952 
MR. 0. REYNOLDS ON THE MOTION OF WATER AND OF 
so as to follow the motion of the water, the expansion of the colour band resolved itself 
into a well-defined waving motion of the band, at first without other disturbance, but 
after two or three waves came a succession of well-defined and distinct eddies. These 
were sufficiently recognisable by following them with the eye, but more distinctly seen 
by a flash from a spark, when they appeared as in fig. 5, p. 942. 
The first time these were seen the velocity of the water was such that the tank fell 
1 inch in 1 minute, which gave a velocity of 0 ra '627, or 2 feet per second. On slightly 
closing the valve the eddies disappeared, and the straight colour band established 
itself. 
Having thus proved the existence of eddies, and that they came into existence at a 
certain definite velocity, attention was directed to the relations between this critical 
velocity, the size of the tube, and the viscosity. 
Two more tubes (2 and 3) were prepared similar in length and mounting to the first, 
but having diameters of about one-half and one-quarter inch respectively. 
In the meantime an attempt was made to ascertain the effect of viscosity by using 
water at different temperatures. The temperature of the water from the main was 
about 45°, the temperature of the room about 54° ; to obtain a still higher tempe¬ 
rature, the tank was heated to 70° by a jet of steam. Then taking, as nearly as we 
could tell, similar disturbances, the experiments which are numbered 1 and 2 in 
Table I. were made. 
To compare these for the viscosity, Poiseuille’s experiments were available, but to 
prevent any accidental peculiarity of the water being overlooked, experiments after 
the same manner as Poiseuille’s were made with the water in the tank. The results 
of these however agreed so exactly with those of Poiseuille that the comparative 
effect of viscosity was taken from Poiseuille’s formula 
P~ ] = l + 0-03368 T-f 0-000221 T 3 
where Pocp, with the temperature and T is temperature centigrade. 
The relative values of P at 47° and 70° Fah. are as 
1-3936 to 1 
while the relative critical velocities at these temperatures were as 
1-45 to 1 
which agreement is very close considering the nature of the experiments. 
But whatever might have been the cause of the previous anomalies, these were 
greatly augmented in the heated tank. After being heated the tank had been 
allowed to stand for an hour or two, in order to become steady. On opening the 
valve it was thought that the eddies presented a different appearance from those in 
the colder water, and the thought at once suggested itself that this was due to 
some source of initial disturbance. Several sources of such disturbance suggested 
