THE LAW OF RESISTANCE IN PARALLEL CHANNELS. 
945 
It thus appeared that there was some difference in the cause of instability in the 
two motions. 
13. Further study of the equations of motion .—Having now definite data to guide 
me, I was anxious to obtain a fuller explanation of these results from the equations of 
motion. I still saw only one way open to account for the instability, namely, by 
assuming the instability of a frictionless fluid to be general. 
Having found a method of integrating the equations for frictionless fluid as far as 
to show whether any particular form of steady motion is stable for a small distur¬ 
bance, I applied this method to the case of parallel flow in a frictionless fluid. The 
result, which I obtained at once, was that flow in one direction was stable, flow in 
opposite directions unstable. This was not what I was looking for, and I spent much 
time in trying to find a way out of it, but whatever objections my method of integra¬ 
tion may be open to, I could make nothing less of it. 
It was not until the end of 1882 that I abandoned further attempts with a 
frictionless fluid, and attempted by the same method the integration of a viscous 
fluid. This change was in consequence of a discovery that in previously considering 
the effect of viscoscity I had omitted to take fully into account the boundary 
conditions which resulted from the friction between the fluid and the solid boundary. 
On taking these boundary conditions into account, it appeared that although the 
tendency of viscoscity through the fluid is to render direct or steady motion stable, 
yet owing to the boundary condition resulting from the friction at the solid surface, 
the motion of the fluid, irrespective of viscoscity, would be unstable. Of course this 
cannot be rendered intelligible without going into the mathematics. But what T 
want to point out is that this instability, as shown by the integration of the equations 
of motion, depends on exactly the same relation 
Hoc^ 
as that previously found. 
This explained all the practical anomalies and particularly the absence of eddies 
below a pure surface of water exposed to the wind. For in this case the surface being 
free, the boundary condition was absent, whereas the film of oil, by its tangential 
stiffness, introduced this condition; this circumstance alone seemed a sufficient 
verification of the theoretical conclusion. 
But there was also the sudden way in which eddies came into existence in the 
experiments with the colour band, and the effect of disturbances to lower the critical 
velocity. These were also explained, for as long as the motion was steady, the 
instability depended upon the boundary action alone, but once eddies were introduced, 
the stability would be broken down. 
It thus appeared that the meaning of the experimental results had been ascertained, 
and the relation between the four leading features and the circumstances on which 
they depend traced for the case of water in parallel flow. 
