1884.J on the Two Manners of Motion of Water. 47 



All this is exactly true for the motion of water. Supposing no 

 disarrangement, the water would move in the manner indicated in 

 theory just as, if there is no disturbance, an egg will stand on its end ; 

 but as there is always slight disturbance, it is only when the condi- 

 tion of steady motion is more or less stable that it can exist. In 

 addition then to the theories either of military tactics or of hydro- 

 dynamics, it is necessary to know under what circumstances the 

 manoeuvres of which they treat are stable or unstable. And it is in 

 definitely separating these conditions that the method of colour-bands 

 has done good service which will remove the discredit in which 

 the theory of hydrodynamics has been held. 



In the first place, it has shown that the property of viscosity or 

 treacliness, possessed more or less by all fluids, is the general influence 

 conclusive to steadiness, while, on the other hand, space and velocity 

 are the counter influence ; and the effect of these influences is subject 

 to one perfectly definite law, which is that a particular evolution 

 becomes unstable for a definite value of the viscosity divided by the 

 product of the velocity and space. This law explains a vast number of 

 phenomena which have hitherto aj)peared paradoxical. One general 

 conclusion is, that with sufficiently slow motion all manners of motion 

 are stable. 



The effect of viscosity is well shown by introducing a band of 

 coloured water across a beaker filled with clear water at rest. Now 

 the water is quite still, I turn the beaker round about its axis. The 

 glass turns but not the water, except that which is close to the glass. 

 The coloured water which is close to the glass is drawn out into 

 what looks like a long smear, but it is not a smear, it is simply a 

 colour-band extending from the point in which the colour touched 

 the glass in a spiral manner inwards, showing that the viscosity was 

 slowly communicating the motion of the glass to the water within. 

 To prove this I have only to turn the beaker back, and the colour 

 band assumes its radial position. Throughout this evolution the 

 motion has been quite steady — quite according to the theory. 



When water flows steadily it flows in streams. Water flowing 

 along a pipe is such a stream bounded by the solid surface of the 

 pipe, but if the water be flowing steadily we can imagine the water 

 to be divided by ideal tubes into a fagot of indefinitely small streams, 

 any of which may be coloured without altering its motion, just as 

 one column of infantry may be distinguished from another by colour. 



If there is internal motion, it is clear that we cannot consider the 

 whole stream bounded by the pipe as a fagot of elementary streams, 

 as the water is continually crossing the pipe from one side to the 

 other, any more than we can distinguish the streaks of colour in a 

 human stream in the corridor of a theatre. 



Solid walls are not necessary to form a stream : the jet from a 

 fire hose, the falls of Niagara, are streams bounded by a free surface. 



A river is a stream half bounded by a solid surface. 



Streams may be parallel, as in a pipe ; converging, as in a conical 



