Oct. 25, 1883] 



NA TURE 



629 



showed themselves reluctantly and irregularly ; whereas when 

 the water on one side of the channel was m >ving in the opposite 

 direction to that on the other, as shown by the curve in Fig. 2, 

 eddies appeared in the middle regularly and readily. 



S. Methods of Investigation. — There appeared to be two ways 

 of proceeding, the one theoretical, the other practical. 



The theoretical method involved the integration of equations 

 for unsteady motion in a way that had not then been accom- 

 plished, and which, considering the general intractability of the 

 equation*, was not promising. 



The practical method was to test the relation between U, 

 - , and c ; this, owing to the simple and definite form of the 



law, seemed to offer, at all events in the first place, a far more 

 promising field of research. 



The law of motion in a straight, smooth tube offered the 

 simplest possible circumstances and the most crucial test. 



The existing experimental .knowledge of the resistance of 



Fig. i. 



water in tubes, although very extensive, was in one important 

 respect incomplete. The previous experiments might be 

 divided into two classes— (1) those made under circumstances 

 in which the law of resistance was as the square of the velocity, 

 and (2) those made under circumstances in which the resistance 

 vanei as the velocity. There had not apparently been any 

 attempt made to determine the exact circumstances under which 

 the change of law took place. 



Again, although it had been definitely pointed out that eddies 

 would explain the resistance as the square of the velocity, it did 

 not appear that any definite experimental evidence of the exis- 

 tence of eddies in parallel tubes had been obtained, and much 

 less was there any evidence as to whether the birth of eddies 

 » as simultaneous with the change in the law of resistance. 



These open points may be be.-t expressed in the form of 

 queries to which the answers anticipated were in the affirmative. 



(1.) What was the exact relation between the diameters of the 

 pipes and the velocities of the water at which the law of resis- 

 tance changed : was it at a certain value of c U ? 



(2.) Did this change depend on the temperature, i.e. the vis- 

 cosity of water ; was it at a certain value of — ? 



ft 



(3.) Were there eddies in parallel tubes? 



(4.) Did steady motion hold up to a critical value and then 

 eddies come in ? 



(5.) Did the eddies come in at a certain value of pf ? 



(6.) Did the eddies first make their appearance as small, and 

 then increase gradually with the velocity, or did they come in 

 suddenly ? 



The bearing of the last query may not be obvious ; but, as will 

 appear in the sequel, its importance was such that, in spite of 

 satisfactory answers to all the other queries, a negative answer to 

 this in respect of one particular class of motions led to the recon- 

 sideration of the supposed cause of instability, and eventually to 

 the discovery of instability caused by fluid friction. 



'1 he queries as they are put suggest two methods of experi- 

 menting : — 



(I.) Measuring the resistances and velocities for different dia- 

 meter--, and with different temperatures of water. 



(2. ) Visual observation as to the appearance of eddies during 

 the flow of water along tubes or open channels. 



Both these methods have been adopted, but as the question 

 relating to eddies had been the least studied, the second method 

 was the fir-t adopted. 



9. Experiments by Visual Observations.— The most important 

 of these experiments related to water moving in one direction 

 along glass tubes. Besides these, however, experiments on fluids 

 flowing in opposite directions in the same tube were made ; also 

 a third class of experiments which related to motion in a flat 

 channel of indefinite breadth. 



These last-mentioned experiments resulted from an incidental 

 observation during some experiments made in 1876 as to the 

 effect of oil to prevent wind waves. As the result of this ob- 

 servation had no small influence in directing the course of this 

 investigation, it may be well to describe it first. 



10. Eddies caused by the Wind beneath the Oiled Surface of 

 Water. — A few drops of oil on the windward side of a pond 

 during a stiff breeze having spread over the pond and completely 

 calmed the surface as regards waves, the sheet of oil, if it may 

 be so called, was observed to drift before the wind, and it was 

 then particularly noticed that close to, and at a considerable 

 distance from, the windward edge, the surface presented the 

 appearance of plate glass ; further from the edge the surface pre- 

 sented that wavering appearance which has already been likened 

 to that of sheet glass, which appearance was at the time noted 

 as showing the existence of eddies beneath the surface. 



Suli-equent observation confirmed this first view.' At a suffi- 

 cient distance from the windward edge of an oil-calmed surface 

 there are always eddies beneath the surface even when the wind 

 is light. But the distance from the edge increases rapidly as the 

 force of the wind diminishes, so that at a limited distance (10 or 

 20 feet) the eddies will come and go with the wind. 



Without oil I was unable to perceive any indication of eddies. 

 At fir.-t I thought that the waves might prevent their appearance 

 even if they were there, but by careful observation I convinced 

 myself that they were not there. It is not necessary to discuss 

 these results here, although, as will appear, they have a very 

 important bearing on the cause of instability. 



11. Experiments by Means of Colour Bands in Glass Tubes. 

 — These were undertaken early in 18S0 ; the final experiments 

 were made on three tubes, Nos. I, 2, and 3. 



The diameters of these were nearly 1 inch, 4 inch, and £ inch. 

 They were all about 4 feet 6 inches long, and fitted with trumpet 

 mouthpieces, so that water might enter without disturbance. 



The water was drawn through the tubes out of a large glass 

 tank in which the tubes were immersed, arrangements being 

 made so that a streak or streaks of highly-coloured water entered 

 the tubes with the clear water. 



The general results were as follows : — 



(1 ) When the velocities were sufficiently low, the streak of 

 colour extended in a beautiful straight line through the tube 

 (Fig. 3)- 



(2.) If the water in the tank had not quite settled to rest, at 

 sufficiently low velocities the streak would shift about the tube, 

 but there was no appearance of sinuosity. 



(3.) As the velocity was increased by small stages at some 

 point in the tube always at a considerable distance from the 

 trumpet or intake, the colour band would all at once mix up with 

 the surrounding water, and fill the rest of the tube with a mass 

 of coloured water, as in Fig. 4. 



Any increase in the velocity caused the point of breakdown to 

 approach the trumpet, but with no velocities that were tried did 

 it reach this. 



On viewing the tube by the light of an electric spark, the mass 

 of colours resolved itself into a mass of more or less distinct 

 curls showing eddies, as in Fig. 5. 



The experiments thus seemed to settle questions 3 and 4 in 

 the affirmative — the existence of eddies and a critical velocity. 



They also settled in the negative question 6 as to the eddies 

 coming in gradually after the critical velocity was reached. 



In order to obtain an answer to question 5 as to the law of the 

 critical velocity, the diameters of the tubes were carefully 

 measured, also the temperature of the water and the rate of 

 discharge. 



{4.) It was then found that with water at a constant tempe- 

 ature and the tank as still as could by any means be brought 



