944 
MR. O. REYNOLDS ON THE MOTION OP WATER AND OP 
the bisulphide caused it to spread along the lower half of the tube, and the surface of 
separation of the two liquids extended along the axis of the tube. On one end of the 
tube being slightly raised the water would flow to the upper end and the bisulphide fall 
to the lower, causing opposite currents along the upper and lower halves of the tube, 
while in the middle of the tube the level of the surface of separation remained 
unaltered. 
The particular purpose of this investigation was to ascertain whether there was a 
critical velocity at which waves or sinuosities would show themselves in the surface of 
separation. 
It proved a very pretty experiment and completely answered its purpose. 
When one end was raised quickly by a definite amount, the opposite velocities of 
the two liquids, which were greatest in the middle of the tube, attained a certain 
maximum value, depending on the inclination given to the tube. When this was 
small no signs of eddies or sinuosities showed themselves; but, at a certain definite 
inclination, waves (nearly stationary) showed themselves, presenting all the appearance 
of wind waves. These waves first made their appearance as very small waves of equal 
lengths, the length being comparable to the diameter of the tube. 
Fig. 7. 
When by increasing the rise the velocities of flow were increased, the waves kept 
the same length but became higher, and when the rise was sufficient the waves would 
curl and break, the one fluid winding itself into the other in regular eddies. 
Whatever might be the cause, a skin formed slowly between the bisulphide and the 
water, and this skin produced similiar effects to that of oil on water; the results 
mentioned are those which were obtained before the skin showed itself. When the 
skin first came on regular waves ceased to form, and in their place the surface was 
disturbed, as if by irregular eddies, above and below, just as in the case of the oiled 
surface of water. 
The experiment was not adapted to afford a definite measure of the velocities at 
which the various phenomena occurred; but it was obvious that the critical velocity 
at which the waves first appeared was many times smaller than the critical velocity in 
a tube of the same size when the motion was in one direction only. It was also clear 
that the critical velocity was nearly, if not quite, independent of any existing 
disturbance in the liquids; so that this experiment shows— 
(1.) That there is a critical velocity in the case of opposite flow at which direct 
motion becomes unstable. 
(2.) That the instability came on gradually and did not depend on the magnitude 
of the disturbances, or in other words, that for this class of motion question 6 must 
be answered in the affirmative. 
