946 
MR. 0. REYNOLDS ON THE MOTION OF WATER AND OF 
But as it appeared that the critical velocity in the case of motion in one direction 
did not depend on the cause of instability with a view to which it was investigated, 
it followed that there must be another critical velocity, which wonld be the velocity 
at which previously existing eddies would die out, and the motion become steady as 
the water proceeded along the tube. This conclusion has been verified. 
14. Results of experiments on the law of resistance in tubes .—The existence of 
the critical velocity described in the previous article could only be tested by allowing 
water in a high state of disturbance to enter a tube, and after flowing a sufficient 
distance for the eddies to die out, if they were going to die out, to test the motion. 
As it seemed impossible to apply the method of colour bands, the test applied was 
that of the law of resistance as indicated in questions (1) and (2) in § 8. The result 
was very happy. 
Two straight lead pipes No. 4 and No. 5, each 16 feet long and having diameters 
of a quarter and a half inch respectively were used. The water was allowed to flow 
through rather more than 10 feet before coming to the first gauge hole, the second 
gauge hole being 5 feet further along the pipe. 
The results were very definite, and are partly shown in fig. 8, and more fully in 
diagram 1, Plate 74. 
Fig. 8. 
(1.) At the lower velocities the pressure was proportional to the velocity, and the 
velocities at which a deviation from the law first occurred were in exact inverse ratio 
of the diameters of the pipes. 
(2.) Up to these critical velocities the discharge from the pipes agreed exactly with 
those given by Poiseuille’s formula for capillary tubes. 
(3.) For some little distance after passing the critical velocity, no very simple 
relations appeared to hold between the pressures and velocities. But by the time the 
velocity reached 1 •2 (critical velocity) the relation became again simple. The pressure 
did not vary as the square of the velocity, but as P722 power of the velocity, this law 
held in both tubes and through velocities ranging from 1 to 20, where it showed no 
signs of breaking down. 
(4.) The most striking result was that not only at the critical velocity, but throughout 
the entire motion, the laws of resistance exactly corresponded for velocities in the 
ratio of 
