CAPILLARY ACTION. 587 



7T~ 

 - Z, 



where z is the least root of the equation 



2 Tl Z 2 Z 4 Z 6 



z ( *>~ ~274 + 2.4 2 .6~2.4 2 .6 2 .8~ l " * C "~ 

 The least root of this equation is 



z~ 3-831 71. 



If h is the height to which the liquid will rise in a capillary tube of 

 unit radius, then the diameter of the largest orifice is 



= 5-4188^. 

 M. Duprez found from his experiments 



EFFECT OF SURFACE-TENSION ON THE VELOCITY OF WAVES*. 



When a series of waves are propagated on the surface of a liquid, the 

 surface-tension has the effect of increasing the pressure at the crests of the 

 waves and diminishing it in the troughs. If the wave-length is X, the equa- 



tion of the surface is 



, x 

 y = b sm ZTT r- . 



A 



The pressure due to the surface-tension T is 



This pressure must be added to the pressure due to gravity gpy. Hence the 

 waves will be propagated as if the intensity of gravity had been 



477* T 7 



instead of g. Now it is shewn in hydrodynamics that the velocity of propa- 

 gation of waves in deep water is that acquired by a heavy body falling through 

 half the radius of the circle whose circumference is the wave-length, or 



277 A./J 



* See Sir W. Thomson, " Hydrokinetio Solutions and Observations," Phil. Mag., Nov. 1871. 



742 



