Section III, 1915 , fi33] Trans. R.S.C. 



Measurement of Surface Tension by Means of a Vertical Jet. 

 By Otto Maass. 



Presented by Dr. D. McIntosh. 



(Read May Meeting, 1915.) 



During the past few years the worth of the absolute values of 

 surface tension as obtained by different methods, especially by those 

 which involve the continual formation of fresh surface of the liquid, 

 has been a subject of some discussion.^ In the following paper a new 

 form of the dynamic measurement of surface tension is described. It 

 is based on the phenomenon that an obstacle placed in the path of a 

 jet of liquid flowing vertically downwards causes waves to travel 

 upwards. Under the proper conditions these waves appear to be 

 stationary and must therefore travel upwards with the same velocity 

 with which the liquid falls. By determining this velocity and the 

 length of the waves, the surface tension of the liquid is measured on a 

 freshly formed surface. 



A wave moving horizontally along the surface of a liquid is pro- 

 pelled onwards by two forces — gravity and surface tension. The 

 velocity with which such a wave is propagated is approximately 

 given by 



where v is the velocity, A the wave-length, g the constant of gravity, 

 T the surface tension and p the specific gravity. Now when a wave 

 travels upwards the force due to gravity is parallel to the surface of 

 the liquid, and plays no part in the propagation of the wave. In 

 this case formula (1) becomes: — 



''l =^ (2) 



Formulae (1) and (2) are derived with the assumption that the waves 

 travel along a plane surface and that the curvature of the waves is 

 in the form of a trochoid. The dynamics of a cylinder of liquid 

 has however been rigorously worked out and the details of the cal- 

 culation are to be found in Lamb's Textbook of Hydrodynamics.^ 



iLenard Sitz. der Heidelberger Akad. d. Wiss. 1910. Bohr. Proc. Roy. Soc. 

 p. 395 A 1911. 



^Lamb's Hydrodynamics p. 450. 



