630 



NATURE 



\Oct. 25, 1883 



about, the critical velocities at which the eddies showed themselves 

 were exactly in the inverse ratios of the diameters of the tubes. 



(5.) That in all the tubes the critical velocity diminished as 

 the temperature increased, the range being from 5° C. to 22° C, 

 and the law of this diminution, so far as could be determined, 

 was in accordance with Poiseuille's experiments. 



Taking T to express degrees Centigrade, then by Poiseuille's 

 experiments — 



- oc P = 1 + crc>336 T + 0-00221 T s , 



p 



Taking a metre as the unit, U, the critical velocity, and D the 

 diameter of the tube, the law of the critical point is completely 



I P 



expressed by the formula U, = — — , where B x = 437. This 



is a complete answer to question 5. 



During the experiments many things were noticed which can- 

 not be mentioned here, but two circumstances should be men- 

 tioned as emphasising the negative answer to question 6. In 

 the first place, the critical velocity was much higher than had 

 been expected in pipes of such magnitude, resistance varying as 

 the square of the velocity had been found at very much smaller 

 velocities than those at which the eddies appeared when the 



flow to the upper end, and the bisulphide fall to the lower, 

 causing opposite currents along the upper and lower halves of 

 the tube, while in the middle of the tube the level of the surface 

 of separation remained unaltered. 



The particular purpose of this investigation was to ascertain 

 whether there was a critical velocity at which waves or sinuosities 

 would show themselves in the surface of separation. It proved 

 a very pretty experiment and completely answered its purpose. 



When one end was raised quickly by a definite amount, the 

 opposite velocities of the two liquids, which were greatest in the 

 middle of the tub?, attained a certain maximum value depending 

 on the inclination given to the tube. When this was small no 

 signs of eddies or sinuosities showed themselves, but at a certain 

 definite inclination waves (nearly stationary) showed themselves, 

 presenting all the appearance of wind waves. 



These waves first made their appearance as very small waves 

 of equal lengths, the length being comparable to the diameter of 

 the tube. 



When by increasing the rise the velocities of flow were in- 

 creased, the waves kept the same length but became higher, and 

 when the rise was sufficient the waves would curl and break, the 

 one fluid winding itself into the other in regular eddies. 



1 



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water in the tank was steady. And in the second place it was 

 1 bserved that the critical velocity was very sensitive to disturb- 

 ance in the water before entering the tubes, and it was only by 

 the greatest care as to the uniformity of the temperature of the 

 tank and the stillness of the water 'that consistent results were 

 obtained. This showed that the steady motion was unstable for 

 disturbances long before the critical velocity was reached, 

 a fact which agreed with the full blown manner in which the 

 eddies appeared. 



12. Experiments with Two Streams in Opposite Directions in 

 the Same Tube. — A glass tube 5 feet long and I '2 inch in dia- 

 meter, having its ends slightly bent up, as shown in Fig. 6, 

 was half filled with bisulphide of carbon, and then filled up with 

 water and both ends corked. The bisulphide was chosen as 

 being a limpid liquid, but little heavier than water and com- 

 pletely insoluble, the surface between the two liquids being 

 clearly distinguishable. When the tube was placed in a hori- 

 zontal direction, the weight of the bisulphide caused it to spread 

 along the lower half of the tube, and the surface of separation 

 of the two liquids extended along the axis of the tube. 



On one end of the tube being slightly raised, the water would 



% 





Whatever might be the cause, a skin formed slowly between 

 the bisulphide and the water, and this skin produced similar 

 effects to that of oil on water ; the results mentioned are those 

 which were obtained before the skin showed itself. When the 

 skin first came on, regular waves ceased to form, and in their 

 place the surface was disturbed as if by irregular eddies above 

 and below, just as in the case of the oiled surface of water. 



The experiment was not adapted to afford a definite measure 

 of the velocities at which the various phenomena occurred, but 

 it was obvious that the critical velocity at which the waves first 

 appeared was many times smaller than the critical velocity in a 

 tube of the same size when the motion was in one direction only. 

 It was also clear that the critical velocity was nearly if not quite 

 independent of any existing disturbance in the liquids. So that 

 this experiment shows — 



(1.) That there is a critical velocity, in the case of opposite 

 flow, at which direct motion becomes unstable. 



f hat the instability came on gradually and did not depend 

 on the magnitude of the disturbances, or, in other words, that 



