[The above theory may be well illustrated by a lecture experiment. A thin-walled glass tube of internal diameter equal to 14½ mm. is ground true at the lower end. The upper end is contracted and is fitted with a rubber tube under the control of a pinch-cock. Water is sucked up from a vessel of moderate size, the rubber is nipped, and by a quick motion the tube and vessel are separated, preferably by a downward movement of the latter. The inverted tube, with its suspended water, being held in a clamp, a beaker containing a few drops of ether is brought up from below until the free surface of the water is in contact with ether vapour. The lowering of tension, which follows the condensation of the vapour, is then strikingly shown by the sudden precipitation of the water.]
Effect of Surface-tension on the Velocity of Waves.—When a series of waves is 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 λ, the equation of the surface is
| y = b sin 2π | x | . |
| λ |
The pressure due to the surface tension T is
| p = −T | d²y | = | 4π² | T y. |
| dx² | λ² |
This pressure must be added to the pressure due to gravity gρy. Hence the waves will be propagated as if the intensity of gravity had been
| ƒ = g + | 4π² | T |
| λ² | ρ |
instead of g. Now it is shown in hydrodynamics that the velocity of propagation 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
| v² = | fλ | = | gλ | + | 2πT | . (1) |
| 2π | 2π | ρλ |
This velocity is a minimum when