Section III, 1919 [129] Trans. R.S.C. 



The Study of the Advance of the Ripple in Front of the Surface of an 

 Ascending Column of Liquid 



By J. C. Thompson, B.A. 



Presented by John Satterly, D.Sc, F. R.S.C. 

 (Read May Meeting, 1919.) 



Many searching investigations have been carried out in respect 

 to waves and ripples. J. Scott Russell was one of the earliest to make 

 a thorough study of the subject. He carried out many researches in 

 respect to the waves on rivers, canals, and artificial reservoirs^ His 

 work was continued by Lord Kelvin and others. Lord Kelvin devel- 

 oped the theory of minimum wave-velocity^, by which the velocity, v, 

 of a wave propagated under the influence of surface tension as well as 

 gravity, is given by the equation 



,J 



Ag 27rT 



In pX 

 where A is the wave-length; T is the surface tension; p is the density; 

 and g is the acceleration due to gravity. The velocity is a minimum 

 when the two terms under the root sign are equal; hence, in the ca.se 

 of water for which T = 75 dynes per cm. 



A = 1 • 7 cm. and v = 23 cm. sec. 

 Hence, no waves or ripples can travel over the surface of water with 

 a smaller velocity than 23 cm. per second. Lord Rayleigh^ and later 

 Dr. Dorsey"* made use of this equation to find the surface tension of 

 various liquids and solutions. 



A ripple, different from those referred to, was noticed by Dr. 

 John Satterly. In carrying out some experiments^ in which he had 

 water repeatedly ascending a tube, a well-defined ripple was observed 

 on the wetted wall of the tube slightly in advance of the moving sur- 

 face of the column of liquid (see AA in Figs. 1 or 2). It was early 

 noticed that the advance of this ripple varied as the velocity of the 

 moving surface varied, which observation gave rise to this research. 



1 J. Scott Russell, "Report on Waves," Brit. Ass. Rep., 1844. 



2 Lord Kelvin, "Hydrokinetic Solutions and Observations," Phil. Mag. (4), 

 XLII, p. 375, 1871. 



3 Lord Rayleigh, Phil. Mag. (S), XXX, p. 386. 



4 Dr. N. E. Dorsey, Phil. Mag. (5), XLIV, p. 369. 



5 Satterly, Trans. R.S.C. 1919, p. 110, Fig. 1, supra. 



