The supply of water to the outside of a long vertical tube was adjusted until the water film was seen to be only just disturbed by a train of travelling waves. Under these conditions the Reynolds number, defined as the discharge per unit width divided by the kinematic viscosity, was 4·4. The wave train was slightly irregular, and average values of the length and velocity of the waves were about 0·45 in. and 5½ in./sec, the temperature being 19° C.