders, and in another by Col. Purdy and the officers of the 

 Darfur Expedition. These maps contain much new geographical 

 matter. The President referred with great satisfaction to 

 Stanley's exploration of the Nyanza, and exhibited a complete 

 chart of the lake drawn by Stanley. As to Col. Gordon, who 

 by last accounts had reached Appudo, 140 miles from the Albert 

 Nyanza, if he could overcome the eight miles of rapids which 

 lay before him, he would probably reach the Albert Nyanza with 

 his steamer the Khedive, beftrC; Stanley. Both Gordon and his 

 assistant Chipendall report, from native information, that the 

 Nile leaves the Albert Nyanza by two channels. Dr. Pogge and 

 Dr. Lasaulx, the only remaining members of the German African 



