88 



Mr. 0. Reynolds. 



[Mar. 15, 



search. Of course, without integration the equations only gave the 

 relation, without showing at all in what way the motion might depend 

 upon it. It seemed, however, to be certain, if the eddies were owing 

 to one particular cause, that integration would show the birth of eddies 

 to depend upon some definite value of — 



cpU 



7. The Cause of Eddies. — There appeared to be two possible causes 

 for the change of direct motion into sinuous. These are best dis- 

 cussed in the language of hydrodynamics ; but as the results of this 

 investigation relate to both these causes, which, although the distinc- 

 tion is subtile, are fundamentally distinct and lead to distinct results , 

 it is necessary that they should be indicated. 



The general cause of the change from steady to eddying motion 

 was, in 1843, pointed out by Professor Stokes as being that, under 

 certain circumstances, the steady motion becomes unstable, so that an 

 indefinitely small disturbance may lead to a change to sinuous motion. 

 Both the causes above referred to are of this kind, and yet they are 

 distinct ; the distinction lying in the part taken in the instability by 

 viscosity. If we imagine a fluid free from viscosity and absolutely 

 free to glide over solid surfaces, then comparing such a fluid with 

 a viscous fluid in exactly the same motion — 



(1.) The frictionless fluid might be unstable and the viscous 

 stable. Under these circumstances the cause of eddies is the insta- 

 bility as a perfect fluid, the effect of viscosity being in the direction 

 of stability. 



(2.) The frictionless fluid might be stable and the viscous fluid 

 unstable ; under which circumstances the cause of instability would 

 be the viscosity. 



It was clear to me that the conclusion I had drawn from the 

 equations of motion immediately related only to the first cause. JS"or 

 could I then perceive any possible way in which instability could 

 result from viscosity. All the same I felt a certain amount of 

 uncertainty in assuming the first cause of instability to be general. 

 This uncertainty was the result of various considerations, but 

 particularly from my having observed that eddies apparently come on 

 in very different ways, according to a very definite circumstance of 

 motion, which may be illustrated. 



When in a channel the water is all moving in the same direction, 

 the velocity being greatest in the middle and diminishing to zero at 

 the sides, as indicated by the cmwe in fig. 1, eddies showed themselves 

 reluctantly and irregularly ; whereas when the water on one side 

 of the channel was moving in the opposite direction to that on 



