THE LAW OF RESISTANCE IN PARALLEL CHANNELS. 
939 
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 instable and the viscous fluid stable. Under 
these circumstances the cause of eddies is the instability 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 conclusions I had drawn from the equations of motion 
immediately related only to the first cause ; nor 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 curve 
in fig. I, eddies showed themselves reluctantly and irregularly; whereas when the 
Fig. 1. 
Fig. 2. 
water on one side of the channel was moving 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. 
8. Methods of investigation .—There appeared to be two ways of proceeding—the 
one theoretical, the other practical. 
The theoretical* method involved the integration of the equations for unsteady 
