938 
MR, 0. REYNOLDS ON THE MOTION OF WATER AND OF 
It is always difficult to trace the dependance of one idea on another. But it may 
be noticed that no idea of dimensional properties as indicated by the dependance of 
the character of motion on the size of the tube and the velocity of the fluid, occurred 
to me until after the completion of my investigation on the transpiration of gases, in 
which was established the dependance of the law of transpiration on the relation 
between the size of the channel and the mean range of the gaseous molecules. 
6. Evidence of dimensional properties in the equations of motion .—The equations of 
motion had been subjected to such close scrutiny, particularly by Professor Stokes, 
that there was small chance of discovering anything new or faulty in them. It seemed 
to me possible, however, that they might contain evidence which had been ovei’looked, 
of the dependance of the character of motion on a relation between the dimensional 
properties and the external circumstances of motion. Such evidence, not only of 
a connexion but of a definite connexion, was found, and this without integration. 
If the motion be supposed to depend on a single velocity parameter U, say the 
mean velocity along a tube, and on a single linear parameter c, say the radius of the 
tube; then having in the usual manner eliminated the pressure from the equations, 
the accelerations are expressed in terms of two distinct types. In one of which 
U 2 
c 3 
is a factor, and in the other 
/HJ 
pc 4 
is a factor. So that the relative values of these terms vary respectively as U and 
p 
cp‘ 
This is a definite relation of the exact kind for which 1 was in 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 he certain if the eddies were owing to one particular cause, 
that integration would show the birth of eddies to depend on some definite value of 
cpTJ 
7. The cause of eddies .—There appeared to be two possible causes for the change of 
direct motion into sinuous. These are best discussed in the language of hydro¬ 
dynamics, but as the results of this investigation relate to both these causes, which, 
although the distinction is subtle, 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 
