50 Professor Osborne Beynolds [March 28, 



theoretical resistance of ships. We see, then, that the motion in the 

 expanding channel is sinuous because the only steady motion is that 

 of a stream through water. Numerous cases in which the motion is 

 sinuous may be explained in the same way, but not all. 



If we have a perfectly parallel channel, neither contracting nor 

 expanding, the steady moving stream will be a fagot of perfectly 

 steady parallel elementary streams all in motion, but moving fastest 

 at the centre. Here we have no stream through steady water. Now 

 when this investigation began it was not known, or imperfectly 

 known, whether such a stream was stable or not, but there was a 

 well-known anomaly in the resistance to motion in parallel channels. 

 In rivers, and all pipes of sensible size, experience had shown that 

 the resistance increased as the square of the velocity, whereas in very 

 small pipes, such as represent the smaller veins in animals, Poiseuille 

 had proved the resistance increased as the velocity. 



Now since the resistance would be as the square of the velocity 

 with sinuous motion, and as the velocity, if direct, it seemed that the 

 discrepancy could be accounted for if the motion could be shown to 

 become unstable for a sufficiently large velocity. This suggested 

 the experiment I am now about to produce before you. 



You see on the screen a pipe with its end open. It is surrounded 

 by clear water and by opening a tap I can draw water through it. 

 This makes no difference to the appearance until I colour one of the 

 elementary streams, when you see a beautiful streak of colour extend 

 all along the pipe. The stream has so far been running steadily, 

 and appears quite stable. I now merely increase the speed ; it is 

 still steady, but the colour-band is drawn down fine. I increase the 

 colour and then again increase the speed. Now you see the colour- 

 band at first vibrates and then mixes so as to fill the tube. This is 

 at a definite velocity ; if the velocity be diminished ever so little the 

 band becomes straight and clear ; increase it again, it breaks up. 

 This critical speed depends on the size of the tube in the exact 

 inverse ratio; the smaller the tube, the greater the velocity; also, 

 the more viscous the water the greater the velocity. 



We have then not only a complete explanation of the difiference in 

 the laws of resistance generally experienced and that found by 

 Poiseuille, but also we have complete evidence of the instability of 

 parallel streams flowing between or over solid surfaces. The cause 

 of the instability is as yet not explained, but this much can be shown, 

 that whereas lateral stiffness in the walls is unimportant, inextensibility 

 or tangential rigidity is essential to the creation of eddies. I cannot 

 show you this because the only way in which we can produce the 

 necessary conditions without a solid channel is by a wind blowing over 

 water. When the wind blows over water it imparts motion to tlie 

 surface of the water just as a moving solid surface ; moving in this 

 ■way, however, the water is not susceptible of eddies. It is unstable, 

 but the result of disturbance is waves. This is proved by an experi- 

 ment long known, but which has recently attracted considerable notice. 



