THE LAW OF RESISTANCE IN PARALLEL CHANNELS. 
955 
In reducing the results the unit taken has been the metre and the temperature is 
given in degrees centigrade. 
The diameters of the three tubes were found by filling them with water. 
The time measured was the time in which the tank fell 1 inch, which in cubic 
metres is given by 
Q = •021237 
In the table the logarithms of P, v, and If are given, as well as the natural numbers 
for the sake of reference. 
The velocities v have been obtained by the formula 
v - 
If being obtained from the formula 
B, 
The final value of If is obtained from the mean value of the logarithm of If. 
23. The results .—The values of log If show a considerable amount of regularity, 
and prove, I think conclusively, not only the existence of a critical velocity at which 
eddies come in, but that it is proportional to the viscosity and inversely proportional 
to the diameter of the tube. 
The fact, however, that this relation has only been obtained by the utmost care to 
reduce the internal disturbances in the water to a minimum must not be lost 
sight of. 
The fact that the steady motion breaks down suddenly shows that the fluid is in a 
state of instability for disturbances of the magnitude which cause it to break down. 
But the fact that in some conditions it will break down for a large disturbance, while 
it is stable for a smaller disturbance shows that there is a certain residual stability so 
long as the disturbances do not exceed a given amount. 
The only idea that I had formed before commencing the experiments was that at 
some critical velocity the motion must become unstable, so that any disturbance from 
perfectly steady motion would result in eddies. 
I had not been able to form any idea as to any particular form of disturbance being 
necessary. But experience having shown the impossibility of obtaining absolutely 
steady motion, I had not doubted but that appearance of eddies would be almost 
simultaneous with the condition of instability. I had not, therefore, considered the 
disturbances except to try and diminish them as much as possible. I had expected to 
see the eddies make their appearance as the velocity increased, at first in a slow or 
feeble manner, indicating that the water was but slightly unstable. And it was a 
matter of surprise to me to see the sudden force with which the eddies sprang into 
existence, showing a highly unstable condition to have existed at the time the steady 
motion broke down. 
4Q 
7r D 3 
P 
v]J 
