| T = | ρλ³ | coth | 2πh | − | gλ²ρ | , (2) |
| 2πτ² | λ | 4π² |
h denoting the depth of the liquid. In observations upon ripples the factor involving h may usually be omitted, and thus in the case of water (ρ = 1)
| T = | λ³ | − | gλ² | (3) |
| 2πτ² | 4π² |
simply. The method has the advantage of independence of what may occur at places where the liquid is in contact with solid bodies.
The waves may be generated by electrically maintained tuning-forks from which dippers touch the surface; but special arrangements are needed for rendering them visible. The obstacles are (1) the smallness of the waves, and (2) the changes which occur at speeds too rapid for the eye to follow. The second obstacle is surmounted by the aid of the stroboscopic method of observation, the light being intermittent in the period of vibration, so that practically only one phase is seen. In order to render visible the small waves employed, and which we may regard as deviations of a plane surface from its true figure, the method by which Foucault tested reflectors is suitable. The following results have been obtained
| Clean | 74.0 |
| Greasy to the point where camphor motions nearly cease | 53.0 |
| Saturated with olive oil | 41.0 |
| Saturated with sodium oleate | 25.0 |
(Phil. Mag. November 1890) for the tensions of various water-surfaces at 18° C., reckoned in C.G.S. measure.
The tension for clean water thus found is considerably lower than that (81) adopted by Quincke, but it seems to be entitled to confidence, and at any rate the deficiency is not due to contamination of the surface.
A calculation analogous to that of Lord Kelvin may be applied to find the frequency of small transverse vibrations of a cylinder of liquid under the action of the capillary force. Taking the case where the motion is strictly in two dimensions, we may write as the polar equation of the surface at time t
r = a + αn cos nθ cos pt, (4)